AE 481 Aircraft Design – Fall 2006

UAVarsity (UAV Team 2) Alex Murray, Manager

Mark Rundle, Deputy Manager

Aerodynamic Analysis Kian Leong Kwek

Yeon Baik Nansi Xue

Structural Design Nathan Blinkilde Marvin Kong

Daniel Campbell Propulsion Matthew Egan

Zhiwei Song Matthew McKeown

CG and Weight Estimates Ingrid Chiles Mark Rundle

Controls Alex Murray

Shareil Elia Jacob Temme

Final Report

December 19, 2006

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Table of Contents

Table of Contents ........................................................................................................................... i Aircraft Specifications Page........................................................................................................ iv List of Symbols .............................................................................................................................. v 1. Introduction................................................................................................................................. 1 2. Mission Description and Analysis .............................................................................................. 2 3. Payload Analysis......................................................................................................................... 4

3.1 Synthetic Aperture Radar...................................................................................................... 4 3.2 Electro-Optic-Infrared Sensor .............................................................................................. 5 3.3 Data Link .............................................................................................................................. 5 3.4 Payload Package ................................................................................................................... 5

4. Current Design Summary ........................................................................................................... 5 5. Weight Estimates ........................................................................................................................ 9

5.1 Fuselage .............................................................................................................................. 10 5.2 Wing .................................................................................................................................... 10 5.3 Tail Surfaces ....................................................................................................................... 11 5.4 Landing Gear ...................................................................................................................... 11 5.5 Power Plant ........................................................................................................................ 12 5.6 Control System .................................................................................................................... 12 5.7 Fuel ..................................................................................................................................... 12 5.8 Payload ............................................................................................................................... 12

6. Center of Gravity ...................................................................................................................... 12 7. Airfoil Selection........................................................................................................................ 13

7.1 Airfoil Selection Criteria..................................................................................................... 13 7.1.1 Maximum Lift Coefficient ............................................................................................ 13 7.1.2 Aerodynamic Efficiency ............................................................................................... 14 7.1.3 Off-design Aerodynamic Characteristics..................................................................... 14

7.2 Analysis of Airfoils.............................................................................................................. 14 8. Wing Design ............................................................................................................................. 18

8.1 Wing Geometry ................................................................................................................... 18 8.2 High Lift Devices ................................................................................................................ 19

8.2.1 Trailing Edge Flaps ..................................................................................................... 19 8.2.2 Flap Type ..................................................................................................................... 19 8.2.3 Flap Location and Dimensioning ................................................................................ 20 8.2.4 Flap Performance Analysis.......................................................................................... 21

9. Aerodynamic Performance at Design Points ............................................................................ 21 9.1 Design Trade-offs................................................................................................................ 21

9.1.1 Taper Ratio .................................................................................................................. 22 9.1.2 Wing Span .................................................................................................................... 22 9.1.3 Root chord.................................................................................................................... 22 9.1.4 Current Design............................................................................................................. 23

9.2 Lift (No Flaps)..................................................................................................................... 23 9.3 Lift (Flaps Deployed) .......................................................................................................... 25 9.4 Drag .................................................................................................................................... 27

10. Power Requirement................................................................................................................. 29

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10.1 Power Requirement Calculations ..................................................................................... 29 10.2 Power Requirement at Cruise Altitude ............................................................................. 30 10.3 Power Requirement for Dash and Loiter.......................................................................... 31 10.5 Flight Envelope ................................................................................................................. 32

11. Engine Selection ..................................................................................................................... 34 12. Propeller Selection .................................................................................................................. 34 13. Fuel Requirements .................................................................................................................. 36 14. Takeoff and Landing Analysis................................................................................................ 37

14.1 Takeoff Analysis ................................................................................................................ 38 14.2 Landing Analysis............................................................................................................... 39

15. Tail Selection .......................................................................................................................... 40 15.1 Vertical Tail ...................................................................................................................... 41

15.1.1 Vertical Tail Maneuverability Requirements............................................................. 42 15.2 Horizontal Tail.................................................................................................................. 43 15.3 Neutral Point..................................................................................................................... 45

16. Landing Gear and Tire Design................................................................................................ 45 17. Air Inlet Sizing........................................................................................................................ 46 18. Trim Analysis.......................................................................................................................... 47

18.1 Required Aerodynamic Information ................................................................................. 48 18.2 Trim Curves ...................................................................................................................... 48

19. Maneuver and Gust Envelope................................................................................................. 52 19.1 Maneuver Loading ............................................................................................................ 52 19.2 Gust Loading..................................................................................................................... 53 19.3 Effect Due to Flaps ........................................................................................................... 53 19.4 V-n Diagrams.................................................................................................................... 53

20. Wing Loading ......................................................................................................................... 55 20.1 Wing Discretization .......................................................................................................... 55 20.2 Aerodynamic Loads .......................................................................................................... 55 20.3 Inertial Loads.................................................................................................................... 56

21. Wing Structure ........................................................................................................................ 60 21.1 Wing Cross Section ........................................................................................................... 60 21.2 Loads................................................................................................................................. 61 21.3 Wing Bending.................................................................................................................... 61

20.3.1 Effective Skin Width ................................................................................................... 61 21.3.2 Allowables.................................................................................................................. 62 21.3.3 Margin of Safety......................................................................................................... 64

21.4 Wing Torsion..................................................................................................................... 65 21.4.1 Shear Flow ................................................................................................................. 65 21.4.2 Shear Stresses ............................................................................................................ 66

21.5 Tresca Yield Criterion....................................................................................................... 66 21.5.1 Principle Stresses....................................................................................................... 66 21.5.2 Tresca Stresses and Margin of Safety ........................................................................ 67

Appendix A: Aircraft Design Comparisons................................................................................ A-1 Appendix B: Aircraft Configuration History.............................................................................. B-1 Appendix C: MATLAB Codes Used in Calculations................................................................. C-1 Appendix D: Aerodynamic Performance Calculations............................................................... D-1

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Appendix E: Takeoff and Landing Calculations .........................................................................E-1 Appendix F: Tail Sizing Calculations and History ......................................................................F-1 Appendix G: Structures Calculations.......................................................................................... G-1 Appendix H: Detailed Fuel Requirement Calculations ............................................................. H-1 Appendix I: V-n Diagram Calculations ........................................................................................I-1 Appendix J: References ............................................................................................................... J-1

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Aircraft Specifications Page

Basic Specifications Maximum gross takeoff weight at end of iteration WTO = 644.8 lbs. Wing Area SW = 74.25 ft2 Horizontal Tail Area SHT = 7.28 ft2 Vertical Tail Area SVT = 7.0 ft2 Frontal Area AF = 27.4 ft2 Wetted Area AW = 183.6 ft2 Wingspan b = 27.0 ft Aircraft Length lAC = 16.1 ft Maximum Wing Lift Coefficient (With Flaps) CLmaxW = 2.25 Maximum Payload Weight WPL = 150 lbs. Powerplant UAV Engines AR801-Carb. Maximum Power 51 hp (@8000 rpm) Weight (with oil, coolant, and propeller) 64.7 lbs.

Performance Specifications Maximum Speed 142.8 kts (140 kts required) Cruise Speed 80 kts (80 kts required) Stall Speed (sea level) 35 kts (35 kts required) Maximum Rate of Climb 31.5 ft/s (16.67 ft/s required) Endurance 21 hr. (with 10 VTI maneuvers) Maximum Range 2080 mi. (with 10 VTI maneuvers) Flight Ceiling 40,100 ft (27,000 ft. required)

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List of Symbols Symbol Definition A Fuselage Cross Sectional Area AF Frontal Area AW Wetted Area AR Aspect Ratio AoA Angle of Attack α Angle of Attack b Wingspan C Wing Chord CD Drag Coefficient CD0 Parasitic Drag coefficient CDi Induced Drag Coefficient CDL&P Air Leakage and Protuberance Drag CDmis Drag from Components with Large Form Drag CDtrim Trim Drag Coefficient Cfc Friction Coefficient CL Lift Coefficient CLac Aircraft Lift Coefficient CLmax Maximum Lift Coefficient CLt Lift Coefficient of the Tail Cl Sectional Lift Coefficient CMacflaps Flaps Pitching Moment CMacw Wing Pitching Moment CMfus Fuselage Pitching Moment Cmac-t Aircraft Pitching Moment without Tail CG Center of Gravity c Airfoil Chord Length cm Lift Curve Slope D Drag e Oswald Efficiency Factor FF Form Factor γ Flight Path Angle K Induced Drag Constant Kf Empirical Pitching Moment Factor Λm Sweep Angle L Lift L/D Lift to Drag Ratio L/Dmax Maximum Lift to Drag Ratio μ Coefficient of Viscosity ηi Engine Efficiency η Viscous Correction Factor θ Upsweep Angle Prequired Required Power Qc Interference Factor

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q Dynamic Pressure ρ Air Density ρsl Air Density at Sea Level S Wing Planform Area SB Braking Distance SC Climb Distance SF Flare Distance SFR Free Roll Distance SG Ground Roll Distance SHT Horizontal Tail Area SR Rotation Distance STR Transition to Climb Distance SVT Vertical Tail Area Sa Approach Distance Swetc Wetted Area t Maximum Airfoil Thickness τ Flap Effectiveness UAV Unmanned Aerial Vehicle V Airspeed Vclimbmax Maximum Climb Velocity Vstall Stall Velocity VTI Visual Target Identification WTO Gross Takeoff Weight

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1. Introduction On August 3rd, 2006, President G.W. Bush introduced the launch of “Operation Jump Start: Acting Now to Secure the Border,” which includes a series of immigration reforms and the tightening of security along the US-Mexico border. As part of the next phase of Operation Jump Start, our team has been awarded a contract from the Department of Homeland Security to design a high-endurance aerial surveillance vehicle to provide real-time border reconnaissance as well as search-and-rescue information in the case of national emergencies. The designation and name for the design is The Big Brother XL4000 (BBXL). Furthermore, the design, as specified by the contract, must meet the following criteria: Mission Capabilities Patrol Area: 2500 sq. mi Patrol Duration: 12 hours of loiter plus 10 visual target identification maneuvers Payload Capability: 1x Synthetic Aperture Radar (SAR), 1x Electro-Optical-Infrared

(EO/I) Sensor, 1x Line-of-Sight Data Link Weight Class: 500 – 1000 lbs Launch Type: Conventional Runway (maximum 3000 ft.) Performance Capabilities Operational Ceiling: 27,000 ft Cruise Speed: 80 kts Top Speed: 140 kts Stall Speed: 35 kts Max Payload Weight: 150 lbs Rate of Climb: 1000 ft/min The primary factors that will be emphasized throughout the design of The Big Brother XL4000 are its effectiveness (ability to satisfy mission requirements), minimization of gross takeoff weight, and its acquisition cost when compared to existing systems. A preliminary design was completed in September 2006, based on comparisons to existing UAV designs, which are available in Appendix A. In the second iteration, the aerodynamic design of Big Brother XL4000 (BBXL) was done in more detail. The airfoil and wing planform geometry were chosen, as well as a preliminary design of flaps. The aerodynamic design of the BBXL was conducted using a MATLAB code to consider many different configurations. The third iteration finalized these aerodynamic parameters and used them to begin aircraft performance estimates. The required power was calculated, and an engine and propeller were chosen. Also, takeoff and landing distances were computed. A summary of the aircraft specifications through each of these iterations is shown in Appendix B. The fourth iteration calculated the trim stability of the aircraft and produced a V-n diagram that determines the range of loads that the aircraft will experience in all flight conditions. The fifth iteration determined the aerodynamic and inertial loads acting on the wing and the resulting wing structure needed to carry these loads.

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This document represents the final iteration of the design of the Big Brother XL4000. All of the calculations have been completed, and a final configuration has been chosen. The purpose of this document is to present an overview of the design of the Big Brother XL4000.

2. Mission Description and Analysis To properly design the Big Brother XL4000 for its mission, analysis must be conducted to gain insight on the flight maneuvers required for the UAV. This section will outline a mission and calculate the duration, flight speed, and distance covered over the various maneuvers. The flight can be broken up into four separate maneuvers:

1. Takeoff, dash to surveillance area, climb to cruise altitude 2. Loiter for a total time of 12 hours 3. Perform a Visual Target Identification (VTI) maneuver when a target is acquired (up

to 10 VTI maneuvers total) 4. Cruise back to base, descend, and land

The UAV will initially take off and then dash at a speed of 140 knots to the center of its 50- by 50-mile surveillance area. A diagram of the mission space is shown in Figure 2.1. When the UAV has reached the loiter area, it will begin to use its synthetic aperture radar to scan the surveillance area while climbing to its cruising altitude of 20,000 ft. at climb rate of 18.3 ft/s.

