workbook - naval air training command
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NAVAL AIR TRAINING COMMAND
NAS CORPUS CHRISTI, TEXAS CNATRA P-421 (Rev. 03-21)
WORKBOOK
INTRODUCTION TO
HELICOPTER AERODYNAMICS
TH-57
2021
DEPARTMENT OF THE NAVY CHIEF OF NAVAL AIR TRAINING250 LEXINGTON BLVD SUITE 102 CORPUS CHRISTI TX 78419-5041
CNATRA P-421 N714 19 Mar 21
CNATRA P-421 (REV. 3-21)
Subj: WORKBOOK, INTRODUCTION TO HELICOPTER AERODYNAMICS, TH-57
1. CNATRA P-421 (Rev. 3-21) PAT, “Workbook, Introduction to Helicopter Aerodynamics, TH-57” is issued for information, standardization of instruction, and guidance to all flight instructors and student military aviators within the Naval Air Training Command.
2. This publication is an explanatory aid to the Helicopter and Tiltrotor curriculums and shall be the authority for the execution of all flight procedures and maneuvers herein contained.
3. Recommendations for changes shall be submitted via the electronic Training Change Request (TCR) form located on the CNATRA Website.
4. CNATRA P-421 (New 02-21) PAT is hereby cancelled and superseded.
D. F. WESTPHALLBy direction
Releasability and distribution: This instruction is cleared for public release and is available electronically only via Chief of Naval Air Training Issuances Website, https://www.cnatra.navy.mil/pubs-pat-pubs.asp.
iii
INTRODUCTION TO HELICOPTER
AERODYNAMICS WORKBOOK
TH-57
Q-2C-3156
iv
LIST OF EFFECTIVE PAGES
Dates of issue for original and changed pages are:
Original.. .0...18 Feb 21 (this will be the date issued)
Revision...1...19 Mar 21
TOTAL NUMBER OF PAGES IN THIS PUBLICATION IS 178 CONSISTING OF THE FOLLOWING:
Page No. Change No. Page No. Change No.
COVER 0 A-1 – A-16 0
LETTER 0 B-1 – B-2 0
iii – xiv 0
1-1 – 1-8 0
2-1 – 2-12 0
3-1 – 3-17 0
3-18 (blank) 0
4-1 – 4-11 0
4-12 (blank) 0
5-1 – 5-18 0
6-1 – 6-16 0
7-1 – 7-28 0
8-1 – 8-19 0
8-20 (blank) 0
9-1 – 9-13 0
9-14 (blank) 0
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INTERIM CHANGE SUMMARY
The following Changes have been previously incorporated in this manual:
CHANGE
NUMBER REMARKS/PURPOSE
The following Interim Changes have been incorporated in this Change/Revision:
INTERIM
CHANGE
NUMBER
REMARKS/PURPOSE
ENTERED
BY
DATE
vi
ACKNOWLEDGEMENTS
The genesis for this text was direction from CNATRA to develop a more comprehensive
helicopter aerodynamics text and course with the ultimate goal of making smarter and therefore
safer pilots. This text was produced through the collective effort of Training Air Wing FIVE
academic instructors, helicopter pilots, the Rotary Wing Aerodynamics Instructor from the U.S.
Navy & Marine Corps School of Aviation Safety, and professors from the U.S. Naval Academy.
The text is a reference that the fleet pilot can use as a single source document, not just as a flight
school workbook. It includes a great deal of information and pictorial items from open internet
sources as well as the books in the reference list. If there are any errors in the interpretation of
these authors’ materials or the sources in the reference list (Appendix A), or the information as
presented, the reader should report them to Training Air Wing FIVE Academic Training
Department. This book is a work in progress and will be updated periodically.
vii
INSTRUCTIONS FOR STUDENT NAVAL AVIATORS
Objective
Upon completion of this course, the student will possess an understanding of basic helicopter
fundamentals and aerodynamic principles. While the student will be required to demonstrate a
functional knowledge of the material presented through successful completion of an end-of-
course examination with a minimum score of 80%, this course is primarily focused on preparing
the student for practical application of that knowledge in future helicopter flight and flight
planning.
Assumptions
1. An engineering background is not required for mastery of the basic concepts of this course.
2. Recent completion of the Fundamentals of Aerodynamics course offered in Aviation
Preflight Indoctrination (or an equivalent course). Review the material if an extended period of
time has passed or the material was not previously mastered.
3. Concurrent completion of interactive courseware (ICWs) augmented by the availability of
knowledgeable instructors and a formal review session prior to testing.
4. This document is an introductory text that serves as an adequate, stand-alone, ready
reference for the military helicopter pilots. A comprehensive helicopter engineering text is not
intended or necessary. A recommended reading list provides options for those with greater
curiosity.
Instructional Approach of this edition
1. This edition was reorganized to be more user friendly. The concepts to be mastered for the
end-of-course exam are described in the corresponding enabling objectives in the basic text.
2. This edition includes the Table of Contents and appendices with a reference/recommended
reading list, Glossary and an Index.
Recommendations for Students
1. Review the enabling objectives before completing ICW’s, study the text and the class
presentation.
2. The utility of this course depends primarily upon the conscientious accomplishment of your
reading and study assignments.
3. Participation in a study group is highly recommended. A study group of four is optimum.
viii
AVIATOR AND INSTRUCTOR GUIDANCE
Every aviator has a “toolbox” with tools they have collected and mastered over the years.
Among other things, that toolbox probably contains emergency procedures, operating
limitations, regulations, or instructions, and an assortment of lessons learned.
A mastery of basic aerodynamic principles is an important tool for the professional aviator,
especially when it comes to the challenging rigors of rotary wing flight in military aviation.
Aerodynamics can save your life. Time after time, mishap reports attribute either a lack of
understanding or the inappropriate misapplication of aerodynamic principles as a causal factor of
the mishap.
The exposure in flight training to these principles and their application is only the first step in the
mastery of the essential concepts. Every profession requires continuing education. As iron
sharpens iron, we learn from one another. It is the responsibility of every naval aviator to
continually sharpen the skills necessary to maintain the “edge” that may one day make the
difference in the accomplishment of the mission and/or your crew’s survival.
Periodic review of both systems and aerodynamic course material will provide for the greatest
retention and immediate recall. Each time an aviator re-reads the text, they will glean some new
fact or relationship to improve their overall understanding, including those who have yet to set
foot in a new aircraft.
A survey of pilots of the Aviation Safety Officer Course reveals that few of the aerodynamic
principles necessary to investigate a mishap were retained from flight training. Each ASO
completes twenty lecture hours of rotary wing aerodynamics in the course. It is clear from this
course that every individual is not only capable of, but also highly motivated toward, making
basic aerodynamic principles an integral part of their toolbox. Their goal is not to develop
mishap investigation skills, but rather to develop mishap avoidance skills they can share.
Therefore, the goal of this text is to present the principles of helicopter aerodynamics in a
straightforward, comprehensible manner, such that both the newest student naval aviator and the
crustiest old instructor pilot may have at their disposal a concise, accurate reference. The best
available tool, however, is only of use to the craftsman who develops and maintains a level of
expertise to make its use second nature.
ix
TABLE OF CONTENTS
LIST OF EFFECTIVE PAGES .................................................................................................. iv INTERIM CHANGE SUMMARY ...............................................................................................v ACKNOWLEDGEMENTS ........................................................................................................ vi INSTRUCTIONS FOR STUDENT NAVAL AVIATORS ..................................................... vii
AVIATOR AND INSTRUCTOR GUIDANCE....................................................................... viii TABLE OF CONTENTS ............................................................................................................ ix TABLE OF FIGURES ................................................................................................................ xii
CHAPTER ONE - INTRODUCTION TO THE HELICOPTER ......................................... 1-1 100. INTRODUCTION .................................................................................................. 1-1
101. HELICOPTER AERODYNAMICS COURSE LEARNING OBJECTIVES ........ 1-1
102. ROTOR SYSTEM .................................................................................................. 1-2 103. ROTOR CONFIGURATIONS ............................................................................... 1-3
104. CONTROLLING FLIGHT ..................................................................................... 1-6
105. FLIGHT CONDITIONS ......................................................................................... 1-7
CHAPTER TWO - THE ATMOSPHERE .............................................................................. 2-1 200. INTRODUCTION .................................................................................................. 2-1 201. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 2-1
202. REVIEW OF BASIC PHYSICS AND AERODYNAMICS .................................. 2-1 203. VECTOR ANALYSIS ............................................................................................ 2-1
204. ESSENTIAL TERMS AND DEFINITIONS ......................................................... 2-3 205. PROPERTIES OF THE ATMOSPHERE .............................................................. 2-4 206. THE STANDARD ATMOSPHERE ...................................................................... 2-5
207. ALTITUDE COMPUTATIONS ............................................................................ 2-6
208. ALTITUDE COMPUTATIONS – DENSITY ALTITUDE................................... 2-8
CHAPTER THREE - HELICOPTER AERODYNAMICS BASICS ................................... 3-1 300. INTRODUCTION .................................................................................................. 3-1 301. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 3-1
302. AIRCRAFT REFERENCE SYSTEM .................................................................... 3-1 303. GENERAL .............................................................................................................. 3-2 304. FORCES ACTING ON THE AIRCRAFT ............................................................. 3-4 305. LIFT ........................................................................................................................ 3-4 306. WEIGHT ................................................................................................................. 3-8
307. THRUST ................................................................................................................. 3-9
308. DRAG ..................................................................................................................... 3-9
309. INTRODUCTION TO LIFT THEORIES ............................................................ 3-12 310. PRESSURE DISTRIBUTION THEORY............................................................. 3-12 311. CIRCULATION THEORY .................................................................................. 3-13 312. MOMENTUM THEORY ..................................................................................... 3-14 313. BLADE ELEMENT THEORY ............................................................................ 3-15
x
CHAPTER FOUR - AIRFOILS ............................................................................................... 4-1 400. INTRODUCTION .................................................................................................. 4-1 401. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 4-1
402. AIRFOIL ................................................................................................................. 4-1 403. AIRFOIL TERMINOLOGY AND DEFINITIONS ............................................... 4-1 404. AIRFOIL TYPES.................................................................................................... 4-3 405. ROTOR AXIS ......................................................................................................... 4-4 406. AIRFLOW AND REACTIONS IN THE ROTOR DISK ...................................... 4-4
407. ROTOR BLADE ANGLES .................................................................................... 4-9
CHAPTER FIVE - POWERED FLIGHT ............................................................................... 5-1 500. INTRODUCTION .................................................................................................. 5-1 501. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 5-1
502. POWERED FLIGHT .............................................................................................. 5-1 503. HOVERING FLIGHT ............................................................................................ 5-1
504. VERTICAL FLIGHT.............................................................................................. 5-7 505. FORWARD FLIGHT ............................................................................................. 5-8
506. SIDEWARD FLIGHT .......................................................................................... 5-16 507. REARWARD FLIGHT ........................................................................................ 5-17
508. TURNING FLIGHT ............................................................................................. 5-18
CHAPTER SIX - AUTOROTATION ...................................................................................... 6-1 600. INTRODUCTION .................................................................................................. 6-1 601. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 6-1
602. GENERAL .............................................................................................................. 6-1 603. VERTICAL AUTOROTATION ............................................................................ 6-2
604. FORWARD FLIGHT AUTOROTATION ............................................................. 6-3 605. AUTOROTATION DESCENT VARIABLES....................................................... 6-5
606. PHASES OF AUTOROTATION ........................................................................... 6-6 607. WINDMILL BRAKE STATE .............................................................................. 6-13 608. HEIGHT-VELOCITY DIAGRAM ...................................................................... 6-13
CHAPTER SEVEN - PERFORMANCE ................................................................................. 7-1 700. INTRODUCTION .................................................................................................. 7-1 701. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 7-1 702. FACTORS AFFECTING PERFORMANCE ......................................................... 7-1 703. GENERAL .............................................................................................................. 7-2 704. POWER REQUIRED ............................................................................................. 7-4
705. POWER AVAILABLE ........................................................................................... 7-8 706. EFFECT OF TAIL ROTOR ON POWER AVAILABLE ...................................... 7-9
707. POWER REQUIRED EXCEEDS POWER AVAILABLE ................................. 7-10 708. HOVER PERFORMANCE .................................................................................. 7-12 709. CLIMB PERFORMANCE ................................................................................... 7-17 710. REVIEW OF OPTIMUM AIRSPEEDS ............................................................... 7-19
xi
CHAPTER EIGHT - FLIGHT PHENOMENA...................................................................... 8-1 800. INTRODUCTION .................................................................................................. 8-1 801. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 8-1
802. GENERAL .............................................................................................................. 8-1 803. FLIGHT ENVELOPE / V-N DIAGRAM .............................................................. 8-1 804. VIBRATION ANALYSIS ...................................................................................... 8-5 805. GROUND VORTEX .............................................................................................. 8-6 806. COMPRESSIBILITY ............................................................................................. 8-7
807. RETREATING BLADE STALL .......................................................................... 8-10 808. GROUND RESONANCE .................................................................................... 8-11 809. DYNAMIC ROLLOVER ..................................................................................... 8-11 810. LOW-G CONDITIONS ........................................................................................ 8-16 811. LOW ROTOR RPM AND ROTOR STALL ........................................................ 8-17
CHAPTER NINE - TAIL ROTOR CONSIDERATIONS ..................................................... 9-1 900. INTRODUCTION .................................................................................................. 9-1 901. LESSON TOPIC LEARNING OBJECTIVES ....................................................... 9-1
902. TORQUE EFFECT ................................................................................................. 9-1 903. VERTICAL STABILIZER ..................................................................................... 9-2
904. TRANSLATING TENDENCY AND HOVER ATTITUDE ................................. 9-3 905. WEATHER VANING ............................................................................................ 9-4 906. TAIL ROTOR FAILURES AND ISSUES ............................................................. 9-4
APPENDIX A - GLOSSARY ................................................................................................... A-1 A100. GLOSSARY .......................................................................................................... A-1
APPENDIX B - REFERENCES AND READING LIST .......................................................B-1
xii
TABLE OF FIGURES
Figure 1-1 Basic Components of the rotor system ............................................................. 1-3 Figure 1-2 Tandem Rotor Helicopters ................................................................................ 1-4 Figure 1-3 Coaxial rotors ..................................................................................................... 1-4 Figure 1-4 HH-43 Hiskie with intermeshing rotors ........................................................... 1-5 Figure 1-5 Basic tail rotor components............................................................................... 1-6
Figure 2-1 Resultant by the Tip-to-Tail Method ............................................................... 2-2 Figure 2-2 Force Vectors on an Airfoil ............................................................................... 2-2 Figure 2-3 Force Vectors on Aircraft in Flight .................................................................. 2-2 Figure 2-4 Static pressure .................................................................................................... 2-4 Figure 2-5 Molecular Energy and Air Temperature ......................................................... 2-5
Figure 2-6 Standard Atmospheric Table ............................................................................ 2-6 Figure 2-7 Pressure Altitude vs. True Altitude with Varying Local Pressures .............. 2-7
Figure 2-8 DA Chart............................................................................................................. 2-9
Figure 2-9 Dew Point Correction Chart ........................................................................... 2-10 Figure 2-10 Thrust Variation with Humidity .................................................................... 2-11 Figure 2-11 Sample Effects of DA Calculations on CH-53D Performance ..................... 2-12
Figure 3-1 Aircraft Reference System ................................................................................ 3-2 Figure 3-2 Area of a Blade ................................................................................................... 3-3
Figure 3-3 Profile of an airfoil ............................................................................................. 3-3 Figure 3-4 Forces acting on a helicopter in forward flight ............................................... 3-4
Figure 3-5 Production of lift ................................................................................................ 3-5 Figure 3-6 Water flow through a tube ................................................................................ 3-6
Figure 3-7 Venturi effect ...................................................................................................... 3-7 Figure 3-8 Notional load factor diagram ............................................................................ 3-9 Figure 3-9 Notional Drag profiles ..................................................................................... 3-10
Figure 3-10 Induced Drag .................................................................................................... 3-11 Figure 3-11 Drag Curve ....................................................................................................... 3-12
Figure 3-12 Pressure Changes Around a Cambered Airfoil ............................................ 3-13 Figure 3-13 Magnus Effect................................................................................................... 3-14
Figure 3-14 Pressure Distribution for Magnus Effect ....................................................... 3-14 Figure 3-15 Induced Velocity Idealized for Momentum Theory ..................................... 3-15 Figure 3-16 Variables in the Blade Element Theory ......................................................... 3-16 Figure 3-17 Airflow over the Airfoil ................................................................................... 3-16 Figure 3-18 Blade Element Diagram .................................................................................. 3-17
Figure 4-1 Aerodynamic terms of an airfoil ....................................................................... 4-2
Figure 4-2 Airfoil Types ....................................................................................................... 4-3 Figure 4-3 Blade Twist ......................................................................................................... 4-4 Figure 4-4 Relative Wind ..................................................................................................... 4-5 Figure 4-5 Horizontal component of relative wind............................................................ 4-5 Figure 4-6 Induced Flow ...................................................................................................... 4-5 Figure 4-7 Spanwise induced flow velocities ...................................................................... 4-6
xiii
Figure 4-8 Rotational Relative Wind .................................................................................. 4-6
Figure 4-9 Resultant relative wind ...................................................................................... 4-7
Figure 4-10 Induced flow in forward flight .......................................................................... 4-7 Figure 4-11 In Ground Effect (IGE) ..................................................................................... 4-8 Figure 4-12 Out of Ground Effect (OGE) ............................................................................ 4-9 Figure 4-13 Angle of Incidence .............................................................................................. 4-9 Figure 4-14 Angle of Attack ................................................................................................. 4-10
Figure 5-1 Translating Tendency ........................................................................................ 5-3 Figure 5-2 Pendular action .................................................................................................. 5-4 Figure 5-3 Coning ................................................................................................................. 5-5 Figure 5-4 Gyroscopic precession ....................................................................................... 5-6 Figure 5-5 Forward Cyclic Input ........................................................................................ 5-7
Figure 5-6 No wind hover .................................................................................................... 5-8 Figure 5-7 Transition to forward flight .............................................................................. 5-8
Figure 5-8 Power vs. airspeed chart.................................................................................... 5-9 Figure 5-9 Airflow in forward flight ................................................................................. 5-10
Figure 5-10 Dissymmetry of lift ........................................................................................... 5-11 Figure 5-11 Effect of flapping .............................................................................................. 5-12
Figure 5-12 Blowback ........................................................................................................... 5-13 Figure 5-13 Airflow with minimal headwind ..................................................................... 5-14 Figure 5-14 Airflow just prior to ETL ................................................................................ 5-14
Figure 5-15 ETL.................................................................................................................... 5-15 Figure 5-16 Sideward Flight ................................................................................................ 5-16
Figure 5-17 Rearward Flight ............................................................................................... 5-17 Figure 5-18 Turning Flight .................................................................................................. 5-18
Figure 6-1 Airflow in an autorotation................................................................................. 6-2 Figure 6-2 Rotor disc regions in autorotation zero speed ................................................. 6-2
Figure 6-3 Rotor blade regions in autorotation ................................................................. 6-4 Figure 6-4 Rotor disc regions in autorotation forward speed .......................................... 6-5
Figure 6-5 Force Vectors in Level-Powered Flight at High Speed................................... 6-6 Figure 6-6 Force Vectors after Power Loss – Reduced Collective ................................... 6-7
Figure 6-7 Force Vectors in Autorotative Steady-State Descent ...................................... 6-8 Figure 6-8 RPM Response to Small RPM Variations ....................................................... 6-9 Figure 6-9 Autorotational Rate of Descent Compared to Airspeed ............................... 6-11 Figure 6-10 Blade Element and Thrust during Steady State Auto and Flare................. 6-12 Figure 6-11 Generic Height Velocity Diagram .................................................................. 6-14
Figure 7-1 Total Drag Curve ............................................................................................... 7-3
Figure 7-2 Power Required Versus Airspeed Curve ......................................................... 7-4 Figure 7-3 Aerodynamic Forces Affecting Power Required ............................................ 7-5 Figure 7-4 Power Required Curves versus Airspeed ........................................................ 7-5 Figure 7-5 Optimum Airspeeds ........................................................................................... 7-7 Figure 7-6 Maximum Range Airspeed Adjustment for Winds ........................................ 7-8 Figure 7-7 Induced Power Required ................................................................................. 7-11
xiv
Figure 7-8 Parasite Power Required ................................................................................. 7-11
Figure 7-9 Decrease in Excess Power as Airspeed Decreases ......................................... 7-12
Figure 7-10 Sample hover problem 1 .................................................................................. 7-14 Figure 7-11 Sample hover problem 2 .................................................................................. 7-15 Figure 7-12 Sample hover problem 3 .................................................................................. 7-16 Figure 7-13 Sample cruise problem .................................................................................... 7-18 Figure 7-14 Sample climb problem ..................................................................................... 7-19 Figure 7-15 Optimum Airspeeds ......................................................................................... 7-20
Figure 7-16 Power Required Chart (CH-46E) ................................................................... 7-21 Figure 7-17 Fuel Flow vs. TAS ............................................................................................ 7-22 Figure 7-18 Excess Power .................................................................................................... 7-22 Figure 7-19 Max Range Altitude vs. Gross Weight ........................................................... 7-23 Figure 7-20 AH-1W - Max Range Airspeed vs. Gross Weight ......................................... 7-24
Figure 7-21 MH-60S – Max Range Airspeed vs. Gross Weight ....................................... 7-25 Figure 7-22 RPM vs. Fuel Flow ........................................................................................... 7-26 Figure 7-23 Excess Power .................................................................................................... 7-27 Figure 7-24 Best Angle of Climb ......................................................................................... 7-28
Figure 7-25 Rate of Climb vs. Best Angle of Climb ........................................................... 7-28
Figure 8-1 V-n Diagram for Fixed Wing Aircraft ............................................................. 8-2 Figure 8-2 AH-64 Apache V-n Diagram ............................................................................. 8-3 Figure 8-3 Vibration Analysis ............................................................................................. 8-6
Figure 8-4 Ground Vortex ................................................................................................... 8-7 Figure 8-5 Critical Mach Number ...................................................................................... 8-9
Figure 8-6 Drag Increase with Mach Number ................................................................... 8-9 Figure 8-7 Dynamic rollover .............................................................................................. 8-13 Figure 8-8 Slope takeoff or landing 1................................................................................ 8-14 Figure 8-9 Slope takeoff or landing 2................................................................................ 8-15
Figure 9-1 Tail Rotor Unbalanced Force ........................................................................... 9-2 Figure 9-2 Yaw Control Mechanisms for Various Configurations .................................. 9-2
Figure 9-3 Vertical Stabilizer .............................................................................................. 9-3 Figure 9-4 Translating Tendency ........................................................................................ 9-4
Figure 9-5 Weather Vaning ................................................................................................. 9-4 Figure 9-6 Effects of Wind Direction on Directional Control .......................................... 9-9 Figure 9-7 LTE in a Right Crosswind .............................................................................. 9-11 Figure 9-8 Fly Home Capability After Loss Of Tail Rotor Thrust ................................ 9-13
INTRODUCTION TO THE HELICOPTER 1-1
CHAPTER ONE
INTRODUCTION TO THE HELICOPTER
100. INTRODUCTION
A helicopter is an aircraft lifted and propelled by one or more horizontal rotors. Each rotor consists
of two or more rotor blades. Helicopters are classified as rotorcraft or rotary-wing aircraft to
distinguish them from fixed-wing aircraft because the helicopter derives its source of lift from the
rotor blades rotating around a mast. The word “helicopter” is adapted from the French hélicoptère,
coined by Gustave de Ponton d’Amécourt in 1861, and linked to the Greek words helix/helikos
(“spiral” or “turning”) and pteron (“wing”).
As an aircraft, the primary advantages of the helicopter are due to the rotor blades that revolve
through the air, providing lift without requiring the aircraft to move forward. This lift allows the
helicopter to hover in one area and to take off and land vertically without the need for runways.
For this reason, helicopters are often used in congested or isolated areas where fixed-wing aircraft
are not able to take off or land.
Piloting a helicopter requires adequate, focused, and safety-orientated training. It also requires
continuous attention to the machine and the operating environment. The pilot must work in three
dimensions and use both arms and both legs constantly to keep the helicopter in a desired state.
Coordination, timing, and control touch require simultaneous use when flying a helicopter.
Although helicopters were developed and built during the first half-century of flight, some even
reaching limited production; it was not until 1942 that a helicopter designed by Igor Sikorsky
reached full-scale production, with 131 aircraft built. Even though most previous designs used
more than one main rotor, it was the single main rotor with an anti-torque tail rotor configuration
that was recognized worldwide as the helicopter.
101. HELICOPTER AERODYNAMICS COURSE LEARNING OBJECTIVES
1. Identify the basic physics principles needed to support helicopter flight
2. Identify the basic aerodynamic factors that are vital to helicopter performance
3. Identify airfoil design considerations
4. Identify the three types of rotor systems
5. Identify rotor system dynamics
6. Identify rotorcraft configurations and airfoil design considerations
7. Identify the basic aerodynamic characteristics of the airframe
8. Identify factors that affect helicopter stability and control
CHAPTER ONE HELICOPTER AERODYNAMICS WORKBOOK
1-2 INTRODUCTION TO THE HELICOPTER
9. Identify factors that affect helicopter power required and power available for flight
10. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
11. Explain the aerodynamics of flight
12. Identify factors that lead to undesirable helicopter phenomena
13. Identify actions that prevent undesirable helicopter phenomena
14. Explain undesirable helicopter phenomena
102. ROTOR SYSTEM
The helicopter rotor system is the rotating part of a helicopter that generates lift. A rotor system
may be mounted horizontally, as main rotors are, providing lift vertically; and it may be mounted
vertically, such as a tail rotor, to provide lift horizontally as thrust to counteract torque effect. In
the case of tilt rotors, the rotor mounts on a nacelle that rotates at the edge of the wing to transition
the rotor from a horizontal mounted position, providing lift horizontally as thrust, to a vertical
mounted position providing lift exactly as a helicopter.
The rotor consists of a mast, hub, and rotor blades. The mast is a hollow cylindrical metal shaft
extending upwards from and driven by the transmission. At the top of the mast is the hub. The
hub is the attachment point for the rotor blades. The rotor blades attach to the hub by several
different methods. Main rotor systems are classified according to how the main rotor blades are
attached and move relative to the main rotor hub. There are three basic classifications: semi rigid,
rigid, or fully articulated, although some modern rotor systems use an engineered combination of
these types.
With a single main rotor helicopter, a torque effect generates as the engine turns the rotor. This
torque causes the body of the helicopter to turn in the opposite direction of the rotor (Newton’s
Third Law: Every action has an equal and opposite reaction. To eliminate this effect, some sort
of anti-torque control must be used with a sufficient margin of power available to allow the
helicopter to maintain its heading and prevent the aircraft from moving unsteadily.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER ONE
INTRODUCTION TO THE HELICOPTER 1-3
Figure 1-1 Basic Components of the rotor system
103. ROTOR CONFIGURATIONS
Most helicopters have a single main rotor but require a separate rotor to overcome torque, which
is a turning or twisting force. This occurs through a variable pitch, anti-torque rotor or tail rotor.
This is the design that Igor Sikorsky settled on for his VS-300 helicopter. It has become the
recognized convention for helicopter design, although designs do vary. Helicopter main rotor
designs from different manufacturers rotate in one of two different directions (clockwise or
counter-clockwise when viewed from above). This can make it confusing when discussing
aerodynamic effects on the main rotor between different designs, since the effects may manifest
on opposite sides of each aircraft. For clarity, throughout this workbook all examples use a
counter-clockwise rotating (when viewed from above) main rotor system.
1. Tandem Rotor. Tandem rotor (sometimes referred to as dual rotor) helicopters have two
large horizontal rotor assemblies, instead of one main assembly and a smaller tail rotor. Single
rotor helicopters need a tail rotor to neutralize the twisting momentum produced by the single
large rotor. Tandem rotor helicopters, however, use counter-rotating rotors, each canceling out
the other’s torque. Counter-rotating rotor blades will not collide with and destroy each other if
they flex into the other rotor’s pathway. This configuration has the advantage of being able to
hold more weight with shorter blades, since there are two blade sets. This configuration allows
all of the power from the engines available for lift, whereas a single rotor helicopter must use
some power to counter main rotor torque. Because of this, tandem helicopters make up some of
the most powerful and fastest rotor system aircraft.
CHAPTER ONE HELICOPTER AERODYNAMICS WORKBOOK
1-4 INTRODUCTION TO THE HELICOPTER
Figure 1-2 Tandem Rotor Helicopters
2. Coaxial Rotors. Coaxial rotors are a pair of rotors turning in opposite directions, but
mounted on a mast with the same axis of rotation, one above the other. This configuration is a
noted feature of helicopters produced by the Russian Kamov helicopter design bureau.
Figure 1-3 Coaxial rotors
3. Intermeshing Rotors. Intermeshing rotors on a helicopter are a set of two rotors turning
in opposite directions, with each rotor mast mounted on the helicopter with a slight angle to the
other so that the blades intermesh without colliding. This arrangement allows the helicopter to
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER ONE
INTRODUCTION TO THE HELICOPTER 1-5
function without the need for a tail rotor. It has high stability and powerful lifting capability.
This configuration is sometimes referred to as a synchropter. The arrangement was developed in
Germany for a small anti-submarine warfare helicopter, the Flettner Fl 282 Kolibri. During the
Cold War, the American Kaman Aircraft company produced the HH-43 Huskie, for USAF
firefighting purposes. The latest Kaman K-MAX model is a dedicated sky crane design used for
construction work.
Figure 1-4 HH-43 Hiskie with intermeshing rotors
4. Tail Rotor. The tail rotor is a smaller rotor mounted vertically or near-vertically on the tail
of a traditional single-rotor helicopter. The tail rotor either pushes or pulls against the tail to
counter the torque. The tail rotor drive system consists of a drive shaft, powered from the main
transmission, and a gearbox mounted at the end of the tail boom. The drive shaft may consist of
one long shaft or a series of shorter shafts connected at both ends with flexible couplings. The
flexible couplings allow the drive shaft to flex with the tail boom.
The gearbox at the end of the tail boom provides an angled drive for the tail rotor and may
include gearing to adjust the output to the optimum rotational speed typically measured in
revolutions per minute (rpm) for the tail rotor. On some larger helicopters, one or more
intermediate gearboxes angle the tail rotor drive shaft from along the tail boom or tail cone to the
top of the tail rotor pylon. These also serve as a vertical stabilizing airfoil to alleviate the power
requirement for the tail rotor in forward flight. The pylon (or vertical fin) may also provide
limited anti-torque within certain airspeed ranges if the tail rotor or the tail rotor flight controls
fail.
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1-6 INTRODUCTION TO THE HELICOPTER
Figure 1-5 Basic tail rotor components
104. CONTROLLING FLIGHT
A helicopter has four primary flight controls: Cyclic, Collective, Anti-torque pedals, and
Throttle
1. Cyclic. The cyclic control is usually located between the pilot’s legs and is commonly
called the “cyclic stick” or simply “cyclic.” On most helicopters, the cyclic is similar to a
joystick. The control is called the cyclic because it can vary the pitch of the rotor blades
throughout each revolution of the main rotor system (i.e., through each cycle of rotation) to
develop unequal lift (thrust). The result is to tilt the rotor disk in a particular direction, resulting
in the helicopter moving in that direction. If the pilot pushes the cyclic forward, the rotor disk
tilts forward, and the rotor produces a thrust in the forward direction. If the pilot pushes the
cyclic to the side, the rotor disk tilts to that side and produces thrust in that direction, causing the
helicopter to hover sideways.
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INTRODUCTION TO THE HELICOPTER 1-7
2. Collective. The collective pitch control, or collective, is located on the left side of the
pilot’s seat with a pilot-selected variable friction control to prevent inadvertent movement. The
collective changes the pitch angle of all the main rotor blades collectively (i.e., all at the same
time) and independently of their positions. Therefore, if a collective input is made, all the blades
change equally, increasing or decreasing total lift or thrust, with the result of the helicopter
increasing or decreasing in altitude or airspeed.
3. Anti-torque Pedals. The anti-torque pedals are located in the same position as the rudder
pedals in a fixed-wing aircraft and serve a similar purpose, namely to control the direction in
which the nose of the aircraft is pointed. Application of the pedal in a given direction changes
the pitch of the tail rotor blades, increasing or reducing the thrust produced by the tail rotor,
causing the nose to yaw in the direction of the applied pedal. The pedals mechanically change
the pitch of the tail rotor, altering the amount of thrust produced.
4. Throttle. Helicopter rotors operate at a specific RPM. The throttle controls the power
produced by the engine, which connects to the rotor by a transmission. The purpose of the
throttle is to maintain enough engine power to keep the rotor RPM within allowable limits to
produce enough lift for flight. In single-engine helicopters, if so equipped, the throttle control is
typically a twist grip mounted on the collective control, but it can also be a lever mechanism in
fully governed systems, as seen in the TH-57. Multi-engine helicopters generally have a power
lever or mode switch for each engine.
105. FLIGHT CONDITIONS
There are two basic flight conditions for a helicopter: hover and forward flight. Hovering is the
most challenging part of flying a helicopter. This is because a helicopter generates its own gusty
air while in a hover, which acts against the fuselage and flight control surfaces. The result is the
need for constant control inputs and corrections by the pilot to keep the helicopter where it is
required to be. Despite the complexity of the task, the control inputs in a hover are simple. The
cyclic is used to eliminate drift in the horizontal direction: forward, backward, right and left.
The collective is used to maintain altitude. The pedals are used to control nose direction or
heading. The interaction of these controls makes hovering so difficult, since an adjustment in
any one control requires an adjustment of the other two, creating a cycle of constant correction.
Displacing the cyclic forward initially causes the nose to pitch down, with a resultant increase in
airspeed and loss of altitude. Aft cyclic initially causes the nose to pitch up, slowing the
helicopter and causing it to climb; however, as the helicopter reaches a state of equilibrium, the
horizontal stabilizer helps level the helicopter to minimize drag, unlike an airplane. Therefore,
the helicopter has very little pitch deflection up or down when the helicopter is stable in a flight
mode. The variation from absolutely level attitude depends on the particular helicopter and the
horizontal stabilizer function.
Increasing collective (power) while maintaining a constant airspeed induces a climb while
decreasing collective causes a descent. Coordinating these two inputs, down collective plus aft
cyclic or up collective plus forward cyclic, results in airspeed changes while maintaining a
constant altitude.
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1-8 INTRODUCTION TO THE HELICOPTER
The pedals serve the same function in both a helicopter and a fixed-wing aircraft, to maintain
balanced flight. This is done by applying pedal input in whichever direction is necessary to
center the ball in the turn and bank indicator.
THE ATMOSPHERE 2-1
CHAPTER TWO
THE ATMOSPHERE
200. INTRODUCTION
The purpose of this chapter is to provide a review of basic physics and atmospherics relevant to
helicopter aerodynamics. Review Fundamentals of Aerodynamics Student Guide
(NAVAVSCOLSCOM-SG-111) from API if necessary.
201. LESSON TOPIC LEARNING OBJECTIVES
1. Identify the basic physics principles needed to support helicopter flight
2. Identify the basic aerodynamic factors that are vital to helicopter performance
3. Identify airfoil design considerations
4. Identify rotor system dynamics
5. Identify rotorcraft configurations and airfoil design considerations
6. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
202. REVIEW OF BASIC PHYSICS AND AERODYNAMICS
Based on the student naval aviator’s recent completion of aviation preflight indoctrination,
vector analysis, physics and atmospherics is abbreviated and includes only those concepts
applicable to rotary wing flight. If necessary, review “Fundamentals of Aerodynamics”
workbook from API. A few concepts, such as density altitude (DA) computation, are introduced
in this section as it relates to the reviewed material.
203. VECTOR ANALYSIS
A scalar is a quantity that describes only magnitude, e.g., time, temperature, or volume. It is
expressed as a single number including units. A vector is a quantity that describes both
magnitude and direction. It commonly represents displacement, velocity, acceleration, or force.
Vectors are represented as arrows. The direction and length of the arrow represent the direction
and magnitude of the vector. Vectors may be added by placing the tail of each succeeding vector
on the head (or tip) of the one preceding it and drawing the resultant vector from the tail of the
first to the tip of the last. This new vector is the resulting magnitude and direction of all the
original vectors working together.
Conversely, a vector may be deconstructed into two or more component vectors that lie in a
desired plane of motion or direction.
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Figure 2-1 Resultant by the Tip-to-Tail Method
Figure 2-2 Force Vectors on an Airfoil
Figure 2-3 Force Vectors on Aircraft in Flight
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THE ATMOSPHERE 2-3
Figures 2-2 and 2-3 show an example of vectors used to depict the forces acting on an airfoil
segment, and an aircraft in flight. Note that the total rotor thrust vector may be resolved into
perpendicular components, a vertical component and a horizontal component. The drag and
weight can also combine to form a resultant of these two forces, which must then be equal and
opposite to the total rotor thrust in equilibrium flight.
204. ESSENTIAL TERMS AND DEFINITIONS
1. Volume (v) is the amount of space occupied by an object.
2. Density ( or ‘rho’) is mass per unit volume.
3. Weight (W) is the force with which a mass is attracted toward the center of the earth by
gravity.
4. A moment (M) is created when a force is applied at some distance from an axis, and tends
to produce rotation about that point. A moment is a vector quantity equal to a force (F) times
the distance (d) from the point of rotation on a line that is perpendicular to the applied
force vector. This perpendicular distance is called the moment arm. Torque (Q) is another
word for a moment created by a force.
5. Work (W) is done when a force acts on a body and moves it. It is a scalar quantity equal
to the force (F) times the distance of displacement (s).
6. Power (P) is the rate of doing work or work done per unit of time.
7. Energy is a scalar measure of a body’s capacity to do work. There are two types of
energy: potential energy and kinetic energy. Energy cannot be created or destroyed, but may be
transformed from one form to another. This principle is called the law of conservation of energy.
8. Potential energy (P.E.) is the ability of a body to do work because of its position or state
of being. It is a function of mass (m), gravity (g), and height (h).
9. Kinetic energy (K.E.) is the ability of a body to do work because of its motion. It is a
function of mass (m) and velocity (V).
Work may be performed on a body to change its position and give it potential energy or work
may give the body motion so that it has kinetic energy. Under ideal conditions, if no work is
being done on an object, its total energy will remain constant. Such an object is considered to be
in a closed system. In a closed system, the total energy will remain constant but potential energy
may be converted to kinetic energy, and vice versa. For example, the kinetic energy of a glider
in forward flight may be converted into potential energy by climbing. As the glider’s altitude
(P.E.) increases, its velocity (K.E.) will decrease.
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205. PROPERTIES OF THE ATMOSPHERE
The atmosphere is composed of approximately 78% nitrogen (N2), 21% oxygen (O2), and 1%
other gases by volume, which includes argon and carbon dioxide. Air is considered a uniform
mixture of these gases and will be examined as a whole rather than as separate gases.
1. Static pressure (PS) is the force each air particle exerts on those around it. On a more
macroscopic scale, ambient static pressure (14.7 psi at sea level on standard day) is equal to the
weight of a column of air over a given area. The force of static pressure acts perpendicularly to
any surface with which the air particles collide. As altitude increases, less air is above you, so
the weight of the column of air decreases. Thus atmospheric static pressure decreases with an
increase in altitude at a rate of approximately 1.0 in-Hg per 1000 feet, near the earth’s surface.
Figure 2-4 Static pressure
2. Air density ( ) is the total mass of air particles per unit of volume. The distance between
individual air particles increases with altitude resulting in fewer particles per unit volume.
Therefore, air density decreases with an increase in altitude.
3. Density Ratio (σ) is the ratio of the density of air at a specific altitude to that of the
standard altitude (sea level).
4. Temperature (T) is a measure of the average kinetic energy of air particles. As
temperature increases, particles begin to move and vibrate faster, increasing their kinetic energy.
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Air temperature decreases linearly with an increase in altitude at a rate of approximately
2 °C (3.57 F) per 1000 ft. up through 36,000 feet MSL. This is called the standard, or
adiabatic lapse rate. Above 36,000 feet lies the isothermal layer where air is at a constant
temperature of -56.5 °C.
Figure 2-5 Molecular Energy and Air Temperature
5. Humidity is the amount of water vapor in the air. As humidity increases, water molecules
displace an equal number of air molecules. Since water molecules have less mass (H2O,
molecular weight (MW) 18) than air (N2, MW 28; and O2, MW 32) and occupy approximately
the same volume, the overall mass in a given volume decreases. Therefore, as humidity
increases, air density decreases. Compared to dry air, the density of air at 100% humidity is
4% less.
6. Viscosity () is a measure of the air's resistance to flow and shearing. Air viscosity can
determine its tendency to either stick to a surface or how easily it flows past it. For liquids, as
temperature increases, viscosity decreases. Recall that the oil in your car flows better or “gets
thinner” when the engine gets hot. Just the opposite happens with air: Air viscosity increases
with an increase in temperature.
206. THE STANDARD ATMOSPHERE
The atmospheric layer were most flying is done is an ever-changing environment. Temperature
and pressure vary with altitude, season, location, time, and even solar sunspot activity. It is
impractical to take all of these into consideration when discussing aircraft performance. In order
to disregard these atmospheric changes, an engineering baseline was developed called the
standard atmosphere. It is a set of reference conditions giving average values of air properties
as a function of altitude. Unless otherwise stated, any discussion of atmospheric properties
in this course will assume standard atmospheric conditions.
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2-6 THE ATMOSPHERE
Figure 2-6 Standard Atmospheric Table
207. ALTITUDE COMPUTATIONS
One of the benefits of a standard atmosphere is the concepts of pressure altitude (PA) and
density altitude (DA). PA is that altitude in the standard atmosphere that corresponds to a
particular static air pressure. An aircraft altimeter senses pressure through the static portion of
the pitot-static system, then shows the altitude at which that pressure would be found in the
standard atmosphere. Early altimeters were referenced to the standard Sea Level pressure of
29.92 inches Hg at sea level. Altitude was estimated by determining the altitude in the standard
atmosphere at which the measured pressure would occur. Modern altimeters are adjusted to
yield accurate altitude at a known point, like an airfield, by changing reference sea level pressure
to an appropriate value. Airport meteorologists measure air pressure, determine what pressure at
sea level would have to exist to yield an accurate altitude reading using standard pressure lapse
rate, and report that setting to pilots. After being set properly, an adjustable altimeter reports the
altitude at which the measured pressure would be found if a standard pressure lapse rate was
applied to a sea level pressure equal to that set by the pilot. Standard pressure lapse rate is
1000 feet of PA for each one inch of Hg. To determine PA (in the standard atmosphere) for use
in calculations a pilot needs only to set 29.92 inches into the altimeter and read the result.
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Properly setting the altimeter and periodically checking for changes in the prescribed setting can
be very important. To properly set the altimeter, pilots should make sure that they are receiving
the altimeter setting in inches of mercury for height above sea level. Three types of settings may
be encountered overseas: QNH, QNE, and QFE.
1. QNH is altitude corrected to standard sea level (provided in ATIS in the United States).
2. QNE is PA (altimeter set to 29.92)
3. QFE is a setting at an airfield to read height above ground at that location (the altimeter
would read zero at the airfield surface).
Overseas, settings are often given in hectopascals (millibars), rather than inches of mercury. To
avoid problems, listen for foreign controllers’ statements of what their pressure reference is and,
if necessary, use the Flight Information Handbook to convert.
Checking for changes in altimeter setting during cross country travel or as weather moves in can
also be important. When station pressure or temperature drops, an altimeter set at the previous
condition will read higher than it should. For example, a flight at 1000 ft. AGL in the standard
atmosphere would have the aircraft at a pressure of 28.92. Note that flight into a high pressure
system would cause the altimeter to read low (actual altitude of 2000 ft. AGL) while flight into a
low pressure system would cause the altimeter to read higher than actual altitude (0 ft. AGL).
REMEMBER: “HIGH TO LOW LOOK OUT BELOW” OR “HOT TO COLD LOOK
OUT BELOW.”
Figure 2-7 Pressure Altitude vs. True Altitude with Varying Local Pressures
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2-8 THE ATMOSPHERE
208. ALTITUDE COMPUTATIONS – DENSITY ALTITUDE
A more appropriate term for correlating aerodynamic performance in the nonstandard
atmosphere is density altitude (DA). DA is that altitude in the standard atmosphere which
corresponds to a particular air density. Changes in air density are caused by variations in
atmospheric pressure, temperature, and humidity. Density altitude (DA) is the PA corrected for
temperature and humidity deviations from the standard atmosphere. If you know the
outside air temperature and humidity, and you can determine the PA, you can derive the DA.
DA is the environmental factor that most significantly affects power available.
Typically, aviators use a chart to determine DA for the ambient PA and temperature. Using
Figure 2-8, enter the chart at the bottom at the appropriate outside air temperature (OAT) and
plot vertically upward to intersect the current PA depicted on the diagonals, determined by
dialing 29.92 into the aircraft altimeter. From this point, read laterally to the left to determine the
DA (not corrected for humidity). In the example depicted, a temperature of 6 °C and 2400’ PA,
results in a 2000’ DA.
Another method for estimating DA is to use the ‘rule of thumb’ equation below.
DA = PA + [(TAmbient – TStd@Altitude)] x 120
For PA, dial in 29.92 " Hg. Temperatures are in C.
The above ‘rule of thumb’ merely requires an accurate understanding of standard temperature at
altitude. Remember that the temperature at sea level for a standard day is 15 °C. With an
average lapse rate of 2 °C / 1000’ MSL, the standard temperature at altitude can be easily
determined; i.e., 5 °C at 5000’ MSL, and -5 °C at 10,000’ MSL. This estimation of DA still fails
to correct for humidity, which is discussed below.
As mentioned earlier, changes in the water vapor content, or humidity, can also greatly affect
the density of the air, in addition to temperature deviations from standard. To recap, as humidity
increases, water molecules with less mass and approximately the same volume as air molecules
displace the more dense air molecules to make the same overall volume containing less actual
mass. Thus, an increase in humidity leads to a decrease in air density, and, therefore, an increase
in DA.
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THE ATMOSPHERE 2-9
Figure 2-8 DA Chart
One way to adjust calculations for humidity is to use a higher temperature than might be
associated with lower density in performance charts. This fictional quantity is known as virtual
temperature, and is defined as OAT corrected for relative humidity. In the same way that wind
chill is applied to a cold day’s temperature to reflect how the wind affects the human body, a
virtual temperature correction may be applied to a temperature measurement to reflect the effect
of humidity on the air’s density. The dew point temperature correction chart accepts dew point
and temperature, and then yields virtual temperature and DA.
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2-10 THE ATMOSPHERE
Figure 2-9 Dew Point Correction Chart
Moisture in the air can be slightly beneficial in controlling engine temperature, but generally
tends to be detrimental to helicopter performance. The decrease in the density of the airflow due
to the presence of water molecules requires more mass flow of air to produce the same amount of
thrust. Since only a limited amount of air can be run through the engine, the effect of water
vapor is to reduce power available.
This loss of power available and aforementioned cooling effects tend to offset each other in
typical helicopter operating scenarios, so engine performance doesn’t change as much with
humidity as it does with temperature.
With respect to rotor systems, reduced air density decreases the lift produced on the rotor blades.
For this reason, the overall effect of humidity degrades helicopter performance.
A common adjustment is the 10% rule of thumb. Add 100 feet to your DA (based on PA and
OAT), for every 10% relative humidity above 0% RH.
DA (corrected for RH) = DA (chart) + (100’ x RH/10%)
The 10% adjustment factor stems from a linear approximation of the curve. Some interpretations
of the curve state that the relative humidity (RH) correction (10% adjustment factor) doesn't go
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THE ATMOSPHERE 2-11
into effect until the RH is above 40% (40% rule). This is because the same curve in Figure 2-10
can be estimated by two distinct slopes, with this 40% rule appearing to give a better
approximation. For example, 0-40% humidity results in no correction, and 50-100% humidity
results in a 100-600 foot altitude correction for humidity (rather than an errant 500-1000 foot
correction) based on the “10% rule.”
Figure 2-10 Thrust Variation with Humidity
A comparison of the three commonly used methods to compute DA indicates that a significant
variation exists between the chosen methods. For example, if we assume an OAT of 30 C
(86 F), PA of sea level and Dew Point of 30 C (RH=100%) we obtain a DA of 1800 feet based
on the DA chart using PA and an uncorrected OAT. If we incorporate the "100 foot-10% RH
rule" for 100% RH the DA is increased by 1000 feet to 2800 feet or to 2400 feet if we only apply
the "rule of thumb" for RH above 40% as some NATOPS manuals dictate. The actual DA
obtained from the DA chart using a corrected OAT yields 2200 feet.
Note the effect of the differences applied to typical aircraft performance data (CH53D) in
Figure 2-11. Making no adjustment might lead to overestimation of capabilities. The difference
is relatively small, but may result in operations conducted close to safe power margins. Ignoring
DA effects could result in exceeding safe margins. Being overly conservative could limit the
ability to complete a mission satisfactorily. The 40% rule offers the most accurate quick
estimate of humidity effects, compared to the more conservative 10% rule.
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DA (corrected for RH >40%) = DA (chart) + 100’ (RH – 40%)/10%
And is only corrected for RH > 40%
Again, for calculations in the field, PA is easily obtained by setting 29.92" Hg in the Kollsman
window of the barometric altimeter. Obtaining the dew point is usually a little more difficult
unless you have access to a weather service. In the absence of any of this information, you can
always assume a worst case scenario of 100% RH which is when the OAT and dew point are the
same.
For comparison purposes, Figure 2-11 depicts for a CH-53D the relative accuracy of the three
techniques for humidity correction of DA with an RH of 100%.
Adjustment DA Max Gross Wt. (HOGE)
NONE 7800 FT 34,800 lbs.
10% RULE 8800 FT 34,000 lbs.
DA COMPUTER 8400 FT 34,500 lbs.
40% RULE 8400 FT 34,500 lbs.
Figure 2-11 Sample Effects of DA Calculations on CH-53D Performance
The 10% Rule provides a more conservative estimate of DA and is the recommended method in
most helicopter NATOPS manuals. If a NATOPS manual does not discuss the effects of
humidity, be conservative and apply the 10% Rule.
HELICOPTER AERODYNAMICS BASICS 3-1
CHAPTER THREE
HELICOPTER AERODYNAMICS BASICS
300. INTRODUCTION
The purpose of this chapter is to introduce the student to aerodynamic principles and
fundamentals that apply to helicopters.
301. LESSON TOPIC LEARNING OBJECTIVES
1. Identify the basic physics principles needed to support helicopter flight
2. Identify the basic aerodynamic factors that are vital to helicopter performance
3. Identify airfoil design considerations
4. Identify rotor system dynamics
5. Identify rotorcraft configurations and airfoil design considerations
6. Identify the basic aerodynamic characteristics of the airframe
7. Identify factors that affect helicopter stability and control
8. Identify factors that affect helicopter power required and power available for flight
9. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
10. Explain the aerodynamics of flight
302. AIRCRAFT REFERENCE SYSTEM
An aircraft's (helicopter or fixed-wing) reference system consists of three mutually perpendicular
lines (axes) intersecting at a single point. This point, called the center of gravity (CG), is the
point at which all weight is concentrated and at which all forces are measured. Theoretically, the
aircraft will balance if suspended at the CG. When in flight, the aircraft will rotate about the CG,
so all moments will be resolved around it as well. The CG will move as fuel burns,
bombs/missiles expended, or cargo shifts.
The longitudinal axis passes from the nose to the tail of the aircraft. Rotation on the
longitudinal axis is roll, or lateral control. Movement along the longitudinal axis is surge.
The lateral axis passes from wingtip to wingtip. Rotation on the lateral axis is pitch, or
longitudinal control. Movement along the lateral axis is sway.
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The vertical axis passes vertically through the CG. Rotation on the vertical axis is yaw, or
directional control. Movement along the vertical axis is heave. As an aircraft moves through
the air, the axis system moves with it. Therefore, the movement of the aircraft can be described
by the movement of its CG.
Figure 3-1 Aircraft Reference System
303. GENERAL
Gravity acting on the mass (the amount of matter) of an object creates a force called weight. The
rotor blade in Figure 3-2 weighs 100 lbs. It is 20 feet long (span) and is 1 foot wide (chord).
Accordingly, its surface area is 20 square feet.
The blade is perfectly balanced on a pinpoint stand, as seen in Figure 3-3, from looking at it from
the end (the airfoil view). The goal is for the blade to defy gravity and stay exactly where it is
when we remove the stand. If we do nothing before removing the stand, the blade will simply
fall to the ground. Can we exert a force (a push or pull) opposite gravity that equals the 100 lb.
weight of the blade? Yes, in helicopters we use aerodynamic force to oppose weight and to
maneuver.
Every object in the atmosphere is surrounded by a gas that exerts a static force of 2,116 lb. per
square foot (a force times a unit area, called pressure) at sea level. However, that pressure is
exerted equally all over the blade (top and bottom) and therefore does not create any useful force
on the blade. We need only create a difference of a single pound of static pressure differential
per square foot of blade surface to have a force equal to the blade’s weight (100 lb. of upward
pressure opposite 100 lb. downward weight).
Total pressure consists of static pressure and, if the air is moving, dynamic pressure (a pressure
in the direction of the air movement). If dynamic pressure is increased the static pressure will
decrease. Due to the design of the airfoil, the velocity of the air passing over the upper surface
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will be greater than that of the lower surface, leading to higher dynamic pressure on the upper
surface than on the lower surface. The higher dynamic pressure on the upper surface lowers the
static pressure on the upper surface. The static pressure on the bottom will now be greater than
the static pressure on the top. The blade will experience an upward force. With just the right
amount of air passing over the blade the upward force will equal one pound per square foot.
This upward force is equal to, and acts opposite the blade’s weight of 100 lb. So, if we now
remove the stand, the blade will defy gravity and remain in its position (ignoring rearward drag
for the moment).
Figure 3-2 Area of a Blade
Figure 3-3 Profile of an airfoil
The force created by air moving over an object (or moving an object through the air) is called
aerodynamic force. Aero means air. Dynamic means moving or motion. Accordingly, by
moving the air over an airfoil we can change the static pressures on the top and bottom thereby
generating a useful force (an aerodynamic force). The portion of the aerodynamic force that is
usually measured perpendicular to the air flowing around the airfoil is called lift and is used to
oppose weight. Drag is the portion of aerodynamic force that is measured as the resistance
created by an object passing through the air (or having the air passed over it). Drag acts in a
stream-wise direction with the wind passing over the airfoil and retards forward movement.
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Figure 3-4 Forces acting on a helicopter in forward flight
304. FORCES ACTING ON THE AIRCRAFT
Once a helicopter leaves the ground, it is acted upon by four aerodynamic forces; thrust, drag,
lift, and weight. Understanding how these forces work and knowing how to control them with
the use of power and flight controls are essential to flight. They are defined as follows:
Lift: opposes the downward force of weight, is produced by the dynamic effect of the air acting
on the airfoil and acts perpendicular to the flightpath through the center of lift.
Weight: the combined load of the aircraft itself, the crew, the fuel, and the cargo or baggage.
Weight pulls the aircraft downward because of the force of gravity. It opposes lift and acts
vertically downward through the aircraft’s center of gravity (CG).
Thrust: the force produced by the power plant/ propeller or rotor. It opposes or overcomes the
force of drag. As a general rule, it acts parallel to the longitudinal axis. However, this is not
always the case, as explained later.
Drag: a rearward, retarding force caused by disruption of airflow by the wing, rotor, fuselage,
and other protruding objects. Drag opposes thrust and acts rearward parallel to the relative wind.
305. LIFT
Lift is generated when an object changes the direction of flow of a fluid or when the fluid is
forced to move by the object passing through it. When the object and fluid move relative to each
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other and the object turns the fluid flow in a direction perpendicular to that flow, the force
required to do this work creates an equal and opposite force that is lift. The object may be
moving through a stationary fluid, or the fluid may be flowing past a stationary object. These
two are effectively identical as, in principle, it is only the frame of reference of the viewer which
differs. The lift generated by an airfoil depends on such factors as:
1. Speed of the airflow
2. Density of the air
3. Total area of the segment or airfoil
4. Angle of attack (AOA) between the air and the airfoil
The AOA is the angle at which the airfoil meets the oncoming airflow (or vice versa). In the
case of a helicopter, the object is the rotor blade (airfoil) and the fluid is the air. Lift is produced
when a mass of air is deflected, and it always acts perpendicular to the resultant relative wind. A
symmetric airfoil must have a positive AOA to generate positive lift. At a zero AOA, no lift is
generated. At a negative AOA, negative lift is generated. A cambered or nonsymmetrical airfoil
may produce positive lift at zero, or even small negative AOA.
The basic concept of lift is simple. However, the details of how the relative movement of air and
airfoil interact to produce the turning action that generates lift are complex. In any case causing
lift, an angled flat plate, revolving cylinder, airfoil, etc., the flow meeting the leading edge of the
object is forced to split over and under the object. The sudden change in direction over the
object causes an area of low pressure to form behind the leading edge on the upper surface of the
object. In turn, due to this pressure gradient and the viscosity of the fluid, the flow over the
object is accelerated down along the upper surface of the object. At the same time, the flow
forced under the object is rapidly slowed or stagnated causing an area of high pressure. This also
causes the flow to accelerate along the upper surface of the object. The two sections of the fluid
each leave the trailing edge of the object with a downward component of momentum, producing
lift.
Figure 3-5 Production of lift
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Bernoulli’s Principle
Bernoulli’s principle describes the relationship between internal fluid pressure and fluid velocity.
It is a statement of the law of conservation of energy and helps explain why an airfoil develops
an aerodynamic force. The concept of conservation of energy states energy cannot be created or
destroyed and the amount of energy entering a system must also exit. Specifically, in this case
the “energy” referred to is the dynamic pressure (the kinetic energy of the air - more velocity,
more kinetic energy) and static air pressure (potential energy). These will change among
themselves, but the total pressure energy remains constant inside the tube.
A simple tube with a constricted portion near the center of its length illustrates this principle. An
example is running water through a garden hose. The mass of flow per unit area (cross-sectional
area of tube) is the mass flow rate. In Figure 3-6 the flow into the tube is constant, neither
accelerating nor decelerating; thus, the mass flow rate through the tube must be the same at
stations 1, 2, and 3. If the cross-sectional area at any one of these stations, or any given point, in
the tube is reduced, the fluid velocity must increase to maintain a constant mass flow rate to
move the same amount of fluid through a smaller area. The continuity of mass flow causes the
air to move faster through the venturi. In other words, fluid speeds up in direct proportion to the
reduction in area.
Figure 3-6 Water flow through a tube
Bernoulli (Ptotal = Pdynamic + Pstatic) states that the increase in velocity will increase the stream-wise
dynamic pressure. Since the total pressure in the tube must remain constant, the static pressure
on the sides of the venturi will decrease. Venturi effect is the term used to describe this
phenomenon.
Figure 3-7 illustrates plates of one square foot in the dynamic flow and on the sides of the tube
indicating static pressure, with corresponding pressure. At point 2, it is easier to visualize the
static pressure reduction on the top of the airfoil as compared to the bottom of the airfoil, which
is depicted as outside of the tube and therefore at ambient static pressure. Keep in mind with
actual blades it is not a simple as this example because the bottom static pressure is influenced
by blade design and blade angle, among other things. However, the basic idea is that it is the
static pressure differential between the top and bottom multiplied by the surface area of the blade
that generates the aerodynamic force.
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Figure 3-7 Venturi effect
Venturi Flow
While the amount of total energy within a closed system (the tube) does not change, the form of
the energy may be altered. Pressure of flowing air may be compared to energy in that the total
pressure of flowing air always remains constant unless energy is added or removed. Fluid flow
pressure has two components, static and dynamic pressure. Static pressure is the pressure
component measured in the flow but not moving with the flow as pressure is measured. Static
pressure is also known as the force per unit area acting on a surface. Dynamic pressure of flow
is that component existing as a result of movement of the air. The sum of these two pressures is
total pressure. As air flows through the constriction, static pressure decreases as velocity
increases. This increases dynamic pressure. Figure 3-7 depicts the bottom half of the constricted
area of the tube, which resembles the top half of an airfoil. Even with the top half of the tube
removed, the air still accelerates over the curved area because the upper air layers restrict the
flow, just as the top half of the constricted tube did. This acceleration causes decreased static
pressure above the curved portion and creates a pressure differential caused by the variation of
static and dynamic pressures.
Newton’s Third Law of Motion
Additional lift is provided by the rotor blade’s lower surface as air striking the underside is
deflected downward. According to Newton’s Third Law of Motion, “for every action there is an
equal and opposite reaction,” the air that is deflected downward also produces an upward
(lifting) reaction.
Since air is much like water, the explanation for this source of lift may be compared to the
planing effect of skis on water. The lift that supports the water skis (and the skier) is the force
caused by the impact pressure and the deflection of water from the lower surfaces of the skis.
Under most flying conditions, the impact pressure and the deflection of air from the lower
surface of the rotor blade provides a comparatively small percentage of the total lift. The
majority of lift is the result of decreased pressure above the blade, rather than the increased
pressure below it.
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306. WEIGHT
Normally, weight is thought of as being a known, fixed value, such as the weight of the
helicopter, fuel, and occupants. To lift the helicopter off the ground vertically, the rotor disk
must generate enough lift to overcome or offset the total weight of the helicopter and its
occupants. Newton’s First Law states: “Every object in a state of uniform motion tends to
remain in that state of motion unless an external force is applied to it.” In this case, the object is
the helicopter whether at a hover or on the ground and the external force applied to it is lift,
which is accomplished by increasing the pitch angle of the main rotor blades. This action forces
the helicopter into a state of motion, without it the helicopter would either remain on the ground
or at a hover.
The weight of the helicopter can also be influenced by aerodynamic loads. When you bank a
helicopter while maintaining a constant altitude, the “G” load or load factor increases. The load
factor is the actual load on the rotor blades at any time, divided by the normal load or gross
weight (weight of the helicopter and its contents). Any time a helicopter flies in a constant
altitude curved flightpath, the load supported by the rotor blades is greater than the total weight
of the helicopter. The tighter the curved flightpath is, the steeper the bank is; the more rapid the
flare or pullout from a dive is, the greater the load supported by the rotor. Therefore, the greater
the load factor must be.
To overcome this additional load factor, the helicopter must be able to produce more lift. If
excess engine power is not available, the helicopter either descends or has to decelerate in order
to maintain the same altitude. The load factor and, hence, apparent gross weight increase is
relatively small in banks up to 30°. Even so, under the right set of adverse circumstances, such
as high-density altitude, turbulent air, high gross weight, and poor pilot technique, sufficient or
excess power may not be available to maintain altitude and airspeed. Pilots must take all of these
factors into consideration throughout the entire flight from the point of ascending to a hover to
landing. Above 30° of bank, the apparent increase in gross weight soars. At 30° of bank, or
pitch, the apparent increase is only 16 percent, but at 60°, it is twice the load on the wings and
rotor disk. For example, if the weight of the helicopter is 1,600 pounds, the weight supported by
the rotor disk in a 30° bank at a constant altitude would be 1,856 pounds (1,600 + 16 percent (or
256)). In a 60° bank, it would be 3,200 pounds; in an 80° bank, it would be almost six times as
much, or 8,000 pounds. It is important to note that each rotor blade must support a percentage of
the gross weight. In a two-bladed system, each blade of the 1,600-pound helicopter as stated
above would have to lift 50 percent or 800 pounds. If this same helicopter had three rotor blades,
each blade would have to lift only 33 percent, or 533 pounds. One additional cause of large load
factors is rough or turbulent air. The severe vertical gusts produced by turbulence can cause a
sudden increase in AOA, resulting in increased rotor blade loads that are resisted by the inertia of
the helicopter.
Each type of helicopter has its own limitations that are based on the aircraft structure, size, and
capabilities. Regardless of how much weight one can carry or the engine power that it may have,
they are all susceptible to aerodynamic overloading. Unfortunately, if the pilot attempts to push
the performance envelope the consequence can be fatal. Aerodynamic forces effect every
movement in a helicopter, whether it is increasing the collective or a steep bank angle.
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Anticipating results from a particular maneuver or adjustment of a flight control is not good
piloting technique. Instead pilots need to truly understand the capabilities of the helicopter under
any and all circumstances and plan never to exceed the flight envelope for any situation.
Figure 3-8 Notional load factor diagram
307. THRUST
Thrust, like lift, is generated by the rotation of the main rotor disk. In a helicopter, thrust can be
forward, rearward, sideward, or vertical. The resultant lift and thrust determines the direction of
movement of the helicopter.
The solidity ratio is the ratio of the total rotor blade area, which is the combined area of all the
main rotor blades, to the total rotor disk area. This ratio provides a means to measure the
potential for a rotor disk to provide thrust and lift. The mathematical calculations needed to
calculate the solidity ratio for each helicopter may not be of importance to most pilots but what
should be are the capabilities of the rotor disk to produce and maintain lift. Many helicopter
accidents are caused from the rotor disk being overloaded. Simply put, pilots attempt maneuvers
that require more lift than the rotor disk can produce or more power than the helicopter’s power-
plant can provide. Trying to land with a nose high attitude along with any other unfavorable
condition (i.e., high gross weight or wind gusts) is most likely to end in disaster.
The tail rotor also produces thrust. The amount of thrust is variable through the use of the anti-
torque pedals and is used to control the helicopter’s yaw.
308. DRAG
The force that resists the movement of a helicopter through the air and is produced when lift is
developed is called drag. Drag must be overcome by the engine to turn the rotor. Drag always
acts parallel to the relative wind. Total drag is composed of three types of drag: profile, induced,
and parasite.
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Figure 3-9 Notional Drag profiles
Profile Drag
Profile drag develops from the frictional resistance of the blades passing through the air. It does
not change significantly with the airfoil’s AOA but increases moderately when airspeed
increases. Profile drag is composed of form drag and skin friction. Form drag results from the
turbulent wake caused by the separation of airflow from the surface of a structure. The amount
of drag is related to both the size and shape of the structure that protrudes into the relative wind.
Skin friction is caused by surface roughness. Even though the surface appears smooth, it may be
quite rough when viewed under a microscope. A thin layer of air clings to the rough surface and
creates small eddies that contribute to drag.
Induced Drag
Induced drag is generated by the airflow circulation around the rotor blade as it creates lift. The
high-pressure area beneath the blade joins the low-pressure area above the blade at the trailing
edge and at the rotor tips. This causes a spiral, or vortex, which trails behind each blade
whenever lift is being produced. These vortices deflect the airstream downward in the vicinity of
the blade, creating an increase in downwash. Therefore, the blade operates in an average relative
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wind that is inclined downward and rearward near the blade. Because the lift produced by the
blade is perpendicular to the relative wind, the lift is inclined aft by the same amount. The
component of lift that is acting in a rearward direction is induced drag.
Figure 3-10 Induced Drag
As the air pressure differential increases with an increase in AOA, stronger vortices form, and
induced drag increases. Since the blade’s AOA is usually lower at higher airspeeds, and higher
at low speeds, induced drag decreases as airspeed increases and increases as airspeed decreases.
Induced drag is the major cause of drag at lower airspeeds.
Parasite Drag
Parasite drag is present any time the helicopter is moving through the air. This type of drag
increases with airspeed. Non-lifting components of the helicopter, such as the cabin, rotor mast,
tail, and landing gear, contribute to parasite drag. Any loss of momentum by the airstream, due
to such things as openings for engine cooling, creates additional parasite drag. Because of its
rapid increase with increasing airspeed, parasite drag is the major cause of drag at higher
airspeeds. Parasite drag varies with the square of the velocity; therefore, doubling the airspeed
increases the parasite drag four times.