Surveillance Area

50 m

iles

50 miles

Loiter Pattern

Airbase

27 miles

6 miles

Surveillance Area

50 m

iles

50 miles

Loiter Pattern

Airbase

27 miles

6 miles

Figure 2.1: Outline of mission space.

Once in the surveillance area, the UAV will follow the pattern outlined in Figure 2.1. The UAV will fly in a 6 mile diameter circle and alternate between the two elliptical flight patterns. This loiter pattern will enable the UAV to observe the entire area, while remaining close to the center

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of the surveillance area. The smallest radius of the loiter pattern is 3 miles, which translates into a 2 degree bank angle. At such small bank angles, negligible additional power is required for maneuvering. The UAV is essentially flying a pattern with alternates between a 6 mile diameter circle and a 27 mile diameter circle. Since the range of the synthetic aperture radar is over 21 miles, a target can be found anywhere within the surveillance area. If a target is found, the UAV will perform a VTI maneuver. A VTI maneuver consists of flying at top speed towards the target, which can be anywhere within the 50- by 50-mile area. If the target is on the edge of the surveillance area, it would be at best 25 miles from the UAV and at worst 35 miles from the UAV. Taking the average of each case, we assumed that for each VTI maneuver, the target is 30 miles from the UAV. Once the UAV has dashed towards the target and descended to 500 ft. altitude, it will loiter in that area for 20 minutes. While loitering, the UAV will collect and transmit optical and infrared imagery using the onboard video cameras. After the UAV has collected sufficient information, it will dash back to the center of the surveillance area, climb to 20,000 ft., and resume loitering. Figure 2.2 describes a VTI maneuver.

Figure 2.2: Description of a VTI maneuver.

For one mission, the UAV will loiter for a total time of 12 hours and will be able to perform 10 VTI maneuvers. After the mission is completed, the UAV will cruise back to the base while descending. For this analysis, it is assumed that the base is within 35 miles of the center of the surveillance area. After calculating each component of the mission, we estimate that a total mission will take approximately 21 hours and will cover a ground track of 2080 miles. These values were used to calculate the amount of fuel needed to complete a mission. The total distance covered and duration of a mission were calculated by breaking up each part of the mission and calculating the speed, duration, and distance covered. Table 2.1 summarizes the total mission and Table 2.2 summarizes the VTI maneuver.

500 ft. 3. Loiter on target 20,000 ft.

1. Loiter at center of surveillance

area 4. Return to center of

surveillance area

2. Descend to target

VTI Maneuver

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Altitude Speed Duration Ground Distance

Event Ft. M Knots m/s Minutes Miles Km Takeoff 0 0 42 21.6 <1 0.5 0.9

Dash to Surveillance Area-While Climbing

20,000 6096 140 72.0 18* 35 56.6

Loiter (total time) 20,000 6096 80 41.2 720 1,104.7 1,777.8 VTI Maneuver (one) varies varies 140-80 72-41.2 49 90.2 145.2 VTI Maneuver (ten) varies varies 140-80 72-41.2 490 902 1452

Cruise Home, Descend and Land

varies varies 80 41.2 25 38 61.15

TOTAL varies varies varies varies 1254 (20.9 hrs.)

2080.4 3397.95

Table 2.1: Description of typical surveillance mission. *Assumes average climb rate of 18.3 ft./s

Altitude Speed Duration Ground Distance Event Ft. M Knots m/s Minutes Miles Km

Dash to Target / Descend to 500 ft.

20,000 6096 140 72.0 11 30 48.3

Loiter 500 152.4 80 41.2 20* 30 48.3 Climb and Dash Back to Surveillance Area

20,000 6096 140 72.0 18 30 48.3

Total varies varies varies varies 49 90 145.2 Table 2.2: Detailed description of a Visual Target Identification (VTI) Maneuver.

*Assumes an average climb rate of 18.3 ft./s

3. Payload Analysis The requirements state that Big Brother XL 4000 must be able to carry 150 pounds of payload, which will consist of a synthetic aperture radar, an electro optic infrared sensor and a line of sight data link. To evaluate these three pieces of equipment, weight and range were the primary criteria. The ideal payload would be lightweight and yet possess a long range. 3.1 Synthetic Aperture Radar The synthetic aperture radar is used for our long range target identification; therefore, a range of at least 21.5 miles is required to survey a 50 mile by 50 mile area with our loiter pattern. We chose the Sandia National labs MiniSAR synthetic Aperture Radar because it is a quarter the weight of other synthetic aperture radars (the MiniSAR weighs 30 pounds) and has a range of 35km (21.75 miles). Other synthetic Aperture Radars were considered, such as the Lynx and TESAR. These were eliminated because of weight concerns; each weighs over 120 pounds [1].

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3.2 Electro-Optic-Infrared Sensor The electro-optic-infrared (EOI) sensor is used for close range target identification; therefore, a range of only 2 miles is required when loitering at 500 ft. A modest range is desired because the UAV may want to observe the targets while not being noticed. The EOI package also must be able to collect imagery in day and night, so a camera and an inferred sensor is required. We chose the Advanced EO/IR sensor from APM UAV Payloads, based in New Jersey. The advanced EO/IR sensor has a 4km range (about 2.5 miles) and has both electro-optical and infrared capabilities [2]. The EO/IR sensor weighs only 50 pounds, so it also meets our weight requirement. 3.3 Data Link A line of sight data link is required to transmit the data collected by the EOI sensor and synthetic aperture radar. The data link is also needed for communicating with the UAV to update any new mission objectives. The data link chosen for our UAV is the UAV Data Link by L-3. This data link is ideal because it has been used previously on other UAVs, has line of sight capabilities and weighs only 0.5 pounds [3]. 3.4 Payload Package The sensor suite of the synthetic aperture radar, the EOI sensor, and line of sight data link can meet all of the mission requirements. These three pieces of equipment in total weigh 80.5 pounds. This leaves 69.5 pounds for auxiliary batteries. The engine chosen comes with an integrated 2kw generator, which will be the primary power supply for the electronics [4]. In event of engine failure, the auxiliary batteries will be able to sustain the UAV until it can reach the base.

4. Current Design Summary This section summarizes the operating parameters of our current UAV design. The following performance parameters are evaluated against mission requirements:

• Flight envelope • Maximum rate of climb • Maximum speed • Maximum range • Maximum endurance • Minimum stall speed • Ceiling • Take off and Landing performance • Payload performance

By comparing these calculated parameters to the specified requirements, we can show that our design is able to meet or exceed all requirements. Range and endurance calculated for average

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case. See section 2 for more information. Table 4.1 compares the performance parameters of Big Brother XL4000 to the design requirements.

Performance Characteristic

As Specified in Requirements

Actual UAV Performance

Meets Requirements?

Max Flight Speed (@ 500 ft.)

≥ 140 Knots 142.8 Knots YES

Max Rate of Climb ≥ 16.67 ft/s 31.5 ft/s YES Max Operating

Altitude (ceiling) ≥ 27,000 ft. 40,100 ft YES

Airstrip Distance to Land

≤ 3,000 ft 847 ft YES

Airstrip Distance to Takeoff

≤ 1,500 ft 605 ft YES

Maximum Payload Weight

150 lbs. 150 lbs. YES

Stall speed (@ Sea level)

≤ 35 Knots 35 Knots YES

Max Endurance Able to loiter for 12 hrs. and 10 VTI’s

2080 miles ( for an average mission)

YES, for most mission applications*

Max Range Able to loiter for 12 hrs. and 10 VTI’s

21 hours (for an average mission)

YES, for most mission applications*

*Range and endurance calculated for average case. See section 2 for more information.

Table 4.1: Analysis of the UAV in meeting mission requirements. The main features of our aircraft were designed to meet the above requirements. In the section below, these features are listed, followed by a description of the key constraints that dictated their size. Feature Description and Constraints Wing Area: 74.25 ft.2; Minimum wing area for sufficient lift at cruise. The minimum

wing area will produce the minimum amount of drag. Tail Area: 7.28 ft.2 (horizontal); 7.0 ft.2 (vertical); Minimum tail area for trimmed

flight at cruise. The minimum tail area will produce the minimum amount of drag.

Flap Area: 8.92 ft.2 (both flaps); Minimum flap area to meet 35 knots stall speed. Flap Deflection: 20 degrees; Minimum flap deflection to meet 35 knots stall speed. Prop Diameter: 60 in; Maximum propeller diameter to maximize propeller efficiency. Engine Power: 51 horsepower (sea level); 50 sea level horsepower required

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Drawings of our current design as of December 19th, 2006, are shown below in Figure 4.1 through Figure 4.6. Dimensions of importance are:

• Total length of aircraft = 16.1 ft • Wingspan = 27.0 ft • Total height of aircraft = 5.8 ft • Fuselage length = 10.0 ft • Distance from nose to center of gravity (full fuel) = 6.24 ft • Distance from nose to center of gravity (no fuel) = 6.21 ft • Propeller Diameter = 5.0 ft • Maximum pitch angle on takeoff: 25°

Figure 4.1: Big Brother XL4000 with landing gear deployed.

Figure 4.2: Big Brother XL4000 with landing gear retracted.

1:64 Scale

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Figure 4.3: Front view of Big Brother XL4000.

Figure 4.4: Left-side view of Big Brother XL4000.

6.0’

2.5’

7.5’ 2.8’

27.0’

5.0’ 5.8’

8.2’

6.24’

25°

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Figure 4.5: Top view of Big Brother XL4000.

Figure 4.6: Internal component layout of Big Brother XL4000.

5. Weight Estimates The weight estimates were calculated based on a gross takeoff weight of 657.1 lbs. at the beginning of the iteration. At the end of the iteration, the new gross takeoff weight is

10.0’

16.1’

x z

Fuel: 183.4 lb. Wing: 65.6 lb.

Tail: 15.0 lb.

Power Plant: 57.7 lb.

Front Gear: 17.3 lb.

Rear Gear: 34.6 lb.

Additional Payload: 69.5 lb.

Control System: 40.0 lb.

1.1 2.38

6.24 6.3

8.3

14.0

EO/I: 50.0 lb

Propeller: 7.0 lb.

SAR: 30.0 lb. Data

Link: 0.5 lb.

10.0 8.0

4.2

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approximately 644.8 lbs. The weight estimates were based on the Cessna aircraft weight estimate procedure and the scaled weights of the Predator. The majority of the weight comes from the wing and fuel, which comprise approximately half of the gross takeoff weight. Table 5.1 shows the weight estimates using both of these methods as well as our initial weight estimates.

Weight (lbs.) Component Cessna Method Predator Scaling Method Our Estimate

Fuselage 77.0 75 75.0 Wing 65.6 66.7 65.6 Tail 15.0 13.3 14.2 Landing Gear 52.0 50 52.0 Power Plant 60.0 90 64.7 Control System 40.0 - 40.0 Fuel 135.1 305 183.4 Payload 150.0 150 150 Total 594.7 750 644.8

Table 5.1: The two methods of weight estimates.

5.1 Fuselage We chose a weight of 75 lbs. based on the Predator scaling method. The Cessna method states that the mass of the fuselage is typically 11% of the gross takeoff weight. This may be a conservative estimate considering the current design for our fuselage is much smaller than a typical Cessna fuselage. Furthermore, the Cessna method is for manned aircraft as opposed to the unmanned aircraft used in our design. 5.2 Wing Our estimate of the weight of the wing was 68.8 lbs. based on the Cessna method. The parameters that go into the Cessna weight estimate of the wing are the design gross takeoff weight, the design load factor, the wing area, the aspect ratio, and the percent thickness of the wing at the chord center-line. The values of these parameters are shown in Table 5.2.

Parameter Value Design GTOW (lb) 700 Design Load Factor 3.5 Wing Area (ft2) 74.25 Aspect Ratio 9.82 Thickness of root chord (%) 17.0

Table 5.2: Parameters for wing weight estimates.

The values of the parameters were picked so that the aircraft could have a reasonable CLmax at stall. The minimum value of CLmax at the stall speed of 35 kts was calculated to be 1.75 from Equation 5.1 and will be attainable based on our MATLAB code analysis.