Total Drag
Total drag for a helicopter is the sum of all three drag forces. As airspeed increases, parasite
drag increases, while induced drag decreases. Profile drag remains relatively constant
throughout the speed range with some increase at higher airspeeds. Combining all drag forces
results in a total drag curve. The low point on the total drag curve shows the airspeed at which
drag is minimized. This is the point where the lift-to-drag ratio is greatest and is referred to as
L/DMAX. At this speed, the total lift capacity of the helicopter, when compared to the total drag
of the helicopter, is most favorable. This is an important factor in helicopter performance.
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Figure 3-11 Drag Curve
309. INTRODUCTION TO LIFT THEORIES
Several theories developed during the last two hundred years to attempt to explain the production
of lift by an airfoil: Pressure Distribution, Circulation, Momentum, and the Blade Element
Theory. One argument says that the pressure differential from the top to bottom of the airfoil
describes lift. Another argument says that the wing deflects the air downward, thus pushing
itself up. Yet another says that there is a net circulation of air around the wing, which causes it
to lift. Each of these ideas is completely legitimate, supported by mathematical proof. Each also
has a set of specific constraints and approximations, which limit its applicability. There will be
situations where one method is more convenient to use than another and other situations that
demand one specific method of investigation.
310. PRESSURE DISTRIBUTION THEORY
The pressure distribution theory evolves from the principle of continuity, and the principle of
conservation of energy as applied to fluid dynamics (Bernoulli’s Equation). To recap, in
considering continuity, as the area (of a stream-tube, for example) decreases, the velocity
increases. Furthermore, from Bernoulli, as the velocity of the air goes up, the static pressure
goes down.
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Therefore, putting the Bernoulli equation together with the continuity principle, we have
the following: as the area decreases, the velocity increases, and as the velocity increases the
static pressure decreases. If the pressure goes down over the top of a wing more so than over
the bottom, then the wing will be lifted up as seen in Figure 3-12. This differential pressure,
accounted for by the continuity principle and the Bernoulli equation, is the method of choice in
describing the mechanics of lift by the pressure distribution theory.
Figure 3-12 Pressure Changes Around a Cambered Airfoil
311. CIRCULATION THEORY
Circulation theory, or the Kutta-Joukowski Theorem, is a method for describing the flow over a
spinning cylinder and, more generally, over any closed area (Figure 3-13). If a non-rotating
circular cylinder is placed in a flow field it will produce no lift. The streamlines and resultant
pressure distributions around a cylinder without circulation (Figure 3-14) generate no net lift
force. When the cylinder is rotated, however, it induces a rotational or circulatory flow and there
is a distinct change in the streamlines and pressure distributions. Air next to the surface of the
cylinder is sped up on the top and slowed down on the bottom by the relative motion of the
cylinder’s surface. The differences in flow speeds cause pressure differences on top and bottom
(Figure 3-14), with the end result being a net lift force perpendicular to the relative velocity.
There have been recent developments in rotary wing flight where circulation theory has shown
nearly direct application. Use of a rotating body to generate pressure differences on top and
bottom surfaces, or viewed alternatively, impart circulation to a flow, is termed Magnus effect.
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Figure 3-13 Magnus Effect
Figure 3-14 Pressure Distribution for Magnus Effect
312. MOMENTUM THEORY
The Momentum Theory of lift relies on Newton’s laws of motion with regard to the air as it
passes over an airfoil and the reaction of the airfoil to the motion of the air. In a hover, this
theory states that a certain amount of air above the rotor system is accelerated to a certain
velocity at a certain distance below the rotor. Since the amount of air has a finite mass and is
given a finite acceleration, its force can be determined through Newton’s second law (F=ma).
Specifically, the theory shows that given an initial velocity (v0) of zero well above the rotor
system, the rotor system accelerates the air downward through the rotors to a particular velocity
(vi, induced velocity) based on the diameter of the rotor, the density of the air and the weight of
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the helicopter. The mass of air is further accelerated by the idealized constraints of the flow to
twice the induced velocity at about the distance of one rotor diameter (Figure 3-15).
Figure 3-15 Induced Velocity Idealized for Momentum Theory
Induced power is that portion of total power used to accelerate air downward and create lift. In
equilibrium, the thrust or force generated by the rotor must equal aircraft weight, so the induced
power required to hover is then a function of aircraft weight. If the helicopter weighs more, it
requires more torque, higher rotor speed, less induced velocity, or some combination of all three.
313. BLADE ELEMENT THEORY
Whereas the Momentum Theory can describe the overall forces on the entire rotor disk, the
Blade Element Theory allows for a greater fidelity in understanding the action and reaction of
individual blades within a rotor disk. The basis of Blade Element Theory is to take a very small
portion of the rotor blade and determine the forces acting on it.
Observe airflow conditions at the blade element in Figure 3-17. The blade “sees” a combination
of linear velocity (sometimes called linear flow) and downward induced velocity as
components of relative wind.
The angle of attack (AOA) is the aerodynamic angle formed between the relative wind and the
chord line (Figure 3-18). The pitch angle is the mechanical angle formed between the tip path
plane (TPP) and the chord line. Lift, which is the component of the total aerodynamic force
perpendicular to the relative wind, is tilted aft. This rearward component generated by lift is
induced drag, formed from the acceleration of a mass of air (downwash) and the energy spent in
the creation of trailing vortices. The remaining arrow labeled profile drag is the result of air
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3-16 HELICOPTER AERODYNAMICS BASICS
friction acting on the blade element and comprised of viscous drag (skin friction) and form drag,
which is the drag produced from the low velocity/low static pressure air formed in the wake of
each blade.
Figure 3-16 Variables in the Blade Element Theory
Figure 3-17 Airflow over the Airfoil
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Figure 3-18 Blade Element Diagram
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AIRFOILS 4-1
CHAPTER FOUR
AIRFOILS
400. INTRODUCTION
The purpose of this chapter is to aid the student in understanding airfoils, terminology, and
airflow and associated reactions in the rotor disk.
401. LESSON TOPIC LEARNING OBJECTIVES
1. Identify airfoil design considerations
2. Identify rotor system dynamics
3. Identify rotorcraft configurations and airfoil design considerations
4. Identify the basic aerodynamic characteristics of the airframe
5. Identify factors that affect helicopter stability and control
6. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
7. Explain the aerodynamics of flight
402. AIRFOIL
Helicopters are able to fly due to aerodynamic forces produced when air passes around the
airfoil. An airfoil is any surface producing more lift than drag when passing through the air at a
suitable angle. Airfoils are most often associated with production of lift. Airfoils are also used
for stability (fin), control (elevator), and thrust or propulsion (propeller or rotor). Certain
airfoils, such as rotor blades, combine some of these functions. The main and tail rotor blades of
the helicopter are airfoils, and air is forced to pass around the blades by mechanically powered
rotation. In some conditions, parts of the fuselage, such as the vertical and horizontal stabilizers,
can become airfoils. Airfoils are carefully structured to accommodate a specific set of flight
characteristics.
403. AIRFOIL TERMINOLOGY AND DEFINITIONS
Blade span: the length of the rotor blade from center of rotation to tip of the blade.
Chord line: a straight line intersecting leading and trailing edges of the airfoil.
Chord: the length of the chord line from leading edge to trailing edge; it is the characteristic
longitudinal dimension of the airfoil section.
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Figure 4-1 Aerodynamic terms of an airfoil
Mean camber line: a line drawn halfway between the upper and lower surfaces of the airfoil.
The chord line connects the ends of the mean camber line. Camber refers to curvature of the
airfoil and subsequent curvature of the mean camber line. The shape of the mean camber is
important for determining aerodynamic characteristics of an airfoil section. Maximum camber
(displacement of the mean camber line from the chord line) and its location help to define the
shape of the mean camber line. The location of maximum camber and its displacement from the
chord line are expressed as fractions or percentages of the basic chord length. By varying the
point of maximum camber, the manufacturer can tailor an airfoil for a specific purpose. The
profile thickness and thickness distribution are important properties of an airfoil section.
Leading edge: the front edge of an airfoil.
Flightpath velocity: the speed and direction of the airfoil passing through the air. For airfoils
on an airplane, the flightpath velocity is equal to true airspeed (TAS). For helicopter rotor
blades, flightpath velocity is equal to rotational velocity, plus or minus a component of
directional airspeed.
Rotational Velocity: Rotational velocity of the blade is constant along the span of the blade.
Rotational velocity is RPM or angular velocity. It does not change. The linear velocity of the
blade element and the relative velocity of the blade element changes and this can be defined as.
rotational relative wind, or the relative velocity of the blade.
Relative wind: defined as the airflow relative to an airfoil and is created by movement of an
airfoil through the air. This is rotational relative wind for rotary-wing aircraft and is covered in
detail later. As an induced airflow may modify flightpath velocity, relative wind experienced by
the airfoil may not be exactly opposite its direction of travel.
Trailing edge: the rearmost edge of an airfoil.
Induced flow: the downward flow of air through the rotor disk.
Resultant relative wind: relative wind modified by induced flow.
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AOA: the angle measured between the resultant relative wind and chord line.
Angle of incidence (AOI): the angle between the chord line of a blade and rotor hub,
commonly referred to as blade pitch angle. For fixed airfoils, such as vertical fins or elevators,
angle of incidence is the angle between the chord line of the airfoil and a selected reference plane
of the helicopter.
Center of pressure: the point along the chord line of an airfoil through which all aerodynamic
forces are considered to act. Since pressures vary on the surface of an airfoil, an average
location of pressure variation is needed. As the AOA changes, these pressures change, and the
center of pressure moves along the chord line.
404. AIRFOIL TYPES
Symmetrical Airfoil
The symmetrical airfoil is distinguished by having identical upper and lower surfaces. The mean
camber line and chord line are the same on a symmetrical airfoil, and it produces no lift at zero
AOA. Most light helicopters incorporate symmetrical airfoils in the main rotor blades.
Nonsymmetrical Airfoil (Cambered)
The nonsymmetrical airfoil has different upper and lower surfaces, with a greater curvature of
the airfoil above the chord line than below. The mean camber line and chord line are different.
The nonsymmetrical airfoil design can produce useful lift at zero AOA. A nonsymmetrical
design has advantages and disadvantages. The advantages are more lift production at a given
AOA than a symmetrical design, an improved lift-to-drag ratio, and better stall characteristics.
The disadvantages are center of pressure travel of up to 20 percent of the chord line (creating
undesirable torque on the airfoil structure) and greater production costs.
Figure 4-2 Airfoil Types
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405. ROTOR AXIS
Because of lift differential due to differing rotational relative wind values along the blade, the
blade should be designed with a twist to alleviate internal blade stress and distribute the lifting
force more evenly along the blade. Blade twist provides higher pitch angles at the root where
velocity is low and lower pitch angles nearer the tip where velocity is higher. This increases the
induced air velocity and blade loading near the inboard section of the blade.
Figure 4-3 Blade Twist
Rotor Blade and Hub Definitions
Hub: on the mast, the attaching point for the root of the blade, and the axis about which the
blades rotate.
Tip: the farthest outboard section of the rotor blade
Root: the inner end of the blade and is the point that attaches to the hub
Twist: the change in blade incidence from the root to the outer blade
The angular position of the main rotor blades (as viewed from above, as they rotate about the
vertical axis of the mast) is measured from the helicopter’s longitudinal axis, and usually from its
nose. The radial position of a segment of the blade is the distance from the hub as a fraction of
the total distance.
406. AIRFLOW AND REACTIONS IN THE ROTOR DISK
1. Relative Wind
Knowledge of relative wind is essential for an understanding of aerodynamics and its practical
flight application for the pilot. Relative wind is airflow relative to an airfoil. Movement of an
airfoil through the air creates relative wind. Relative wind moves in a direction parallel to but
opposite of the movement of the airfoil. There are two parts to wind passing a rotor blade:
Horizontal part: caused by the blades turning plus movement of the helicopter through the air
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Vertical part: caused by the air being forced down through the rotor blades plus any movement
of the air relative to the blades caused by the helicopter climbing or descending
Figure 4-4 Relative Wind
Figure 4-5 Horizontal component of relative wind
Figure 4-6 Induced Flow
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Figure 4-7 Spanwise induced flow velocities
2. Rotational Relative Wind (Tip-Path Plane)
The rotation of rotor blades as they turn about the mast produces rotational relative wind
(tip-path plane). The term rotational refers to the method of producing relative wind. Rotational
relative wind flows opposite the physical flightpath of the airfoil, striking the blade at 90° to the
leading edge and parallel to the plane of rotation; and it is constantly changing in direction
during rotation. Rotational relative wind velocity is highest at blade tips, decreasing uniformly
to zero at the axis of rotation (center of the mast).
Figure 4-8 Rotational Relative Wind
3. Resultant Relative Wind
The resultant relative wind at a hover is rotational relative wind modified by induced flow. This
is inclined downward at some angle and opposite the effective flightpath of the airfoil, rather
than the physical flightpath (rotational relative wind). The resultant relative wind also serves as
the reference plane for development of lift, drag, and total aerodynamic force (TAF) vectors on
the airfoil. When the helicopter has horizontal motion, airspeed further modifies the resultant
relative wind. The airspeed component of relative wind results from the helicopter moving
through the air. This airspeed component is added to, or subtracted from, the rotational relative
wind depending on whether the blade is advancing or retreating in relation to helicopter
movement. Introduction of airspeed relative wind also modifies induced flow. Generally, the
downward velocity of induced flow is reduced. The pattern of air circulation through the disk
changes when the aircraft has horizontal motion. As the helicopter gains airspeed, the addition
of forward velocity results in decreased induced flow velocity. This change results in an
improved efficiency (additional lift) being produced from a given blade pitch setting.
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Figure 4-9 Resultant relative wind
Induced Flow (Downwash): At flat pitch, air leaves the trailing edge of the rotor blade in the
same direction it moved across the leading edge; no lift or induced flow is being produced. As
blade pitch angle is increased, the rotor disk induces a downward flow of air through the rotor
blades creating a downward component of air that is added to the rotational relative wind.
Because the blades are moving horizontally, some of the air is displaced downward. The blades
travel along the same path and pass a given point in rapid succession. Rotor blade action
changes the still air to a column of descending air. Therefore, each blade has a decreased AOA
due to the downwash. This downward flow of air is called induced flow (downwash). It is most
pronounced at a hover under no-wind conditions.
Figure 4-10 Induced flow in forward flight
In Ground Effect (IGE): Ground effect is the increased efficiency of the rotor disk caused by
interference of the airflow when near the ground. The air pressure or density is increased, which
acts to decrease the downward velocity of air. Ground effect permits relative wind to be more
horizontal, lift vector to be more vertical, and induced drag to be reduced. These conditions
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allow the rotor disk to be more efficient. Maximum ground effect is achieved when hovering
over smooth hard surfaces. When hovering over surfaces as tall grass, trees, bushes, rough
terrain, and water, maximum ground effect is reduced. Rotor efficiency is increased by ground
effect to a height of about one rotor diameter (measured from the ground to the rotor disk) for
most helicopters. Since the induced flow velocities are decreased, the AOA is increased, which
requires a reduced blade pitch angle and a reduction in induced drag. This reduces the power
required to hover IGE.
Figure 4-11 In Ground Effect (IGE)
Out of Ground Effect (OGE): The benefit of placing the helicopter near the ground is lost
above IGE altitude. Above this altitude, the power required to hover remains nearly constant,
given similar conditions (such as wind). Induced flow velocity is increased, resulting in a
decrease in AOA and a decrease in lift. Under the correct circumstances, this downward flow
can become so localized that the helicopter and locally disturbed air will sink at alarming rates.
This effect is called vortex ring state (formerly referenced as settling-with-power) and is
discussed later. A higher blade pitch angle is required to maintain the same AOA as in IGE
hover. The increased pitch angle also creates more drag. This increased pitch angle and drag
requires more power to hover OGE than IGE.
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Figure 4-12 Out of Ground Effect (OGE)
407. ROTOR BLADE ANGLES
There are two angles that enable a rotor disk to produce the lift required for a helicopter to fly:
angle of incidence and angle of attack.
Angle of Incidence: Angle of incidence is the angle between the chord line of a main or tail
rotor blade and its rotor disk. It is a mechanical angle rather than an aerodynamic angle and is
sometimes referred to as blade pitch angle. In the absence of induced flow, AOA and angle of
incidence are the same. Whenever induced flow, up flow (inflow), or airspeed modifies the
relative wind, the AOA is different from the angle of incidence. Collective input and cyclic
feathering change the angle of incidence. A change in the angle of incidence changes the AOA,
which changes the coefficient of lift, thereby changing the lift produced by the airfoil.
Figure 4-13 Angle of Incidence
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Angle of Attack: AOA is the angle between the airfoil chord line and resultant relative wind. It
is an aerodynamic angle and not easy to measure. It can change with no change in the blade
pitch angle (angle of incidence, discussed earlier).
Figure 4-14 Angle of Attack
When the AOA is increased, air flowing over the airfoil is diverted over a greater distance,
resulting in an increase of air velocity and more lift. As the AOA is increased further, it becomes
more difficult for air to flow smoothly across the top of the airfoil. At this point, the airflow
begins to separate from the airfoil and enters a burbling or turbulent pattern. The turbulence
results in a large increase in drag and loss of lift in the area where it is taking place. Increasing
the AOA increases lift until the critical angle of attack is reached. Any increase in the AOA
beyond this point produces a stall and a rapid decrease in lift.
Several factors may change the rotor blade AOA. The pilot has little direct control over AOA
except indirectly through the flight control input. Collective and cyclic feathering help to make
these changes. Feathering is the rotation of the blade about its longitudinal axis by
collective/cyclic inputs causing changes in blade pitch angle. Collective feathering changes
angle of incidence equally and in the same direction on all rotor blades simultaneously. This
action changes AOA, which changes coefficient of lift (CL), and affects overall lift of the rotor
disk.
Cyclic feathering changes the blade’s AOA differentially around the rotor disk and creates a
differential lift. Aviators use cyclic feathering to control attitude of the rotor disk. It is the
means to control rearward tilt of the rotor (blowback) caused by flapping action and (along with
blade flapping) counteract dissymmetry of lift (discussed later). Cyclic feathering causes attitude
of the rotor disk to change but does not change the amount of net lift the rotor disk is producing.
Most of the changes in AOA come from change in airspeed and rate of climb or descent; others
such as flapping occur automatically due to the rotor system design. Flapping is the up and
down movement of rotor blades about a hinge on a fully articulated rotor system. A semi-rigid
system does not have a hinge but flap as a unit. A rigid rotor system has no vertical or horizontal
hinges, so the blades cannot flap or drag, but they can flex. By flexing, the blades themselves
compensate for the forces which previously required rugged hinges. It occurs in response to
changes in lift due to changing velocity or cyclic feathering. No flapping occurs when the
tip-path plane is perpendicular to the mast. The flapping action alone, or along with cyclic
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER FOUR
AIRFOILS 4-11
feathering, controls dissymmetry of lift. Flapping is the primary means of compensating for
dissymmetry of lift.
Pilots adjust AOA through normal control manipulation of the pitch angle of the blades. If the
pitch angle is increased, the AOA increases; if the pitch angle is reduced, the AOA is reduced.
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POWERED FLIGHT 5-1
CHAPTER FIVE
POWERED FLIGHT
500. INTRODUCTION
This chapter introduces powered flight analysis and associated effects.
501. LESSON TOPIC LEARNING OBJECTIVES
1. Identify rotor system dynamics
2. Identify rotorcraft configurations and airfoil design considerations
3. Identify the basic aerodynamic characteristics of the airframe
4. Identify factors that affect helicopter stability and control
5. Identify factors that affect helicopter power required and power available for flight
6. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
7. Explain the aerodynamics of flight
502. POWERED FLIGHT
In powered flight (hovering, vertical, forward, sideward, or rearward), the total lift and thrust
forces of a rotor are perpendicular to the rotor disk.
503. HOVERING FLIGHT
1. General
Hovering is the most challenging part of flying a helicopter. This is because a helicopter
generates its own gusty air while in a hover, which acts against the fuselage and flight control
surfaces. The end result is constant control inputs and corrections by the pilot to keep the
helicopter where it is required to be. Despite the complexity of the task, the control inputs in a
hover are simple. The cyclic is used to eliminate drift in the horizontal plane, controlling
forward, backward, right and left movement or travel. The throttle, if not governor controlled, is
used to control revolutions per minute (RPM). The collective is used to maintain altitude. The
pedals are used to control nose direction or heading. It is the interaction of these controls that
makes hovering difficult, since an adjustment in any one control requires an adjustment of the
other two, creating a cycle of constant correction. During hovering flight, a helicopter maintains
a constant position over a selected point, usually a few feet above the ground. The ability of the
helicopter to hover comes from the both the lift component, which is the force developed by the
main rotor(s) to overcome gravity and aircraft weight, and the thrust component, which acts
horizontally to accelerate or decelerate the helicopter in the desired direction. Pilots direct the
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5-2 POWERED FLIGHT
thrust of the rotor disk by using the cyclic to rotate the rotor disk plane relative to the horizon.
They do this in order to induce travel or compensate for the wind and hold a position. At a hover
in a no-wind condition, all opposing forces (lift, thrust, drag, and weight) are in balance; they are
equal and opposite. Therefore, lift and weight are equal, resulting in the helicopter remaining at
a stationary hover.
While hovering, the amount of main rotor thrust can be adjusted to maintain the desired hovering
height. This is done by changing the angle of incidence (by moving the collective) of the rotor
blades, and hence their AOA. Changing the AOA changes the drag on the rotor blades, and the
power delivered by the engine must change as well to keep the rotor speed constant (The Nf
governor in the TH-57 works to accomplish this resultant constant RPM, or Nr).
The weight that must be supported is the total weight of the helicopter and its occupants. If the
amount of lift is greater than the actual weight, the helicopter accelerates upwards until the lift
force equals the weight of the helicopter; if lift is less than weight, the helicopter accelerates
downward.
The drag of a hovering helicopter is mainly induced drag incurred while the blades are producing
lift. There is, however, some profile drag on the blades as they rotate through the air and a small
amount of parasite drag from the non-lift-producing surfaces of the helicopter, such as the rotor
hub, cowlings, and landing gear. Throughout the rest of this discussion, the term “drag” includes
induced, profile and parasite drag.
An important consequence of producing thrust is torque. As discussed earlier, Newton’s Third
Law states: for every action there is an equal and opposite reaction. Therefore, as the engine
turns the main rotor disk in a counterclockwise direction, the helicopter fuselage wants to turn
clockwise. The amount of torque is directly related to the amount of engine power being used to
turn the main rotor disk. As power changes, torque changes.
To counteract this torque-induced turning tendency, an anti-torque rotor or tail rotor is
incorporated into most helicopter designs. A pilot can vary the amount of thrust produced by the
tail rotor in relation to the amount of torque produced by the engine. As the engine supplies
more power to the main rotor, the tail rotor must produce more thrust to overcome the increased
torque effect. This control change is accomplished through the use of anti-torque pedals.
2. Translating Tendency (Drift)
During hovering flight, a single main rotor helicopter tends to move in the direction of tail rotor
thrust. This lateral (or sideward) movement is called translating tendency.
To counteract this tendency, one or more of the following features may be used. All examples
are for a counterclockwise rotating main rotor disk.
a. The main transmission is mounted at a slight angle to the left (when viewed from
behind) so that the rotor mast has a built-in tilt to oppose the tail rotor thrust.
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POWERED FLIGHT 5-3
b. Flight controls can be rigged so that the rotor disk is tilted to the left slightly when the
cyclic is centered. Whichever method is used, the tip-path plane is tilted slightly to
the left in the hover.
c. The transmission is mounted so the rotor shaft is vertical with respect to the fuselage,
the helicopter “hangs” left skid low in the hover. (The opposite is true for rotor disks
turning clockwise when viewed from above.)
d. The helicopter fuselage will also be tilted when the tail rotor is below the main rotor
disk and supplying anti-torque thrust. The fuselage tilt is caused by the imperfect
balance of the tail rotor thrust against the main rotor torque in the same plane. The
helicopter tilts due to two separate forces, the main rotor disk tilt to neutralize the
translating tendency and the lower tail rotor thrust below the plane of the torque
action.
e. In forward flight, the tail rotor continues to push to the right, and the helicopter makes
a small angle with the wind when the rotors are level and the slip ball is in the middle.
This is called inherent sideslip. For some larger helicopters, the vertical fin or
stabilizer is often designed with the tail rotor mounted on them to correct this side slip
and to eliminate some of the tilting at a hover. (By mounting the tail rotor on top of
the vertical fin or pylon, the anti-torque is more in line with or closer to the horizontal
plane of torque, resulting in less airframe (or body) lean from the tail rotor.) Also,
having the tail rotor higher off the ground reduces the risk of objects coming in
contact with the blades, but at the cost of increased weight and complexity.
Figure 5-1 Translating Tendency
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3. Pendular Action
Since the fuselage of the helicopter, with a single main rotor, is suspended from a single point
and has considerable mass, it is free to oscillate either longitudinally or laterally in the same way
as a pendulum. This pendular action can be exaggerated by over controlling; therefore, control
movements should be smooth and not exaggerated.
Figure 5-2 Pendular action
The horizontal stabilizer helps to level the helicopter in forward flight. However, in rearward
flight, the horizontal stabilizer can press the tail downward, resulting in a tail strike if the
helicopter is moved rearward into the wind. Normally, with the helicopter mostly into the wind,
the horizontal stabilizer experiences less headwind component as the helicopter begins rearward
travel (downwind). When rearward flight groundspeed equals the wind speed, then the
helicopter is merely hovering in a no-wind condition. However, rearward hovering into the wind
requires considerable care and caution to prevent tail strikes.
It is important to note that there is a difference in the amount of pendular action between a semi
rigid system and a fully articulated system. Because of the hard connection (offset) of the latter,
the centrifugal force pulling out on the blades is transferred to the fuselage, and the fuselage
tends to follow the rotor attitude. The semi rigid system is a true pendulum, with thrust required
to create a moment around the fuselage CG to allow for control of the fuselage.
4. Coning
In order for a helicopter to generate lift, the rotor blades must be turning. Rotor disk rotation
drives the blades into the air, creating a relative wind component without having to move the
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airframe through the air as with an airplane or glider. Depending on the motion of the blades and
helicopter airframe, many factors cause the relative wind direction to vary. The rotation of the
rotor disk creates centrifugal force (inertia), which tends to pull the blades straight outward from
the main rotor hub: the faster the rotation, the greater the centrifugal force, the slower the
rotation, the smaller the centrifugal force. This force gives the rotor blades their rigidity and, in
turn, the strength to support the weight of the helicopter. The maximum centrifugal force
generated is determined by the maximum operating rotor revolutions per minute (RPM).
As lift on the blades is increased (in a takeoff, for example), two major forces are acting at the
same time—centrifugal force acting outward, and lift acting upward. The result of these two
forces is that the blades assume a conical path instead of remaining in the plane perpendicular to
the mast. This can be seen in any helicopter when it takes off; the rotor disk changes from flat to
a slight cone shape.
Figure 5-3 Coning
If the rotor RPM is allowed to go too low (below the minimum power-on rotor RPM, for
example), the centrifugal force becomes smaller and the coning angle becomes much larger. In
other words, should the RPM decrease too much, at some point the rotor blades fold up with no
chance of recovery.
5. Coriolis Effect
The Coriolis Effect is also referred to as the law of conservation of angular momentum. It states
that the value of angular momentum of a rotating body does not change unless an external force
is applied. In other words, a rotating body continues to rotate with the same rotational velocity
until some external force is applied to change the speed of rotation. Angular momentum is the
moment of inertia (mass times distance from the center of rotation squared) multiplied by the
speed of rotation.
Changes in angular velocity, known as angular acceleration and deceleration, take place as the
mass of a rotating body is moved closer to or farther away from the axis of rotation. The speed
of the rotating mass varies proportionately with the square of the radius.
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An excellent example of this principle in action is a figure skater performing a spin on ice skates.
The skater begins rotation on one foot, with the other leg and both arms extended. The rotation
of the skater’s body is relatively slow. When a skater draws both arms and one leg inward, the
moment of inertia (mass times radius squared) becomes much smaller and the body is rotating
almost faster than the eye can follow. Because the angular momentum must, by law of nature,
remain the same (no external force applied), the angular velocity must increase.
The rotor blade rotating about the rotor hub possesses angular momentum. As the rotor begins to
cone due to G-loading maneuvers, the diameter of the rotor disk shrinks. Due to conservation of
angular momentum, the blades increase speed even though the blade tips have a shorter distance
to travel due to reduced disk diameter. The action results in an increase in rotor RPM which
causes a slight increase in lift. Most pilots arrest this increase of RPM with an increase in
collective pitch. This increase in blade RPM lift is somewhat negated by the slightly smaller
disk area as the blades cone upward.
6. Gyroscopic Precession
The spinning main rotor of a helicopter acts like a gyroscope. As such, it has the properties of
gyroscopic action, one of which is precession. Gyroscopic precession is the resultant action or
deflection of a spinning object when a force is applied to this object. This action occurs
approximately 90° in the direction of rotation from the point where the force is applied
(or 90° later in the rotation cycle).
Figure 5-4 Gyroscopic precession
Examine a two-bladed rotor disk to see how gyroscopic precession affects the movement of the
tip-path plane. Moving the cyclic pitch control increases the angle of incidence of one rotor
blade with the result of a greater lifting force being applied at that point in the plane of rotation.
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This same control movement simultaneously decreases the angle of incidence of the other blade
the same amount, thus decreasing the lifting force applied at that point in the plane of rotation.
The blade with the increased angle of incidence tends to flap up; the blade with the decreased
angle of incidence tends to flap down. Because the rotor disk acts like a gyro, the blades reach
maximum deflection at a point approximately 90° later in the plane of rotation. Figure 5-5
illustrates the result of a forward cyclic input. The retreating blade angle of incidence is
increased, and the advancing blade angle of incidence is decreased resulting in a tipping forward
of the tip-path plane, since maximum deflection takes place 90° later when the blades are at the
rear and front, respectively.
Figure 5-5 Forward Cyclic Input
In a rotor disk using three or more blades, the movement of the cyclic pitch control changes the
angle of incidence of each blade an appropriate amount so that the end result is the same.
504. VERTICAL FLIGHT
Hovering is actually an element of vertical flight. Increasing the angle of incidence of the rotor
blades (pitch) while keeping their rotation speed constant generates additional lift and the
helicopter ascends. Decreasing the pitch causes the helicopter to descend. In a no-wind
condition in which lift and thrust are less than weight and drag, the helicopter descends
vertically. If lift and thrust are greater than weight and drag, the helicopter ascends vertically.
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5-8 POWERED FLIGHT
Figure 5-6 No wind hover
505. FORWARD FLIGHT
In steady forward flight, with no change in airspeed or vertical speed, the four forces of lift,
thrust, drag, and weight must be in balance. Once the tip-path plane is tilted forward, the total
lift-thrust force is also tilted forward. This resultant lift-thrust force can be resolved into two
components—lift acting vertically upward and thrust acting horizontally in the direction of
flight. In addition to lift and thrust, there is weight (the downward acting force) and drag
(the force opposing the motion of an airfoil through the air).
Figure 5-7 Transition to forward flight
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POWERED FLIGHT 5-9
In straight-and-level, un-accelerated forward flight (straight-and-level flight is flight with a
constant heading and at a constant altitude), lift equals weight and thrust equals drag. If lift
exceeds weight, the helicopter accelerates vertically until the forces are in balance; if thrust is
less than drag, the helicopter slows down until the forces are in balance. As a helicopter initiates
a move forward, it begins to lose altitude because lift is lost as thrust is diverted forward.
However, as the helicopter begins to accelerate from a hover, the rotor disk becomes more
efficient due to translational lift. The result is excess power over that which is required to hover.
Continued acceleration causes an even larger increase in airflow through the rotor disk (up to a
maximum determined by drag and the engine’s limit of power), and more efficient flight. In
order to maintain un-accelerated flight, the pilot must understand that with any changes in power
or in cyclic movement, the helicopter begins either to climb or to descend. Once straight-and-
level flight is obtained, the pilot should make note of the power (torque setting) required and not
make major adjustments to the flight controls.
Figure 5-8 Power vs. airspeed chart
1. Airflow in forward flight
Airflow across the rotor disk in forward flight varies from airflow at a hover. In forward flight,
air flows opposite the aircraft’s flightpath. The velocity of this air flow equals the helicopter’s
forward speed. Because the rotor blades turn in a circular pattern, the velocity of airflow across
a blade depends on the position of the blade in the plane of rotation at a given instant, its
rotational velocity, and airspeed of the helicopter. Therefore, the airflow meeting each blade
varies continuously as the blade rotates. The highest velocity of airflow occurs over the right
side (3 o’clock position) of the helicopter (advancing blade in a rotor disk that turns
counterclockwise) and decreases to rotational velocity over the nose. It continues to decrease
until the lowest velocity of airflow occurs over the left side (9 o’clock position) of the helicopter
(retreating blade). As the blade continues to rotate, velocity of the airflow then increases to
rotational velocity over the tail. It continues to increase until the blade is back at the 3 o’clock
position.
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The advancing blade in Figure 5-9 position A moves in the same direction as the helicopter. The
velocity of the air meeting this blade equals rotational velocity of the blade plus wind velocity
resulting from forward airspeed. The retreating blade (position C) moves in a flow of air moving
in the opposite direction of the helicopter. The velocity of airflow meeting this blade equals
rotational velocity of the blade minus wind velocity resulting from forward airspeed. The blades
(positions B and D) over the nose and tail move essentially at right angles to the airflow created
by forward airspeed; the velocity of airflow meeting these blades equals the rotational velocity.
This results in a change to velocity of airflow all across the rotor disk and a change to the lift
pattern of the rotor disk.
Figure 5-9 Airflow in forward flight
Advancing Blade: As the relative wind speed of the advancing blade increases, the blade gains
lift and begins to flap up. It reaches its maximum up-flap velocity at the 3 o’clock position,
where the wind velocity is the greatest. This up-flap creates a downward flow of air and has the
same effect as increasing the induced flow velocity by imposing a downward vertical velocity
vector to the relative wind which decreases the AOA.
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Retreating Blade: As relative wind speed of the retreating blade decreases, the blade loses lift
and begins to flap down. It reaches its maximum down-flap velocity at the 9 o’clock position,
where wind velocity is the least. This down-flap creates an upward flow of air and has the same
effect as decreasing the induced flow velocity by imposing an upward velocity vertical vector to
the relative wind which increases the AOA.
Dissymmetry of Lift: Dissymmetry of lift is the differential (unequal) lift between advancing
and retreating halves of the rotor disk caused by the different wind flow velocity across each
half. This difference in lift would cause the helicopter to be uncontrollable in any situation other
than hovering in a calm wind. There must be a means of compensating, correcting, or
eliminating this unequal lift to attain symmetry of lift.
When the helicopter moves through the air, the relative airflow through the main rotor disk is
different on the advancing side from the retreating side. The relative wind encountered by the
advancing blade is increased by the forward speed of the helicopter, while the relative wind
speed acting on the retreating blade is reduced by the helicopter’s forward airspeed. Therefore,
as a result of the relative wind speed, the advancing blade side of the rotor disk can produce
more lift than the retreating blade side.
Figure 5-10 Dissymmetry of lift
If this condition were allowed to exist, a helicopter with a counterclockwise main rotor blade
rotation would roll to the left because of the difference in lift. In reality, the main rotor blades
flap and feather automatically to equalize lift across the rotor disk. Articulated rotor disks,
usually with three or more blades, incorporate a horizontal hinge (flapping hinge) to allow the
individual rotor blades to move, or flap up and down as they rotate. A semi-rigid rotor disk
(two blades) utilizes a teetering hinge, which allows the blades to flap as a unit. When one blade
flaps up, the other blade flaps down.
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As shown in Figure 5-11, as the rotor blade reaches the advancing side of the rotor disk (A), it
reaches its maximum up flap velocity. When the blade flaps upward, the angle between the
chord line and the resultant relative wind decreases. This decreases the AOA, which reduces the
amount of lift produced by the blade. At position (C), the rotor blade is now at its maximum
down flapping velocity. Due to down flapping, the angle between the chord line and the
resultant relative wind increases. This increases the AOA and thus the amount of lift produced
by the blade.
Figure 5-11 Effect of flapping
The combination of blade flapping and slow relative wind acting on the retreating blade normally
limits the maximum forward speed of a helicopter. At a high forward speed, the retreating blade
stalls because of a high AOA and slow relative wind speed. This situation is called retreating
blade stall and is evidenced by a nose pitch up, vibration, and a rolling tendency, usually to the
left in helicopters with counterclockwise blade rotation.
Pilots can avoid retreating blade stall by not exceeding the never-exceed speed. This speed is
designated VNE and is indicated on a placard and marked on the airspeed indicator by a red line.
Blade flapping compensates for dissymmetry of lift in the following way. At a hover, equal lift
is produced around the rotor disk with equal pitch (AOI) on all the blades and at all points in the
rotor disk (disregarding compensation for translating tendency). The rotor disk is parallel to the
horizon. To develop a thrust force, the rotor disk must be tilted in the desired direction of
movement. Cyclic feathering changes the angle of incidence differentially around the rotor disk.
For a counterclockwise rotation, forward cyclic movement decreases the angle of incidence on
the right of the rotor disk and increases it on the left.
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When transitioning to forward flight either from a hover or taking off from the ground, pilots
must be aware that as the helicopter speed increases, translational lift becomes more effective
and causes the nose to rise or pitch up (sometimes referred to as blowback). This tendency is
caused by the combined effects of dissymmetry of lift and transverse flow. Pilots must correct
for this tendency by maintaining a constant rotor disk attitude that will move the helicopter
through the speed range in which blowback occurs. If the nose is permitted to pitch up while
passing through this speed range, the aircraft may also tend to roll to the right. To correct for
this tendency, the pilot must continuously move the cyclic forward as velocity of the helicopter
increases until the takeoff is complete, and the helicopter has transitioned into forward flight.
Figure 5-12 illustrates the tilting forward of the rotor disk, which is the result of a change in pitch
angle with forward cyclic. At a hover, the cyclic is centered and the pitch angle on the
advancing and retreating blades is the same. At low forward speeds, moving the cyclic forward
reduces pitch angle on the advancing blade and increases pitch angle on the retreating blade.
This causes a slight rotor disk tilt. At higher forward speeds, the pilot must continue to move the
cyclic forward. This further reduces pitch angle on the advancing blade and further increases
pitch angle on the retreating blade. As a result, there is even more tilt to the rotor disk than at
lower speeds.
Figure 5-12 Blowback
A horizontal lift component (thrust) generates higher helicopter airspeed. The higher airspeed
induces blade flapping to maintain symmetry of lift. The combination of flapping and cyclic
feathering maintains symmetry of lift and desired attitude on the rotor disk and helicopter.
2. Translational lift
Improved rotor efficiency resulting from directional flight is called translational lift. The
efficiency of the hovering rotor disk is greatly improved with each knot of incoming wind gained
by horizontal movement of the aircraft or surface wind. As the incoming wind produced by
aircraft movement or surface wind enters the rotor disk, turbulence and vortices are left behind
and the flow of air becomes more horizontal. In addition, the tail rotor becomes more
aerodynamically efficient during the transition from hover to forward flight.
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Figure 5-13 Airflow with minimal headwind
Figure 5-14 Airflow just prior to ETL
Effective Translational Lift (ETL): While transitioning to forward flight at about 16 to 24
knots, the helicopter goes through effective translational lift (ETL). As mentioned earlier in the
discussion on translational lift, the rotor blades become more efficient as forward airspeed
increases. Between 16 and 24 knots, the rotor disk completely outruns the recirculation of old
vortices and begins to work in relatively undisturbed air. The flow of air through the rotor disk
is more horizontal, which reduces induced flow and drag with a corresponding increase in angle
of attach and lift. The additional lift available at this speed is referred to as the ETL, which
makes the rotor disk operate more efficiently. This increased efficiency continues with increased
airspeed until the best climb airspeed is reached, and total drag is at its lowest point.
As speed increases, translational lift becomes more effective, nose rises or pitches up, and
aircraft rolls to the right. The combined effects of dissymmetry of lift, gyroscopic precession,
and transverse flow effect cause this tendency. It is important to understand these effects and
anticipate correcting for them. Once the helicopter is transitioning through ETL, the pilot needs
to apply forward and left lateral cyclic input to maintain a constant rotor-disk attitude.
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Figure 5-15 ETL
Translational Thrust: Translational thrust occurs when the tail rotor becomes more
aerodynamically efficient during the transition from hover to forward flight. As the tail rotor
works in progressively less turbulent air, this improved efficiency produces more anti-torque
thrust, causing the nose of the aircraft to yaw left (with a main rotor turning counterclockwise)
and forces the pilot to apply right pedal (decreasing the AOA in the tail rotor blades) in response.
In addition, during this period, the airflow affects the horizontal components of the stabilizer
found on most helicopters which tends to bring the nose of the helicopter to a more level attitude.
3. Induced flow
As the rotor blades rotate, they generate what is called rotational relative wind. This airflow is
characterized as flowing parallel and opposite the rotor’s plane of rotation and striking
perpendicular to the rotor blade’s leading edge. This rotational relative wind is used to generate
lift. As rotor blades produce lift, air is accelerated over the foil and projected downward.
Anytime a helicopter is producing lift, it moves large masses of air vertically and down through
the rotor disk. This downwash or induced flow can significantly change the efficiency of the
rotor disk. Rotational relative wind combines with induced flow to form the resultant relative
wind. As induced flow increases, resultant relative wind becomes less horizontal. Since AOA is
determined by measuring the difference between the chord line and the resultant relative wind, as
the resultant relative wind becomes less horizontal, AOA decreases.
4. Transverse flow effect
As the helicopter accelerates in forward flight, induced flow drops to near zero at the forward
disk area and increases at the aft disk area. These differences in lift between the fore and aft
portions of the rotor disk are called transverse flow effect. This increases the AOA at the front
disk area causing the rotor blade to flap up and reduces AOA at the aft disk area causing the
rotor blade to flap down. Because the rotor acts like a gyro, maximum displacement occurs 90°
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in the direction of rotation. The result is a tendency for the helicopter to roll slightly to the right
as it accelerates through approximately 20 knots or if the headwind is approximately 20 knots.
Transverse flow effect is recognized by increased vibrations of the helicopter at airspeeds around
12 to 15 knots and can be produced by forward flight or from the wind while in a hover. This
vibration happens at an airspeed just below ETL on takeoff and after passing through ETL
during landing. The vibration happens close to the same airspeed as ETL because that is when
the greatest lift differential exists between the front and rear portions of the rotor system. As
such, some pilots confuse the vibration felt by transverse flow effect with passing through ETL.
To counteract transverse flow effect, a cyclic input to the left may be needed.
506. SIDEWARD FLIGHT
In sideward flight, the tip-path plane is tilted in the direction that flight is desired. This tilts the
total lift-thrust vector sideward. In this case, the vertical or lift component is still straight up and
weight straight down, but the horizontal or thrust component now acts sideward with drag acting
to the opposite side.
Figure 5-16 Sideward Flight
Sideward flight can be a very unstable condition due to the parasitic drag of the fuselage
combined with the lack of horizontal stabilizer for that direction of flight. Increased altitudes
help with control and the pilot must always scan in the direction of flight. Movement of the
cyclic in the intended direction of flight causes the helicopter to move, controls the rate of speed,
and ground track, but the collective and pedals are key to successful sideward flight. Just as in
forward flight, the collective keeps the helicopter from contacting the ground and the pedals help
maintain the correct heading; even in sideward flight, the tail of the helicopter should remain
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER FIVE
POWERED FLIGHT 5-17
behind you. Inputs to the cyclic should be smooth and controlled, and the pilot should always be
aware of the tip-path plane in relation to the ground.
Contacting the ground with the skids during sideward flight will most likely result in a dynamic
rollover event before the pilot has a chance to react. Extreme caution should be used
when maneuvering the helicopter sideways to avoid such hazards from happening.
507. REARWARD FLIGHT
For rearward flight, the tip-path plane is tilted rearward, which, in turn, tilts the lift-thrust vector
rearward. Drag now acts forward with the lift component straight up and weight straight down.
Figure 5-17 Rearward Flight
Pilots must be aware of the hazards of rearward flight. Because of the position of the horizontal
stabilizer, the tail end of the helicopter tends to pitch downward in rearward flight, causing the
probability of hitting the ground to be greater than in forward flight. Another factor to consider
in rearward flight is skid design. Most helicopter skids are not turned upward in the back, and
any contact with the ground during rearward flight can put the helicopter in an uncontrollable
position leading to tail rotor contact with the ground. Pilots must do a thorough scan of the area
before attempting to hover rearward, looking for obstacles and terrain changes. Slower airspeeds
can help mitigate risk and maintain a higher-than-normal hover altitude.
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5-18 POWERED FLIGHT
508. TURNING FLIGHT
In forward flight, the rotor disk is tilted forward, which also tilts the total lift-thrust force of the
rotor disk forward. When the helicopter is banked, the rotor disk is tilted sideward resulting in
lift being separated into two components. Lift acting upward and opposing weight is called the
vertical component of lift. Lift acting horizontally and opposing inertia (centrifugal force) is the
horizontal component of lift (centripetal force).
As the angle of bank increases, the total lift force is tilted more toward the horizontal, thus
causing the rate of turn to increase because more lift is acting horizontally. Since the resultant
lifting force acts more horizontally, the effect of lift acting vertically is decreased. To
compensate for this decreased vertical lift, the AOA of the rotor blades must be increased in
order to maintain altitude. The steeper the angle of bank is, the greater the AOA of the rotor
blades required to maintain altitude. Thus, with an increase in bank and a greater AOA, the
resultant lifting force increases, and the rate of turn is higher. Simply put, collective pitch must
be increased in order to maintain altitude and airspeed while turning. Collective pitch controls
the angle of incidence and along with other factors, determines the overall AOA in the rotor disk.
Figure 5-18 Turning Flight
AUTOROTATION 6-1
CHAPTER SIX
AUTOROTATION
600. INTRODUCTION
This chapter introduces the conceptual and aerodynamic principles involved during
autorotational flight.
601. LESSON TOPIC LEARNING OBJECTIVES
1. Identify airfoil design considerations
2. Identify rotor system dynamics
3. Identify rotorcraft configurations and airfoil design considerations
4. Identify the basic aerodynamic characteristics of the airframe
5. Identify factors that affect helicopter stability and control
6. Identify factors that affect helicopter power required and power available for flight
7. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
8. Explain the aerodynamics of flight
9. Identify factors that lead to undesirable helicopter phenomena
10. Identify actions that prevent undesirable helicopter phenomena
11. Explain undesirable helicopter phenomena
602. GENERAL
In a helicopter, an autorotative descent is a power-off maneuver in which the engine is
disengaged from the main rotor disk and the rotor blades are driven solely by the upward flow of
air through the rotor. In other words, the engine is no longer supplying power to the main rotor.
At the instant of engine failure, the main rotor blades are producing lift and thrust from their
angle of attack (AOA) and velocity. By lowering the collective (which must be done
immediately in case of an engine failure), lift and drag are reduced, and the helicopter begins an
immediate descent, thus producing an upward flow of air through the rotor disk. This upward
flow of air through the rotor disk provides sufficient thrust to maintain rotor RPM throughout the
descent. The tail rotor is driven by the main rotor transmission during autorotation, so heading
control is maintained with the anti-torque pedals as in normal flight.
CHAPTER SIX HELICOPTER AERODYNAMICS WORKBOOK
6-2 AUTOROTATION
Autorotation is further defined as the state of flight where the main rotor disk of a helicopter is
being turned by the action of air moving up through the rotor rather than engine power driving
the rotor. In normal, powered flight, air is drawn into the main rotor disk from above and
exhausted downward, but during autorotation, air moves up into the rotor disk from below as the
helicopter descends. Autorotation is permitted mechanically by a freewheeling unit: a clutch
mechanism that allows the main rotor to continue turning even if the engine is not running. If
the engine fails, the freewheeling unit automatically disengages the engine from the main rotor
allowing the main rotor to rotate freely. It is the means by which a helicopter can be landed
safely in the event of an engine failure.
Figure 6-1 Airflow in an autorotation
603. VERTICAL AUTOROTATION
Most autorotations are performed with forward speed. For simplicity, the following
aerodynamic explanation describes a vertical autorotative descent (no forward speed) in still air.
Under these conditions, the forces that cause the blades to turn are similar for all blades
regardless of their position in the plane of rotation. Therefore, dissymmetry of lift resulting from
helicopter airspeed is not a factor.
Figure 6-2 Rotor disc regions in autorotation zero speed
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SIX
AUTOROTATION 6-3
During vertical autorotation, the rotor disk is divided into three regions: driven region, driving
region, and stall region. Figure 6-3 shows three blade sections that illustrate force vectors.
Part A is the driven region, B and D are points of equilibrium, part C is the driving region, and
part E is the stall region. Force vectors are different in each region because rotational relative
wind is slower near the blade root and increases continually toward the blade tip. Also, blade
twist gives a more positive AOA in the driving region than in the driven region. The
combination of the inflow up through the rotor with rotational relative wind produces different
combinations of aerodynamic force at every point along the blade.
The driven region, also called the propeller region, is nearest the blade tips. Normally, it consists
of about 30 percent of the radius. In the driven region, part A of Figure 6-3 the TAF acts behind
the axis of rotation, resulting in an overall drag force. The driven region produces some lift, but
that lift is offset by drag. The overall result is a deceleration in the rotation of the blade. The
size of this region varies with the blade pitch, rate of descent, and rotor RPM. When changing
autorotative RPM blade pitch, or rate of descent, the size of the driven region in relation to the
other regions also changes.
There are two points of equilibrium on the blade, one between the driven region and the driving
region, and one between the driving region and the stall region. At points of equilibrium, TAF is
aligned with the axis of rotation. Lift and drag are produced, but the total effect produces neither
acceleration nor deceleration.
The driving region, or autorotative region, normally lies between 25 to 70 percent of the blade
radius. Part C of Figure 6-3 shows the driving region of the blade, which produces the forces
needed to turn the blades during autorotation. Total aerodynamic force in the driving region is
inclined slightly forward of the axis of rotation, producing a continual acceleration force. This
inclination supplies thrust, which tends to accelerate the rotation of the blade. Driving region
size varies with blade pitch setting, rate of descent, and rotor RPM.
By controlling the size of this region, a pilot can adjust autorotative RPM. For example, if the
collective pitch is raised, the pitch angle increases in all regions. This causes the point of
equilibrium to move inboard along the blade’s span, thus increasing the size of the driven region.
The stall region also becomes larger while the driving region becomes smaller. Reducing the
size of the driving region causes the acceleration force of the driving region and RPM to
decrease. A constant rotor RPM is achieved by adjusting the collective pitch so blade
acceleration forces from the driving region are balanced with the deceleration forces from the
driven and stall regions.
The inner 25 percent of the rotor blade is referred to as the stall region and operates above its
maximum AOA (stall angle), causing drag, which tends to slow rotation of the blade. Part E of
Figure 6-3 depicts the stall region.
604. FORWARD FLIGHT AUTOROTATION
Autorotative force in forward flight is produced in exactly the same manner as when the
helicopter is descending vertically in still air. However, because forward speed changes the
CHAPTER SIX HELICOPTER AERODYNAMICS WORKBOOK
6-4 AUTOROTATION
inflow of air up through the rotor disk, all three regions move outboard along the blade span on
the retreating side of the disk where AOA is larger. With lower AOA on the advancing side
blade, more of the blade falls in the driven region. On the retreating side, more of the blade is in
the stall region. A small section near the root experiences a reversed flow; therefore, the size of
the driven region on the retreating side is reduced.
Prior to landing from an autorotative descent (or autorotation), the pilot must flare the helicopter
in order to decelerate. The pilot initiates the flare by applying aft cyclic. As the helicopter flares
back, the airflow patterns change around the blades causing the RPM to increase. Pilots must
adjust the collective as necessary to keep the RPM within operating limits.
Figure 6-3 Rotor blade regions in autorotation
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SIX
AUTOROTATION 6-5
Figure 6-4 Rotor disc regions in autorotation forward speed
605. AUTOROTATION DESCENT VARIABLES
Performance in the descent depends upon the forces acting upon the rotor. Airspeed affects the
aerodynamic force on all blades and total power required for flight. Most autorotations are flown
at a 13-17 degree glide angle which offers the lowest descent rate in autorotation. It is worth
noting that very low speed autorotations, while possible, have very high associated descent rates.
Aircraft trim and gross weight also affect power required, so they also affect performance. As an
aircraft moves further out of trim the parasite drag increases, power required increases, and
hence descent rate increases. Gross weight determines RPM at a given collective pitch. At high
gross weight, more blade pitch is required to maintain a desired RPM, so higher gross weights
result in a slower rate of descent, assuming all other variables remain the same. RPM also varies
in descent with altitude (both PA and DA). Higher DA requires higher blade pitch to maintain a
given RPM but, due to the lower air density, a higher rate of descent will still occur.
The factors affecting autorotative descent performance are: Airspeed, Trim, Gross Weight, DA,
and RPM
RPM tradeoffs. RPM is adjusted by varying collective. Adjusting RPM in an autorotation
affects rate of descent and energy stored in the rotor. Selection of a good autorotation rotor
speed depends upon desired performance. High RPM stores energy well and but involves a
higher descent rate. Low RPM provides a slower descent and longer glide, but provides less
stored power for use in the flare. Taken to an extreme, low RPM can stall an excessive portion
of the rotor and make recovery extremely difficult. Specific considerations follow:
CHAPTER SIX HELICOPTER AERODYNAMICS WORKBOOK
6-6 AUTOROTATION
High RPM
1. Centrifugal loads on hub.
2. Excessive propeller region so higher rate of descent.
3. Rotational energy to trade off in a flare.
4. Good for high inertia systems which would have difficulty building RPM rapidly in a flare.
Low RPM
1. Higher AOA therefore a slower rate of descent.
2. Excessive stall region if RPM gets too low resulting in an increase in rate of descent.
3. Less rotational energy to trade off in a flare.
4. Good for low inertia systems which can build RPM rapidly in a flare.
5. Rotor blades lose centrifugal stiffness and cone upwards reducing the effective disk area,
increases material stresses, and increases the rate of descent.
606. PHASES OF AUTOROTATION
Autorotations are divided into three distinct phases: entry, steady-state descent, and deceleration
(flare) and touchdown. Each phase is aerodynamically different from the others.
Level Powered Flight at High Speed. Figure 6-5 shows the airflow and force vectors for a
blade in this configuration. The lift and drag vectors are large, and the total aerodynamic force is
inclined well to the rear of the axis of rotation. An engine failure in this mode will cause rapid
rotor RPM decay. To prevent this, the aviator must lower the collective quickly to reduce drag
and incline the total aerodynamic force vector forward, nearer the axis of rotation.
Figure 6-5 Force Vectors in Level-Powered Flight at High Speed
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SIX
AUTOROTATION 6-7
Entry. This phase is entered after loss of engine power. The loss of engine power and rotor
RPM is more pronounced when the helicopter is at high gross weight or high forward speed or in
high-DA conditions. Any of these conditions demand increased power and a more abrupt
reaction to the loss of that power. In most helicopters, it takes only seconds for the RPM decay
to fall into a minimum safe range, requiring a quick response from the aviator.
After an engine failure the pilot enters an autorotation by lowering the collective. AOA lessens
as airflow begins to move less downward, then shifts to an upward flow. The net result is that
lower AOA and less pitch make a smaller aerodynamic force that is not tilted as far aft
(Figure 6-6). Vertical force is reduced, so a descent begins, but the associated reduction in drag
keeps the rotor from losing too much RPM.
Collective Pitch Reduction. Figure 6-6 shows the airflow and force vectors for a blade
immediately after power loss and the subsequent collective reduction, yet before the aircraft has
begun to descend. Lift and drag are reduced, with the total aerodynamic force vector inclined
further forward than it was in powered flight. As the helicopter begins to descend, the airflow
begins to flow upward from under the rotor system. This causes the total aerodynamic force to
incline further forward until it reaches an equilibrium that maintains a safe operating RPM
(Figure 6-7).
Figure 6-6 Force Vectors after Power Loss – Reduced Collective
Possible aircraft initial reactions are based upon sudden loss of torque on the main rotor. Thus,
the helicopter will yaw left due to a reduction in anti-torque required (before pedals are
adjusted), and may roll right due to residual tail rotor force. The primary concern should be
controlling RPM. To make the entry a success, blade pitch must be lowered in a timely manner.
The rate of rotor speed decay will determine how quickly the collective must be lowered, and the
rate of decay will be determined by rotor inertia and power required. Rotor inertia is a rotor
head’s resistance to changes in velocity. A high-inertia rotor head will tend to remain at the
same RPM longer after a loss of power or in a flare than a low-inertia rotor head. Power
required is related to induced power, so it is affected by density and airspeed. In practical terms,
this means that the following factors affect successful autorotation entry:
1. Rotor blade pitch (dependent on flight condition - airspeed, gross weight, climb/descent,
etc.)
CHAPTER SIX HELICOPTER AERODYNAMICS WORKBOOK
6-8 AUTOROTATION
2. Rotor inertia
a. High inertia - RPM builds and decays slowly.
b. Low inertia - RPM builds and decays rapidly.
3. Pilot reaction time.
4. Entry altitude (time to establish a stabilized autorotation)
5. Entry airspeed
Steady-State Descent. Figure 6-7 shows the airflow and force vectors for a blade in a
steady-state autorotative descent. Airflow is now upward through the rotor disk because of the
descent. This up-flow of air creates a larger AOA, although blade pitch angle has not changed
since the descent began. Total aerodynamic force on the blade increases and is inclined further
forward until equilibrium is established, rate of descent and rotor RPM stabilize, and the
helicopter is descending at a constant angle. Angle of descent is normally 13 - 17 degrees,
depending on airspeed, DA, wind, and the type of helicopter.
Figure 6-7 Force Vectors in Autorotative Steady-State Descent
When autorotation is established, up-flow tilts the relative wind downward, which moves the net
aerodynamic force forward. In a stabilized autorotation the component of lift in the horizontal
direction balances out the horizontal component of drag so that drag does not reduce the rotor
RPM.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SIX
AUTOROTATION 6-9
RPM Stability. In an autorotation, transient changes in aircraft attitude or wind shifts can
change the airflow through the rotor system, therefore affecting RPM. However, the rotor
system demonstrates RPM stability in response to small changes. Figure 6-8 graphically
describes the blade region variations with RPM changes. In autorotation, the blade is at flat pitch
(or near flat pitch), which is designed to maintain a constant RPM at a given descent rate. When
an external force (winds/airflow etc., vice a change in collective setting) causes a small transient
increase in the RPM, the regions shift inboard, enlarging the driven (prop) region and associated
drag, while also reducing the moment arm for the driving (auto) region on the blades. This
reduction in the driving region causes the RPM to decrease back towards the original RPM. Just
the opposite happens with slight decreases in RPM. Thus, for minor RPM variations, the rotor
system has RPM stability.
However, with a large decrease in RPM, even though the driving region of the blade increases,
the stall region and drag it produced also increases. The increased moment arm for the driving
region may not be sufficient to regain the lost RPM before the aircraft reaches the ground.
Figure 6-8 RPM Response to Small RPM Variations
Since the amount of blade surface producing positive autorotative driving force varies according
to RPM and this driving force is synonymous with thrust produced, it is obvious the pilot has
additional control over rate of descent by changing pitch through collective application.
Excessively high Nr produces less driving force and a higher rate of descent, and very low Nr
leads to low driving force in proportion to high drag associated with a stalled profile. There is an
optimum RPM range, which produces the greatest net driving force and minimum descent rate.
It is in the best interest of the pilot to strive for this RPM range until reaching flare altitude. The
pilot must monitor RPM throughout the autorotation to ensure RPM stays within limits.
When steady state autorotation is achieved, the pilot has the option of stretching his glide to a
CHAPTER SIX HELICOPTER AERODYNAMICS WORKBOOK
6-10 AUTOROTATION
distant landing zone (LZ) or increasing his loiter time in the air, provided sufficient altitude
exists.
Rate of Descent and Glide Distance in Autorotation. Rather than using power required/power
available charts for autorotation, many NATOPS manuals contain charts specifically for
autorotation (Figure 6-9). Helicopter airspeed is probably the most significant factor that affects
rate of descent in autorotation. The rate of descent is high at very low airspeeds, decreases to a
minimum at some intermediate speed, and increases again at faster speeds. Minimum rate of
descent occurs at the bucket airspeed because this is where the minimum power is required to
remain airborne. If there is an available field immediately in front of you, you may use this
speed for extra time aloft to ensure crew readiness for landing or make a prudent radio
transmission, but there are other factors to consider as the helicopter approaches the ground.
If the engine failed and there was not a suitable landing site immediately in front of you, but
there was one further away, consider fling at maximum glide range airspeed. Maximum glide
distance occurs where the ratio of power required to airspeed is a minimum so that the aircraft
will fly the furthest horizontally with the smallest descent rate. A line drawn from the point of
origin tangent to the total drag curve illustrates the airspeed for maximum glide distance, much
the same as for powered flight. There are tradeoffs, and in this case, higher speed and distance
over the ground reduces time aloft.
The airspeeds for minimum rate of descent and maximum glide distance vary by helicopter type.
Individual operator’s manuals cover this information.
As the ground approaches the range of safe airspeed/rotor RPM combinations narrow and precise
management of kinetic energy is necessary. The new goal is to reduce kinetic energy along the
flight path to zero at the same time contact is made with the ground. Trade off the stored kinetic
energy in rotor RPM for thrust to maintain power requirements for flight before the blades reach
a stalled condition.
Deceleration and Touchdown. From either of the two extreme airspeed range examples
previously discussed (max glide/min rate of descent), we will assume a suitable LZ is now easily
within range. If we were at max glide at a high forward speed and associated high rate of
descent, it is only logical we slow down (low rate of descent at ground contact = less pain). How
slow? Minimum rate of descent sounds logical. But, even at this airspeed, the helicopter's
landing gear cannot absorb the amount of energy the helicopter is carrying at ground contact.
Therefore, it may be advantageous to carry five to ten knots extra airspeed over minimum rate of
descent airspeed at flare altitude - banking on another tradeoff – extra forward airspeed for high
rotor RPM. The fact is, maximum range airspeed is associated with greater rate of steady-state
descent, but the greater flare through minimum rate of descent airspeed to maximum decelerative
attitude provides a greater decelerative force both horizontally and vertically than a flare started
from min rate of descent speed. The challenge, therefore, is timing the deceleration
approximately from max range airspeed, which is more difficult than from the standard auto at
min rate of descent.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SIX
AUTOROTATION 6-11
Figure 6-9 Autorotational Rate of Descent Compared to Airspeed
The Last 100 Feet. It can be assumed that autorotation ends at 100 feet (depending on aircraft
and speed), and the landing procedure then begins. To execute a power-off landing for rotary-
wing aircraft, the aviator exchanges airspeed for lift by decelerating the aircraft during the last
100 feet. When executed correctly, deceleration is applied and timed so that rate of descent and
forward airspeed are minimized just before touchdown. At about 15 feet, this energy exchange
is essentially complete. The primary remaining control input is application of collective pitch to
cushion the touchdown. Because all helicopter types are slightly different, aviator experience in
that particular aircraft is the most useful tool for predicting the useful energy exchange available
CHAPTER SIX HELICOPTER AERODYNAMICS WORKBOOK
6-12 AUTOROTATION
at 100 feet and the appropriate amount of deceleration and collective pitch needed to execute that
exchange safely and effectively to land the aircraft successfully.
Flare and Touchdown. Figure 6-10 shows the airflow and force vectors for a blade in an
autorotative deceleration. To make an autorotative landing, the aviator reduces airspeed and rate
of descent just before touchdown. The aviator can partially accomplish both actions by applying
aft cyclic, which changes the attitude of the rotor disk in relation to the relative wind. A nose-up
cyclic flare tilts the rotor disk rearward which inclines the resultant thrust of the rotor system
to the rear, slowing forward speed. It also increases AOA on all blades by changing the
direction of airflow through the rotor system. The resulting increase in AOA creates more lift
along with the lift vector becoming more vertical, which decreases rate of descent. Moreover,
the downward shift in relative wind tilts the lift vector at blade element more forward, resulting
in a larger pro-autorotative force; this increases rotor RPM. The increase in RPM can be used
to cushion the landing but must be monitored to prevent overspeeding the rotor head.
Additionally, the flare exposes more of the fuselage to the airstream, thereby increasing
fuselage parasitic drag, further aiding in slowing the aircraft down. The flare should be
maintained in an effort to reach a point where forward speed is five to ten knots at close
proximity to the ground (10-15 feet). At this point, increasing collective increases thrust (trading
RPM for lift) and augments braking action, using up part of the stored rotational energy. Due to
the aft-tilted thrust vector and the addition of collective, the pilot must put in a little forward
cyclic to level the aircraft and use that last rotational energy by pulling collective to cushion the
landing. Since there is no torque from the engine, drivetrain drag may cause the fuselage to
“follow” the rotor system when collective is pulled, causing the nose to yaw to the left and
requiring some right rudder, the opposite of powered flight. The key is to maintain heading
control throughout the autorotation using the rudder pedals as necessary.
Figure 6-10 Blade Element and Thrust during Steady State Auto and Flare
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SIX
AUTOROTATION 6-13
If one chooses to arrive at flare altitude at less than minimum rate of descent airspeed, there is
little or no forward speed to trade off for this advantageous increase in rotor RPM and braking
action. Forward speed is already low, and if too much flare is combined with an improperly
timed flare (too high), forward speed may reduce to zero at a high altitude. This condition is
known as becoming “vertical,” and since the rotor system already has little stored energy, there
will not be enough thrust available with collective increase to slow rate of descent at touchdown
to a non-destructive level.
Arriving at the altitude for maximum decelerative effectiveness just prior to collective pull is
extremely useful because it involves trading kinetic energy from the descent for kinetic energy in
the rotor. If the attitude was achieved and held for an extended period of time, the reduction in
velocity would cause a greatly increased descent rate, which would increase the size of the stall
region on the blades and cause a loss of RPM.
Factors affected by the flare are: RPM, Thrust vector direction and magnitude, and Fuselage
attitude.
607. WINDMILL BRAKE STATE
Windmill Brake State. If the rotor somehow entered a descent at a rate in excess of
approximately 180% of induced velocity, too much potential energy would be diverted to
powering the rotor. Excessive rotor speed would create a very dangerous condition. In the
windmill brake state virtually all flow is “up” relative to the rotor, and energy may be extracted
from the system. This is the condition in which windmills extract energy from the passing air,
but it is not a normal operating state for any helicopter. The one time that a rotorcraft is put into
a descending flow state that approaches windmill brake is during the cyclic flare of an
autorotation. During that transient phase, kinetic energy is increased in the rotor by increasing
up-flow in order to make it available for use in the landing. However, RPM must be
monitored and controlled to prevent excessive buildup and overspeeding of the rotor head.
608. HEIGHT-VELOCITY DIAGRAM
No matter how well the pilot can execute an autorotation, there remain some combinations of
initial altitudes and airspeeds from which a safe autorotational landing will be extremely difficult
to perform. In fact, at some combinations of altitude and forward speed, it is almost impossible
to demonstrate safe autorotative landings at a vertical touchdown speed within the design limits
of the landing gear. The boundaries of these combinations define the height-velocity diagram or
"The Deadman's Curve." (Figure 6-11)
The purpose of an H–V diagram is to identify the portions of the flight envelope from which a
safe landing can be made in the event of a sudden engine failure. The H–V diagram also
generally depicts two areas to be avoided: The low-airspeed/high-hover altitude (low flight
altitude) region and the high-airspeed/low-altitude region. These are named with respect to
takeoff from the IGE Hover. At a hover, 200 – 300’ is considered a high altitude. Above
60 KIAS, flight below 20’ is considered low altitude.
CHAPTER SIX HELICOPTER AERODYNAMICS WORKBOOK
6-14 AUTOROTATION
There are H-V diagrams for each type of helicopter. They are found in their respective NATOPS
manuals. Helicopter pilots should be familiar with these diagrams.