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max

212TO sea L StallW L SC vρ= = (Eqn. 5.1)

Given the sea-level density of 1.225 kg/m3, the wing area (S) and stall speed, we calculated the minimum CLmax needed to generate sufficient lift at the stall speed that is equivalent to the WTO. Our calculations indicate that we can achieve a CLmax greater than 1.75, which is sufficient for the stall requirement. 5.3 Tail Surfaces The Cessna method predicts our tail weight to be 15.0 lbs. This estimate is a function only of the horizontal and vertical tail areas, which are 7.28 ft2 and 7.0 ft2, respectively. The Predator method determined a smaller tail weight of 13.3 lbs. Since our aircraft does not carry passengers, the design requirements for the tail do not have to meet as strict requirements as needed for transport aircraft. Thus, we chose to use the average of the two estimates for our tail weight. The resulting tail weight is 14.2 lbs. 5.4 Landing Gear The landing gear weight estimate was based on a modified Cessna method. The Cessna landing gear estimate is a function of only the gross takeoff weight. The landing gear used for the estimate is a retractable tri-gear configuration. The Cessna landing gear estimate is based on the Equation 5.2. TOGear Weight = 0.019 W + 38⋅ (Eqn. 5.2) The constant term in the equation seemed too big for our aircraft since the Cessna model is for aircraft up to 5000 lbs. We scaled the constant by multiplying it by the ratio of the UAV WTO /5000 lbs. Thus the modified equation is show below. TOGear Weight = 0.019 W + 5.7⋅ (Eqn. 5.3) Using this formula, we were able to get more reasonable numbers, which were closer to the estimate using the Predator scaling method. We chose a retractable landing gear configuration because we concluded that it is more efficient than a static landing gear. Similar UAVs, such as the General Atomics Predator and GNAT-750, use a retractable landing gear. The weight estimate of 52.0 lbs. for the landing gear is very similar to a scaled-down weight estimate of the Predator with retractable landing gear. Also, using analytical calculations we determined that the weight penalty is not as large as the drag penalty. The increase in weight for retractable landing gear compared to a fixed landing gear is about 34 lbs. However, the increase in the parasitic drag coefficient for fixed landing gear is approximately 20%. This requires approximately a 20% increase in power for cruise which results in a significant weight penalty in extra fuel burned.

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5.5 Power Plant We chose a weight estimate for a power plant that is less than the calculations by both the Cessna and Predator methods. We made this decision based on information for brand new, ultra high efficiency engines that are currently available on the market. The model that we are implementing is the AR801, manufactured by UAV Engines Ltd. in Lichfield, U.K. This engine produces a maximum power of 51 hp at 8000 RPM, which is sufficient for all required flight conditions. The estimated weight of 64.7 lbs. includes a dry weight of 43 lbs. plus an additional 14.7 lbs. for oil, coolant, and installation hardware [5]. Also, propeller weight of 7.0 lbs. was included in the weight estimate. 5.6 Control System The control system consists of flight and engine controls. According to Cessna weight estimates, 40 lbs. is used for light single fixed propeller engine aircraft. Since our UAV has a single pushback propeller as the initial design, 40 lbs. seems reasonable. No information was available on the weight of the control system on the Predator. 5.7 Fuel The fuel weight was calculated to be 183.4 lbs. based on our mission requirements. These requirements include takeoff, cruise for 12 hours, 10 VTI maneuvers, cruise back to the landing strip, and landing. The detailed fuel calculations are carried out in Section 13. 5.8 Payload The maximum payload of the UAV is set at 150 lbs. This value includes the three payload components: a Synthetic Aperture Radar sensor, an Electro-Optic-Infrared sensor, and a line of sight data link. It also includes the mounting hardware, batteries, and other electrical equipment necessary to integrate these components into the UAV. A payload weight of 150 lbs. must be accounted for, even if lighter payload components can be found.

6. Center of Gravity Using the mass calculations from the previous section and layouts, we determined the location of the center of gravity of the UAV to be 6.24 ft behind the nose of the aircraft when the fuel tanks are full. The CG moves forward to 6.21 ft behind the nose when the fuel tanks are empty. The center of gravity is slightly forward of the aerodynamic center of the wing (located at 6.3 ft.) to ensure aircraft stability. The center of gravity of the aircraft was determined based on the spreadsheet shown in Table 6.1.

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Components Weight Distance from Nose Moment Wing 65.6 6.30 413.1 Tail 14.2 14.00 198.3 Propeller 7.0 10.00 70.0 Powerplant 57.7 8.30 478.9 Front Gear 17.3 2.38 41.2 Rear Gear 34.6 10.00 346.4 SAR 30.0 1.80 54.0 EO/I 50.0 1.10 55.0 Data Link 0.5 2.50 1.3 Additional Payload 69.5 8.00 556.0 Fuel 183.4 6.30 1155.4 Fuselage 53.6 5.00 267.9 Twin Boom 21.4 10.15 217.5 Control System 40.0 4.20 168.0 GTOW 644.8 4023.0 Dry Weight 461.4

CG (Full Fuel) 6.24 CG (Empty Fuel) 6.21

Table 6.1: Spreadsheet created for CG calculations.

The CG calculations assume that the components have point mass at their respective locations. In addition, it assumes that fuel is concentrated at the wing aerodynamic center.

7. Airfoil Selection The selected airfoil must be able to meet all the aerodynamics requirements as given on the aircraft specification sheet. Furthermore, we would like to select an airfoil with excellent aerodynamic performance throughout its mission. To this end, we have developed three criteria with which we would able to judge each airfoil. 7.1 Airfoil Selection Criteria The three criteria used for selecting an airfoil are maximum lift coefficient, aerodynamic efficiency, and off-design aerodynamic performance. The next three sections outline the importance of each of these criteria. 7.1.1 Maximum Lift Coefficient One of the most desirable characteristics of our airfoil is its lift coefficient. The lift coefficient dictates how well the aircraft will generate lift during lift-intensive maneuvers, such as takeoff and landing. The aircraft must have a design sea-level stall speed of 35 knots. The minimum lift coefficient required to maintain the flight condition at stall speed is given by:

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212TO sea L StallW L SC vρ= = (Eqn. 7.1)

Given that the airfoil generally has a lift coefficient higher than that of the entire wing, the airfoil to be chosen has to have a maximum lift coefficient higher than the value calculated by Equation 7.1. In addition to meeting the maximum lift coefficient requirement, we would like an airfoil which has superior lift characteristics in order to minimize the wing area. Wings with a larger lift coefficient tend to produce more induced drag as well. Therefore, through iterations between our airfoil selection and wing design, we will choose the best airfoil and wing design which creates the necessary lift while minimizing drag. 7.1.2 Aerodynamic Efficiency The second most important criterion is the aerodynamic efficiency, given by the maximum lift-to-drag ratio. To reduce drag and thereby conserve fuel, the aircraft will have to fly in such a state as to achieve maximum aerodynamic efficiency. Since the aircraft spends the majority of its flight time either cruising or loitering, the airfoil selected must have the highest aerodynamic efficiency at cruising and loitering conditions. 7.1.3 Off-design Aerodynamic Characteristics The final criterion we considered was off-design performance of the airfoil. Having a high efficiency at a single angle of attack does not guarantee reasonable aerodynamic performance throughout the entire flight envelope. Therefore, the airfoil should have a reasonable lift-to-drag ratio over a broad range of angles of attack. The airfoil must also operate over a wide range of conditions. Our airfoil must be able to generate negative lift and have reasonable aerodynamic efficiencies over a broad range of angles of attack 7.2 Analysis of Airfoils Our team analyzed a wide range of airfoils before choosing the NASA GA(W)-1 (ls417) airfoil, illustrated in Figure 7.1, as the best choice for our UAV. We analyzed Mark Drela’s DAE low drag airfoils as well as NACA 5-digit 63-series and 23-series. We compared these with the NASA Langley general aviation airfoil series. Our analysis shows that the high lift coefficient and excellent off-design characteristics make the NASA GA(W)-1 (ls417) the best airfoil for the Big Brother XL4000.

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Figure 7.1: NASA GA(W)-1 airfoil cross section.

Airfoils were analyzed at the Reynolds number for each flight condition and at various angles of attack. We considered the following conditions in the flight profile: cruise, dash, loiter, takeoff and landing. The XFOIL inputs for each of these conditions are given in Table 7.1.

Cruise Dash Loiter Takeoff/Landing Reynolds Number 1.66E+06 2.90E+06 2.44E+06 1.38E+06

Mach Number 0.13 0.23 0.12 0.07 Altitude (m) 6096 6096 152.4 0

Table 7.1: Aerodynamic characteristics of different flight configurations.

The NASA GA(W)-1 (ls417) airfoil outperformed all other airfoils in maximum sectional lift coefficient. Figure 7.2 below shows the drag polar diagram of the airfoils that we analyzed. The NASA GA(W)-1 (ls417) had the highest maximum sectional lift coefficient (CLmax = 1.94) of the airfoils analyzed. The thicker NACA 23018 had the next highest CL of 1.71. While the NASA GA(W)-1 (ls417) had the best maximum lift performance, it was important to analyze the drag performance of the airfoil.

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0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

-1.5 -1 -0.5 0 0.5 1 1.5 2

Sectional Lift Coefficient

Sect

iona

l Dra

g C

oeff

icie

ntNACA 63-015ANACA 63212NACA 63-215NACA 63-412NACA 64-012ANACA 64-212NACA 64-215

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Sectional Lift Coefficient

Sect

iona

l Dra

g C

oeff

icie

nt

NACA 23015NACA 23012NACA 23018NASA GWA-1 (ls417)NACA 23010

Very low sectional drag at low lift coefficients

CLmax ≈ 1.5

Negative lift can be generated

Negative lift can be generated

NACA 23-series have significantly lower CLmax than NASA GA(W)-1 (ls417)

NACA 23-series and NASA GA(W)-1 (ls417) have similar sectional drags

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0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

-1.5 -1 -0.5 0 0.5 1 1.5 2

Sectional Lift Coefficient

Sect

iona

l Dra

g C

oeff

icie

ntLS013LS413LS413MODLS417MOD

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Sectional Lift Coefficient

Sect

iona

l Dra

g C

oeff

icie

nt

NACA 2412NACA 6712DAE 11DAE 21DAE 31

Figure 7.2: Drag polar plots of analyzed airfoils.

Negative lift can be generated

No Negative lift can be generated

Slightly higher sectional drag at low lift coefficients

NASA GA(W)-1 (LS417Mod) CLmax = 1.94

Good aerodynamic efficiencies

But very poor off-design performance

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The NASA GA(W)-1 (ls417) airfoil has slightly higher drag coefficients than most of the airfoils analyzed. Because most of the UAV mission requires loitering and dashing at high speed, we compared the sectional drag coefficients at sectional lift coefficients around CL=0.5, which is near the cruise lift coefficient. The DAE 31, NASA LS413 and NACA 63-series airfoils had CD values of approximately 0.005 near CL = 0.5. The NACA 23-series airfoils had CD values of 0.7-0.8, depending on sectional thickness. The NASA GA(W)-1 (ls417) airfoil has a CD value of approximately 0.8 at CL = 0.5. While the NASA GA(W)-1 (ls417) airfoil had a slightly higher sectional drag coefficient, it was still comparable to its competitors. While the sectional drag coefficient can give a good indicator of performance, the overall wing performance is the deciding factor for airfoil selection. The NASA GA(W)-1 (ls417) airfoil has excellent off-design characteristics. The airfoil can generate CL ≈ -0.5 at -8 degrees angle of attack for dive conditions. It also has a wide range of sectional lift coefficients that generate low sectional drag. While the NASA GA(W)-1 (ls417) airfoil meets all of the airfoil criteria, it is also important to analyze the overall wing performance to pick the best airfoil. The performance characteristics of the NASA GA(W)-1 (ls417) airfoil are shown below in Table 7.2.

Parameter NASA GA(W)-1 Lift curve slope m 0.112 degrees-1

Zero-Lift Angle of Attack αL0 -4.0 degrees Maximum Sectional Lift Coefficient Clmax 1.94 Sectional Pitching Moment CmAC -0.1

Table 7.2: Performance characteristics of the selected NASA GA(W)-1 (ls417) airfoil.

The next section will discuss the current wing design. As a result of calculating wing iterations with the NASA GA(W)-1 (ls417), NASA ls413 and NACA 23015 airfoils, we found the NASA GA(W)-1 (ls417) airfoil to be the best. The high maximum lift coefficient allows us to minimize the required wing area. The wing area reduction with the NASA GA(W)-1 (ls417) airfoil outweighs the greater sectional drag of the airfoil. As a result the NASA GA(W)-1 (ls417) airfoil allows us to minimize the engine power required, fuel consumption and thus our gross takeoff weight.

8. Wing Design The wing planform shape and high lift devices were selected so that the desirable stall speed and maximum range requirements were met. We chose a design that met these two parameters for cost reasons. The wing design is currently a tapered, un-swept, un-twisted wing with simple flaps for low speed flight. This section outlines the design of the wing and high lift devices in more detail. 8.1 Wing Geometry To find the optimal wing planform area, the MATLAB program Liftline.m was used to calculate the induced drag and the lift distribution. Following our aerodynamic design iterations, we have

19

decided on a wing with a root chord of 3.1 ft. and a tip cord of 2.4 ft. (Figure 8.1). We chose this current baseline design to reduce the induced drag of our UAV. The reduced drag lessens the amount of fuel required, the power required, and overall weight of the aircraft.

Figure 8.1: Finalized wing geometry.