Taking a closer look at the H-V diagram, we see several definite points define the curve, the first
being the low hover height. Up to this height, a pilot can handle a power failure by coming
straight down, using collective increase to cushion the landing. Above that altitude in
combination with low speed, the rotor blades will slow down and stall if collective setting
remains constant, or the helicopter will impact the ground too hard if collective is lowered.
Enough altitude does not exist to acquire enough forward airspeed by the time flare altitude is
reached to successfully execute a flare. This height is a function of the power required to hover,
rotor inertia, blade area and stall characteristics, and the capability of the landing gear to absorb
the landing forces without sustaining damage.
The unsafe hover area runs from the low hover height to the high hover height. Above this
altitude, there is enough altitude to make a diving transition into forward flight autorotation and
execute a normal flare.
Beyond the knee of the curve, a power failure is survivable at any altitude above the high-
airspeed/low-altitude region. The three problems associated with the high-airspeed/low-altitude
region are pilot reaction time, lack of time and altitude for the induced flow to reverse before
ground impact, and possibility of tail rotor stinger strike in response to cyclic flare to trade
altitude for airspeed.
Figure 6-11 Generic Height Velocity Diagram
Skilled test pilots, who try to make their reactions simulate those of the average reaction time of
a pilot, establish H-V diagrams. This is done by specifying a definite delay time following the
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SIX
AUTOROTATION 6-15
engine failure before initiating control input. The military assumes their pilots may be distracted
during an engine failure due to focused attention to assigned missions, allowing a two-second
delay before response during any flight condition.
A few regions of operation are apparent on the H-V diagram.
1. Low-speed region. The largest region noticed on the diagram occurs where potential
energy is not sufficient to offset low aircraft kinetic energy state for transition to an autorotative
glide path. In other words, not enough altitude is available to establish a steady-state glide and
minimum flare airspeed. When the engine fails in this sector a rapid rate of descent will occur,
but with little or no forward airspeed a flare will not be capable of arresting the descent prior to
landing. Application of collective will cause the RPM to decay excessively resulting in a hard
landing (limited rotor rotational kinetic energy available).
2. Low-altitude/high-speed region. At low altitude and high speed, a quick cyclic flare can
transfer kinetic energy to the rotor, provided time is sufficient to initiate the maneuver before
ground impact. In the low-altitude/high-speed region, velocity is too great for a safe taxiing
auto, but altitude is too low for flare initiation. By the time the pilot reacts (using typical
reaction time) with a flare or zoom climb, the tail sinks enough to impact the ground.
3. High hover height. At altitudes above the low airspeed avoid region, the pilot can enter
autorotation by making a diving transition to forward flight, reaching the desired autorotation
airspeed and then executing a normal flare.
4. Low hover height. Below the low airspeed avoid region the helicopter can simply be
landed straight down with no forward airspeed and cushioned with collective and/or landing
gear. Rotor stored kinetic energy is traded in the cushion.
The size of the avoid region is affected by several variables. Pilot response time varies, but
charts are drawn on the basis of average pilot response times. Airspeed affects the ability to
establish an autorotation at an acceptable rate of descent. Rotor inertia determines how quickly
the rotor loses speed. A low-inertia system would be more likely to lose valuable RPM before
establishment of autorotation, so it would have a larger avoid area than a helicopter with high
rotor inertia. Increased gross weight increases power required for flight, which in turn increases
rate of descent and thus increases the size of the avoid area. DA decreases rotor efficiency and
increases power required, so it has the same effect as increased gross weight on size of the avoid
area.
The variables that directly affect the size of the height-velocity diagram avoid area are:
1. Rotor Inertia. High inertia reduces shaded region because RPM does not decay as fast as
a low-inertia system. High inertia moves the “knee” left.
2. Gross Weight. Power requirements increase. High gross weight moves the “knee” right.
3. DA. Same effect as gross weight. High DA moves the “knee” right.
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6-16 AUTOROTATION
H-V Guidelines in the TH-57. During normal takeoff, airspeed should be 40 KIAS by 20’ AGL
and 65 KIAS by 50’ AGL to minimize the risk near the H-V diagram avoid areas, transitioning
through the caution area into the green area as quickly as possible. In Chapter Four of NATOPS,
protracted operations in the AVOID and CAUTION areas of the height-velocity diagram are
prohibited. Realize that mission operations such as rescue hoisting, externals, etc., all require
“high” altitude hovers. One just needs to realize that if an engine failure occurs during those
operations, options may be limited!
PERFORMANCE 7-1
CHAPTER SEVEN
PERFORMANCE
700. INTRODUCTION
This chapter correlates helicopter aerodynamics principles with engine and aircraft performance.
701. LESSON TOPIC LEARNING OBJECTIVES
1. Identify rotor system dynamics
2. Identify rotorcraft configurations and airfoil design considerations
3. Identify the basic aerodynamic characteristics of the airframe
4. Identify factors that affect helicopter stability and control
5. Identify factors that affect helicopter power required and power available for flight
6. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
7. Explain the aerodynamics of flight
702. FACTORS AFFECTING PERFORMANCE
Moisture (Humidity): Humidity alone is usually not considered an important factor in
calculating density altitude and helicopter performance; however, it does contribute. There are
no rules of thumb used to compute the effects of humidity on density altitude, but some
manufacturers include charts with 80 percent relative humidity columns as additional
information. There appears to be an approximately 3–4 percent reduction in performance
compared to dry air at the same altitude and temperature, so expect a decrease in hovering and
takeoff performance in high humidity conditions. Although 3–4 percent seems insignificant, it
can be the cause of a mishap when already operating at the limits of the helicopter.
Weight: Weight is one of the most important factors because the pilot can control it. Most
performance charts include weight as one of the variables. By reducing the weight of the
helicopter, a pilot may be able to take off or land safely at a location that otherwise would be
impossible. However, if ever in doubt about whether a takeoff or landing can be performed
safely, delay your takeoff until more favorable density altitude conditions exist. If airborne, try
to land at a location that has more favorable conditions, or one where a landing can be made that
does not require a hover.
In addition, at higher gross weights, the increased power required to hover produces more torque,
which means more anti-torque thrust is required. In some helicopters during high altitude
operations, the maximum anti-torque produced by the tail rotor during a hover may not be
sufficient to overcome torque even if the gross weight is within limits.
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7-2 PERFORMANCE
Winds: Wind direction and velocity also affect hovering, takeoff, and climb performance.
Translational lift occurs any time there is relative airflow over the rotor disk. This occurs
whether the relative airflow is caused by helicopter movement or by the wind. Assuming a
headwind, as wind speed increases, translational lift increases, resulting in less power required to
hover.
The wind direction is also an important consideration. Headwinds are the most desirable as they
contribute to the greatest increase in performance. Strong crosswinds and tailwinds may require
the use of more tail rotor thrust to maintain directional control. This increased tail rotor thrust
absorbs power from the engine, which means there is less power available to the main rotor for
the production of lift. Some helicopters even have a critical wind azimuth or maximum safe
relative wind chart. Operating the helicopter beyond these limits could cause loss of tail rotor
effectiveness.
Takeoff and climb performance is greatly affected by wind. When taking off into a headwind,
effective translational lift is achieved earlier, resulting in more lift and a steeper climb angle.
When taking off with a tailwind, more distance is required to accelerate through translation lift.
703. GENERAL
Helicopter aircraft and engine performance require an understanding of the power required
curves, power available, and the relationship between them.
Power is required to overcome the drag produced by the rotors and the fuselage. The power
available to meet this power requirement is produced by a turboshaft engine. Turbojet aircraft
produce thrust directly from their engines and do not turn a propeller or rotor. As such, jet
aircraft performance charts only slightly resemble helicopter drag curves. For each pound of
drag generated by the aircraft at a specific airspeed, a pound of thrust must be generated by the
jet in order to maintain level flight. The amount of thrust produced by a jet engine is directly
proportional to fuel flow and therefore endurance and range performance may be determined
from an aircraft total drag curve.
The differences between the two types of performance curves can be attributed to the different
contributions of profile and induced drag in the helicopter. The helicopter rotor also produces
thrust, but the production of thrust is not directly related to the fuel flow for turbo-shaft engines.
Turbo-shaft fuel flow is more closely related to how much power is being produced by the
engine. Accordingly, a total drag curve cannot be used in the same way as a performance chart
for helicopters.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SEVEN
PERFORMANCE 7-3
Figure 7-1 Total Drag Curve
Instead, “power required curves” (or more specifically, “fuel flow curves”) are presented in
operator’s manuals for use in mission planning. Power is simply the rate of doing work. Most
turbine helicopters are equipped with a gauge for measuring torque which may be viewed by the
aviator in the cockpit. Since power equals torque times RPM, if the RPM remains constant, the
torque is a direct representation of current engine power output. Further, a fuel flow scale is
usually provided opposite the torque scale of a cruise chart, thereby enabling the aviator to
convert torque directly to fuel flow.
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7-4 PERFORMANCE
Figure 7-2 Power Required Versus Airspeed Curve
It is important to note that the lowest point on the power required curve is the point of minimum
power required (best lift to drag ratio) and not necessarily the point of minimum drag (as is the
lowest point on the total drag curve). The point of minimum power results in the lowest fuel
flow and is therefore the airspeed for maximum endurance. The airspeed for minimum power
is slower than the airspeed for minimum drag because a decrease in velocity to the minimum
power airspeed decreases the power required, even though flying at any airspeed below
minimum drag actually increases drag. However, because the bottom of the drag curve is nearly
flat, the slight increase in drag is more than offset by the decrease in velocity, which slows the
work rate and therefore results in an overall reduction in power required.
704. POWER REQUIRED
For a helicopter to remain in steady, level flight, forces and moments must balance. These forces
exist in the vertical plane, horizontal plane, and about the CG in the form of pitching moments.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SEVEN
PERFORMANCE 7-5
Figure 7-3 Aerodynamic Forces Affecting Power Required
Figure 7-4 Power Required Curves versus Airspeed
In a hover, two types of power are necessary - induced and profile power. Induced power is
power associated with the production of rotor thrust. This value is at its highest during a hover
(60 – 85 percent of total main rotor power) and decreases rapidly as the helicopter accelerates
into forward flight. During forward flight, the increase in mass flow of air introduced to the
rotor system reduces the amount of work the rotors must produce to maintain a constant thrust,
therefore, induced power required continues to go down with increasing airspeed.
Profile power, which can be thought of as "main rotor turning power," accounts for 15 – 40
percent of main rotor power in a hover and is used to overcome friction drag on the blades. It
increases slightly with increasing airspeed.
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7-6 PERFORMANCE
In forward flight, parasite power joins forces with induced and profile power to overcome the
parasite drag generated by all the aircraft components, excluding the rotor blades. Parasite
power can be thought of as the power required to move the aircraft through the air. This power
requirement increases in proportion to forward airspeed cubed. Obviously, this is
inconsequential at low speed, but is significant at high speed and is an important consideration
for helicopter designers to minimize drag.
In addition to the drag curves which are the basis for the power required curves, there is a fourth
power requirement, labeled “miscellaneous,” which is taken into account when power required
curves are developed for specific rotorcraft. This is the power required to run the tail rotor and
accessories such as generators, hydraulics, etc. Accessory power requirements remain relatively
constant independent of airspeed, while tail rotor power required tends to decrease with
increasing airspeed. Depending on the charts used, this additional power requirement is
sometimes combined with the profile power requirement, creating a “total rotor profile power”
required to maintain a given rotor RPM, taking into account the rotor profile drag as well as the
tail rotor and accessory requirements.
The smaller horizontal force, H-force, is produced by the unbalanced profile and induced drag
(or in-plane drag in some books) of the main rotor blades. Tilting the rotor disk forward from a
fraction of a degree at low speed to about 10° at max speed compensates for this.
Different flight regimes are performed more efficiently at different forward speeds. The bowl-
shape of the power required curve graphically illustrates the reason why. Optimum speeds
determined by this curve are maximum loiter time (endurance), minimum rate of descent in
autorotation, best rate of climb and maximum range airspeed.
Best rate of climb airspeed is formed at the point where the difference is a maximum between
power required and power available. The bottom of the curve is called the bucket airspeed.
Since the goal of achieving maximum loiter time is making the available fuel last as long as
possible, and since fuel flow is proportional to engine power, maximum loiter time should also
be at this point.
Near this speed, minimum rate of descent in an autorotation is also found, since the power
required to keep the aircraft airborne is at a minimum.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SEVEN
PERFORMANCE 7-7
Figure 7-5 Optimum Airspeeds
The point on the power required curve corresponding to the point of minimum drag versus
airspeed on the drag curve is at an airspeed greater than that for minimum power (bucket
airspeed). This is the airspeed for maximum range and is where the ratio of fuel flow to
velocity is at a minimum value. This point is shown in at the point of tangency of the power
required curve and a straight line drawn from the origin, providing the best power or fuel flow to
airspeed (thus drag) ratio. Maximum range speed is found on the fuel flow curve by drawing a
line tangent to the curve from the origin. This ratio of speed to fuel flow shows the distance one
can travel on a pound of fuel on a no-wind day. If there is a headwind, the line should be
originated at the headwind value, which derives a higher speed and lower range. For a tailwind,
the optimum airspeed decreases, but the range increases significantly. On generic charts the
speed for maximum range and autorotation maximum glide distance sometimes appear to be the
same. Best airspeed for maximum glide in an autorotation is also affected by headwinds and
tailwinds just like maximum range airspeed. However, when using aircraft specific charts, that
is not usually the case and the two speeds are different.
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7-8 PERFORMANCE
Figure 7-6 Maximum Range Airspeed Adjustment for Winds
705. POWER AVAILABLE
Air density (DA) is the environmental factor which most significantly affects power available.
Less dense air requires that the engine works harder to produce the same amount of mass flow.
Power available is directly affected by density to such a degree that power available at a given
DA can be calculated by simply multiplying power available at standard sea level by the density
ratio in the ambient conditions.
Poweravail = Powersea level x density ratio ()
This is generally true in regions of relatively normal temperature variation. However, in
locations of extremely wide temperature variations such as the desert environment, the
temperature can have an extra degrading effect on engine power available.
Other factors limiting power available. Operating conditions that affect fuel flow or airflow
directly affect the ability of the engine to generate power. Some of those factors follow:
1. Fuel Flow Limitation (cold) - As temperature decreases the density of air increases so the
fuel flow must increase in order to maintain the stoichiometric fuel/air ratio for complete
combustion. However, the amount of fuel flow through the fuel nozzles has a limit; therefore at
cold temperatures the fuel/air ratio will not be optimum, and incomplete (lean) combustion will
occur, resulting in less power available.
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PERFORMANCE 7-9
2. Turbine Temperature Limitation (hot) - The materials used to build turbines have definite
stress and temperature limits. To avoid unacceptable creep or component failure, turbine
temperature must be limited. Depending on aircraft manufacturer this can be called exhaust gas
temperature (EGT), turbine outlet temperature (TOT) or turbine inlet temperature (TIT).
3. Ng-Gas Generator Limitation (hot) - As the OAT increases the density of air decreases,
therefore the gas turbine has to rotate faster in order to deliver the same mass flow rate. This
increased rotational speed required at higher temperatures can approach limits that have been
established to counter centrifugal loads on the gas turbine blades.
4. Age of the engine - Compressor blades erode with time, and their degradation results in
loss of blade area that will degrade engine performance.
5. Component rating degradation - Transmission components have material limitations, so
their torque capacity must be considered.
6. Humidity/Moisture Effect - Increases in humidity/moisture have a counteracting effect in
that the associated decrease in air density is detrimental while the reduced combustor inlet temp
(T3) is beneficial. Hence humidity/moisture has a negligible effect on gas turbine engines.
7. Torque limits - drive train limits, including drive shaft and transmission.
8. Airspeed effects (ram air) - Airspeed increases the flow rate into the engine, but at the
speed at which rotorcraft operate this effect is negligible.
706. EFFECT OF TAIL ROTOR ON POWER AVAILABLE
Since the engine drives both the main rotor and the tail rotor, the tail rotor does not affect the
power available that the engine produces; rather, it requires that the power be shared between the
two rotor systems, reducing power available for the main rotor. The tail rotor uses 5-15% of the
total power available, therefore leaving only 85-95% for the main rotor. Although other
frictional losses of the drive train may be significant, the tail rotor robs the greatest amount of
power from the main rotor. The tail rotor makes its greatest demands on the engine power
available when the greatest requirements are on the main rotor. For example, in the climb,
termination of a steep approach, when power required to perform a maneuver is equal to or
exceeding the power available, and/or when rotor RPM is drooping, the main rotor system is
creating the greatest amount of torque, therefore, the anti-torque requirements from the tail rotor
are greatest. However, since the main rotor and tail rotor are driven by a common system, when
main rotor RPM droops, tail rotor demand is highest and it is most sensitive to its own decreased
RPM.
For each of these maneuvers, the time to insure adequate power is available to maintain tail rotor
and main rotor authority is prior to the maneuver. This highlights the critical importance of in-
depth performance planning prior to flight, as well as careful re-evaluation during flight should
the mission require any alteration to the planned flight. When the margin for error is minimal,
unnecessary maneuvering should be kept to a minimum, and increased vigilance is required to be
CHAPTER SEVEN HELICOPTER AERODYNAMICS WORKBOOK
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best prepared for any unanticipated situation. As with any other aspect of aviation, expect the
unexpected, and then vortex ring state (VRS), PR Exceeds PA, or even an engine failure will not
catch you unprepared.
707. POWER REQUIRED EXCEEDS POWER AVAILABLE
When power required for a maneuver exceeds power available (PR>PA) under the ambient
conditions, an un-commanded descent or deceleration will result. Aggravating factors include:
high G-loading, high gross weight, high DA, rapid maneuvering (quick stops), slow spool up
time, loss of wind effect, loss of wind direction, and loss of ground effect (transiting from the
deck of a ship).
PR>PA Indications. Power required exceeding power available becomes dangerous when
operating in close proximity to obstructions where the pilot may not have maneuvering airspace
to recover prior to impacting the obstacle. Along with the un-commanded descent or
deceleration, rotor droop and associated loss of tail rotor authority (LTA) may result.
In addition to proper performance planning and situational awareness of the above aggravating
factors, the pilot should avoid excessive maneuvering, high descent rates, and downwind
takeoffs and landings, especially in environmental conditions where power available may be
marginal.
Power required exceeding power available is differentiated from vortex ring state (VRS) by un-
commanded descent being associated with max allowable torque and/or rotor droop and possible
LTA. VRS is not normally associated with either rotor droop or LTA.
Induced power. Induced power requirements change as forward airspeed increases. The
requirement for a mass flow of air still exists, but forward velocity increases the mass flow rate
so the rotor does not need to apply as much work on the air, thus less power is required. At
speeds beyond that at which the tip vortices are outrun (speed for translational lift) the rotor disk
acts in a manner that is similar to a conventional wing.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SEVEN
PERFORMANCE 7-11
Figure 7-7 Induced Power Required
Parasite power. Just as high induced power requirements can cause a power required exceeding
power available situation at a hover or slow airspeeds, parasite power requirements can cause the
situation at higher speeds.
Figure 7-8 Parasite Power Required
The point where power required exceeds engine power available at high speed is commonly
referred to as VH or the maximum speed in level flight at maximum power without an un-
commanded descent developing. VH should not be confused with VNE (Velocity never exceed)
which is a structural limitation. VNE of an aircraft is the V speed which refers to the velocity that
should never be exceeded due to risk of structural failure, due to calculated factors such as wing,
tail, or airframe deformation or due to aero elastic 'flutter' (unstable airframe or control
oscillation). VNE is specified as a red line on many airspeed indicators. This speed is specific to
the aircraft model, and represents the edge of its performance envelope in terms of speed.
Excess Power. Because power required exceeding power available is often associated with
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7-12 PERFORMANCE
lower airspeeds, the induced power requirement may become critical. As airspeed decreases
during the approach or maneuvering, induced power required increases, so deceleration with a
constant collective setting moves the helicopter into a regime where excess power (difference
between available and required) steadily decreases. Each aircraft is inherently different, and
experiences a different amount of translational lift at different airspeeds. The determining factor
in the amount of "extra lift" available is determined by the slope of the induced power required
curve. Typically, translational lift is experienced during transition from hover into forward flight
at airspeeds between 13 - 24 knots, depending on disk size, blade area, and RPM.
Figure 7-9 Decrease in Excess Power as Airspeed Decreases
It is a fact that when a helicopter transitions from forward flight to a hover, it experiences
decreased performance because of increased induced power requirements that stem from the tip
vortices that are generated in a hover. As airspeed decreases to near 13 - 24 knots the entire rotor
begins to experience recirculation of vortices, and vortices impact the fuselage and tail. Power
required increases and if power available is marginal, or the aircraft is not in ground effect,
conditions are ripe for an un-commanded descent, rotor droop, and/or LTA.
708. HOVER PERFORMANCE
Helicopter performance revolves around whether or not the helicopter can be hovered. More
power is required during the hover than in any other flight regime. Obstructions aside, if a hover
can be maintained, a takeoff can be made, especially with the additional benefit of translational
lift. Hover charts are provided for in ground effect (IGE) hover and out of ground effect (OGE)
hover under various conditions of gross weight, altitude, temperature, and power. The IGE
hover ceiling is usually higher than the OGE hover ceiling because of the added lift benefit
produced by ground effect. A pilot should always plan an OGE hover when landing in an area
that is uncertain or unverified.
As density altitude increases, more power is required to hover. At some point, the power
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SEVEN
PERFORMANCE 7-13
required is equal to the power available. This establishes the hovering ceiling under the existing
conditions. Any adjustment to the gross weight by varying fuel, payload, or both, affects the
hovering ceiling. The heavier the gross weight, the lower the hovering ceiling. As gross weight
is decreased, the hover ceiling increases.
Sample Hover Problem 1
You are to fly to a remote location for training. Using Figure 7-10 can you safely hover in
ground effect at your departure point with the following conditions?
Pressure Altitude..............................8,000 feet
Temperature..........................................+15 °C
Takeoff Gross Weight.........................1,250 lb.
RPM...............................................104 percent
First enter the chart at 8,000 feet pressure altitude (point A), then move right until reaching a
point midway between the +10 °C and +20 °C lines (point B). From that point, proceed down to
find the maximum gross weight where a 2 foot hover can be achieved. In this case, it is
approximately 1,280 pounds (point C). Since the gross weight of your helicopter is less than
this, you can safely hover with these conditions.
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7-14 PERFORMANCE
Figure 7-10 Sample hover problem 1
Sample Hover Problem 2
Once you reach the remote location in the previous problem, you will need to hover OGE for
training. The pressure altitude at the remote site is 9,000 feet, and you will use 50 pounds of fuel
getting there. (The new gross weight is now 1,200 pounds.) The temperature will remain at
+15 °C. Can you accomplish the mission?
Enter the chart at 9,000 feet (point A) and proceed to point B (+15 °C). From there, determine
that the maximum gross weight to hover OGE is approximately 1,130 pounds (point C). Since
your gross weight is higher than this value, you will not be able to hover in these conditions. To
accomplish the mission, you will need to remove approximately 70 pounds before you begin the
flight.
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PERFORMANCE 7-15
Figure 7-11 Sample hover problem 2
These two sample problems emphasize the importance of determining the gross weight and
hover ceiling throughout the entire flight operation. Being able to hover at the takeoff location
with a specific gross weight does not ensure the same performance at the landing point. If the
destination point is at a higher density altitude because of higher elevation, temperature, and/or
relative humidity, more power is required to hover there. You should be able to predict whether
hovering power will be available at the destination by knowing the temperature and wind
conditions, using the performance charts in the helicopter flight manual, and making certain
power checks during hover and in flight prior to commencing the approach and landing.
For helicopters with dual engines, performance charts provide torque amounts for both engines.
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Sample Hover Problem 3
Determine what torque is required to hover. Use the following conditions:
Pressure Altitude ............................................9,500 feet
Outside Air Temperature.........................................0 °C
Gross Weight.....................................................4,250 lb.
Desired Skid Height ..............................................5 feet
First, enter the chart at 9,500 feet pressure altitude, then move right to outside air temperature,
0 °C. From that point, move down to 4,250 pounds gross weight and then move left to 5-foot
skid height. Drop down to read 66 percent torque required to hover.
Figure 7-12 Sample hover problem 3
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PERFORMANCE 7-17
709. CLIMB PERFORMANCE
Most of the factors affecting hover and takeoff performance also affect climb performance. In
addition, turbulent air, pilot techniques, and overall condition of the helicopter can cause climb
performance to vary.
A helicopter flown at the best rate-of-climb speed (VY) obtains the greatest gain in altitude over a
given period of time. This speed is normally used during the climb after all obstacles have been
cleared and is usually maintained until reaching cruise altitude. Rate of climb must not be
confused with angle of climb. Angle of climb is a function of altitude gained over a given
distance. The VY results in the highest climb rate, but not the steepest climb angle, and may not
be sufficient to clear obstructions. The best angle of climb speed (VX) depends upon the power
available. If there is a surplus of power available, the helicopter can climb vertically, so VX is
zero.
Wind direction and speed have an effect on climb performance, but it is often misunderstood.
Airspeed is the speed at which the helicopter is moving through the atmosphere and is unaffected
by wind. Atmospheric wind affects only the groundspeed, or speed at which the helicopter is
moving over the Earth’s surface. Thus, the only climb performance affected by atmospheric
wind is the angle of climb and not the rate of climb.
When planning for climb performance, it is first important to plan for torque settings at level
flight. Climb performance charts show the change in torque, above or below torque, required for
level flight under the same gross weight and atmospheric conditions to obtain a given rate of
climb or descent.
Sample Cruise or Level Flight Problem
Determine torque setting for cruise or level flight using the following conditions:
Pressure Altitude............................................. 8,000 feet
Outside Air Temperature..................................... +15 °C
Indicated Airspeed...............................................80 knots
Maximum Gross Weight .....................................5,000 lb.
With this chart, first confirm that it is for a pressure altitude of 8,000 feet with an OAT of 15°.
Begin on the left side at 80 knots indicated airspeed (point A) and move right to maximum gross
weight of 5,000 lb. (point B). From that point, proceed down to the torque reading for level
flight, which is 74 percent torque (point C). This torque setting is used in the next problem to
add or subtract cruise/descent torque percentage from cruise flight.
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Figure 7-13 Sample cruise problem
Sample Climb Problem
Determine climb/descent torque percentage using the following conditions:
Rate of Climb or Descent .....................................500 fpm
Maximum Gross Weight......................................5, 000 lb.
With this chart, first locate a 500-fpm rate of climb or descent (point A), and then move to the
right to a maximum gross weight of 5,000 lb. (point B). From that point, proceed down to the
torque percentage, which is 15 percent torque (point C). For climb or descent, 15 percent torque
should be added/subtracted from the 74 percent torque needed for level flight. For example, if
the numbers were to be used for a climb torque, the pilot would adjust torque settings to
89 percent for optimal climb performance.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SEVEN
PERFORMANCE 7-19
Figure 7-14 Sample climb problem
710. REVIEW OF OPTIMUM AIRSPEEDS
Optimum Airspeeds. Choosing appropriate level-flight airspeed is an important part of
obtaining the most appropriate performance for a mission. Airspeeds for maximum speed,
maximum range, and maximum endurance are distinct, and vary with aircraft loading and
environment. In a given set of conditions, one performance parameter may be more crucial than
others, so flight at the airspeed that would maximize that potential makes sense. For example, if
holding while awaiting deck landing space is important, the pilot should fly at the airspeed that
gives the best endurance. In a long over-water mission, best range may be appropriate.
Maximum speed is required in a time critical situation. Fortunately, the required airspeed for
any of these situations is easily found on a power required versus airspeed chart.
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Figure 7-15 Optimum Airspeeds
Speeds for endurance and range. As a previous lesson pointed out, power required varies with
weight, altitude, and airspeed. The chart section of a NATOPS manual contains power required
curves that are divided up typically by PA (pressure altitude). They depict power requirements
at a variety of aircraft weights in a format similar to that used here. The shape of this curve has
been likened, by some, to be just like a collective position curve; the collective is highest in a no-
wind hover, decreases with increasing forward airspeed to the "bucket," and increases again as
airspeed approaches VNE.
The power required curve also depicts fuel flow required at various airspeeds because power has
a direct relationship to the amount of fuel introduced into a gas turbine. In a no-wind hover,
power required is the highest, so fuel flow is also the highest. Power and fuel flow decrease as
forward velocity is increased toward the "bucket,” and then increase again as airspeed
approaches VNE. Thus, a relationship between fuel flow and forward speed can be visualized.
Minimum fuel flow occurs at the bucket airspeed, so the bucket airspeed is identified as the point
of maximum endurance.
The airspeed for maximum range is determined by drawing a tangent line from the origin to the
fuel flow/power required curve. The slope, or the change in the vertical direction with respect to
the change in the horizontal direction, is fuel flow/airspeed. Units of the slope are lb. /hr divided
by NM/hr. When the hours are cancelled in the slope, the units of slope are pounds of fuel used
per nautical mile traveled. Minimizing the slope translates to finding the point at which the least
fuel is burned for each nautical mile of travel (pound/NM). The least fuel per nautical mile is the
same as the most distance covered for the least amount of fuel used, or maximum range.
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PERFORMANCE 7-21
Figure 7-16 Power Required Chart (CH-46E)
So how do winds factor into this situation? Winds do not affect endurance airspeed because
distance over the ground is not important in endurance calculations. Endurance solely deals with
time aloft at minimum power, minimum amount of fuel burned, and airspeed felt at the rotor is
the same whether wind is present or not.
Maximum range, however, is affected by winds because it involves maximizing movement over
the ground with minimal fuel flow. Speed over the ground is faster with a tailwind and slower
with a headwind, so the origin (zero point) of the airspeed axis must be shifted by the amount of
the headwind. Thought of another way, with a headwind the aircraft does not go as far and with
a tailwind it goes further.
Repeated use of the above system of determining wind correction has given results at typical
maximum range airspeeds that are predictable even without chart work. A good rule of thumb,
based upon consistently close approximations, is to add 1/4 of the headwind component on to no-
wind maximum range airspeed and to subtract 1/6 of the tailwind component. It should be noted
that these percentages will change with gross weight, ambient air conditions, and aircraft T/M/S.
The aviator is recommended to thoroughly sift through his own power and airspeed charts in
order to validate these trends. The difference between the two adjustments has to do with the
shape of the curve and the effect of shifting the origin and the resulting point of intersection of
the tangent line.
Maximum rate of climb and minimum rate of descent. The airspeed to fly for maximum
endurance (the bucket airspeed) is also suitable for maximizing performance in two other
regimes: maximum rate of climb and minimum rate of descent with power off. Maximum rate
of climb occurs at the bucket because minimum power required subtracted from a fairly constant
power available yields the largest amount of excess power available. If airspeed is maintained
constant, excess power can be used to climb or maneuver. Likewise, in a descent, the point of
minimum power required for flight is the point at which power deficit, which relates directly to
sink rate, would occur in a power-off situation. Note that max endurance and max rate of climb
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7-22 PERFORMANCE
are found at the bucket of a power chart, while minimum rate of descent is found at the bucket of
an autorotation chart.
Figure 7-17 Fuel Flow vs. TAS
Figure 7-18 Excess Power
How does fuel consumption change with altitude? The specific fuel consumption of the gas
turbine varies with two primary operating parameters: temperature and power output. The
specific fuel consumption is defined as nautical miles per pound of fuel.
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PERFORMANCE 7-23
As density is decreased, both the fuel flow and SHP decrease proportionally, so it can be said
that density variations do not by themselves influence specific fuel consumption (disregarding
profile and parasitic drag). However, as altitude is increased, temperature normally decreases.
Because the turbine may deliver a given thrust output with less fuel at a lower inlet temperature,
the specific fuel consumption normally improves (decreases) with altitude. If the atmosphere
can be considered to be standard, the specific fuel consumption decreases to the tropopause and
then remains constant until the efficiency of the compressor begins to break down at sufficiently
high altitudes. The standard atmosphere has a temperature decrease up to the tropopause
(approx. 36,000 feet).
Figure 7-19 Max Range Altitude vs. Gross Weight
Specific fuel consumption also varies quite noticeably with power output. The gas turbine is
designed so that it operates most efficiently at high power outputs. This means that the specific
fuel consumption is lowest at higher power settings, and that 100% Ng is the optimum speed for
greatest efficiency. Note that total fuel consumption does not go down at high power settings;
specific fuel consumption, or pound of fuel per hour per SHP does. For a given amount of shaft
horsepower output, the least amount of fuel is burned (highest efficiency) at high power settings.
This situation poses an interesting problem for helicopters. Because helicopters use turboshaft
engines, the fuel efficiency of the aircraft is determined by the efficiency of both the engine and
the rotor system. An increase in DA requires more work by the rotor system for the same flight
profile. Engine efficiency gains at altitude are balanced by rotor efficiency losses. Actual fuel
efficiency obtained at altitude thus depends upon rotor system efficiency, installed aircraft
engine characteristics, work output requirement, and total fuel load. In general, at low gross
weights one gets better range at higher altitude while at high gross weights a better range is
achieved at sea level.
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7-24 PERFORMANCE
As might be expected, fuel flow increases at higher gross weights. As aircraft gross weight
increases, power required increases and hence fuel flow increases. Also, the airspeed for
maximum range also increases due to the shift in the power required curve. Maximum range and
endurance airspeeds increase with increasing gross weight. This is true because increased gross
weights shift the power required curve up and to the right. This trend is universally true for
maximum endurance airspeeds, but varying shapes of the power required curve for some
helicopters make the trend of best range airspeed unpredictable. A survey of several fleet
helicopters reveals that maximum range airspeed shifts depend upon the aircraft and operating
environment.