8.2 High Lift Devices High lift devices such as trailing edge flaps and leading edge flaps are often employed in aircraft to generate additional lift during takeoff, create drag during landing, and decrease take-off distance. In order to meet our mission requirements, our team analyzed the advantages and its associated trade-offs of incorporating such devices in our design. 8.2.1 Trailing Edge Flaps To achieve a successful takeoff, the amount of lift generated must balance the weight of the aircraft. Since the amount of lift generated is directly related to the lift coefficient and the speed of the aircraft, a takeoff scenario would require a high lift coefficient to counter the low speed. If the wing of the airplane is unable to provide the required lift coefficient, then trailing edge flaps may be used to increase the camber of the wing and improve the wing lift coefficient. While this is beneficial during the take-off process, the deployment of flaps also results in a substantial increase in the drag coefficient of the wing. Thus, the flaps may also be deployed during the landing phase to create additional drag and aid in the deceleration of the aircraft. 8.2.2 Flap Type To maintain simplicity and optimize weight, two particular flaps may be considered: the split flap and the plain flap. As shown by Figure 8.2, the plain flap rotates about a simple hinge while the split flap uses an upper and lower surface, of which the lower rotates about a simple hinge while the upper remains immobile. The plain flap is the simplest to implement while the split flap is more complex but offers better structural strength. In our case of a low speed lightweight vehicle, the performance of the plain flap is more advantageous than the structural benefits of the split flap.

Root Chord= 3.1 ft.

Wing Span = 27 ft.

Tip Chord= 2.5 ft. Tip Chord= 2.4 ft.

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Figure 8.2: Diagram showing the plain flap and split flap design. [6]

In addition to structural advantages, plain flap is more efficient than split flaps. As shown by Figure 8.3, plain flap performs 20% better than split flap with 20 degree flap deflection angle.

Figure 8.3: Plain flap performs better than split flaps at 20 degree flap deflection angle.

8.2.3 Flap Location and Dimensioning The positioning of the flap with respect to the wing centerline is important in optimizing the structural and flow behavior in that region. The flap must be positioned where it is as close as possible to the fuselage (for stress optimization) but far enough to minimize the boundary layer effects due to the proximity of the fuselage. Thus, we chose to position the inner side of the flap a distance roughly equivalent to 2 fuselage diameters (4 feet) from the wing centerline (Figure 8.4). In choosing the dimensions of the flap, our team decided to implement 20% flap chord to wing chord ratio. The maximum flap chord to wing chord ratio was limited to 30% due to wing structural consideration. From the MATLAB code, we have iterated the flap dimension process and we came up with the flap span of 7.0 ft, which was approximately 45% of the half-span of the wing.

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Figure 8.4 Diagram showing flap positioning and dimensioning.

8.2.4 Flap Performance Analysis To determine the performance impact of the flaps on the aircraft during takeoff and landing, we inputted the flap geometry and flight conditions into our main MATLAB solver to determine the lift and drag coefficients at the two flight conditions. For simplicity, a maximum flap deflection angle of 20 degrees was assumed throughout the analysis. From our analysis, it was determined that the utilization of flaps increases the maximum lift coefficient by 26.2%. A summary of the sectional airfoil performance with the flaps is shown below in Table 8.1.

Parameter Value Lift curve slope m 0.112 degrees-1

Zero-Lift Angle of Attack αL0 -7.3 degrees Maximum Sectional Lift Coefficient Clmax 2.612 Sectional Pitching Moment CmAC -0.252

Table 8.1: Sectional airfoil performance with flaps deployed at 20°.

9. Aerodynamic Performance at Design Points The aerodynamic performance characteristics of the aircraft were computed at the various design points of takeoff, cruise, dash, and landing. A MATLAB code was used to perform these calculations, and it is included in Appendix C. 9.1 Design Trade-offs To come up with the optimal parameters for the aerodynamic design, our team considered different geometric parameters of the aircraft. We also took design restraint parameters into consideration such that our initial aerodynamic design parameters do not clash with other design considerations. The only major design restraint was at dash condition. Our engines will not meet the dash requirements if the wing area and CD0 values were too high.

3.1 ft

cf/c = 0.2

7.0 ft

4 ft 2.4 ft

13.5 ft

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9.1.1 Taper Ratio Taper ratio is defined as the ratio between the tip chord length and root chord length. Various taper ratios were considered while restricting other parameters. Table 9.1 tabulates the aerodynamic parameter changes according to the taper ratio.

b = 27cr (ft) ct (ft) taper Able to Takeoff? AR Sw (ft^2) L/D @ cruise L/D @ Dash Cdo @ cruise Cdo @ dash3.5 3.5 1.000 y 7.71 94.5 15.35 16.17 0.0185 0.01623.5 3 0.857 y 8.31 87.75 16.06 16.96 0.0191 0.01683.5 2.5 0.714 y 9 81 16.8 17.78 0.0199 0.0175

Table 9.1: Table showing aerodynamic parameters as a function of taper ratio.

First condition to look for was whether the aircraft was able to takeoff with decreased taper ratio. As the taper ratio is decreased, the wing area decreases, which reduces the lift generated by the wing. A decrease in the taper ratio also increases the aspect ratio, which in return reduces the induced drag. This is observed in the L/D values as taper is decreased. Most importantly, CD0 increases as taper increases. Therefore, iteration was necessary to find best taper ratio which maximizes aircraft’s L/D while not increasing CD0 at dash condition. 9.1.2 Wing Span Wing span was also considered in the sizing of the wing. Table 9.2 shows aerodynamic parameter changes as a function of wing span.

Wing Span (ft) Able to Takeoff? AR Sw (ft^2) L/D @ cruise L/D @ Dash Cdo @ cruise Cdo @ dash26 y 9.45 71.5 16.91 17.95 0.0212 0.018628 y 10.18 77 17.75 18.83 0.0205 0.01830 y 10.91 82.5 18.56 19.67 0.02 0.0175

Table 9.2: Increase in wing span decreases CD0 values.

As the wing span is increased it reduced the CD0 values. This is a result of increased wing area and weight of the wing. Due to our design constraint, it was not recommended to increase the wing area too much. The optimal wing span was calculated to be 27 ft. from the iteration. 9.1.3 Root chord Lastly, the root chord was changed to see how it affects other aerodynamic parameters. Table 9.3 shows the results.

cr (ft) taper Able to Takeoff? AR Sw (ft^2) L/D @ cruise L/D @ Dash Cdo @ cruise Cdo @ dash3 1 y 10 90 17.61 18.61 0.0191 0.0168

3.5 1 y 8.57 105 16.31 17.16 0.0178 0.01574 1 y 7.5 120 15.02 15.71 0.0167 0.0148

Table 9.3: Increasing root chord harms the L/D ratio.

From the table, it is clear that increasing the root chord decreases the CD0 value. However, the cost of increasing has a large negative effect. The aspect ratio decreases and as a result, a large

23

induced drag is experienced by the aircraft. This drag increase harms the L/D ratio and this would correlate to the amount of fuel it requires to complete the mission. 9.1.4 Current Design Current design has a root chord of 3.1 with taper ratio of 0.774. Table 9.4 tabulates the current design.

b cr ct Able to Takeoff? AR Wing Area L/D @ cruise L/D @ Dash Cdo @ cruise Cdo @ dash27 3.1 2.4 y 9.82 74.25 17.2 18.2 0.021 0.018

Table 9.4: Optimal design configuration.

Current long endurance UAVs have L/D values ranging between 15 and 20. Our calculated UAV L/D values are comparable to similar aircrafts. With the current configuration, our UAV is able to meet the dash condition. 9.2 Lift (No Flaps) When the flaps are retracted, we are interested in the maximum angle of attack of the aircraft when the sectional lift coefficient reaches 1.94. Table 9.1 is the plot illustrating this point.

Figure 9.1: Wing sectional lift coefficient profile at takeoff conditions without flaps [7].

The maximum angle of attack without flaps was calculated to be 16 degrees. Table 9.5 summarizes the aircraft aerodynamic coefficients at various angles of attack. The lift coefficient of the aircraft was based on the sectional life coefficient values output by Liftline.m. The drag coefficient calculation will be discussed on section 8.4. The coefficient of moment without the tail calculation can be found in Appedix D.

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AoA CL(wing) CL(ac) Cmac-t CD(ac)0 0.36166 0.32323 -0.10000 0.026471 0.45208 0.41601 -0.09118 0.028862 0.54250 0.50879 -0.08237 0.031813 0.63291 0.60158 -0.07355 0.035334 0.72333 0.69436 -0.06474 0.039415 0.81374 0.78714 -0.05592 0.044066 0.90416 0.87992 -0.04711 0.049277 0.99458 0.97271 -0.03829 0.055058 1.08499 1.06549 -0.02948 0.061399 1.17541 1.15827 -0.02066 0.0683010 1.26582 1.25106 -0.01185 0.0757711 1.35624 1.34384 -0.00303 0.0838112 1.44666 1.43662 0.00579 0.0924113 1.53707 1.52940 0.01460 0.1015814 1.62749 1.62219 0.02342 0.1113115 1.71790 1.71497 0.03223 0.1216016 1.80832 1.80775 0.04105 0.13246

Table 9.5: Aerodynamic parameters at takeoff conditions without flaps.

The pitching moment increases as the aircraft pitches. The main contribution comes from the fuselage pitching moment. Given these coefficient of drag and lift at various angles of attack, we were able to investigate whether the UAV was able to takeoff without flaps. The lift generated by the aircraft is limited by the wing stall angle of attack. A lift greater than 644.8 lbf. is needed to take off.

Figure 9.2: UAV will not be able to takeoff without the flaps.

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As observed in Figure 9.2, the wing without flaps deployed at stall angle of attack of approximately 16 degrees gives lift of 555 lbf., which is incapable of generating sufficient lift for takeoff with a given stall speed of 35 kts at sea-level. To calculate the stall speed at cruise condition, Equation 8.1 was used.

max)(

2

LCSWV

⋅⋅⋅

=ρ

(Eqn. 9.1)

Using Equation 9.1 and using the CLmax of the wing at 16 degree angle of attack, we calculated the stall speed at cruise conditions to be 50.9 kts. Hence, the UAV will be able to cruise at 80 kts. Mission requirements specify that the aircraft must perform dash maneuvers with an air speed of 140 kts and at an altitude of 500 ft. Based on our calculations, our UAV will be able to sustain steady level flight at these conditions. Using the same approach as cruise condition calculation, we calculated the stall speed at dash to be 38.3 kts. Therefore, the UAV will be able to dash at 140 kts. 9.3 Lift (Flaps Deployed) When the flaps are deployed, we are interested in the maximum angle of attack of the aircraft as well as the maximum lift coefficient generated by the flaps. Figure 9.3 illustrates this point.

Figure 9.3: Wing sectional lift coefficient profile with flaps deployed.

The corresponding angle of attack at this condition was approximately 17 degrees. Therefore our stall angle of attack with flaps deployed is 17 degrees. Table 9.6 summarizes the aircraft aerodynamic coefficients in the flap deployed configuration.

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AoA CL(wing) CL(ac) Cmac-t CD(ac)0 0.71635 0.62129 -0.25153 0.051701 0.80677 0.71407 -0.24271 0.055982 0.89719 0.80685 -0.23390 0.060823 0.98760 0.89964 -0.22508 0.066234 1.07802 0.99242 -0.21627 0.072215 1.16843 1.08520 -0.20745 0.078756 1.25885 1.17799 -0.19864 0.085857 1.34927 1.27077 -0.18982 0.093528 1.43968 1.36355 -0.18100 0.101759 1.53010 1.45633 -0.17219 0.1105510 1.62051 1.54912 -0.16337 0.1199111 1.71093 1.64190 -0.15456 0.1298412 1.80135 1.73468 -0.14574 0.1403413 1.89176 1.82747 -0.13693 0.1513914 1.98218 1.92025 -0.12811 0.1630215 2.07259 2.01303 -0.11930 0.1752016 2.16301 2.10581 -0.11048 0.1879617 2.25343 2.19860 -0.10167 0.20127

Table 9.6: Aerodynamic parameters at take-off conditions (flaps deployed).

The necessary lift coefficient needed to takeoff was calculated to be approximately 2.14, which occurs between 16 and 17 degrees angle of attack. The pitching moment is significantly more negative with flaps because flaps increase the lift generated by the wing and as a result, they will produce more negative pitching moment. Also notice the increase in CD as the flaps contribute more induced drag. The drag contribution due to the flaps can be found in section 8.4. Without the flaps, we have shown that the aircraft is unable to generate sufficient lift for takeoff and cruise at sea-level without the flaps. With the flaps deployed we came to conclusion that the aircraft will generate sufficient lift for takeoff with a flap deflection angle of 20 degrees.

Figure 9.4: Aircraft will generate sufficient lift for takeoff with flaps deployed.