For example, the AH-1W and MH-60S show decreased maximum range airspeed at higher gross
weights for the conditions given.
Figure 7-20 AH-1W - Max Range Airspeed vs. Gross Weight
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER SEVEN
PERFORMANCE 7-25
Figure 7-21 MH-60S – Max Range Airspeed vs. Gross Weight
Effect of rotor speed on range and endurance. In some situations, a helicopter may consume
less fuel at a rotor speed below 100%. This benefit only occurs when profile power is a major
contributor to power required, so it only applies to a certain extent. When the rotor speed gets
too slow the increase in AOA required to generate lift at a slower rotational speed generates
excessive drag forces.
In addition to possible drag increases, decreasing Nr for fuel efficiency can present other
problems. Decreased main rotor speed produces lower tail rotor speed, so loss of tail rotor
efficiency can increase power demands and, in the most extreme case, make LTA more likely.
Additionally, in the event of an engine failure, rotor RPM will decay to dangerous levels more
quickly.
Nonetheless, it is true that in some cases a decrease in Nr can yield a decreased fuel flow that will
increase range and endurance. Figure 7-22 shows that fuel flow increases below 100% Nr at
high gross weights because the rotor system is attempting to lift a heavier aircraft at slower than
optimal rotor speed. This feature is overwhelmingly obvious with the CH-53D but the trend is
the same for all aircraft.
Thus, fuel conservation benefits occur primarily at lower percentages of maximum gross weight.
Even at lower gross weights, use of this technique should be carefully considered for its
necessity, thoroughly planned, and not used routinely. One hundred percent Nr is established by
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7-26 PERFORMANCE
Figure 7-22 RPM vs. Fuel Flow
Another use for Bucket Airspeed. Several fleet helicopter mishaps involving gearbox failures
have addressed the selection of an airspeed to fly in cases of impending catastrophic component
failure while flying over water. NATOPS manuals provide some guidance in this area, and it is
no coincidence that recommended speeds are generally in the vicinity of that recommended for
maximum endurance. The best airspeed would be that which demands the lowest power
requirements, thereby imposing the smallest load on the defective transmission/gearbox
components in an attempt to delay failure. The smallest load occurs at the bucket airspeed,
which is the same as the airspeed for maximum rate of climb, airspeed for minimum rate of
descent in a power-off situation, and airspeed for maximum endurance. In at least one case
(the CH-53E), an airspeed range is recommended for main gear box oil system failure, but the
text recommends specifically that airspeed be reduced to minimum power required for flight: the
bucket.
For a given gross weight and altitude, one airspeed, the bucket, provides the performance point
which maximizes potential climb rate for achieving communication/navigation reception,
minimizes fuel flow if required to loiter until assistance arrives and/or a positive fix is obtained,
provides for a minimum rate of descent in the event of a power loss and subsequent ditching, and
minimizes the mechanical loads on the failing components to the point of possibly delaying their
demise long enough to reach terra firma or some other suitable platform.
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PERFORMANCE 7-27
The bucket is a very useful airspeed to keep in mind. Although the bucket shifts a little with
changes in gross weight (fuel burn-off) and altitude, an average speed target that works well for
the most common operating profiles is worthy of remembering. In fact, some NATOPS manuals
define a "best" airspeed that implies some average value over the normal gross weight/altitude
operating range.
Of course, nothing supersedes sound judgment and good headwork in adjusting to a particular
emergency situation. Selection of the most favorable airspeed can depend on desired closure
rates, maximum range requirements or other considerations once catastrophic failure is
imminent.
Excess Power. Power available (PA) is almost constant throughout all velocities, hence,
maximum excess power occurs at the "bucket" airspeed where power required (PR) is a
minimum. The airspeed for maximum excess power equates to airspeed for maximum rate of
climb, as previously discussed.
Figure 7-23 Excess Power
Best Angle of Climb. Excess power in a HOGE means that the best angle of climb is straight
up. If power is not sufficient for a vertical climb, then the best angle of climb occurs at an
airspeed that involves maximum vertical velocity per unit of horizontal velocity. That airspeed
is obtained by drawing a tangent line from the power available line at zero airspeed to the power
required curve. The tangent yields the best rate of climb for the least velocity or the most
vertical distance traveled for the least horizontal distance traveled, because it identifies the point
at which the most excess power occurs relative to the true airspeed. Typically, best rate of climb
is denoted by VY and best angle of climb by VX. Both are affected by altitude and gross weight
variations due to their association with the power required curve. An increase in weight shifts
the power required curve up and to the right so that the VX airspeed increases as the aircraft gets
heavier. It also happens that VX tends to be about 3/4 of VY.
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7-28 PERFORMANCE
Figure 7-24 Best Angle of Climb
Figure 7-25 Rate of Climb vs. Best Angle of Climb
FLIGHT PHENOMENA 8-1
CHAPTER EIGHT
FLIGHT PHENOMENA
800. INTRODUCTION
This lesson introduces various phenomena associated with helicopter flight.
801. LESSON TOPIC LEARNING OBJECTIVES
1. Identify airfoil design considerations
2. Identify rotor system dynamics
3. Identify rotorcraft configurations and airfoil design considerations
4. Identify the basic aerodynamic characteristics of the airframe
5. Identify factors that affect helicopter stability and control
6. Identify factors that affect helicopter power required and power available for flight
7. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
8. Explain the aerodynamics of flight
9. Identify factors that lead to undesirable helicopter phenomena
10. Identify actions that prevent undesirable helicopter phenomena
11. Explain undesirable helicopter phenomena
802. GENERAL
Maneuvering flight can place both the aircraft and the pilot under stress. Knowing the
maneuvering limitations is critical. In combat, the aircraft may be flown on the edge of the
envelope, as dictated by the mission or to save lives. In training, the student will be introduced
to the envelope gradually. Develop a comfort zone. Learning the dangers associated with flight
discussed in this chapter, as well as the methods for their avoidance/recovery, are critical to a
career in aviation.
803. FLIGHT ENVELOPE / V-N DIAGRAM
A helicopter’s design is dictated by the expected use. Performance and load bearing
requirements are set by the customer in the case of military aircraft or by the FAA and the
engineering and sales departments for civil aircraft. Anticipated strength requirements to meet
design criteria at a range of speeds are consolidated in a V-n diagram.
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8-2 FLIGHT PHENOMENA
The V-n diagram or V-G diagram is a graph that summarizes an aircraft's structural and
aerodynamic limitations at a particular weight, altitude and configuration. The horizontal axis is
indicated airspeed. The vertical axis of the graph is load factor, or G's. V-n diagrams define the
maneuvering envelope for fixed-wing aircraft and rotary-wing aircraft. Helicopter NATOPS
manuals typically do not have V-n diagrams because most helicopters do not have G-meters,
therefore pilots are unable to gauge loading. Rather, AOB limitations are developed with
consideration for associated load factors and general maneuver restrictions keep the aircraft in
the envelope.
Figure 8-1 V-n Diagram for Fixed Wing Aircraft
Several critical factors are identified on the V-n diagram. Even though NATOPS typically does
not include a V-n diagram, consideration of the following factors goes into development of those
maneuver limits and are worth knowing about before flying in critical situations:
Limit Load Factor. The top and bottom of the V-n diagram are established by the structural
limit line, or limit load factor. Limit load factor is the greatest load factor an aircraft can sustain
without any risk of permanent deformation. It is the maximum load factor anticipated in normal
daily operations. If the limit load factor is exceeded, some structural damage or permanent
deformation may occur. Aircraft will have both positive and negative limit load factors.
Overstress/Over-G is the condition of possible permanent deformation or damage that results
from exceeding the limit load factor. This type of damage will reduce the service life of the
aircraft because it weakens the aircraft's basic structure. Overstress/over-G may occur without
visibly damaging the airframe. Inside the aircraft are a variety of components, such as hydraulic
actuators and engine mounts, which are not designed to withstand the same loads that the
airframe can.
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FLIGHT PHENOMENA 8-3
Figure 8-2 AH-64 Apache V-n Diagram
Ultimate load factor. Ultimate load factor is the maximum load factor that the aircraft can
withstand without structural failure. There will be some permanent deformation at the ultimate
load factor, but no actual failure of the major load-carrying components should occur. If you
exceed the ultimate load factor, structural failure is imminent (something major on the aircraft
will break). The ultimate load factor is 150% of the limit load factor.
Increases in gross weight and altitude require increases in AOA and lifting forces so that the
G envelope is reduced due to increased structural bending and blade flapping limits.
So far, in the roughly 70 years that helicopters have been operating, no really high load-factor
maneuver has been identified as a prohibitively hard to attain design consideration. Because
rotor blades are attached to the aircraft with a hinge or a relatively soft blade root, and because
centrifugal force tends to bend the blade down, a rotor blade flaps up but doesn’t bend
significantly when developing high thrust. As a consequence, the pilot need not worry about
causing a permanent set while doing an extreme maneuver. This is not to say, however, that no
structural damage has been done. Experience shows that high load-factor maneuvers raise the
level of oscillatory loads in the blades, hub, control system, and rotor-support structure. Usually
the pilot has a sense of these loads in the level of vibration they feel. Depending on the design of
the various components, the higher-than-normal oscillatory loads may cause fatigue damage that
shortens the useful life of the part.
Lift Limit. The left-hand side of the V-n diagram is the lift limit. This is the maximum load
factor available at a given airspeed. An aerodynamic limit of rotor thrust exists at speeds less
than maneuver speed because air mass flow through the rotor is decreasing and the rotor can't
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8-4 FLIGHT PHENOMENA
generate high transient thrust levels. Attempted hard aft cyclic maneuvering at low speeds will
result in further reduced speed and "G available." Many helicopters have the capability of
generating in excess of four transient G's at high speed; it is unusual for a helicopter to be able to
sustain more than two G's.
Limit Airspeed. The vertical line on the right side is called the redline airspeed, or VNE
(Velocity never-to-exceed). Redline airspeed is the highest airspeed that an aircraft is allowed to
fly. Flight at speeds above VNE can cause structural damage. VNE is determined primarily by
excessive structural loads and power available, but may also be affected by controllability
limits, MCRIT, or airframe temperature.
Excessive structural loads may be encountered on components other than the main structural
members. Control surfaces, stabilizers, and other external components are often not able to
withstand the same forces that the wings (rotor disc) or fuselage can withstand. Maneuvering at
very high airspeeds may create sufficient forces to twist or break at their attachment point.
If an aircraft or component (advancing blade) reaches its critical Mach number (MCRIT) and is
not designed to withstand supersonic airflow, the shock waves generated may damage the
structure of the aircraft. Redline airspeed for these aircraft will be slightly below the airspeed at
which they will achieve MCRIT.
Redline airspeed may also be used to set limits on airframe temperature. As airspeed increases,
the aircraft encounters more air particles producing friction which heats up the airframe. This
heating can be extreme and hazardous at high speeds. Once the temperature becomes excessive,
the airframe may suffer creep damage.
Controllability may determine the redline airspeed on aircraft with conventional control systems.
At high airspeeds, dynamic pressure may create forces on the control surfaces which exceed the
pilot's ability to overcome. Or, due to the aeroelasticity of the control surfaces, full deflection of
the cockpit controls may cause only small deflection of the control surfaces. In either case, the
pilot will be unable to provide sufficient control input to safely maneuver the aircraft.
In fixed wing aircraft, the never exceed airspeed is established to preclude structural damage
from flutter. In a helicopter, never exceed speed is based upon power available or component
wear considerations.
VAFT. The maximum allowable rearward speed. This may be a structural limit, but
rotor/airframe configuration and rearward visibility from the cockpit are also factors, and VAFT
may be made as high as it is thought safe to test for.
Maneuvering Speed. The intersection of lift limit and structural limit lines occurs at the
maneuvering airspeed. Maneuvering airspeed (Va), also known as the corner airspeed, is the
maximum speed at which full control deflection can be abruptly applied without
overstressing the aircraft. Va varies with aircraft weight, just as the size of the maneuvering
envelope changes with weight. Above maneuver speed, the rotor can generate high aerodynamic
loads in excess of the limit load or can be pushed into retreating blade stall. Below maneuver
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER EIGHT
FLIGHT PHENOMENA 8-5
speed an aerodynamic limit of rotor thrust exists. At the maneuver speed the aircraft can achieve
limit load at a low speed, so it offers maximum turn rate and minimum turn radius.
Gust loading. Gust loading refers to the increase in the G load due to vertical wind gusts. The
load imposed by a gust is dependent upon the velocity of the gust. The higher the velocity, the
greater the increase in load. If an aircraft were generating the limit load factor during a
maximum performance turn and hit a vertical gust, the gust will instantaneously increase the
AOA of the airfoils and increase the lift on the rotor blades, enough to raise the G load above the
limit load factor. This is why "intentional flight through severe or extreme turbulence and
thunderstorms is prohibited" in many aircraft.
Vertical gusts of up to 30 feet per second may be encountered in moderate turbulence. This
could produce up to two G's of acceleration on the aircraft. Because gust loading is cumulative
with pilot-induced loading, the limit load factor due to pilot-induced loads should be reduced
to two-thirds of the normal limit load factor. For this reason, if you make the mistake of
entering a thunderstorm, consideration should be given to continuing to the other side since
maneuvering increases the pilot-induced loads.
Turbulence penetration also requires that you slow the aircraft to a speed that will reduce the
effects of stress caused by gust loading. Since a thunderstorm gives no assurance of positive G
loading, thunderstorm penetration airspeeds may reflect the intersection between the negative
load and negative lift lines.
804. VIBRATION ANALYSIS
Everything from your eyeballs to your aircraft has a natural frequency. This natural frequency is
determined by the components' mass and stiffness and is normally modeled as a spring mass
system in various modes of bending, and torsion.
Nodes are points where no motion occurs. As such, a node is a good place to suspend the rotor
system or locate crew or passenger seats for maximum comfort and minimum vibration.
The main source of vibrations for helicopters comes from the main rotor system. Vibrations
referred to as 1P, 2P, and 3P vibes are equal to the main rotor rotating frequency or multiples of
that frequency (vibrations per revolution). The frequency of the main rotor is a function of the
speed at which it rotates in revolutions per minute.
Figure 8-3, Vibration Analysis, provides a quick reference for basic analysis of vibrations
typically felt in the cockpit while flying. The number or beats of vibration related to the main
rotor blades can vary depending on the number of rotor blades installed, i.e., on an H-53E with
seven blades, several blades could be out of track rather than just one.
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8-6 FLIGHT PHENOMENA
CATEGORY INDICATIONS CAUSE
LOW FREQUENCY (most
common)
1:1 LATERAL
1:1 VERTICAL
MRB out of balance
MRB out of track
2:1 Inherent in two-bladed helicopter.
Increase indicates worn rotating
control part of rotor hub part.
MEDIUM FREQUENCY 4:1 TO 6:1 Change in A/C ability to absorb
normal vibrations. Loose
component (landing gear most
common), loose cargo etc.
HIGH FREQUENCY TOO FAST TO COUNT
BUZZ IN PEDALS
Anything that rotates or vibrates at
the speed of the tail rotor
(transmission, engine, driveshaft).
Figure 8-3 Vibration Analysis
Tail shake. A problem that is usually worse in autorotation than in other flight conditions is
“tail shake.” This has been a significant problem on the prototypes of a number of helicopter
designs during their first test flights.
It is usually traced to unsteady airflow that arises at the main-rotor pylon or at the rotor hub, and
reaches the position of the tail rotor or empennage surfaces with high turbulence. If the
frequency of the turbulence happens to match one of the empennage’s natural frequencies, the
resulting resonance causes vibrations that can be felt throughout the entire helicopter.
The usual cure for this is to install special pylon fairings that act as low aspect ratio wings.
These produce tip vortices that tend to organize the flow and lower the turbulence downstream.
The unsteady flow from the hub can be suppressed by the installation of a round cap or “beanie”
that also produces vortices. Neither of these fixes should be done unless flight test results show
that they are necessary, since both add weight and drag to the helicopter.
Sometimes even these changes are not sufficient and it is necessary to avoid resonance by adding
weights which lower the natural frequencies of the vertical or horizontal stabilizer structure, or
raise the natural frequency with structural stiffening.
Other sources of vibrations due to external loads or airflows through the rotor system can also
cause excitement of component natural frequencies. The vibration caused by an oscillating
external load has at numerous times forced aircrew to pickle the load or, in a worse case, caused
the crash of an Israeli CH-53D that killed several personnel on board.
805. GROUND VORTEX
Occasionally during a discussion of takeoff operations, pilots will hear the term “ground vortex”
mentioned. As previously discussed, in a hover the rotor downwash travels outward from the
aircraft after impacting the ground. The height of this outward traveling airflow is
approximately equal to 1/3 the rotor diameter and has a curling tendency. This is called the
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FLIGHT PHENOMENA 8-7
Ground Vortex. The speed of the vortex as it moves further from the aircraft slows due to
friction from the ground. As the helicopter moves forward, it catches up with the ground vortex,
and the rotor downwash mixes with increased relative wind to create a rotating vortex, which
eventually causes an increased downwash through the rotor system. This simulates a climbing
situation, increasing power required. Eventually this vortex is overrun at a higher speed.
Figure 8-4 Ground Vortex
806. COMPRESSIBILITY
Because the forward speed of the helicopter is added to the rotational velocity of the advancing
blade, the highest relative wind velocities occur at the tip of the advancing blade. When the
Mach number of the tip section of the advancing blade exceeds the Critical Mach number for
the rotor blade section, the results are compressibility effects. The principal effect of
compressibility is a large increase in drag and rearward shift of the airfoil aerodynamic center
(AC). Compressibility effects on the helicopter increase the power required to maintain rotor
RPM and cause rotor roughness, vibration, cyclic shake, and an undesirable structural twisting of
the rotor blade. Compressibility effects become more severe at higher lift coefficients (higher
blade angles of attack) and higher Mach numbers.
Adverse Compressibility Conditions. The following operating conditions represent the
conditions that contribute to compressibility:
1. High airspeed.
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8-8 FLIGHT PHENOMENA
2. High rotor RPM.
3. High gross weight.
4. High DA.
5. High-G maneuvers.
6. Low temperature—the speed of sound is proportional to the square root of the absolute
temperature; therefore, it decreases as temperature decreases.
7. Turbulent air—sharp gusts momentarily increase the blade AOA and thus lower the
Critical Mach number to the point where compressibility effects may be encountered on the
blade.
Corrective Actions. Corrective actions are any actions that will decrease the AOA or velocity
of the airflow. There are similarities in the critical conditions for compressibility and retreating
blade stall, with one notable exception: compressibility occurs at high rotor RPM, and retreating
blade stall occurs at low rotor RPM. With the exception of RPM control, the recovery technique
is identical for both. Such techniques include decreasing:
1. Blade pitch by lowering collective, if possible.
2. Rotor RPM.
3. Severity of maneuver.
4. Airspeed.
Critical Mach Number. Critical Mach Number is the flow speed at which the local velocity at
some point on an airfoil first reaches sonic speed. Because airfoils speed up flow on the upper
surface to generate lift, the flow over the top is faster than the free stream. When the free stream
past a section of the rotor blade is going about Mach .72, at the point of maximum velocity over
the airfoil’s surface the local speed may reach Mach 1.0, or the speed of sound (Figure 10-25).
That flow Mach number, .72, is known as the Critical Mach Number. Actual Critical Mach
Number depends upon the shape of the airfoil.
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FLIGHT PHENOMENA 8-9
Figure 8-5 Critical Mach Number
Drag Divergence Mach Number (MDD). Drag Divergence Mach is a speed that exists above
the critical Mach number but below sonic velocity. At speed above the Critical Mach Number,
air becomes more and more compressible. It begins to form a shock wave that increases drag
and disrupts flow. As the flow over the airfoil moves faster and faster, stronger shock waves
begin to form on the airfoil. The flow disruption and strong pressure disturbances greatly
increase drag and cause airflow separation. Drag due to compression starts out small at lower
speeds, but at some point before sonic velocity begins to dramatically increase. The Mach
number at which the drag dramatically increases is called Drag or Force Divergence Mach
Number.
Figure 8-6 Drag Increase with Mach Number
The highest speed encountered by the blades in forward flight occurs at a rotor blade’s tip as it
passes the 3 o’clock position. At that point the velocity equals the RPM times the blade radius,
plus the helicopter’s forward velocity. When velocity at the tip on the advancing side
approaches MDD an increase in power is required to overcome extra drag. The fact that drag
increases at one point on the rotor disk and not at others is felt as a vibration. Also, as
compressibility increases near MDD on the advancing blade, there is an increase in vibrations and
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8-10 FLIGHT PHENOMENA
structural stress as the AC of the rotor blade migrates rearward in the transonic region. An
additional undesirable effect is noise as blades repeatedly “break the sound barrier” as they go
around the disc’s advancing side.
The solutions typically used to deal with advancing blade compressibility effects are sweeping
the leading edge of the rotor blades back, varying the airfoil thickness along the span, and
varying the airfoil section along the span. Sweep reduces the velocity that the blade tip "sees"
thereby delaying drag divergence and reduces the CL max of the airfoil.
Variation of airfoil thickness and of airfoil section serve to change the properties of the airfoil.
As the rotational velocity increases out towards the end of the blade, the thickness decreases or
the overall qualities of the airfoil change to take advantage of the increase in speed.
807. RETREATING BLADE STALL (RBS)
In forward flight, the relative airflow through the main rotor disk is different on the advancing
and retreating side. The relative airflow over the advancing side is higher due to the forward
speed of the helicopter, while the relative airflow on the retreating side is lower. This
dissymmetry of lift increases as forward speed increases.
To generate the same amount of lift across the rotor disk, the advancing blade flaps up while the
retreating blade flaps down. This causes the AOA to decrease on the advancing blade, which
reduces lift, and increase on the retreating blade, which increases lift. At some point as the
forward speed increases, the low blade speed on the retreating blade, and its high AOA cause a
stall and loss of lift.
Retreating blade stall is a factor in limiting a helicopter’s never-exceed speed (VNE ) and its
development can be felt by a low frequency vibration, pitching up of the nose, and a roll in the
direction of the retreating blade. High weight, low rotor RPM, high density altitude, turbulence
and/or steep, abrupt turns are all conducive to retreating blade stall at high forward airspeeds. As
altitude is increased, higher blade angles are required to maintain lift at a given airspeed. Thus,
retreating blade stall is encountered at a lower forward airspeed at altitude. Most manufacturers
publish charts and graphs showing a VNE decrease with altitude.
When recovering from a retreating blade stall condition caused by high airspeed, moving the
cyclic aft only worsens the stall as aft cyclic produces a flare effect, thus increasing the AOA.
Pushing forward on the cyclic also deepens the stall as the AOA on the retreating blade is
increased. While the first step in a proper recovery is usually to reduce collective, RBS should
be evaluated in light of the relevant factors discussed in the previous paragraph and addressed
accordingly. For example, if a pilot at high weight and high DA is about to conduct a high
reconnaissance prior to a confined area operation where rolling into a steep turn causes onset of
RBS, the recovery is to roll out of the turn. If the cause is low rotor RPM, then increase the
RPM.
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FLIGHT PHENOMENA 8-11
808. GROUND RESONANCE
Helicopters with articulating rotors (usually designs with three or more main rotor blades) are
subject to ground resonance, a destructive vibration phenomenon that occurs at certain rotor
speeds when the helicopter is on the ground. Ground resonance is a mechanical design issue that
results from the helicopter’s airframe having a natural frequency that can be intensified by an
out-of-balance rotor. The unbalanced rotor disk vibrates at the same frequency (or multiple
thereof) of the airframe’s resonant frequency, and the harmonic oscillation increases because the
engine is adding power to the system, increasing the magnitude (amplitude) of the vibrations
until the structure or structures fail. This condition can cause a helicopter to self-destruct in a
matter of seconds.
Hard contact with the ground on one corner (and usually with wheel-type landing gear) can send
a shockwave to the main rotor head, resulting in the blades of a three-blade rotor disk moving
from their normal 120° relationship to each other. This movement occurs along the drag hinge
and could result in something like 122°, 122°, and 116° between blades. When another part of
the landing gear strikes the surface, the unbalanced condition could be further aggravated.
If the RPM is low, the only corrective action to stop ground resonance is to close the throttle
immediately and fully lower the collective to place the blades in low pitch. If the RPM is in the
normal operating range, fly the helicopter off the ground, and allow the blades to re-phase
themselves automatically. Then, make a normal touchdown. If a pilot lifts off and allows the
helicopter to firmly re-contact the surface before the blades are realigned, a second shock could
move the blades again and aggravate the already unbalanced condition. This could lead to a
violent, uncontrollable oscillation.
This situation does not occur in rigid or semi-rigid rotor disks because there is no drag hinge. In
addition, skid-type landing gear is not as prone to ground resonance as wheel-type landing gear,
since the rubber tires' resonant frequency typically can match that of the spinning rotor, unlike
the condition of a rigid landing gear.
809. DYNAMIC ROLLOVER
A helicopter is susceptible to a lateral rolling tendency, called dynamic rollover, when it is in
contact with the surface during takeoffs or landings. For dynamic rollover to occur, some factor
must first cause the helicopter to roll or pivot around a skid or landing gear wheel, until its
critical rollover angle is reached. The angle at which dynamic rollover occurs will vary based on
helicopter type. Then, beyond this point, main rotor thrust continues the roll and recovery is
impossible. After this angle is achieved, the cyclic does not have sufficient range of control to
eliminate the thrust component and convert it to lift. If the critical rollover angle is exceeded, the
helicopter rolls on its side regardless of the cyclic corrections made.
Dynamic rollover begins when the helicopter starts to pivot laterally around its skid or wheel.
For dynamic rollover to occur the following three factors must be present:
1. A rolling moment
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8-12 FLIGHT PHENOMENA
2. A pivot point other than the helicopter’s normal CG
3. Thrust greater than weight
This can occur for a variety of reasons, including the failure to remove a tie down or skid-
securing device, or if the skid or wheel contacts a fixed object while hovering sideward, or if the
gear is stuck in ice, soft asphalt, or mud. Dynamic rollover may also occur if you use an
improper landing or takeoff technique or while performing slope operations. Whatever the
cause, dynamic rollover is possible if not using the proper corrective technique.
Once started, dynamic rollover cannot be stopped by application of opposite cyclic control alone.
For example, the right skid contacts an object and becomes the pivot point while the helicopter
starts rolling to the right. Even with full left cyclic applied, the main rotor thrust vector and its
moment follows the aircraft as it continues rolling to the right. Quickly reducing collective pitch
is the most effective way to stop dynamic rollover from developing. Dynamic rollover can occur
with any type of landing gear and all types of rotor disks.
It is important to remember rotor blades have a limited range of movement. If the tilt or roll of
the helicopter exceeds that range (5–8°), the controls (cyclic) can no longer command a vertical
lift component and the thrust or lift becomes a lateral force that rolls the helicopter over. When
limited rotor blade movement is coupled with the fact that most of a helicopter’s weight is high
in the airframe, another element of risk is added to an already slightly unstable center of gravity.
Pilots must remember that in order to remove thrust, the collective must be lowered as this is the
only recovery technique available.
Critical Conditions
Certain conditions reduce the critical rollover angle, thus increasing the possibility for dynamic
rollover and reducing the chance for recovery. The rate of rolling motion is also a consideration
because, as the roll rate increases, there is a reduction of the critical rollover angle at which
recovery is still possible. Other critical conditions include operating at high gross weights with
thrust (lift) approximately equal to the weight.
1. The following conditions are most critical for helicopters with counterclockwise rotor
rotation:
2. Right side skid or landing wheel down, since translating tendency adds to the rollover
force.
3. Right lateral center of gravity (CG).
4. Crosswinds from the left.
5. Left yaw inputs.
For helicopters with clockwise rotor rotation, the opposite conditions would be true.
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FLIGHT PHENOMENA 8-13
Figure 8-7 Dynamic rollover
Cyclic Trim
When maneuvering with one skid or wheel on the ground, care must be taken to keep the
helicopter cyclic control carefully adjusted. For example, if a slow takeoff is attempted and the
cyclic is not positioned and adjusted to account for translating tendency, the critical recovery
angle may be exceeded in less than two seconds. Control can be maintained if the pilot
maintains proper cyclic position and does not allow the helicopter’s roll and pitch rates to
become too great. Fly the helicopter into the air smoothly while keeping movements of pitch,
roll, and yaw small; do not allow any abrupt cyclic pressures.
Normal Takeoffs and Landings
Dynamic rollover is possible even during normal takeoffs and landings on relatively level
ground, if one wheel or skid is on the ground and thrust (lift) is approximately equal to the
weight of the helicopter. If the takeoff or landing is not performed properly, a roll rate could
develop around the wheel or skid that is on the ground. When taking off or landing, perform the
maneuver smoothly and carefully adjust the cyclic so that no pitch or roll movement rates build
up, especially the roll rate. If the bank angle starts to increase to an angle of approximately 5–8°,
and full corrective cyclic does not reduce the angle, the collective should be reduced to diminish
the unstable rolling condition. Excessive bank angles can also be caused by landing gear caught
in a tie down strap, or a tie down strap still attached to one side of the helicopter. Lateral loading
imbalance (usually outside published limits) is another contributing factor.
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8-14 FLIGHT PHENOMENA
Slope Takeoffs and Landings
During slope operations, excessive application of cyclic control into the slope, together with
excessive collective pitch control, can result in the downslope skid or landing wheel rising
sufficiently to exceed lateral cyclic control limits, and an upslope rolling motion can occur.
When performing slope takeoff and landing maneuvers, follow the published procedures and
keep the roll rates small. Slowly raise the downslope skid or wheel to bring the helicopter level,
and then lift off. During landing, first touchdown on the upslope skid or wheel, then slowly
lower the downslope skid or wheel using combined movements of cyclic and collective. If the
helicopter rolls approximately 5–8° to the upslope side, decrease collective to correct the bank
angle and return to level attitude, then start the landing procedure again.
Figure 8-8 Slope takeoff or landing 1
Use of Collective
The collective is more effective in controlling the rolling motion than lateral cyclic, because it
reduces the main rotor thrust (lift). A smooth, moderate collective reduction, at a rate of less
than approximately full up to full down in two seconds, may be adequate to stop the rolling
motion. Take care, therefore, not to dump collective at an excessively high rate, as this may
cause a main rotor blade to strike the fuselage. Additionally, if the helicopter is on a slope and
the roll starts toward the upslope side, reducing collective too fast may create a high roll rate in
the opposite direction. When the upslope skid or wheel hits the ground, the dynamics of the
motion can cause the helicopter to bounce off the upslope skid or wheel, and the inertia can
cause the helicopter to roll about the downslope ground contact point and over on its side.
Under normal conditions on a slope, the collective should not be pulled suddenly to get airborne
because a large and abrupt rolling moment in the opposite direction could occur. Excessive
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER EIGHT
FLIGHT PHENOMENA 8-15
application of collective can result in the upslope skid or wheel rising sufficiently to exceed
lateral cyclic control limits. This movement may be uncontrollable. If the helicopter develops a
roll rate with one skid or wheel on the ground, the helicopter can roll over on its side.
Figure 8-9 Slope takeoff or landing 2
Precautions
To help avoid dynamic rollover:
1. Always practice hovering autorotations into the wind, and be wary when the wind is gusty
or greater than 10 knots.
2. Use extreme caution when hovering close to fences, sprinklers, bushes, runway/taxi lights,
tie-down cables, deck nets, or other obstacles that could catch a skid or wheel. Aircraft parked
on hot asphalt overnight might find the landing gear sunk in and stuck as the ramp cooled during
the evening.
3. Always use a two-step lift-off. Pull in just enough collective pitch control to be light on the
skids or landing wheels and feel for equilibrium, then gently lift the helicopter into the air.
4. Hover high enough to have adequate skid or landing wheel clearance from any obstacles
when practicing hovering maneuvers close to the ground, especially when practicing sideways or
rearward flight.
5. Remember that when the wind is coming from the upslope direction, less lateral cyclic
control is available.
6. Avoid tailwind conditions when conducting slope operations.
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8-16 FLIGHT PHENOMENA
7. Remember that less lateral cyclic control is available due to the translating tendency of the
tail rotor when the left skid or landing wheel is upslope. (This is true for counterclockwise rotor
disks.)
8. Keep in mind that the lateral cyclic requirement changes when passengers or cargo are
loaded or unloaded.
9. Be aware that if the helicopter utilizes interconnecting fuel lines that allow fuel to
automatically transfer from one side of the helicopter to the other, the gravitational flow of fuel
to the downslope tank could change the CG, resulting in a different amount of cyclic control
application to obtain the same lateral result.
10. Do not allow the cyclic limits to be reached. If the cyclic control limit is reached, further
lowering of the collective may cause mast bumping. If this occurs, return to a hover and select a
landing point with a lesser degree of slope.
11. During a takeoff from a slope, begin by leveling the main rotor disk with the horizon or
very slightly into the slope to ensure vertical lift and only enough lateral thrust to prevent sliding
on the slope. If the upslope skid or wheel starts to leave the ground before the downslope skid or
wheel, smoothly and gently lower the collective and check to see if the downslope skid or wheel
is caught on something. Under these conditions, vertical ascent is the only acceptable method of
lift-off.
12. Be aware that dynamic rollover can be experienced during flight operations on a floating
platform if the platform is pitching/rolling while attempting to land or takeoff. Generally, the
pilot operating on floating platforms (barges, ships, etc.) observes a cycle of seven during which
the waves increase and then decrease to a minimum. It is that time of minimum wave motion
that the pilot needs to use for the moment of landing or takeoff on floating platforms. Pilots
operating from floating platforms should also exercise great caution concerning cranes, masts,
nearby boats (tugs) and nets.
810. LOW-G CONDITIONS
“G” is an abbreviation for acceleration due to the earth’s gravity. A person standing on the
ground or sitting in an aircraft in level flight is experiencing one G. An aircraft in a tight, banked
turn with the pilot being pressed into the seat is experiencing more than one G or high-G
conditions. A person beginning a downward ride in an elevator or riding down a steep track on a
roller coaster is experiencing less than one G or low-G conditions. The best way for a pilot to
recognize low G is a weightless feeling similar to the start of a downward elevator ride.