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From Figure 9.4, we can clearly see that at stall angle of attack of approximately 17 degrees, the aircraft will be able to takeoff with 675.1 lbf lift force. This is slightly higher than our gross takeoff weight of 644.8 lbf. Our goal was meet the gross takeoff weight at stall speed since the UAV will be flying at 1.15 times greater than the stall speed during normal takeoff session. At 1.15Vstall, the UAV will generate approximately 894.5 lbf of lift force and it will have 6 degree of error margin between stall angle of attack and minimum lift angle of attack. Deploying the flaps will result in changes to aerodynamic properties of the wing. The sectional lift coefficient of the wing as well as the aerodynamic pitching moment will be affected due to the flaps. The equations used to calculate these changes are shown in Appendix D. 9.4 Drag The total drag coefficient can be calculated by adding the parasite drag coefficient, induced drag coefficient, trim drag coefficient, and the added induced drag due to the flaps. Equation 9.2 illustrates this point. ( )0 trimD D D Di Dflaps

C C C C C= + Δ + + (Eqn. 9.2)

Each component contributing to the total drag was calculated individually. These calculations can be found in Appendix D. The total drag coefficient of the aircraft at takeoff, cruise and dash conditions were plotted and a 2nd degree polynomial fit operation was done to calculate the K value for CD = KCL

2 + CD0. Table 9.7 shows the table of CD0 and K values for all 4 configurations.

CD0 K(ac) Takeoff (No Flaps) 0.0222 0.0336

Takeoff (With Flaps) 0.0375 0.0339 Cruise 0.0205 0.0336 Dash 0.0181 0.0336

Table 9.7: CD0 and K values at different configurations.

To illustrate this relationship, a drag polar plot for takeoff condition was constructed. This is shown in Figure 9.5.

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Drag Polar at Takeoff Condition (-17 deg. to 17 deg.)

0

0.05

0.1

0.15

0.2

0.25

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

CL(ac)

CD(a

c)

Without Flaps With Flaps

Figure 9.5: Drag polar at Takeoff Condition

As you can see from the plot, the y-intercept (CD0) increased with the flaps deployed. This is expected due to increase in induced drag as well as the trim drag. The K value did not change much going from retracted to deployed configuration. The slope of drag polar curve remains the same for both configurations due to this constant K. The parasite drag coefficient is the major contribution of the drag when the aircraft is at steady level flight. Table 9.8 shows the breakdown of each component contributing to the parasite drag at dash condition.

Component CD0 Wing 0.0100

Fuselage 0.0025 Booms 0.0020

Tail 0.0021 Deployed Landing Gear 0.0034

Table 9.8. CD0 contribution by different components at dash condition.

As seen from the table, the major contribution of the parasite drag is the wing. By examining the equations, the wing surface area was the major parameter related to the wing parasite drag. Therefore, our team focused on optimizing the wing surface area as much as possible in order to minimize the wing parasite drag. Another component to observe is the landing gear. When the landing gear was not retracted, the resultant parasite drag coefficient contribution was approximately 33% of the wing parasite drag. This was the main motivation behind retractable landing gear configuration. Additionally, the fuselage and boom wetted areas were directly calculated from CAD software since this was the most accurate way to calculate it.

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9.5 Cruise and Dash Performance During dash, the aircraft is traveling approximately twice as fast at near sea level altitude compared to cruise conditions. From the lift section, we have calculated that our stall velocity at cruise is below 80 kts. Additionally, at dash condition, the stall speed was below 140 kts at maximum angle of attack. This implies that our aircraft should be able to carry out its mission with targeted airspeed for both conditions. For cruise and dash conditions, it is important to consider L/D ratio since this will directly affect the fuel efficiency of the aircraft. Table 9.9 tabulates the maximum L/D ratio for both conditions as well as the CLmax and equivalent stall speeds.

L/Dmax AoA (Degree) CLmax(ac) Vstall (kts) Cruise 17.2 5 1.81 50.9 Dash 18.2 5 1.81 38.3

Table 9.9: Maximum L/D ratio occurs near 5 degree angle of attack.

Our UAV will have approximately L/D ratio of 17 for both conditions near 5 degree angle of attack. This is similar to the L/D ratio of similar aircrafts we have considered at the beginning of our project.

10. Power Requirement In order for our aircraft to meet the various speed and altitude requirements, the UAV must have a sufficiently powerful engine and propeller configuration. To select an appropriate engine, our team calculated the power requirements based on the current aerodynamic and weight estimates of the aircraft. The power required was computed at the various design points of cruise, dash and loiter. Our calculations indicate that with the chosen propeller, a 51 hp engine will be required to meet all performance specifications. 10.1 Power Requirement Calculations In steady level flight, the aircraft is flying at a constant altitude and velocity. At this flight condition, the required thrust is equal to the drag acting on the aircraft. For a propeller aircraft, the measured output is in horse power and must be converted to thrust. A MATLAB code was written to perform these calculations and is included in Appendix C.

To maintain steady, level flight, the engine must generate an available power that is greater than or equal to the power required. The power available, at a specific altitude, in an engine that has a rated sea level horse power Pshp is given by:

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0.85 ( )altitudeAval i shp sealevel

sealevel

P Pρηρ

= (Eqn. 10.1)

It is clear from this equation that power available drops as the altitude increases. Also the term ηi is a measure of the propeller efficiency and is a function of flight speed and propeller diameter. The maximum airspeed attainable at a certain altitude occurs when the available power output is equal to the power required. 10.2 Power Requirement at Cruise Altitude The power requirement at the cruise altitude of 20,000 ft was calculated and is given in Figure 10.1. These power requirements are calculated assuming our aircraft is at our GTOW of 644.8 lbs. The power required to cruise at 80 kts is 8.1 hp. With a 51 hp engine, the output gives us a maximum air speed of 138.9 kts and is also able to meet the power required at the stall speed of 42 kts.

Figure 10.1: Power available and power needed at cruise altitude.

Based on our mission analysis, a large part of our mission profile consists of cruising at 80 kts at an altitude of 20,000 ft. Therefore, it is important that the cruise speed be close to the airspeed that requires the minimum amount of power. Given our aerodynamic configuration, the least power required for steady level flight is 7.6 hp and occurs at a flight speed of 62 kts. Although we will be cruising with 0.5 hp greater than the optimum, the trade off is necessary in order to meet our other aerodynamic specifications.

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10.3 Power Requirement for Dash and Loiter At the dash and loiter altitude of 500 ft, the power requirement was calculated and is given in Figure 10.2. These power requirements are calculated assuming our aircraft is at our GTOW of 644.8 lbs. The power required for dash at 140 kts is 39.7 hp. The power required for loiter is 9.4 hp. The engine also delivers enough power to fly at the stall speed of 40.9 kts and attain a maximum speed of 142.8 kts. From this analysis, we conclude that the 51 hp engine meets our requirements.

Figure 10.2: Power required and power available at dash/loiter altitude with 51 hp engine.

10.4 Maximum Climb Rate Our UAV is required to have a rate of climb of 16.67 ft/s at sea level. The maximum rate of climb, max climb rateV can be determined by first calculating the horizontal velocity at which maximum climb rate is attained, max rateV . max rateV and subsequently max climb rateV for a certain altitude is given by:

0

max rate2

3 d

W KVS Cρ

⎛ ⎞= ⎜ ⎟⎝ ⎠

(Eqn. 9.2)

3max climb rate max rate

( ) 1 ( )2

shp SL Dp

SL

P C SV VW W

ρ η ρρ

= − (Eqn. 9.3)

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Figure 10.3 depicts how the maximum climb rate of our UAV varies with altitude. The weight of the aircraft was assumed to be the GTOW of 644.8 lbs. It shows that our aircraft easily meets the required sea level climb rate even at maximum weight. Figure 10.3 also shows that our flight ceiling is 40,100 ft. The flight ceiling is given by the altitude at which the maximum climb rate is zero. Our aircraft has a maximum climb rate of 31.5 ft/s at sea level.

Figure 10.3: Maximum climb rate for our UAV at maximum weight and flaps retracted.

10.5 Flight Envelope The flight envelope depicts the range of speeds that our aircraft can fly at a specific altitude in steady level flight. The stall boundary line is the locus of our UAV’s stallV at each respective altitude, and is determined purely from the aerodynamic properties of our aircraft. The power boundary line represents the maximum and minimum speeds at which the engine is able to power the aircraft in steady level flight. The maximum and minimum speed occurs when the maximum power available from the engine matches the power required for steady level flight. Since the stall boundary is ahead of the lower power boundary for most of the altitudes, the minimum airspeeds that our UAV will be able to maintain is usually stall limited. These flight envelopes are calculated assuming our aircraft is at our GTOW of 644.8 lbs. Figure 10.4 demonstrates that our UAV, with flaps retracted is able to fly at all the required flight points with the exception of the sea level stall requirement. However, it can be seen in Figure 10.5 that with flaps deployed, our UAV is able to satisfy stall requirements.

33

Figure 10.4: Flight envelope of the UAV with flaps retracted.

Figure 10.5: Flight envelope of the UAV with flaps deployed.

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11. Engine Selection We chose to implement the AR801 engine, manufactured by UAV Engines of Lichfield, United Kingdom, as the power plant of our aircraft. The engine is a very important part of the aircraft design. The engine must be able to perform to the demands of the different flight conditions that our UAV will encounter. The engine must be able to provide adequate power during dash and take-off, yet be fuel efficient enough to minimize the fuel weight required. To these ends, we have selected several different engines that meet the maximum power requirement and are relatively fuel efficient. Table 11.1 shows some different characteristics of the chosen engines.

AR801 [5] Rotax 582 UL [8] HKS 700E [9] Type of Engine Rotary 2 Stroke 4 Stroke

Manufacturer UAV Engines BRP-Rotax HKS Location United Kingdom Austria Japan Horsepower (bhp) 51 65 60 Weight (lbs) 53.7 110.2 121 Average Fuel Consumption (lb/hr) 15 24 14.3 Dimensions (in) 12.8 X 9.8 X 12 20 X 16.4 X 29.5 25.3 X 17.1 X 18.4 Evaluation Best Option Fuel Inefficient Too Big

Table 11.1: Engine comparison chart. Our ideal engine will be light, fuel efficient, small, and easy to use. As can be seen from Table 11.1, the AR801, which is made by UAV Engines Ltd., is both light, small, and fuel efficient. The Rotax 582 UL is heavier and the least fuel efficient of the group. It also is a 2 stroke engine which requires the extra step of adding oil to the fuel. The HKS 700 E is the most fuel efficient, but its size is relatively large in comparison to the AR801 due to its horizontally opposed cylinders. After considering these differences, we chose the AR801 engine to power our UAV. Its compact rotary engine is perfect for our narrow fuselage. In addition, its low weight and good fuel consumption will make the fuel weight and therefore overall weight of our UAV minimal, which is desirable. Appendix H details the fuel consumption of the AR801.

12. Propeller Selection We chose to use a composite-wood two-bladed propeller that is 5 ft in diameter for our initial design. Two blades and a composite-wood construction were selected because of weight considerations. A composite two bladed propeller typically weighs less than 7 lbs. [10]. A two bladed propeller is also the least destabilizing propeller configuration during powered flight. Proper propeller selection is important because the propeller’s geometry plays an important role in the propulsion systems overall efficiency and aircraft stability. The initial propeller selection was conducted by looking at the diameters of propellers for engines of similar power (about 50 hp). A propeller diameter of 52-72 inches was a typical size used on engines ranging in power of 50-70 horsepower [11]. Therefore, no matter what engine is chosen in the 50 horsepower range, the maximum prop size is 72 inches. To find the optimum propeller size, different propeller geometries were evaluated based on the following criteria (in order of importance):

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1. Ability of propeller to fit in current configuration 2. Efficiency of the propeller 3. Weight 4. Ease of installation/operation 5. Contribution to destabilizing downwash on aircraft stability

The efficiency of the propeller is directly related to its size. Therefore, we chose the largest propeller reasonably possible to get the largest efficiency possible. The design parameters that limit the size of the propeller are the ground clearance when rotating for takeoff and the maximum distance between the twin booms (6.28 ft.) Some propellers can vary their pitch to increase the efficiency. However, the efficiency increase is only realized at low speeds, and a variable pitch propeller is more complicated and heavier than a fixed pitch propeller. For these reasons, we chose a fixed-pitch propeller. From Figure 12.1 below, it is evident that the propeller efficiency is lower at lower speeds. This is fine for our configuration because the UAV is not power-limited at low speeds; we are power limited at high speeds. At high speeds, the propeller efficiency is at its maximum (0.98 for our case) and is adequate to meet our dash requirement.

Figure 12.1: Propeller efficiency as function of flight speed.

Using the knowledge of actuator disk theory and research conducted on propellers we were able to construct a trade-study matrix. We used the trade study matrix in Table 12.1 to evaluate the best possible configuration and size of the propeller. The design tradeoffs are summarized in the trade study matrix below.