Helicopters rely on positive G to provide much or all of their response to pilot control inputs.
The pilot uses the cyclic to tilt the rotor disk, and, at one G, the rotor is producing thrust equal to
aircraft weight. The tilting of the thrust vector provides a moment about the center of gravity to
pitch or roll the fuselage. In a low-G condition, the thrust and consequently the control authority
are greatly reduced.
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FLIGHT PHENOMENA 8-17
Although their control ability is reduced, multi-bladed (three or more blades) helicopters can
generate some moment about the fuselage independent of thrust due to the rotor hub design with
the blade attachment offset from the center of rotation. However, helicopters with two-bladed
teetering rotors rely entirely on the tilt of the thrust vector for control. Therefore, low-G
conditions can be catastrophic for two-bladed helicopters.
At lower speeds, such as initiation of a takeoff from hover or the traditional recovery from vortex
ring state, forward cyclic maneuvers do not cause low G and are safe to perform. However, an
abrupt forward cyclic input or pushover in a two-bladed helicopter can be dangerous and must be
avoided, particularly at higher speeds. During a pushover from moderate or high airspeed, as the
helicopter noses over, it enters a low-G condition. Thrust is reduced, and the pilot has lost
control of fuselage attitude but may not immediately realize it. Tail rotor thrust or other
aerodynamic factors will often induce a roll. The pilot still has control of the rotor disk, and may
instinctively try to correct the roll, but the fuselage does not respond due to the lack of thrust. If
the fuselage is rolling right, and the pilot puts in left cyclic to correct, the combination of
fuselage angle to the right and rotor disk angle to the left becomes quite large and may exceed
the clearances built into the rotor hub. This results in the hub contacting the rotor mast, which is
known as mast bumping. Low-G mast bumping has been the cause of numerous military and
civilian fatal accidents. It was initially encountered during nap-of-the-earth flying, a very low-
altitude tactical flight technique used by the military where the aircraft flies following the
contours of the geographical terrain. The accident sequence may be extremely rapid, and the
energy and inertia in the rotor system can sever the mast or allow rotor blades to strike the tail or
other portions of the helicopter.
Turbulence, especially severe downdrafts, can also cause a low-G condition and, when combined
with high airspeed, may lead to mast bumping. Typically, helicopters handle turbulence better
than a light airplane due to smaller surface area of the rotor blades. During flight in turbulence,
momentary excursions in airspeed, altitude, and attitude are to be expected. Pilots should
respond with smooth, gentle control inputs and avoid over controlling. Most importantly, pilots
should slow down, as mast bumping is less likely at lower airspeeds.
Multi-bladed rotors may experience a phenomenon similar to mast bumping known as droop
stop pounding if flapping clearances are exceeded, but because they retain some control authority
at low G, occurrences are less common than for teetering rotors.
811. LOW ROTOR RPM AND ROTOR STALL
Rotor RPM is a critically important parameter for all helicopter operations. Just as airplanes will
not fly below a certain airspeed, helicopters will not fly below a certain rotor RPM. Safe rotor
RPM ranges are marked on the helicopter’s tachometer and specified in the Rotorcraft Flight
Manual (RFM). If the pilot allows the rotor RPM to fall below the safe operating range, the
helicopter is in a low RPM situation. If the rotor RPM continues to fall, the rotor will eventually
stall.
Rotor stall should not be confused with retreating blade stall, which occurs at high forward
speeds and over a small portion of the retreating blade tip. Retreating blade stall causes vibration
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8-18 FLIGHT PHENOMENA
and control problems, but the rotor is still very capable of providing sufficient lift to support the
weight of the helicopter. Rotor stall, however, can occur at any airspeed, and the rotor quickly
stops producing enough lift to support the helicopter, causing it to lose lift and descend rapidly.
Rotor stall is very similar to the stall of an airplane wing at low airspeeds. The airplane wing
relies on airspeed to produce the required airflow over the wing, whereas the helicopter relies on
rotor RPM. As the airspeed of the airplane decreases or the speed of the helicopter rotor slows
down, the AOA of the wing/rotor blade must be increased to support the weight of the aircraft.
At a critical angle (about 15°), the airflow over the wing or the rotor blade will separate and stall,
causing a sudden loss of lift and increase in drag. An airplane pilot recovers from a stall by
lowering the nose to reduce the AOA and adding power to restore normal airflow over the wing.
However, the falling helicopter is experiencing upward airflow through the rotor disk, and the
resulting AOA is so high that even full down collective will not restore normal airflow. In the
helicopter when the rotor stalls, it does not do so symmetrically because any forward airspeed
will produce a higher airflow on the advancing side than on the retreating side. This causes the
retreating blade to stall first, and its weight makes it descend as it moves aft while the advancing
blade is climbing as it goes forward. The resulting low aft blade and high forward blade become
a rapid aft tilting of the rotor disc sometimes referred to as rotor “blow back” or “flap back.” As
the helicopter begins to descend, the upward flow of air acting on the bottom surfaces of the tail
boom and any horizontal stabilizers tend to pitch the aircraft nose down. These two effects,
combined with any aft cyclic by the pilot attempting to keep the aircraft level, allow the rotor
blades to blow back and contact the tail boom, in some cases actually severing the tail boom.
Since the tail rotor is geared to the main rotor, in many helicopters the loss of main rotor RPM
also causes a significant loss of tail rotor thrust and a corresponding loss of directional control.
Rotor stalls in helicopters are not recoverable. At low altitude, rotor stall will result in an
accident with significant damage to the helicopter, and at altitudes above approximately 50 feet
the accident will likely be fatal. Consequently, early recognition of the low rotor RPM condition
and proper recovery technique is imperative.
Low rotor RPM can occur during power-off and power-on operations. During power-off flight, a
low RPM situation can be caused by the failure to quickly lower the collective after an engine
failure or by raising the collective at too great a height above ground at the bottom of an
autorotation. However, more common are power-on rotor stall accidents. These occur when the
engine is operating normally but the pilot demands more power than is available by pulling up
too much on the collective. Known as “overpitching,” this can easily occur at higher density
altitudes where the engine is already producing its maximum horsepower and the pilot raises the
collective. The corresponding increased AOA of the blades requires more engine horsepower to
maintain the speed of the blades; however, the engine cannot produce any additional horsepower,
so the speed of the blades decreases. A similar situation can occur with a heavily loaded
helicopter taking off from a confined area. Other causes of a power-on low rotor RPM condition
include the pilot rolling the throttle the wrong way in helicopters not equipped with a governor or
a governor failure in helicopters so equipped.
As the RPM decreases, the amount of horsepower the engine can produce also decreases. Engine
horsepower is directly proportional to its RPM, so a 10 percent loss in RPM due to overpitching,
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER EIGHT
FLIGHT PHENOMENA 8-19
or one of the other scenarios above, will result in a 10 percent loss in the engine’s ability to
produce horsepower, making recovery even slower and more difficult than it would otherwise
be. With less power from the engine and less lift from the decaying rotor RPM, the helicopter
will start to settle. If the pilot raises the collective to stop the settling, the situation will feed
upon itself rapidly leading to rotor stall.
There are a number of ways the pilot can recognize the low rotor RPM situation. Visually, the
pilot can not only see the rotor RPM indicator decrease but also the change in torque will
produce a yaw; there will also be a noticeable decrease in engine noise, and at higher airspeeds
or in turns, an increase in vibration. Many helicopters have a low RPM warning system that
alerts the pilot to the low rotor RPM condition.
To recover from the low rotor RPM condition the pilot must simultaneously lower the collective,
increase throttle if available and apply aft cyclic to maintain a level attitude. At higher airspeeds,
additional aft cyclic may be used to help recover lost RPM. Recovery should be accomplished
immediately before investigating the problem and must be practiced to become a conditioned
reflex.
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8-20 FLIGHT PHENOMENA
THIS PAGE UNTENTIONALLY LEFT BLANK
TAIL ROTOR CONSIDERATIONS 9-1
CHAPTER NINE
TAIL ROTOR CONSIDERATIONS
900. INTRODUCTION
The purpose of this chapter is to aid the student in understanding tail rotor design. Tail rotor
design considerations include both performance and rotor configuration requirements.
901. LESSON TOPIC LEARNING OBJECTIVES
1. Identify airfoil design considerations
2. Identify rotorcraft configurations and airfoil design considerations
3. Identify the basic aerodynamic characteristics of the airframe
4. Identify factors that affect helicopter stability and control
5. Identify factors that affect helicopter power required and power available for flight
6. Identify aerodynamic terms, concepts, and diagrams vital to helicopter aerodynamics
7. Explain the aerodynamics of flight
8. Identify factors that lead to undesirable helicopter phenomena
9. Identify actions that prevent undesirable helicopter phenomena
10. Explain undesirable helicopter phenomena
902. TORQUE EFFECT
For purposes of uniformity, conventional main rotor direction is chosen to be counterclockwise
as viewed from above. A single main rotor imparts a moment on the fuselage which, if left
unbalanced, would cause the fuselage to rotate clockwise around the vertical axis. This moment
is compensated for by placing an anti-torque tail rotor a certain distance from the center of
gravity of the aircraft. The thrust of the anti-torque tail rotor multiplied by the distance to the
CG results in a moment in the opposite direction to that generated by the main rotor. If the
forces and moments involved are considered in combination, the moments balance, but the
forces do not. The unbalanced force of the tail rotor causes a right translating tendency that is
most noticeable in a hover and occurs to a lesser extent in forward flight. Additionally, any
change in power setting will change the torque and therefore yaw. The effects of wind on the tail
rotor’s effectiveness must also be considered if the helicopter is to be usable in a wide range of
operating conditions.
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9-2 TAIL ROTOR CONSIDERATIONS
Figure 9-1 Tail Rotor Unbalanced Force
Pilots of helicopters with a clockwise rotation (and thus a left main rotor moment) simply need to
consider the effects in the opposite direction.
Figure 6-2 below illustrates the method of torque balance and directional control for both the tail
rotor configuration and alternate methods.
Helicopter Configuration
Torque Balance Directional Control
Yaw Moment
Single MR, TR TR Thrust TR Collective
Coaxial MR diff torque MR diff collective
Tandem MR diff torque MR diff cyclic
Side-by-side MR diff torque MR diff cyclic
Figure 9-2 Yaw Control Mechanisms for Various Configurations
903. VERTICAL STABILIZER
A vertical stabilizer can help quite a bit in reducing the amount of tail rotor thrust required in
forward flight. Shaped like a wing, a vertical stabilizer provides lift (thrust) in the direction of
anti-torque. The vertical stabilizer can be either a cambered airfoil or a symmetrical airfoil
mounted on an offset angle. The higher the aircraft’s velocity, the more the vertical stabilizer
will be contributing to the anti-torque effort. At higher speeds, tail rotor power requirements are
significantly reduced, therefore more engine power is now available to drive the main rotor
system.
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TAIL ROTOR CONSIDERATIONS 9-3
Design tradeoffs have precluded the production of any military helicopters that can actually fly
in level, balanced flight with a complete tail rotor failure because of the power interactions
between the tail rotor and vertical fin. Making a large enough tail fin that could completely
compensate for a lost tail rotor would compromise sideward flight capability. The Apache and
Blackhawk, however, were designed to be able to fly straight in a controlled descent (at a
specified airspeed) without the tail rotor operating.
Figure 9-3 Vertical Stabilizer
904. TRANSLATING TENDENCY AND HOVER ATTITUDE
While the tail rotor system produces anti-torque effect, it also produces thrust in the horizontal
plane, causing the aircraft to drift right laterally in a hover, for a counterclockwise rotating,
single-rotor helicopter. The aviator must compensate for this right translating tendency of the
helicopter by tilting the main rotor disk to the left. This lateral tilt creates an equal but opposite
main rotor force to the left that compensates for the tail rotor thrust to the right. These two
horizontal forces, however, are often offset from each other vertically. The main rotor force to
the left coupled with the tail rotor force to the right commonly causes a left skid low hover
attitude during flight.
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9-4 TAIL ROTOR CONSIDERATIONS
Figure 9-4 Translating Tendency
905. WEATHER VANING
In a no-wind hover, the tail rotor provides all of the anti-torque compensation. As the aircraft
moves into forward flight, the tail rotor is assisted in this compensatory effort by the weather-
vaning effect and the vertical stabilizer. The increased parasitic drag produced on the
longitudinal surface of the aircraft as the relative wind increases causes the aircraft to "steer" into
the relative wind. This weather-vaning effect will increase proportionally with airspeed and
provide minor assistance to the anti-torque effect.
Figure 9-5 Weather Vaning
906. TAIL ROTOR FAILURES AND ISSUES
Anti-torque malfunctions may occur through a number of mechanisms: a loss of the entire
gearbox/components; a fixed pedal setting, left, right, or neutral; driveshaft failure; loss of tail
rotor authority/loss of tail rotor effectiveness (LTA/LTE). Also, even though an engine failure
removes the need for anti-torque compensation, directional control at touchdown may be limited
in a number of situations.
1. LTA and LTE
The ability of the tail rotor to provide anti-torque and yaw control can be greatly reduced by two
factors that are easily confused. LTA is related to power available to the main and tail rotor.
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TAIL ROTOR CONSIDERATIONS 9-5
LTE is related to the direction from which the wind strikes the tail rotor in a hover and tends to
be labeled as an aerodynamic phenomenon compared to LTA, which is most often described as a
mechanical phenomenon.
2. LTA
This occurs when power required for hover exceeds power available. Power supplied to the
main rotor is delivered as a torque at a certain RPM.
Power = Torque x RPM
When the engines are providing the maximum that they are capable of at 100% RPM it will
translate to a certain amount of torque. If the pilot demands more performance by continuing to
increase collective the AOA on the main rotor blades will increase. Lift will increase, but so will
drag. Because power is a constant, the main rotor response to the increased drag will be an
increase in torque and a decrease in RPM.
Tail rotor thrust required for flight is a function of main rotor torque. Tail rotor thrust available
is a function of RPM squared. When the main rotor slows down it also slows down the tail rotor,
providing less tail rotor thrust. Thus, the increased tail rotor thrust required to counteract
increasing main rotor torque with drooped turns is not available. The pilot can call for more
tail rotor thrust by increasing tail rotor torque with increased left pedal, but at some point the
ability to increase tail rotor AOA runs out. When tail rotor thrust required exceeds tail rotor
thrust available, LTA occurs and the nose of the aircraft yaws to the right.
3. LTE
Loss of tail rotor effectiveness (LTE) or an unanticipated yaw is defined as an un-commanded,
rapid yaw towards the advancing blade which does not subside of its own accord. It can result in
the loss of the aircraft if left unchecked. It is very important for pilots to understand that LTE is
caused by an aerodynamic interaction between the main rotor and tail rotor and not caused from
a mechanical failure. Some helicopter types are more likely to encounter LTE due to the normal
certification thrust produced by having a tail rotor that, although meeting certification standards,
is not always able to produce the additional thrust demanded by the pilot.
A helicopter is a collection of compromises. Compare the size of an airplane propeller to that of
a tail rotor. Then, consider the horsepower required to run the propeller. For example, a Cessna
172P is equipped with a 160-horsepower (HP) engine. A Robinson R-44 with a comparably
sized tail rotor is rated for a maximum of 245 HP. If you assume the tail rotor consumes 50 HP,
only 195 HP remains to drive the main rotor. If the pilot were to apply enough collective to
require 215 HP from the engine, and enough left pedal to require 50 HP for the tail rotor, the
resulting engine overload would lead to one of two outcomes: slow down (reduction in RPM) or
premature failure. In either outcome, anti-torque would be insufficient and total lift might be
less than needed to remain airborne.
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9-6 TAIL ROTOR CONSIDERATIONS
Every helicopter design requires some type of anti-torque system to counteract main rotor torque
and prevent spinning once the helicopter lifts off the ground. A helicopter is heavy, and the
power-plant places a high demand on fuel. Weight penalizes performance, but all helicopters
must have an anti-torque system, which adds weight. Therefore, the tail rotor is certified for
normal flight conditions. Environmental forces can overwhelm any aircraft, rendering the
inherently unstable helicopter especially vulnerable.
As with any aerodynamic condition, it is very important for pilots to not only to understand the
definition of LTE, but more importantly, how and why it happens, how to avoid it, and lastly,
how to correct it once it is encountered. We must first understand the capabilities of the aircraft
or even better what it is not capable of doing. For example, if you were flying a helicopter with a
maximum gross weight of 5,200 lb., would you knowingly try to take on fuel, baggage and
passengers causing the weight to be 5,500 lb.? A wise professional pilot should not ever exceed
the certificated maximum gross weight or performance flight weight for any aircraft. The
manuals are written for safety and reliability. The limitations and emergency procedures are
stressed because lapses in procedures or exceeding limitations can result in aircraft damage or
human fatalities. At the very least, exceeding limitations will increase the costs of maintenance
and ownership of any aircraft and especially helicopters.
Overloaded parts may fail before their designed lifetime. There are no extra parts in helicopters.
The respect and discipline pilots exercise in following flight manuals should also be applied to
understanding aerodynamic conditions. If flight envelopes are exceeded, the end results can be
catastrophic.
LTE is an aerodynamic condition and is the result of a control margin deficiency in the tail rotor.
It can affect all single-rotor helicopters that utilize a tail rotor. The design of main and tail rotor
blades and the tail boom assembly can affect the characteristics and susceptibility of LTE but
will not nullify the phenomenon entirely. Translational lift is obtained by any amount of clean
air through the main rotor disk. The same holds true for the tail rotor. As the tail rotor works in
less turbulent air, it reaches a point of translational thrust. At this point, the tail rotor becomes
aerodynamically efficient and the improved efficiency produces more anti-torque thrust. The
pilot can determine when the tail rotor has reached translational thrust. As more anti-torque
thrust is produced, the nose of the helicopter yaws to the left (opposite direction of the tail rotor
thrust), forcing the pilot to correct with right pedal application (actually decreasing the left
pedal). This, in turn, decreases the AOA in the tail rotor blades. Pilots should be aware of the
characteristics of the helicopter they fly and be particularly aware of the amount of tail rotor
pedal typically required for different flight conditions.
LTE is a condition that occurs when the flow of air through a tail rotor is altered in some way, by
altering the angle or speed at which the air passes through the rotating blades of the tail rotor
disk. As discussed in the previous paragraph, an effective tail rotor relies on a stable and
relatively undisturbed airflow in order to provide a steady and constant anti-torque reaction. The
pitch and AOA of the individual blades will determine the thrust. A change to either of these
alters the amount of thrust generated. A pilot’s yaw pedal input causes a thrust reaction from the
tail rotor. Altering the amount of thrust delivered for the same yaw input creates an imbalance.
Taking this imbalance to the extreme will result in the loss of effective control in the yawing
plane, and LTE will occur.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER NINE
TAIL ROTOR CONSIDERATIONS 9-7
This alteration of tail rotor thrust can be affected by numerous external factors. The main factors
contributing to LTE are:
a. Airflow and downdraft generated by the main rotor blades interfering with the airflow
entering the tail rotor assembly.
b. Main blade vortices developed at the main blade tips entering the tail rotor disk.
c. Turbulence and other natural phenomena affecting the airflow surrounding the tail
rotor.
d. A high-power setting, hence large main rotor pitch angle, induces considerable main
rotor blade downwash and hence more turbulence than when the helicopter is in a low
power condition.
e. A slow forward airspeed, typically at speeds where translational lift and translational
thrust are in the process of change and airflow around the tail rotor will vary in
direction and speed.
f. The airflow relative to the helicopter;
i. Worst case—relative wind within ±15° of the 10 o’clock position, generating
vortices that can blow directly into the tail rotor. This is dictated by the
characteristics of the helicopters aerodynamics of tail-boom position, tail rotor
size and position relative to the main rotor and vertical stabilizer, size and
shape.
ii. Weathercock stability—tailwinds from 120° to 240°, such as left crosswinds,
causing high pilot workload.
iii. Tail rotor vortex ring state (210° to 330°). Winds within this region will result
in the development of the vortex ring state of the tail rotor.
g. Combinations (i, ii, iii) of these factors in a particular situation can easily require
more anti-torque than the helicopter can generate and in a particular environment
LTE can be the result.
Certain flight activities lend themselves to being at higher risk of LTE than others. For example,
power line and pipeline patrol sectors, low speed aerial filming/photography as well as in the
Police and Helicopter Emergency Medical Services (EMS) environments can find themselves in
low-and-slow situations over geographical areas where the exact wind speed and direction are
hard to determine.
Unfortunately, the aerodynamic conditions that a helicopter is susceptible to are not explainable
in black and white terms. LTE is no exception. There are a number of contributing factors, but
what is more important in preventing LTE is to note them, and then to associate them with
CHAPTER NINE HELICOPTER AERODYNAMICS WORKBOOK
9-8 TAIL ROTOR CONSIDERATIONS
situations that should be avoided. Whenever possible, pilots should learn to avoid the following
combinations:
a. Low and slow flight outside of ground effect.
b. Winds from ±15º of the 10 o’clock position and probably on around to 5 o’clock
position.
c. Tailwinds that may alter the onset of translational lift and translational thrust, and
hence induce high power demands and demand more anti-torque (left pedal) than the
tail rotor can produce.
d. Low speed downwind turns.
e. Large changes of power at low airspeeds.
f. Low speed flight in the proximity of physical obstructions that may alter a smooth
airflow to both the main rotor and tail rotor.
Pilots who put themselves in situations where the combinations above occur should know that
they are likely to encounter LTE. The key is not to put the helicopter in a compromising
condition, while at the same time being educated enough to recognize the onset of LTE and
being prepared to react quickly to it before the helicopter cannot be controlled.
Early detection of LTE, followed by the immediate flight control application of corrective action,
applying forward cyclic to regain airspeed, applying right pedal not left as necessary to maintain
rotor RPM, and reducing the collective (thus reducing the high-power demand on the tail rotor),
is the key to a safe recovery. Pilots should always set themselves up when conducting any
maneuver to have enough height and space available to recover in the event they encounter an
aerodynamic situation such as LTE.
Understanding the aerodynamic phenomenon of LTE is by far the most important factor in
preventing an LTE-related accident, and maintaining the ability and option either to go around if
making an approach or pull out of a maneuver safely and re-plan, is always the safest option.
Having the ability to fly away from a situation and re-think the possible options should always be
part of a pilot's planning process in all phases of flight. Unfortunately, there have been many
pilots who have idled a good engine and fully functioning tail rotor disk and autorotated a
perfectly airworthy helicopter to the crash site because they misunderstood or misperceived both
the limitations of the helicopter and the aerodynamic situation.
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER NINE
TAIL ROTOR CONSIDERATIONS 9-9
Figure 9-6 Effects of Wind Direction on Directional Control
4. Weathercock Stability (120 - 240 degrees)
In this region, the helicopter attempts to weathervane, or weathercock, its nose into the relative
wind. Unless a resisting pedal input is made, the helicopter starts a slow, un-commanded turn
either to the right or left, depending upon the wind direction. If the pilot allows a right yaw rate
to develop and the tail of the helicopter moves into this region, the yaw rate can accelerate
rapidly. In order to avoid the onset of LTE in this downwind condition, it is imperative to
maintain positive control of the yaw rate and devote full attention to flying the helicopter.
5. Tail Rotor VRS (210 - 330 degrees)
Winds within this region cause a tail rotor vortex ring state to develop. The result is a non-
uniform, unsteady flow into the tail rotor. The vortex ring state causes tail rotor thrust variations,
which result in yaw deviations. The net effect of the unsteady flow is an oscillation of tail rotor
thrust. Rapid and continuous pedal movements are necessary to compensate for the rapid
changes in tail rotor thrust when hovering in a left crosswind. Maintaining a precise heading in
this region is difficult, but this characteristic presents no significant problem unless corrective
action is delayed. However, high pedal workload, lack of concentration, and over controlling
can lead to LTE.
When the tail rotor thrust being generated is less than the thrust required, the helicopter yaws to
the right. When hovering in left crosswinds, concentrate on smooth pedal coordination and do
not allow an un-commanded right yaw to develop. If a right yaw rate is allowed to build, the
helicopter can rotate into the wind azimuth region where weathercock stability then accelerates
the right turn rate. Pilot workload during a tail rotor vortex ring state is high. Do not allow a
right yaw rate to increase.
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9-10 TAIL ROTOR CONSIDERATIONS
6. Main Rotor Disk Vortex (285 - 315 degrees)
Winds at velocities of 10–30 knots from the left front cause the main rotor vortex to be blown
into the tail rotor by the relative wind. This main rotor disk vortex causes the tail rotor to operate
in an extremely turbulent environment. During a right turn, the tail rotor experiences a reduction
of thrust as it comes into the area of the main rotor disk vortex. The reduction in tail rotor thrust
comes from the airflow changes experienced at the tail rotor as the main rotor disk vortex moves
across the tail rotor disk.
The effect of the main rotor disk vortex initially increases the AOA of the tail rotor blades, thus
increasing tail rotor thrust. The increase in the AOA requires that right pedal pressure be added
to reduce tail rotor thrust in order to maintain the same rate of turn. As the main rotor vortex
passes the tail rotor, the tail rotor AOA is reduced. The reduction in the AOA causes a reduction
in thrust and right yaw acceleration begins. This acceleration can be surprising, since previously
adding right pedal to maintain the right turn rate. This thrust reduction occurs suddenly, and if
uncorrected, develops into an uncontrollable rapid rotation about the mast. When operating
within this region, be aware that the reduction in tail rotor thrust can happen quite suddenly, and
be prepared to react quickly to counter this reduction with additional left pedal input.
7. AOA Reduction (060 - 120 degrees)
In a right crosswind, the relative wind shifts toward a tail rotor blades’ chord line because of
effectively increased induced velocity. The shifted relative wind impacts at a lower AOA, which
develops lower lift and results in less thrust. The pilot will automatically compensate by adding
more left pedal, but in some cases can reach pedal travel limits before adequate thrust can be
generated.
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TAIL ROTOR CONSIDERATIONS 9-11
Figure 9-7 LTE in a Right Crosswind
8. Loss of Translational Lift (All Azimuths)
The loss of translational lift results in increased power demand and additional anti-torque
requirements. If the loss of translational lift occurs when the aircraft is experiencing a right turn
rate, the right turn will be accelerated as power is increased unless corrective action is taken by
the pilot.
9. Reducing the Onset of LTE
To help reduce the onset of LTE, follow these steps:
a. Maintain maximum power-on rotor RPM. If the main rotor RPM is allowed to
decrease, the anti-torque thrust available is decreased proportionally.
b. Avoid tailwinds below airspeeds of 30 knots. If loss of translational lift occurs, it
results in an increased power demand and additional anti-torque pressures.
c. Avoid OGE operations and high-power demand situations below airspeeds of
30 knots at low altitudes.
d. Be especially aware of wind direction and velocity when hovering in winds of about
8–12 knots. A loss of translational lift results in an unexpected high power demand
and an increased anti-torque requirement.
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9-12 TAIL ROTOR CONSIDERATIONS
e. Be aware that if a considerable amount of left pedal is being maintained, a sufficient
amount of left pedal may not be available to counteract an unanticipated right yaw.
f. Be alert to changing wind conditions, which may be experienced when flying along
ridge lines and around buildings.
g. Execute right turns slowly. This limits the effects of rotating inertia, and decreases
loading on the tail rotor to control yawing.
10. Recovery Technique
If a sudden unanticipated right yaw occurs, the following recovery technique should be
performed. Apply full left pedal. Simultaneously, apply forward cyclic control to increase
speed. If altitude permits, reduce power. As recovery is affected, adjust controls for normal
forward flight. A recovery path must always be planned, especially when terminating to an OGE
hover and executed immediately if an un-commanded yaw is evident.
Collective pitch reduction aids in arresting the yaw rate but may cause an excessive rate of
descent. Any large, rapid increase in collective to prevent ground or obstacle contact may
further increase the yaw rate and decrease rotor RPM. The decision to reduce collective must be
based on the pilot’s assessment of the altitude available for recovery.
If the rotation cannot be stopped and ground contact is imminent, an autorotation may be the best
course of action. Maintain full left pedal until the rotation stops, then adjust to maintain heading.
For more information on LTE, see Advisory Circular (AC) 90-95, Unanticipated Right Yaw in
Helicopters.
11. Tail Rotor Failure and Engine Failure
Loss of engine power. Should the aircraft lose power the aircraft will tend to yaw left. The yaw
inputs made prior to the engine failure compensate for a much greater torque than that which is
instantly delivered with a reduction in engine power. The tail rotor continues to provide thrust
whether it is powered by one engine in a single engine failure, or through windmilling in a
complete engine failure. Initial response to engine failures must include a right pedal input.
Tail rotor failure. Tail rotor failure, whether a control failure (stuck pedal) or a complete loss
of tail rotor thrust, can be a survivable event. With a control failure, most designs allow for the
tail rotor to operate at some intermediate setting. If the pilot chooses an appropriate speed,
balanced flight associated with that tail rotor setting can be attained.
A complete loss of tail rotor thrust requires more attention to airspeed. With increased airspeed
the main rotor operates more efficiently so it generates less torque. As velocity increases, both
the power required and anti-torque required decrease until the aircraft reaches its minimum
power required or "bucket" airspeed. After the bucket airspeed the power and anti-torque
required again increases up to VNE. The best airspeed to fly during a tail rotor failure would be
that requiring the least amount of anti-torque. An even better option is to fly in the flight regime
HELICOPTER AERODYNAMICS WORKBOOK CHAPTER NINE
TAIL ROTOR CONSIDERATIONS 9-13
in which the engines produce no torque, that is, an autorotation. However, the impact of the
vertical stabilizer (fin) must be taken into account as indicated below.
A vertical stabilizer can help quite a bit in reducing the amount of tail rotor thrust required in
forward flight. Shaped like a wing, a vertical stabilizer provides lift (thrust) in the direction of
anti-torque. The higher the aircraft's velocity the more the vertical stabilizer will be contributing
to the anti-torque effort. Making a tail fin that could completely compensate for a lost tail rotor
would compromise sideward flight capability. The Apache and Blackhawk, however, were
designed to be able to fly straight in a controlled descent (at an appropriate airspeed) without the
tail rotor operating.
Figure 9-8 Fly Home Capability After Loss Of Tail Rotor Thrust
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9-14 TAIL ROTOR CONSIDERATIONS
THIS PAGE LEFT INTENTIONALLY BLANK
GLOSSARY A-1
APPENDIX A
GLOSSARY
A100. GLOSSARY
Acceleration: The time rate of change of velocity.
Advancing blade: The rotor blade experiencing an increased relative wind because of airspeed.
Aerodynamics: 1The science that treats the motion of air and other gaseous fluids and the forces
acting on bodies when the bodies move through such fluids or when such fluids move against or
around the bodies. 2aThe actions and forces resulting from the movement or flow of gaseous
fluids against or around bodies. 2bThe properties of a body or bodies with respect to these
actions or forces. 3The application of the principles of gaseous fluid flows and their actions
against and around bodies to the design and construction of bodies intended to move through
such fluids.
Aerodynamic center (AC): Point along the chord line about which changes in AOA do not
result in a change of moment.
Aerodynamic force: The vector summation of lift and drag vectors depicted on the blade
element diagram.
Aerodynamic twist: The twist of an airfoil having different absolute angles of incidence at
different span-wise stations.
Air density/Atmospheric density: Mass of air per unit volume (D = M/V). It is the single most
important atmospheric variable with regards to aircraft performance.
Airfoil: A structure designed to produce lift as it moves through the air.
Airfoil characteristics: 1Any aerodynamic quality peculiar to a particular airfoil, especially to
an airfoil section or profile, usually a specified AOA. Airfoil characteristics are expressed
variously as the coefficients of lift or drag, the pitching moment, the zero-lift angle, the lift-drag
ratio, and so on. 2A feature of any particular airfoil or airfoil section such as the actual or
relative amount of span, taper, or thickness.
Airfoil section: 1A section of an airfoil, especially a cross section, taken at right angles to the
span axis or some other specified axis of the airfoil. 2The form or shape of an airfoil section; an
airfoil profile or the area defined by the profile.
Airspeed: The speed of an aircraft in relation to the air through which it is passing. Typically in
terms of forward airspeed but can be sideways or rearward also.
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A-2 GLOSSARY
Angle-of-Attack (AOA): The angle at which a body, such as an airfoil or fuselage, or a system
of bodies, such as a helicopter rotor, meets a flow. Usually expressed as the acute angle between
the chord line of an airfoil and the resultant relative wind.
Angle of climb: The angle between a horizontal plane and the flight path of a climbing aircraft.
Angle of incidence: Fixed airfoils (wings, horizontal and vertical fins, stabilizers): the acute
angle between the chord line of the airfoil and a selected reference plane, usually the longitudinal
axis of the aircraft. Rotating airfoils (helicopters’ main and tail rotors, propellers): the acute
angle between the chord line of the airfoil and the tip path plane. Angle of incidence is normally
called pitch angle for main rotor, tail rotor, and propeller blades.
Angular acceleration: A simultaneous change in both speed and direction of movement. An
example of this is an airplane in a spin.
Anti-autorotative force: In autorotational flight, the decelerating horizontal component of the
aerodynamic force along the driven and no-lift regions.
Anti-torque device: A method used to counteract torque reaction, for example a tail rotor,
Fenestron, or NOTAR to name a few.
Articulated rotor system: A rotor system in which the hub is mounted rigidly to the mast and
the individual blades are mounted on hinge pins, allowing them to flap up and down and move
forward and backward (lead and lag). Individual blades are allowed to feather by rotating about
the blade grip retainer bearing.
Aspect Ratio: Length of a blade divided by its width.
Attitude: The position of a body as determined by the inclination of the axes to some frame of
reference. If not otherwise specified, this frame of reference is fixed to the earth (horizon).