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Criteria Compatibility with configuration

Efficiency of Propeller Weight Ease of

Installation Contribution to

stability Conclusion

Design Considered

Configuration Considerations 2 Blade-Fixed

Pitch Excellent Adequate Excellent Excellent Excellent Design Chosen

2 Blade-Variable Pitch Excellent Excellent Unsatisfactory Unsatisfactory Excellent

Too heavy and

complicated>2 Blade-

Fixed Pitch Excellent Adequate Poor Excellent Unsatisfactory

Too heavy, complicated and stability

problems > 2 Blade-

Variable Pitch Excellent Excellent Poor Unsatisfactory Unsatisfactory

Too heavy, complicated and stability

problems Size Considerations

Propeller; <5feet

diameter Excellent Poor Excellent Excellent Excellent Not efficient

enough

Propeller; 5 feet diameter Excellent Adequate Excellent Excellent Excellent Design

Chosen Propeller; >5 feet diameter

Poor; cannot fit a prop with

diameter > 5 ft

Poor; tip exceeds Mach 1

Unsatisfactory Excellent Unsatisfactory Will not fit in current

design

Table 12.1: Propeller Design Trade study. From the trade study matrix, it is clear that a 5 ft. diameter propeller in the 2 blade, fixed pitch configuration is the best design choice for our design. The propeller will be attached to a 2.3:1 reduction drive that is part of the AR801 engine. The belt drive’s reduction ratio was chosen so that the propeller blade tips will not exceed Mach 1.

13. Fuel Requirements Big Brother XL4000 will need 183.4 lbs of fuel to complete the flight profile detailed in the Mission Description section. In order to meet the requirements, the aircraft must carry enough fuel to perform all of its required objectives: take off, perform 10 VTI maneuvers, cruise for 12 hours, and land. Figure 13.1 shows the estimated fuel requirements for each phase of the mission.

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Figure 13.1 Breakdown of the amount of fuel required for each segment of the mission profile. From a fuel consumption perspective, the entire mission profile comprises of 3 types of maneuvers: climb, steady level flight and a powered descent. In order to perform the more complex calculations for climb and steady level flight, MATLAB codes (fuel_climb.m, fuel_levelflight.m) were written and are included in Appendix C. The MATLAB codes calculate the power required for each maneuver at the specified altitude. Using the engine manufacture’s data for fuel consumption, we are able to calculate the fuel flow rate required for each power setting required during the flight. The MATLAB code iterates every 1 second during flight. After every iteration the weight is recalculated based on fuel burned off (and hence weight lost by the UAV) during each second. The code updates the weight throughout the flight like a Breguet’s equation simulation, however our simulation accounts for a variable throttle setting, which Breguet’s equation does not. We believe that our simulation is a better model of the actual fuel required than Breguet’s equation because our simulation is tailored for our mission profile and considers more variables. The detailed calculations we used for calculating the fuel requirements of our aircraft is detailed in Appendix H.

14. Takeoff and Landing Analysis The Big Brother XL4000 will be able to both take off and land well within the distance specified by our requirements. Our design requirements state that the aircraft must be able to take off and land on a 3000-foot runway and clear a 50-foot tall obstacle at the end of the field. Our UAV

Fuel Used During 10 VTI Maneuvers 116.10 lbs

Fuel Used During 12 hr Cruise 59.45 lbs

Fuel Used During Takeoff + Climb + Dash to Surveillance Area 5.93 lbs

Fuel Used During Return to Base 1.89 lbs

Total Fuel Required: 183.4 lbs

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sufficiently meets these requirements. The UAV with flaps deployed and running at full throttle will take off and reach 50 ft elevation within 605 ft of where it started. For landing, the UAV is able to clear the obstacle, descend at a -5 degree climb angle and come to a complete stop in 847 ft. Our analysis shows that the UAV design can take off and land on very short runways. This allows our design to operate on a much larger range of airfields. The detailed calculations used in this analysis are available in Appendix E. 14.1 Takeoff Analysis The takeoff procedure is illustrated below in Figure 14.1.

Figure 14.1: Diagram of takeoff distance for UAV. [6]

The total takeoff distance is the sum of the ground roll, SG, the rotation distance, SR, the transition to climb, STR, and the climb distance, SC.

TOT G R TR CS S S S S= + + + (Eqn. 14.1)

The full equations for each of these terms are found in Appendix E, and the results of our calculations are shown in Table 14.1. The velocities used for takeoff and landing are available in Table 14.2. The UAV is able to takeoff well within the regulations at its max power of 51 hp on normal fields of concrete or firm dirt. We also computed the minimum power required to takeoff within the regulated distance and found it to be 16.5 hp. This minimum power yields a takeoff distance of roughly 2220 ft with actual lift off from the ground occurring before the half-field point of 1500 ft. At worst case conditions of a wet grass runway, our design can still takeoff in 654 ft. The most important factors in minimizing takeoff distance are weight and power. A

39

decrease in weight or an increase in power will shorten the takeoff distance. Therefore we decided to take off at maximum power to allow for the minimum possible takeoff distance. 14.2 Landing Analysis The landing procedure is illustrated below in Figure 14.2.

Figure 14.2: Landing procedure of UAV. [6]

The total landing distance is the sum of the approach distance, Sa, the flare distance, SF, the free roll distance, SFR, and the braking distance, SB.

L a F FR BS S S S S= + + + (Eqn. 14.2)

The equations for each of these terms are also found in Appendix E, and values for each are listed in Table 14.1; the input parameters are also listed in Table 14.3. Our design lands well within the 3000 ft limits at a distance of 847 ft on a concrete or firm dirt strip. On the worst case field of wet grass, our aircraft can land in a distance of 1007 ft.

Takeoff Landing SG = 264 ft Sa = 536 ft SR = 65 ft SF = 71 ft

STR = 195 ft SFR = 68 ft SC = 81 ft SB = 172 ft

STotal = 605 ft STotal = 847 ft

Table 14.1: Takeoff and landing distances.

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Takeoff Landing Takeoff Velocity 65 ft/s Approach Velocity 76.7 ft/s Transition Velocity 67.9 ft/s Flare Veloctiy 72.57 ft/s Climb Velocity 70.8 ft/s Touchdown Velocity 67.85 ft/s

Table 14.2: Aircraft velocities during takeoff and landing.

Propulsion Power 51 hp Propulsion Efficiency 0.748 Aerodynamic Performance for Takeoff S 74.25 ft2 CL 0.1 Cdo 0.0375 K 0.0336 Aerodynamic Performance for Landing S 74.25 ft2

CL 0 Cdo 0.0375 K 0.0336 Landing Weight 461.4 lbs Gross Takeoff Weight 644.8 lbs Descent Angle 5 degrees

Table 14.3: Input Parameters.

In our calculations for landing distance we chose a descent angle of -5° instead of the specified angle of -3°. A steeper descent angle will yield a shorter the landing distance. We attempted to keep the landing distance as short as possible so as to allow our UAV to make use of the shortest possible field. A descent angle of -3° will produce a landing distance of 1216 ft., which still meets our requirements but results in a much longer runway needed. To show that the aircraft is capable of descending at -5°, we considered the following equation which relates the flight path angle to the thrust, drag, and the weight of the aircraft.

W

DT −=)sin(γ (Eqn. 14.3)

For the minimum flight path angle, the thrust is set to zero. At a speed of 1.15 times the stall speed and the stall angle of attack, the total drag on the aircraft is 86 lbs. For landing, the aircraft with all its fuel used up will weigh 461.4 lbs. Solving for γ, we find the minimum flight path angle to be -10.5°, which is more than we need. Thus, our aircraft is capable of descending at a flight path angle of at least -5°.

15. Tail Selection In choosing the optimum tail configuration for BBXL 4000, we considered numerous tail designs used by existing UAVs. In particular, we studied three tail configurations: V-tail, twin-boom tail,

41

and tailless or flying wing (Appendix F). An H-shaped, twin-boom tail design was chosen as the final configuration. It offers two distinct advantages over other designs. First, it allows the extension of the moment arm of tail without the weight and drag penalties of a full fuselage. Second, it also enables the placement of heavy engine machinery closer to the center of gravity and hence maintaining the stability of aircraft by keeping the center of gravity close to the aerodynamic center. The horizontal and vertical tails are essential for the aircraft’s longitudinal and lateral stability. The customer requires that the UAV be statically stable in yaw and pitch for all configurations. In order for the aircraft to be stable, both the lateral stability derivative (Cnψ) and the longitudinal stability derivative (Cm/CL) have to be negative. To meet these requirements, we chose a total vertical tail area of 7.0 ft2 and a horizontal tail area of 7.28 ft2. The rudder size is 0.875 ft2 per tail while the elevator size is 2.9 ft2. An illustration of the tail configuration is shown in Figure 15.1.

Figure 15.1 Vertical and horizontal tail dimensions. Diagram not to scale

15.1 Vertical Tail To calculate the vertical tail size, the yawing effects of the wing, fuselage, propeller, and wing-body interference were considered. A detailed description of our calculation of this value is outlined in Appendix F. A desired stability derivative for the aircraft (Cnψ) was calculated based on our aircraft configuration, and then the vertical tail area was adjusted to meet this specification. The result of our calculation was a vertical tail area of 4.34 ft2. This value of vertical tail generates a Cnψ of -1.6x10-4. This indicates that the aircraft is laterally stable. However, while the vertical tail size of 4.34 ft2 is sufficient to provide directional stability to the aircraft, it does not guarantee that the aircraft has enough maneuverability. The relation between the vertical tail size and the maneuverability is explained in the following section.

0.5

1.87

1.43

1.08

1.92

1.68

0.4

0.64

6.28

1.16

0.46

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15.1.1 Vertical Tail Maneuverability Requirements The mission of the BBXL 4000 is to provide patrol and reconnaissance. Given that the intended targets may do everything in their power to avoid detection and tracking, we require BBXL 4000 to be able to perform high-mobility maneuvers while loitering. This is to prevent targets from eluding the tracking of BBXL 4000. Therefore, it is important to have adequate tail control surfaces to provide the required lateral mobility to the aircraft. In our context maneuverability is defined as the yaw rate of the aircraft. We would like the aircraft to have enough yaw acceleration to complete a 180° level rotation in less than 15 seconds and to complete a 360° level rotation in less than 20 seconds. To determine the yaw rate of the aircraft and thus the required vertical tail size, we fix the rudder area to be 25% of the vertical tail area and the maximum deflection angle of the rudder to be 30°. The parameters are fixed based on study of similar aircraft. We also assume that the UAV has to perform high maneuverability moves when it is loitering at 500 ft. The yawing rate is related to the vertical tail size area by:

(Eqn. 15.1)

Where Izz = the polar moment of inertia about z-axis, calculated to be 666.3 slug/ft2;

LVT = the distance between vertical tail aerodynamic center and the wing aerodynamic center;

ρ = air density at the loiter altitude of 500 ft: 0.0024slug/ft3; V = loiter velocity: 135 ft/sec;

r

nv

ddCδ

= rudder power, given by the equation:

41083.3 −×=−= vVT

W

VTv

r

nv

bL

SSa

ddC ητδ

(Eqn. 15.2)

δr = deflection angle of rudder, given in degrees; SVT = vertical tail area

With the original vertical tail size of 4.34ft2, we can obtain a maximum yaw rate of:

242 0126.034.41083.37.71350024.0

3.66621

srad

=⋅×⋅⋅⋅⋅

= −ψ (Eqn. 15.3)

With a yaw rate of 0.0126 rad/s2, the aircraft does not have enough maneuverability to meet our turning requirement. Working backwards from the required yaw acceleration, we found that 7 ft2 will allow the aircraft to meet our maneuverability requirement. The comparison of the yawing moment and the rotating time of the aircraft are presented in Table 15.1.

( ) VTrr

nvVTzz S

ddCLVI δδ

ρψ 2

21

=

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Tail Area (ft2) Yaw rate (rad/s2) 90° turn time (s) 180° turn time (s) 360° turn time (s)

4.52 0.0126 15.8 22.3 31.6 7.0 0.0315 10.0 14.1 20.0

Table 15.1: Comparison of time requirement for prescribed turn angles of the iterated vertical

tail area sizing calculation of 4.34 ft2 and increased area 7 ft2.

The rotation time shows that vertical tail size of 7.0 ft2 is the minimum area needed to meet our maneuverability requirement. The lateral stability derivate at this tail area is -1.2x10-4 and this shows that the aircraft still has adequate lateral stability despite enlarging the vertical tail by 60%. As such, the vertical tail area of the UAV will be 7.0 ft2, or 3.5 ft2 for each tail. 15.2 Horizontal Tail The horizontal tail size is determined by the elevator power to maintain the aircraft at equilibrium at maximum lift condition. Elevator size is fixed at 40% of the horizontal tail and maximum elevator deflection is fixed at 20°. The values of the fixed parameters are based on study of similar aircrafts. Even though ground effect is not required for the horizontal tail sizing, we felt that it would be advisable to leave a margin of safety to account for the ground effect at landing. Therefore, we used a most forward C.G. location of 6 ft instead of 6.21 ft from the nose, which was calculated from the weight component analysis. In addition to satisfying equilibrium condition at maximum lift, the horizontal tail has to be able to provide longitudinal stability as well. For the horizontal tail, a more complicated iteration was required to account for the pitching moment effects of the fuselage, wing, CG location, and elevator deflections. The first iteration of this calculation is outlined in Appendix F. Convergence was determined when the output value of the tail area was within 1% of the input value. By starting with an initial horizontal tail of 18.56 ft2, we obtain a final horizontal tail size of 7.28 ft2 after 27 iterations. The tail area obtained after every iteration and its convergence are presented in Figure 15.2 and Figure 15.3.

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Figure 15.2: Horizontal tail size against number of iterations.

Figure 15.3: Horizontal tail size converged to within 1% of original tail size.

The convergence of less than 1% is achieved after 27 iterations, with the final horizontal tail size of 7.28 ft2. We also attempted to initialize the iteration with an initial tail area of more than 18.7 ft2. Results show that the final value at convergence is approximately 7.3 ft2 as well. The tail area yields a longitudinal directional derivate (Cm/CL) value of -0.15, which is stabilizing. Therefore, the aircraft is able to maintain longitudinal stability with the given tail area.

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15.3 Neutral Point One of the parameters calculated for the horizontal tail sizing is the neutral point, which determines the farthest allowed aft location of the center of gravity for the aircraft to be stable. Following the calculations in Appendix F, the stable most rear location of the center of gravity is 6.66 ft behind the nose of the aircraft. The actual farthest aft location of the aircraft’s CG is 6.24 ft, which is forward of the aft limit of the center of gravity. Thus, our aircraft meets the stability requirements of the neutral point and the actual C.G. locations are within the usable C.G. range.

16. Landing Gear and Tire Design The landing gear and tire sizing were calculated using a statistical approach. A statistical tire sizing table was provided by Raymer [6]. This method assumed 90% of the aircraft weight to be carried by the rear tires while the remaining 10% was carried by the front tires. Equation 16.1 was used to calculate the diameter and width of rear and front tires in inches. ( ) B

wDiameter orWidth in AW= (Eqn. 16.1) A and B in Equation 16.1 is a constant term given by Raymer. Ww is the weight carried by each tire. Given our gross takeoff weight of 644.8 lbs, the weight carried by the front and rear tires were 580.3 lbs and 64.5 lbs respectively. Since we are planning to install 2 rear landing gears, the weight will be evenly distributed among the two, making the Ww for each landing gear 290.15 lbs. Table 16.1 shows the values of A and B as well as the final diameter and width sizing of front and rear tires.

A B Front (in) Rear (in) Diameter (in.) 1.51 0.349 6.48 11.00

Width (in.) 0.715 0.312 2.63 4.22

Table 16.1: Summary of diameter and width calculation. Our UAV will implement a retractable landing gear system, and the approximate tire dimensions can be obtained from Table 16.1. To maintain stability of the aircraft, the rear landing gears are to be stored within the twin booms. Storing the landing gear in the booms also increases the space inside the fuselage while making use of twin boom inner capacity. Figure 16.1 and Figure 16.2 illustrates how the landing gears will be retracted into the twin booms.

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Figure 16.1: Front landing gear retraction.

Figure 16.2: Rear landing gear retraction.

As seen from the figures above, the front landing gear retracts backwards, and the rear landing gears retract forward. The rear landing gears in their down position were located slightly rear of the CG such that the rotation during takeoff can be maneuvered without a large pitching moment. A simple hinge mechanism and electric motor were incorporated to retract the landing gears.

17. Air Inlet Sizing Our engine requires an air inlet of 80 in2. Our UAV needs an air inlet because the engine is mounted inside its fuselage. In addition to providing a necessary component for combustion, air is needed to dissipate heat from the radiator of our liquid cooled rotary engine.

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We determined the required inlet area required by taking into consideration the following: engine displacement of 294 cm3, engine revolution limit of 8000 rpm and stall speed of our aircraft at about 35 knots. Using this information and simple volume flow rate calculations, we conclude that a maximum area of about 40 in2 is necessary for our engine’s intake. In addition, it has been found that typical radiators for this size of engine have approximately 60 to 70 in2 of surface area [12]. However, because our radiator will not be placed directly over the air inlet, but will be set back several inches, air will have time to disperse and diffuse to a larger area than what our inlet allows. Based on this we have found that an area of about 40 in2 will be sufficient for our radiator cooling. With the combined area required for the engine’s intake and the radiator, we determined that the air inlet area will need to be 80 in2, 40 for the engine’s intake and 40 for cooling the radiator. This inlet will be placed on the top side of the fuselage to prevent debris from being sucked in during takeoff and landing, thus helping to prevent damage or clogging of engine components (see Figure 17.1).

Figure 17.1: Engine air inlet located on top of fuselage.

18. Trim Analysis In order to sustain steady flight, trim analysis must be performed to determine if the aircraft is able to balance its aerodynamic forces in equilibrium. Also, for a particular symmetric maneuver or gust as specified by the V-n diagram, we will need to evaluate the aerodynamic loads acting on the UAV in a trimmed condition. Trim curves generated at the critical design points are also

Engine air inlet (80 in2)

48

needed for determining the structural stability of the aircraft when subjected to the velocity-load factor combinations for symmetric maneuvers (zero pitching acceleration). 18.1 Required Aerodynamic Information Aerodynamic information such as of CL, CD and CM is needed to obtain trim curves. This information is needed for the power-off and tail-off configurations within the range of operating angles of attack, -17° < α < 16°. The three aerodynamic quantities are obtained from Section 9, which details the aerodynamic performance at design points.

18.2 Trim Curves The following ten graphs show the trim curves for five different configurations and conditions. The first set of four graphs (Figure 18.1) shows the trim curves for major flight conditions at full fuel. The next set three graphs (Figure 18.2) shows the trim curves for major flight conditions at empty fuel. Since takeoff with no fuel is not a feasible maneuver, we have not included the trim curve for this configuration. Also, because the fuel is located in the wing at the aircraft’s center of gravity, the change in center of gravity between full-fuel and empty-fuel conditions is negligible. As a result, the trim curves in Figure 18.1 and Figure 18.2 are essentially the same.

49

50

Figure 18.1: Trim curves for major flight maneuvers with full fuel.

51

Figure 18.2: Trim curves for major flight maneuvers with no fuel.

Each trim curve demonstrates the variation of four sets of non-dimensionalized force coefficients as functions of angle of attack. The vertical force coefficient for the entire aircraft, CZA, shows the resultant force in the vertical direction from aerodynamic forces over the entire aircraft and is given by Equation 18.1.

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⎟⎟⎠

⎞⎜⎜⎝

⎛+=

W

TZTZZA S

SCCC (Eqn. 18.1)

The vertical force coefficient of the wing, CZ, gives the resultant vertical aerodynamic force on the wing of the aircraft (Eqn. 18.2).

)sin()cos( αα DLZ CCC += (Eqn. 18.2) Both of these values increase as the angle of attack increases. Since we assume that the wing and tail are the only surfaces contributing significantly to the overall vertical aerodynamics force, the difference between the CZA and CZ shows the necessary vertical force from the tail required to achieve trimmed longitudinal flight. This will eventually determine the amount of elevator deflection needed. Furthermore, the horizontal force coefficient for the entire aircraft, CX, shows the variation of the resultant force in the horizontal direction from aerodynamic forces as a function of angle of attack (Eqn. 18.3)

)cos()sin( αα DLX CCC +−= (Eqn. 18.1) We assumed that CXA and CX are approximately equal, since the force contribution from the tail in the longitudinal axis of the aircraft is negligible. As shown in Figure 18.1, CX decreases as angle of attack increases. Lastly, the moment coefficient of the aircraft neglecting the effects of the tail, CMACT, shows the necessary moment generated by the tail needed to sustain trimmed-flight at varying angles of attack.

19. Maneuver and Gust Envelope To further demonstrate the aircraft’s capabilities and performance, V-n diagrams were created to show the variation in load factor with increasing airspeed for in-flight maneuvers and wind gusts. 19.1 Maneuver Loading Flight load factors represent the ratio of aerodynamic force normal to the aircraft’s longitudinal axis to the aircraft’s weight. The diagram illustrates the general maneuvering flight envelope and the limit loads (or the maximum aerodynamic loads the airframe must be able to sustain without permanent deformation) during various flight design points. Since current regulations and specifications do not specifically define the allowable load factors for an unmanned reconnaissance aircraft, the limit load factors were instead predetermined partially by the customer and by FAR Part 23.

From Customer Specifications: Maximum Positive Design Load Factor: +3.50 Minimum Negative Design Load Factor: -1.90

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From FAR Part 23: VC (Cruise Velocity): 80 knots VD (Dive Velocity): 115 knots

Load Factor at Point E: -1.00

19.2 Gust Loading During regular flight, atmospheric conditions such as a sudden or sharp gust will affect the aerodynamic forces acting on an aircraft and thus its load factor. Due to the absence of reliable gust loading specifications for UAV type aircraft, the customer has suggested using the parameters as defined in FAR Part 23. FAR regulations specify the vertical gust velocities at various design points that must be considered. These gust velocities at the design points are shown below.

Design Point Positive & Negative Gust Velocity (ft/s) VC (80 kt) 50

VD (115 kt) 25 Table 19.1: Sharp in flight vertical gust velocities, as specified by FAR Part 23.

19.3 Effect Due to Flaps The V-n diagram must also show the structural loading due to flap deployment. Although the amount of time spent in flight with the flaps deployed is much less than the amount of time without, it introduces higher structural loading than un-deployed at the same speed. Consequently, this region is shown in green in the diagrams following. As defined by FAR Part 23 [13], the limiting load factors for flaps deployed are listed below.

Maximum Positive Design (with Flaps) Load Factor: +2.00 Minimum Negative Design (with Flaps) Load Factor: 0.00

19.4 V-n Diagrams By including the effects of the sharp gusts at the specified design velocities in the V-n diagram, we are able to display both the maneuvering flight envelope as well as the associated gust envelope. The complete V-n diagrams for both cases of retracted and deployed flaps in empty and full fuel configurations are displayed in Figure 19.1 and Figure 19.2. The velocities corresponding to each design point are listed on each diagram. For a full description of the analysis process, please refer to Appendix I.

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Figure 19.1: V-n diagram for the Big Brother XL4000 at dry weight.

Figure 19.2: V-n diagram for the Big Brother XL4000 with full fuel.

The four critical loading conditions (design points) are shown in the diagrams above (A,D,E,and G). The respective velocities and load factors at these points were compiled and shown in the table below.

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Design Point

Velocity (Full Fuel) (kt)

Velocity (Empty Fuel) (kt)

Load Factor (full fuel)

Load Factor (empty fuel)

A 63.60 53.99 3.50 3.50 D 115.00 115.00 3.50 3.50 E 115.00 115.00 -1.00 -1.00 G 61.23 51.97 -1.90 -1.90

Table 19.2: Maneuver velocity and load factors at critical load conditions.

20. Wing Loading Before designing and analyzing the structure of the wing, we have to determine the wing loads at the critical points in the V-n diagram. The loading conditions for both empty- fuel and full-fuel conditions will have to be considered. The loads acting on the wing consist of aerodynamic loads such as lift, drag, pitching moment as well as inertial loads such as wing structural weight, fuel weight and twin boom weight. In calculating the distribution of loads across the span of the wing, all of the forces and moments have to be accounted for. The reference axes of the wing have to be chosen before we can determine the wing loading. The x-axis is the aircraft reference axis, pointing aft. The y-axis is the quarter-chord line of the wing in span-wise direction, with the origin at the root of the wing and pointing towards the right wing tip. The z-axis completes the orthonormal axes, pointing in the direction of the lift forces. 20.1 Wing Discretization The overall load distribution is calculated by dividing each wing into 100 strips along the y-axis, with the first strip at the wing tip and the 100th strip closest to the fuselage. The widths of the strips are smaller nearer the wing tip to better capture the variation of the load distribution near the tip. The forces acting on the wing are then given as force per length in the span-wise direction. 20.2 Aerodynamic Loads The aerodynamic forces acting on the wing are namely the lift, drag and the pitching moments. The lift acts in the z-direction, the drag acts in the x-direction and the pitching moment acts in the y-direction. To calculate the distribution of the aerodynamic loads along the span, we will first need to calculate the aircraft’s total lift coefficient, Cza, which is obtained using the Eqn 20.1, where nz is the load factor and Veq is the equivalent velocity corresponding to the critical design points in the V-n diagram.

weq

z

SV

WnCza

2

21 ρ

= (Eqn. 20.1)

Subsequently from the trim curve, we can obtain the wing angle of attack corresponding to Cza. Using the wing angle of attack from the trim curve, we will be able to obtain the sectional lift, drag and moment coefficient at each span-wise station from the MATLAB code LiftLine.m. The forces and moments acting at each station can then be calculated by multiplying the coefficients

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by the respective chord length and dynamic pressure. Finally the loads acting on each strip are calculated as the averages of the loads acting on the two stations spanning the strip. 20.3 Inertial Loads The wings are estimated to have a structural weight of 68.8 lb or 34.4 lb per wing. To simplify our calculation, we assume that the structural weight is uniform across the span, with the center of gravity of the structure located at ⅓ of the chord behind the leading edge. In addition, the twin booms are attached to the wing at 2⅓ ft to 3⅔ ft away from the root. Therefore, the span-wise stations that fall within this distance will have to carry the additional weight of the booms. The total fuel required is 183.4 lb, or 91.7 lb of fuel per wing. We designed our fuel tank to carry 101 lb of fuel per wing or 15 lb of extra fuel than what is required for the entire mission. The fuel container is assumed to be a container that has the following rectangular cross section at each span-wise station:

Figure 20.1: Fuel tank position in airfoil.