Autorotation: Descending flight of a helicopter without engine power where the air
approaching from below the rotor disk (upward induced flow) keeps the rotor blades turning at
an operational speed. May be divided into four distinct phases: entry, steady state descent, flare
and touchdown.
Axis: 1A line passing through a body about which the body rotates or may be assumed to rotate.
Any arbitrary line of reference such as a line about which the parts of a body or system are
symmetrically distributed. A line along which a force is directed; for example, an axis of thrust. 2Specifically, any one of a set or system of mutually perpendicular reference axes—usually
intersecting at the CG of an aircraft, rocket projectile, or the like—about which the motions,
moments, and forces of roll (longitudinal), pitch (lateral), and yaw (vertical) are measured.
Balancing tab: A moveable tab linked to the trailing edge of a control surface. When the
control surface is deflected the tab is deflected in an opposite direction, creating a force which
aids in moving the larger surface. Sometimes called a servo tab.
HELICOPTER AERODYNAMICS WORKBOOK APPENDIX A
GLOSSARY A-3
Blade element theory: Utilizes graphically depicted representation of the airflow and
aerodynamic forces applied to a selected airfoil section. Gives a more accurate representation of
rotor performance than does Momentum Theory. It also details the movement of individual
blades around the disk.
Blowback: The pitch-up tendency as the aircraft accelerates due to the flapping which
compensates for dissymmetry of lift. The separation of the virtual axis from the control axis.
Boundary-layer control: The control of the flow in the boundary layer about a body, or of the
region of flow near the surface of the body, to reduce or eliminate undesirable aerodynamic
effects and hence to improve performance.
Camber: The curvature of the surfaces of an airfoil or airfoil section from leading edge to
trailing edge.
Camber Line: Line equidistant from the upper and lower surface of the airfoil; same as chord
line for a symmetrical airfoil.
Center of gravity (CG): The balancing point for a body, generally expressed along the
longitudinal or lateral axis.
Center of pressure: Point along chord line about which all aerodynamic forces (distributed lift
along upper and lower surfaces) are acting.
Center-of-pressure travel: The movement of the center of pressure of an airfoil along the
chord with changing AOA; the amount of this movement is expressed in percentages of the
chord length from the leading edge.
Centrifugal force: The outward force created by the rotation of the main rotor and opposed by
centripetal force. The large centrifugal force is what allows the weight of the helicopter to be
distributed across otherwise flexible rotor blades. Centrifugal force is proportional to the square
of Nr and increases dynamic blade rigidity.
Centripetal force: The accelerative force acting on a body moving in a curved path. It is the
component of force that is directed toward the center of curvature or axis of rotation. Centripetal
force causes a change in the direction of the linear velocity vector of a body in motion, resulting
in an acceleration of the body. Centripetal force is the out-of-balance force that causes an
aircraft to turn. It is the horizontal component of lift that is directed toward the center of the
turn.
Chord: The distance between the leading and trailing edges of an airfoil along the chord line.
Chord line: A straight line intersecting the leading and trailing edges of an airfoil.
Coefficient of drag (CD): A dimensionless number indicating the inefficiency of an airfoil
which is determined by AOA and airfoil design. It is derived from wind tunnel testing.
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A-4 GLOSSARY
Coefficient of lift (CL): A dimensionless number indicating the efficiency of the airfoil which is
determined by AOA and airfoil design. It is derived from wind tunnel testing.
Collective feathering: The equal and simultaneous mechanical change of blade pitch (the angle
of incidence) of all rotor blades in a rotor system.
Compressibility: At high forward airspeeds, the advancing rotor blade creates large pressure
changes, which result in significant air density changes. As the blade’s velocity approaches the
speed of sound, the blade becomes less efficient because of a nose-down pitching moment and a
significant increase in drag.
Compressible flow: Flow at speeds high enough that density changes in the fluid can no longer
be neglected.
Coning: The upward displacement of the main rotor blades due to increased lift and balanced
somewhat by centrifugal force.
Coning angle: The angle between the tip path plane and the main rotor blades.
Control surface: A movable airfoil designed to be rotated or otherwise moved to change the
speed or direction of an aircraft.
Critical Mach number: The free-stream Mach number at which a local Mach number of 1.0 is
attained at any point on the body under consideration.
Cyclic feathering: The mechanical change of blade pitch (the angle of incidence), of individual
rotor blades independently of the other blades in the system.
Density altitude (DA): PA corrected for temperature and humidity; or, the altitude in the
standard atmosphere corresponding to a particular value of air density. The denser an air mass
(cold, dry air), the lower the corresponding value corrected to a standard atmosphere will be
(High density = Low DA). The opposite is also true. Additionally, DA increases as temperature
and/or relative humidity increases. Therefore DA is inversely proportional to atmospheric
density and directly proportional to temperature and relative humidity.
Disk Area: The area of the circle inscribed by the tip path plane with the rotors turning. The
coning angle of the blades changes the disk area.
Disk loading: The weight (thrust) of the helicopter divided by the rotor disk area (lb./sq.in).
Dissymmetry of lift: In forward flight the advancing blade experiences an increase in linear
flow. The increased linear flow increases the lift on the advancing blade. Likewise, the
retreating blade sees a decrease in linear flow and therefore a decrease in lift. Compensated for
primarily by flapping.
Downwash: The induced downward flow of air resulting from the passage of an airfoil
(induced flow).
HELICOPTER AERODYNAMICS WORKBOOK APPENDIX A
GLOSSARY A-5
Downwash angle: The angle, measured in a plane parallel to the plane of symmetry of an
aircraft, between the direction of downwash and the direction of the undisturbed airstream. This
angle is positive when the deflected stream is downward. (See Up-wash angle.)
Drag: The aerodynamic force in a direction opposite that of flight and caused by the resistance
to movement brought to bear on an aircraft by the atmosphere through which it passes.
Droop snoot airfoil: nonsymmetrical airfoil design used by the TH-57. The droop snoot design
incorporates a symmetrical blade design with a nonsymmetrical nose. A droop snoot design
provides good stall characteristics at high angles of attack and produces very low pitching
moments.
Dynamic pressure: The pressure of a fluid resulting from its motion; it is equal to one-half the
fluid density times the fluid velocity squared (q = 1/2V2). In incompressible flow, dynamic
pressure is the difference between total pressure and static pressure.
Dynamic rollover: The lateral rolling of the helicopter onto its side due to exceeding the critical
rollover angle for a critical roll rate, regardless of cyclic corrections. For dynamic rollover to
occur the helicopter must have a ground pivot point.
Dynamic stability: The property that causes a body, such as an aircraft or a rocket, to dampen
the oscillations set up by restoring moments and to return gradually to its original state when
disturbed from the original state of steady flight or motion.
Effective translational lift: The pronounced increased in translational lift during transition to
forward flight (approximately 13-24 knots) due to the rotor disk experiencing a significantly
decreased induced airflow.
Empennage: The assembly of stabilizing and control surfaces at the tail of an aircraft.
Endurance: The time an aircraft can continue flying under given conditions without refueling.
Equivalent airspeed: Calibrated airspeed of an aircraft corrected for adiabatic compressible
flow for the particular altitude. Equivalent airspeed is equal to calibrated airspeed in standard
atmosphere at sea level.
Feathering: A mechanical change in the angle of incidence, or pitch, of an airfoil segment.
Fin: A fixed airfoil that aids directional stability.
Flapping: Vertical blade movement, normally about a central hinge pin, which allows the rotor
disk to tilt and helps compensate for dissymmetry of lift.
Flight path: The line connecting the continuous positions occupied or to be occupied by an
aircraft as it moves with reference to the vertical or horizontal planes.
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A-6 GLOSSARY
Flow separation/boundary layer separation: The breakaway of flow from a surface; the
condition of a flow separated from the surface of a body and no longer following its contours.
Fuselage: The body to which the wings, landing gear, and tail are attached.
Geometric imbalance: Occurs when the radius of the center of mass for a single rotor blade
changes due to excessive flapping and is no longer equidistant from the center of rotation relative
to the individual centers of mass for the other rotor blade(s). This phenomenon may lead to
excessive hunting. If the center of mass for an individual rotor blade shifts towards the center of
rotation, that blade has a tendency to lead; likewise, if the center of mass shifts away from the
center of rotation, the blades will have a tendency to lag. Ground resonance may result if this
excessive flapping creates excessive hunting oscillations.
Geometric twist: An engineered design of the rotor blade span-wise, that incorporates a twist
beginning with an increased angle of incidence at the root of the rotor blade which decreases
from the root to the tip. Geometric twist helps to distribute lift more equally across the rotor
blade.
Gravity: An attraction of two objects for each other that depends on their mass and the distance
between them.
Gross weight: The total weight of an aircraft and its contents.
Ground effect: The increased efficiency (decreasing power requirement) of the rotor system of
the helicopter beginning at approximately one rotor diameter above the surface and increasing as
the helicopter approaches the ground. The aerodynamic effect can be largely attributed to the
reduction of the velocity of the induced flow because the ground interrupts the airflow beneath
the helicopter. Additionally, the ground interrupts the formation of tip vortices, reducing their
contribution to induced flow. The decrease in induced flow increases AOA, providing an
increase in lift with a reduction in blade pitch setting/power setting.
Ground resonance: Normally associated with the fully articulated rotor system and an
inoperative blade dampener, ground resonance is a destructive oscillation caused when the
helicopter is in contact with the ground and one or more rotor blades are displaced due to a gust
of wind, sudden control movement, or a hard landing. When this occurs, the CG of the rotor
system spirals violently outward. (See Geometric imbalance)
Ground vortex: During a normal transition to forward flight, the helicopter’s downwash creates
a vortex in front of the path of flight. As the helicopter accelerates, the aircraft flies through the
vortex. This serves to increase the induced flow causing an increase in the power required.
Gyroscopic precession: A phenomenon in rotating systems that results in all forces applied
perpendicular to the plane of rotation being manifested 90° later from the point of force in the
direction of rotation.
Horsepower: A unit of power equal to the power necessary to raise 550 pounds one foot in one
second. Thus a 1000-horsepower engine develops 1000 times 550 foot-pounds of work per
HELICOPTER AERODYNAMICS WORKBOOK APPENDIX A
GLOSSARY A-7
second. It is common to represent this power in terms of minutes instead of seconds. Thus,
equations routinely have conversion factors of 33,000.
Induced drag: The horizontal component of lift (parallel to the tip path plane) attributed to a
downward induced velocity.
Induced flow (V-ind): Vertical/axial component of relative wind. Generally, in powered flight
the induced velocity is downward and in non-powered flight the induced velocity is upward
through the rotor disk. Also known as induced airflow.
In-plane drag: The summation of all decelerating forces in the plane of rotation (induced drag +
horizontal component of profile drag).
Kinetic energy: The energy of a system because of motion.
Lag: In a rotating system, this is the occurrence of a momentary decrease in the rotational
velocity, normally about a vertical hinge pin in an articulated system.
Laminar flow: A smooth flow in which no cross flow of fluid particles occurs, hence a flow
conceived as made up of layers.
Laminar separation: The separation of a laminar-flow boundary layer from a body.
Lateral axis: An axis going from side to side of an aircraft, rocket, missile, and so on. It is
usually the side-to-side body axis passing through the CG. The axis about which pitching action
occurs. Sometimes called a Transverse axis.
Lateral stability: The tendency of a body, such as an aircraft, to resist rolling or, sometimes,
lateral displacement; the tendency of an aircraft to remain wings-level, either in flight or at rest.
Lead: Opposite of lag, or, a momentary increase in the rotational velocity in a rotating system.
Leading edge: The forward edge of an airfoil, blade, and the like. The edge which normally
meets the air or fluid first.
Lift: The component of the total aerodynamic force (thrust on a blade element), which is
perpendicular to the relative wind.
Lift component: A force acting on an airfoil perpendicular to the direction of its motion through
the air.
Lift-drag ratio: The ratio of lift to induced drag, obtained by dividing the lift by the induced
drag or the coefficient of lift by the coefficient of drag.
Linear flow: Horizontal/lateral component of resultant relative wind in a rotating system, the
V-rotational flow +/- the V-translational, adjusted for any existing wind condition.
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A-8 GLOSSARY
Load: 1The forces acting on a structure. These may be static (as with gravity), dynamic (as with
centrifugal force), or a combination of static and dynamic. 2Used to describe an aircraft’s cargo.
Load factor: the sum of the loads on a structure, including the static and dynamic loads;
expressed in units of G.
Longitudinal acceleration: Acceleration substantially along the longitudinal axis of an aircraft,
a rocket, or the like.
Longitudinal axis: A straight line through the CG of an aircraft fore and aft in the plane of
symmetry.
Mach number: The ratio of the velocity of a body to that of sound in the surrounding medium.
Thus a Mach number of 1.0 indicates a speed equal to the speed of sound; 0.5, a speed one-half
the speed of sound; 5.0, a speed five times the speed of sound, and so on.
Mach wave: 1A shock wave theoretically occurring along a common line of intersection of all
the pressure disturbances emanating from an infinitesimally small particle moving at a
supersonic speed through a fluid medium; such a wave is considered to exert no changes in the
condition of the fluid it is passing through. The concept of the Mach wave is used in defining
and studying the realm of certain disturbances in a supersonic field of flow. 2A very weak shock
wave appearing, for example, at the nose of a very sharp body where the fluid undergoes no
substantial change in direction.
Maneuver: Any planned motion of an aircraft in the air or on the ground.
Maneuverability: The ease with which an aircraft will move out of its equilibrium position.
Maneuverability and stability are opposites.
Maximum endurance airspeed: The lowest point on the power required curve where the ratio
of lift versus drag is maximized (also called bucket airspeed).
Maximum range airspeed: The point where a line drawn from the origin (corrected for winds)
is tangent to the power required curve.
Maximum rate of climb airspeed: The lowest point on the power required curve. Ratio of lift
versus the drag is maximized thereby allowing for the greatest power excess. (Also referred to
as best rate of climb)
Mean aerodynamic chord: The chord of an imaginary rectangular airfoil that would have
pitching moments throughout the flight range the same as those of an actual airfoil or
combination of airfoils under consideration, calculated to make equations of aerodynamic forces
applicable.
Mean camber line: A line drawn halfway between the upper and lower surfaces of an airfoil.
The curvature of the mean camber line in relation to the chord line is very important in
determining the aerodynamic characteristics of an airfoil section. The maximum camber
(displacement of the mean line from the chord) and the location of the maximum camber help to
HELICOPTER AERODYNAMICS WORKBOOK APPENDIX A
GLOSSARY A-9
define the shape of the mean camber line. These quantities are expressed as fractions or a
percent of the basic chord length. A typical low-speed airfoil may have a maximum camber of
4% located 40% aft of the leading edge. On symmetrical airfoils, the mean camber line and the
chord line are the same.
Mechanical axis: The extension of the centerline of the rotor mast (the actual axis of the rotor
head).
Momentum theory: Theory that helps explain rotary wing lift production, primarily based on
Isaac Newton’s three Laws of Motion. The action of accelerating a mass of air downward
produces a reaction that lifts the helicopter. Momentum theory is most applicable in hovering
and forward flight.
Neutral stability: The stability of a body such that after it is disturbed, it tends neither to return
to its original state nor to move further from it; that is, its motions or oscillations neither increase
nor decrease in magnitude.
Newton’s Laws of Motion:
1. Newton’s First Law (The Law of Equilibrium) “A body at rest tends to remain at rest and a
body in motion tends to remain in motion in a straight line at a constant velocity unless acted
upon by some unbalanced force.”
2. Newton’s Second Law (The Law of Acceleration) “The acceleration (a) of a body is
directly proportional to the force (F) exerted on the body, is inversely proportional to the mass
(m) of the body, and is in the same direction as the force.” "F = ma"
3. Newton’s Third Law (The Law of Interaction)” “For every action, there is an equal and
opposite reaction.”
Nonsymmetrical airfoil: An airfoil with a different shape or size above and below the chord
line.
Parasite drag: Drag incurred from components of an aircraft not contributing to lift.
Pendulum effect: Un-commanded nose-up tendency during deceleration that occurs in response
to an increase in collective pitch before mechanical and virtual axes are realigned. Compensated
for by pilot-induced feathering through forward cyclic.
Phase lag: When a rotating system in resonance receives a periodic excitation force sympathetic
with the natural frequency of the system, the response to the applied force is a maximum
displacement up to 90° after the force is applied. A phenomenon of the rotor system analogous
to gyroscopic precession which occurs as a result of a continuous excitation force.
Pitch angle: Angle between the chord line and the tip path plane. (See also Angle of incidence).
Pitching moment: A moment about a lateral axis of an aircraft, rocket, airfoil, and so on. This
moment is positive when it tends to increase the AOA or to nose the body upward.
APPENDIX A HELICOPTER AERODYNAMICS WORKBOOK
A-10 GLOSSARY
Positive G: The foot ward inertial force produced by a headward acceleration. The force occurs
in a gravitational field or during an acceleration when the human body is so positioned that the
force of inertia acts on it in a head-to-foot direction.
Positive lift: Lift acting in an upward direction.
Potential energy: The energy of a system derived from position.
Power: The rate of doing work; often expressed in units of horsepower.
Power available (PA or Pavail): The amount of power an engine is capable of producing for given
conditions. As DA increases, engine power available decreases.
Power excess/Excess power: Ratio of power available to the power required. If the ratio is less
than 1 then power required exceeds the power available.
Power required (PR or Preq): The amount of power necessary to turn the rotor system at a
constant speed. As the DA increases, the pitch angle of the rotor blades must increase to
generate the same amount of lift. This creates more drag forces on the rotor system and therefore
more power is required to maintain a constant rotor speed.
Power required exceeds power available (PR > PA): An un-commanded rate of descent and/or
loss of rotor RPM caused by the power required exceeding the power available (also called
settling with power). Conditions that contribute to higher power required are high gross weights,
high G-loading, rapid maneuvering, high-density altitudes, loss of ground effect, and loss of
translational lift. High DA also contributes to loss of engine power available.
Power Settling: A term often used interchangeably with “settling with power” by different
services and texts. See “Vortex Ring State” and “power required exceeds power available” for
preferred terminology.
Preconing: The engineered design used to reduce stress associated with flexing on the root of
the rotor blades, the yoke, and the blade grips.
Pressure altitude (PA): The altitude of a given pressure in the standard atmosphere. See
Standard atmosphere. As pressure increases, density increases and DA decreases.
Pressure gradient: A change in the pressure of a gas or fluid per unit of distance.
Pro-autorotative force: In unpowered flight, the accelerating horizontal component of the total
aerodynamic force vector in the region where it is tilted forward of vertical/axial (driving
region).
Profile drag: Result of air friction acting on the blade element (parallel to the relative wind).
NOTE:
In a hover, profile drag accounts for 15-45 percent of the total
power consumption.
HELICOPTER AERODYNAMICS WORKBOOK APPENDIX A
GLOSSARY A-11
Rate of climb: The rate at which an aircraft gains altitude; that is, the vertical component of its
airspeed in climbing.
Rate of descent: The rate at which an aircraft descends; that is, the vertical component of its
airspeed in descending; the rate at which a parachute and its burden descend.
Relative velocity: Velocity of the resultant relative wind.
Relative wind resultant: The vector resultant of the linear velocity + induced velocity as
depicted on the blade element diagram.
Retreating blade: The rotor blade experiencing a decreased relative wind because of airspeed.
Retreating blade stall: Aggravated case of dissymmetry of lift which results in the aircraft
pitching up and rolling left. As airspeed increases the retreating blade’s linear flow is reduced,
the blade flaps down, decreasing induced flow and increasing AOA. Eventually, as airspeed
increases further, the blade will exceed the critical AOA and will stall. With current blade
designs, a helicopter’s forward airspeed is primarily limited by retreating blade stall.
Reynolds number: The product of a typical length and the fluid speed divided by the kinematic
viscosity of the fluid. It expresses the ratio of the internal forces to the viscous forces.
Rigid rotor system: Sometimes referred to as “hingeless” since the rotor blades are fixed
rigidly to the hub without mechanical hinges for flapping, lead and lag (hunting), and on some
systems pitch change (feathering). Flapping and hunting occur through the flexing and bending
of the composite hub or “flextures.” Some systems also allow for pitch change through the
twisting of the materials rather than a pitch-change hub.
Roll: Movement around the longitudinal axis of an aircraft.
Rotational velocity (V-rot): The component of the relative wind produced by rotation of the
rotor blades i.e., the velocity of airflow across the airfoil due to its rotation about the mechanical
axis.
Rotor disk: Area of the circle inscribed in the tip path plane.
Rotor system: General term referring primarily to the design that holds the rotor blades to the
mast. The three general types of rotor systems are: fully-articulated, semi-rigid and rigid.
Semi-rigid rotor system: A rotor system in which the blades are connected to the mast by a
trunnion that allows blades to flap. Pitch change (feathering) is allowed at the hub about the
blade grip retainer bearing.
Separated flow: Flow over or about a body that has broken away from the surface of the body
and no longer follows its contours.
APPENDIX A HELICOPTER AERODYNAMICS WORKBOOK
A-12 GLOSSARY
Settling with power: Also known as “Power Required Exceeds Power Available,” is a
hazardous helicopter flight condition in which the power required for a given maneuver or flight
regime is greater than the power available under the current ambient conditions. The terms
“settling with power” and “power settling” are used differently by Army and Navy helicopter
pilots, therefore the term “power required exceeds power available” is preferred. This should not
be confused with “Power Settling” which is more correctly called “Vortex Ring State.”
Sideslip: A movement of an aircraft such that the relative wind has a velocity component along
the lateral axis.
Skid: Rate of turn is greater than normal for a degree of bank established.
Slip: The rate of turn is less than normal for the degree of bank established.
Span: 1aThe dimension of an airfoil from end to end, from tip to tip, or from root to tip. 1bThe
dimension of an aircraft, measured between lateral extremities. 2The dimension of an airfoil
from tip to tip, measured in a straight line. Where ailerons or elevators extend beyond the tips of
the airfoil proper, their extension is included in the span. Sweeping an airfoil or giving it
dihedral decreases the span.
Speed: The rate at which an object moves in relation to time and distance.
Speed of sound: The speed at which sound travels in a given medium under specified
conditions.
Stabilator: A horizontal surface that pivots as a whole; it is distinct from the usual combination
of fixed and movable surfaces.
Stability: The property of an aircraft to maintain its attitude or to resist displacement and, if
displaced, to develop forces and moments tending to restore the original condition.
Stabilizer: A fixed or adjustable airfoil or vane that provides stability for an aircraft; that is, a
fin or more specifically the horizontal stabilizer on an aircraft.
Stall: 1aA condition in which a wing or other dynamically lifting body flies at an AOA greater
than that for maximum lift, resulting in a loss of lift and an increase of drag. 1bA loss of lift and
an increase of drag brought on by a shock wave; that is, a shock stall. 2The flight condition or
behavior of an aircraft flying at an angle greater than the angle of maximum lift; any of various
aircraft performances involving a stall.
Stall speed: The airspeed at which, under a given set of conditions, an aircraft will stall.
Stalling AOA: 1The minimum AOA of an airfoil or airfoil section or other dynamic lifting body
at which a stall occurs; that is, a critical AOA. 2The angle of maximum lift.
Standard atmosphere: A model of atmospheric conditions that vary with altitude above sea
level, namely: pressure, temperature, and density. The model was derived from global averages
and is used in performance.
HELICOPTER AERODYNAMICS WORKBOOK APPENDIX A
GLOSSARY A-13
Standard lapse rate: In a thermodynamic system, the rate of heat loss of two degrees Celsius
per every 1000 feet due to an expansion of the atmosphere corresponding to an increase in
altitude. Also referred to as average or adiabatic lapse rate.
Static pressure: The atmospheric pressure of the air through which an aircraft is flying.
Sweepback: The backward slant from root to tip (or inboard end to outboard end) of an airfoil
or of the leading edge or other reference line of an airfoil. Sweepback usually refers to a design
in which both the leading and trailing edges of the airfoil have a backward slant.
Symmetrical airfoil: An airfoil with the same size and shape above and below the chord line.
Tab: A small auxiliary airfoil set into the trailing edge of an aircraft control surface (or
something set into or attached to another surface such as a rotor blade) and used for trim or to
move or assist in moving the larger surface.
Tail rotor: The anti-torque device of a single-rotor helicopter. Control of this rotor is through
the foot pedals.
Tandem rotor system: A main lifting rotor is used at each end of the helicopter. The rotor
systems rotate in opposite directions to counteract torque.
Taxi: 1The operation of an airplane or helicopter under its own power on the ground, except that
movement incident to actual takeoff and landing. 2The forward movement of a helicopter at a
hover is referred to as a hover taxi.
Thrust: Rotor thrust is the vector sum of forces produced in the rotor system.
Thrust axis: A line or axis through an aircraft, rocket, and so on along which the thrust acts; an
axis through the longitudinal center of a jet or rocket engine along which the thrust of the engine
acts; a center of thrust. For helicopters, the total rotor thrust acts perpendicular to the tip path
plane through the rotor head and is called virtual axis.
Tip path plane: The path inscribed by the tips of the main rotor blades as they rotate. The tip
path plane contains the rotor disk, and rotor thrust is perpendicular to the TPP.
Tip vortex: A vortex springing from the tip of a wing because of the flow of air around the tip
from the high-pressure region below the surface to the low-pressure region above it.
Torque: Mathematically, torque is a force times a distance. It causes the fuselage to react in
yaw due to the fact that the drive train turns the rotor.
Torque effect: In a counterclockwise rotating rotor system, due to the momentum of the
advancing rotor blade on the right side of the aircraft, there is an equal and opposite reaction
(torque) which causes the helicopter to rotate to the right. The tail rotor counteracts torque
effect. Remember Newton’s Third Law of Motion which states that every action has an equal
and opposite reaction.
APPENDIX A HELICOPTER AERODYNAMICS WORKBOOK
A-14 GLOSSARY
Trailing edge: The rearmost edge of an airfoil.
Trailing vortex: A vortex that is shed from a wing or other lifting body and is trailing behind it,
especially such a vortex trailing from a wingtip or from the end of a bound vortex. It is
sometimes referred to as wake turbulence.
Translating tendency: Tendency for a helicopter to translate laterally due to tail rotor thrust.
Translational flight: Any horizontal movement of a helicopter with respect to the air.
Translational lift: The increased efficiency of the rotor system in the production of lift by
increasing the horizontal mass flow of air through the rotor disk, reducing the induced flow and
vortices. (See also Effective translational lift)
Translational velocity (V-trans): Airflow through a rotor system or across a blade element due
to movement of the aircraft. Added geometrically to v-rotational on the advancing blade and
subtracted on the retreating blade.
Transverse flow effect: A non-uniform induced velocity flow pattern across the rotor disk that
produces a pronounced rolling tendency and lateral vibrations during transition through
approximately 10-20 knots.
Trim: The condition of a heavier-than-air aircraft in which it maintains a fixed attitude with
respect to the wind axes, with the moments about the aircraft axes being in equilibrium. The
word “trim” is often used with special reference to the balance of control forces.
Trim tab: A tab that is deflected to a position where it remains to keep the aircraft in the desired
trim. Adjustment of a trim tab on a rotor blade causes the blade to maintain a given track or
plane of motion.
True airspeed: Equivalent airspeed corrected for error that is due to air density (altitude and
temperature).
Turbulence: An agitated condition of the air or other fluids; a disordered, irregular, mixing
motion of a fluid or fluid flow such as that about a body in motion through the air.
Turbulent boundary layer: A boundary layer characterized by random fluctuations of a
velocity and by pronounced layer mixing of the fluid.
Turbulent flow: A flow characterized by turbulence; that is, an irregular, eddying, fluctuating
flow; a flow in which the velocity of a given point varies erratically in magnitude and direction
with time.
Underslinging: Attachment of the rotor head occurs with a pivot point above the blade grips
and centered midway between the opposing blade centers of gravity. Semi-rigid rotor head
design which compensates for geometric imbalance by keeping the individual centers of mass for
HELICOPTER AERODYNAMICS WORKBOOK APPENDIX A
GLOSSARY A-15
each rotor blade equidistant from the center of rotation. Allows for flapping, but geometric
design minimizes hunting.
Uniform flow: An idealized flow in which the streamlines are parallel and the velocity is
constant throughout.
Unsteady flow: A flow whose velocity components vary with time at any point in the fluid.
Unsteady flow is of fixed pattern if the velocity at any point changes in magnitude but not
direction and of variable pattern if the velocity at any point changes in direction.
Up-wash: A flow deflected upward by a wing, rotor, rotor blade, and so on.
Up-wash angle: A negative downwash angle; that is, the acute angle, measured in a plane
parallel to the plane of symmetry of an aircraft, between the direction of up-wash and the
direction of the undisturbed airstream.
Useful load: The difference, in pounds, between the empty weight and maximum authorized
gross weight of an aircraft.
V-rotational: See “Rotational velocity.”
V-translational: See “Translational velocity.”
Vector: A quantity having both magnitude and direction. Also a graphic illustration of such a
quantity.
Velocity: 1Speed. 2A vector quantity that includes both magnitude (speed) and direction relative
to a given frame of reference. 3Time rate of motion in a given direction.
Venturi: A converging-diverging passage for fluid that increases the fluid velocity and lowers
its static pressure; a venturi tube.
Vertical axis: An axis passing through an aircraft from top to bottom and usually passing
through the CG. The axis about which yaw occurs. Also called a Normal axis.
Vertical stabilizer: A vertical fin mounted approximately parallel to the longitudinal axis of an
aircraft to which a rudder may be attached. The vertical stabilizer aids in directional stability.
Also called a vertical fin.
Virtual axis: The axis of rotation perpendicular to the tip path plane, as opposed to the
mechanical axis. As the rotor disk tilts with control inputs, the virtual axis tilts and remains
perpendicular to the plane of rotation. Rotor thrust acts through the virtual axis.
Vortex Ring State (VRS): Settling of the helicopter into its own downwash. During VRS,
airflow is downward over the outer portion of the rotor disk and upward both in an area
expanding outward from the hub as well as the area outside the tip path plane. This rapidly
decaying phenomenon may result in zero net lift. The prescribed limits to avoid entry into VRS
APPENDIX A HELICOPTER AERODYNAMICS WORKBOOK
A-16 GLOSSARY
for the TH-57 are: avoid descent rates in excess 800 ft. /min at airspeeds less than 40 KIAS, and
avoid descent gradients greater than 45°. VRS has also been called “power settling,” a term
commonly confused with the term “settling with power.”
Wake Turbulence: (See Trailing vortex.)
Weathervane: The tendency of an aircraft on the ground to face into the wind.
Weight: A measure of the mass of an object under the acceleration of gravity.
Work: A force exerted over a given distance.
Yaw: A movement about the vertical axis.
Zero AOA: The position of an airfoil, fuselage, or other body when no AOA exists between two
specified or understood reference lines.
Zero-lift AOA: The geometric AOA at which no lift is created. Often called the angle of zero
lift or the zero-lift angle.
REFERENCES AND READING LIST B-1
APPENDIX B
REFERENCES AND READING LIST
1. Rotary Wing Aerodynamics for Naval Aviators, School of Aviation Safety, Department of
the Navy, May 2004.
2. Fundamentals of Aerodynamics (NAVAVSCOLSCOM-SG-111), Naval Aviation Schools
Command, Pensacola, FL, April 2008.
3. Fundamentals of Flight, FM 1-203, Headquarters, Department of the Army,
October 1988.
4. Rotary Wing Flight, FM 1-51, Headquarters, Department of the Army, 16 April 1979.
5. Meteorology for Army Aviators, FM 1-230, Headquarters, Department of the
Army, September 1982.
6. Anderson, John D, Fundamentals of Aerodynamics - 2nd Ed., McGraw-Hill
Inc., U.S.A. 1991, 1984.
7. Anderson, John D. Jr. A History of Aerodynamics - Cambridge University Press,
Cambridge, United Kingdom, 1999.
8. Dole, Charles E., Flight Theory and Aerodynamics - A Practical Guide for
Operational Safety, John Wiley & Sons, Inc. 1981.
9. Hurt, Hugh. Aerodynamics for Naval Aviators (NAVWEPS 00-80T-80).
Washington, D.C.: U.S. Government Printing Office, 1960.
10. Johnson, Wayne, Helicopter Theory Dover Publications, Inc., New York New York, 1980.
11. Leishman, J. Gordon, Principles of Helicopter Aerodynamics, Cambridge University
Press, Cambridge, United Kingdom, 2000.
12. Montgomery, John R, Sikorsky Helicopter Flight Theory for Pilots and
Mechanics, Sikorsky Aircraft, Division of United Aircraft Corporation, U.S.A. 1964.
13. Prouty, R.W., Helicopter Aerodynamics, PJS Publications Inc., Peoria IL, 1985.
14. Prouty, R.W., Even More Helicopter Aerodynamics, PJS Publications Inc., Peoria IL,
1985.
15. Prouty, R.W., Helicopter Performance, Stability. And Control, Krieger
Publishing Company, Inc., Malabar, FL, 1995.
16. Rolls-Royce, The Jet Engine, Rolls-Royce Limited, 1969.
APPENDIX B HELICOPTER AERODYNAMICS WORKBOOK
B-2 REFERENCES AND READING LIST
17. Saunders, George H., Dynamics of Helicopter Flight, John Wiley & Sons, lnc., 1975.
18. Seddon, J., Basic Helicopter Aerodynamics, AIAA, 1990.
19. Spence, Charles F., editor, AIM/FAR 1998, McGraw-Hill, 1998.
20. Stepniewski, W. Z., Keys, C. N., Rotary-Wing Aerodynamics, Dover
Publications, Inc., 31 East 2nd Street. Mineola, N.Y. 11501
21. Treager, Irwin E., Aircraft Gas Turbine Engine Technology, McGraw-Hill, Inc.,
1970.
22. Wagtendonk, Walter J., Principles of Helicopter Flight, Aviation Supplies &
Academics, Inc., Newcastle, Washington, 1996.
23. Helicopter Flying Handbook, U.S. Department of Transportation, Federal Aviation
Administration, Flight Standards Service, FAA-H-8083-21B, 2019.