The length of the fuel tank at each station is ½ of the chord length and the height is 45% of the maximum airfoil thickness. Since the structural wing box covers 50% of the chord, the design of the fuel tank ensures that the fuel container is contained within the wing box. After determining all the forces acting on the wing, the resultant loads on the wing can be determined. The forces are decomposed along the reference axes and then added together to give the resultant loads along the reference axes, namely VX, VZ, MT, MX and MZ. 20.4 Maximum Wing Loading The wing loading distribution will be performed at the four critical design points as indicated in the V-n diagram, for both empty-fuel and full-fuel configurations. The following five graphs show the various load distributions that the wing is subjected to.

0.5c

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Figure 20.2: Comparision of vertical shear loading Vz at various design points.

From the above Vz graph, the maximum shear force in the z-direction will occur at Design Point D for the full-fuel configuration. Design Point D corresponds to low positive angle of attack. A kink in the Vz graph can be noticed at ⅓ ft to 3⅔ ft from the root, which is caused by the offset from the fuel and twin boom inertial loads.

Figure 20.3: Comparison of horizontal shear loading Vx at various design points.

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From the above Vx graph, the wing experiences the most x-direction shear force at Design Point A, which corresponds to high positive angle of attack at full-fuel configuration.

Figure 20.4: Comparison of torsional moment distribution MT at various design points.

The above graph shows the torsional moment distribution about the y-axis. The maximum torsion will occur at Design Point E for the empty-fuel configuration.

Figure 20.5: Comparison of bending momnet distribution about the x-axis Mx at various design points.

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The Mx graph shows that the maximum bending moment about the x-axis occurs at Design Point D, which corresponds to low positive angle of attack, for the full-fuel configuration.

Figure 20.6: Comparing of bending moment about the z-axis Mz at various design points.

The Mz graph shows the bending moment distribution along the span of the wing about the z-axis. The maximum bending moment will occur at Design Point A, which corresponds to high-positive angle of attack, for the full-fuel configuration. The following table presents the maximum shear stress and moments that the wing will experience at 0% span (wing root), 27% span, 60% span and 75% span. Wing structural analysis will be performed at these four cross-sections at the design points where the wing experiences maximum shear stresses and moments.

0% span 27% span 60% span 75% span Design Point Vz (lbf) 871.1 670 332.5 179.6 D (Fuelled) Vx (lbf) -223.4 -148.3 -61.5 -28.6 A (Fuelled) MT (lbf-ft) 441.7 314.2 156.8 93.7 E (Empty) Mx (lbf-ft) 5655 2990 760 250.3 D (Fuelled) Mz (lbf-ft) 46.9 29.7 10.1 3.81 A (Fuelled)

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21. Wing Structure During flight, the aerodynamic loads from drag and lift will place the wing structure in bending as well as torsion. For the stability and safety of the aircraft, it is crucial that any loading up to the limit loads of the aircraft not cause permanent deformation of the wing. The wing cross section will be examined and defined in four locations: at 75% of the span (a required location), at 60% of the span (the fuel tank is present from 0% of the span up to 60%), at 27% of the span (note that the cross section at 25% of the span is required to be examined, however 27% represents the edge of boom, and clearly it makes more sense to define the structural cross section at this point rather than at 25%), and lastly at 0% of the span. For this analysis, the cross section will be assumed constant between analyzed locations. Thus, the cross section at 75% will be the constant cross section between 75% and 100%, the cross section at 60% will be the constant cross section between 60% and 75%, and so on. Note that this is conservative since the stress the cross section needs to carry increases from the tip chord to the root chord. The right hand coordinate system being used in this analysis is defined as follows: +y outboard of the left side of the aircraft, +x forward to the nose of the aircraft, and +z is vertical (up). 21.1 Wing Cross Section The overall layout of a cross section of the wing at an arbitrary wing station is shown Figure 21.1. There are two spars (numbered 5 and 6) and four flanges acting as spar supports (numbered 1, 2, 3, and 4). Note that angle spars are being used since they are relatively easy to machine to variable area cross sections that retain their overall shape compared to ‘hat’ and ‘zee’ stringers. Since the Big Brother 4000XL is a relatively small aircraft, 0.032” thick 2024-T3 clad aluminum will be used for the skin in the analysis of the aircraft. This thickness of skin is assumed due to manufacturing and assembly concerns.

Figure 21.1: Cross section of the wing at an arbitrary wing station. Note the stringers and flanges are not

drawn to scale with the airfoil shape.

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21.2 Loads The critical loads for each spanwise station under consideration are shown in Table 21.1. Note that the bending loads and shear loads (Mx, Mz, Vz, and Vz) correspond to Design Point D on the V-n Diagram of the aircraft at maximum weight. The twisting moment (MT,) corresponds to Design Point E on the V-n Diagram of the aircraft at maximum weight. Station Vz (lbf) Vx (lbf) Mt (ft-lbf) Mx (ft-lbf) Mz (ft-lbf) 75% 164.4 11.70 91.45 213.9 -1.54 60% 325.7 18.37 154.0 732.0 -3.01 27% 670.0 31.59 304.2 2,989.5 -6.35 0% 871.1 42.76 417.9 5,654.8 -8.99

Table 21.1: Critical loading at the spanwise stations being analyzed. 21.3 Wing Bending Bending forces on the wing are created by the lift and drag forces across the span of the wing. The majority of these stresses will be carried by the flanges that are reinforcing the wing and supporting the spars. These items are shown in Figure 21.1. Also note that the skin in the vicinity of the rivet rows attaching the stringers and flanges to the skin of the aircraft will carry some of this bending stress within an effective width. The analysis in this section follows what is outlined by E.F. Bruhn in Chapter 19 of Reference 14. Note that because of the low wing loading, the inclusion of stringers in the design of the aircrafts wing is not necessary. 20.3.1 Effective Skin Width While the bending stresses of the wing in flight are primarily carried by the stringers and flanges of the wing, the full width of skin in tension can be considered to carry some of this load, and an effective width of skin in compression will also carry some of the bending load. The effective width is defined since the thin sheets that comprise skin tend to buckle at low loads, and the stress in the skin varies in between the stringers, as is shown in Figure 21.2.

Figure 21.2 The stress distribution of stiffeners and sheet. Note that the stress on the sheet is variable. [14]

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Instead of trying to account for this variable stress in the sheet, the effective width is defined for ease of calculation by determining the width of skin around a stiffener over which the stress is constant. Graphically, this is shown in Figure 21.3. Note that the width is defined per row of rivets attaching the stiffener to the skin. The equation used for the effective width (w) in this report is dependent upon the skin thickness (t), the modulus of elasticity of the skin (E), as well as the stress in the stringer (σst). This formula is shown in Eqn. 21.1.

st

Etwσ

**90.1*2 = (Eqn. 21.1)

Figure 21.3: The effective skin width. Note that the stress over the width is constant. [14]

Note, however, that when the skin is in tension, there is no effective width, and the entire width of the skin is assumed to carry load. 21.3.2 Allowables As stated before, the material making up the skin of the aircraft is 2024-T3 clad aluminum sheet. From Mil-Handbook 5-J, Reference 23, the material allowables are shown below in Figure 21.4. Note that the compression yield value for 0.032” thick sheet, 36 ksi, is the critical value for design considerations in bending. For the shear flow calculations, the ultimate shear allowable is 37 ksi.

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Figure 21.4: Mechanical properties of 2024-T3 Aluminum. [15]

The material comprising the stiffeners is 2024-T351 clad aluminum extrusions. Once again from Mil-Handbook 5-J, the material allowables are shown below in Figure 21.5. As with the sheet, the critical allowable is the compression yield stress, in this case 34 ksi.

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Figure 21.5: Mechanical properties of 2024-T3 Aluminum. [15]

21.3.3 Margin of Safety While passenger aircraft are required by FAR Part 23 and 25 to maintain design margins of safety of 1.50, military aircraft are not so strictly regulated, and there is leeway in determining the appropriate margin of safety levels for the aircraft. As this is an unmanned drone, we believe that a margin of 1.50 would be over designing the flight vehicle, and that a margin of safety of 1.35 is adequate. Additionally note that if the margin of safety is in excess of +3.00, it will be noted as +HIGH. A sample calculation of the steps to calculating the margin of safety for the wing elements in bending is shown below inTable 21.2. For a more complete explanation of the calculations that went into this table, refer to Appendix G. The margin of safety equation is shown in Eqn. 21.2, and is dependent on the applied stress as well as the allowable stress. Note that the minimum margin of safety in the wing section at 27% of the span is +HIGH, which surpasses the 35% established in the above paragraph.

1.. −=essAppliedStrtressAllowableSSM (Eqn. 21.2)

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Wing Station: 27% Chord: 34.932 inchesFlange No Strng A Rivet Rows Total Area Z' AZ' AZ'2 X' AX'

1 0.008 1 0.12787249 3.2027404 0.40954 1.311658 6.88 0.8798252 0.008 1 0.153584285 2.7005231 0.41476 1.120063 24.3 3.7318723 0.1756736 1 0.1756736 -1.189365 -0.20894 0.248506 24.3 4.2686094 0.1756736 1 0.1756736 -2.081353 -0.36564 0.761024 6.88 1.20872

Totals 0.632803974 0.24972 3.441251 10.08903Flange No AX'2 AX'Z' Z=Z'-Zbar X=X'-Xbar Sigmab P=sigb*A M.S. Pass?

1 6.053623041 2.81785076 2.80811352 -9.06288 -2766.03 -353.7 11.3 Yes2 90.67897138 10.078005 2.305896156 8.3551584 -1875.29 -288.014 17.1 Yes3 103.7209074 -5.07693335 -1.583991636 8.3551584 1641.56 288.379 21.5 Yes4 8.316579711 -2.51577296 -2.475980256 -9.06288 2011.32 353.335 17.4 Yes

Totals 208.7700815 5.30314949 -5.7E-14 Table 21.2: A sample margin of safety results made at 27% of the span. For a more thorough explanation,

refer to Appendix G. In Table 21.3 the minimum margin of safety present at each spanwise station is noted. Clearly the margins are well above what is required, however the stringer areas have not been further reduced so as to not make machining impractical. Note that all stringer areas are 0.032 square inches from 0% of the span to 27% of the span, and 0.008 square inches starting at 27% of the span and extending to the tip of the wing. All of the individual stringer areas as well as their corresponding margins of safety are presented in Appendix G. 75% Span 60% Span 27% Span 0% Span Minimum M.S. +HIGH +HIGH +HIGH +HIGH Table 21.3: Minimum margins of safety at each span of the wing. Note that these margins vastly exceed what

is required, however stringer areas have not been reduced out of manufacturing concerns [16]. 21.4 Wing Torsion Aerodynamic forces on the wing create a torsional moment on the wing, denoted Mt in the loads section above. This twisting action causes a shear flow in the skin covering the wing, as well as in the forward and aft spars. Only the skin is assumed to carry this shear flow.

21.4.1 Shear Flow The shear center is the point in a cross section of a structure about which applied forces cause the structure to only bend, and not twist. When the twisting moment MT is applied about this point, it creates pure shearing stresses in the skin of the wing. Externally applied forces Vx and Vz create additional shear stresses if these forces are not applied at the shear center of the cross section of our wing. We calculated the shear flow in each section of the wing making use of the Matlab code provided, written by Nagaraj Banavara. As input, this code takes the location and cross sectional areas of the stringers and sparcaps, as well as the location and thicknesses of the spars and the aircraft skin. The input forces of MT, Vz, and Vx are used to compute the shear stress present in each section of the skin, as well as the stress present in the spars of the aircraft.

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It is important to note that the trailing edge section of the wing is assumed to provide no structural support in the calculation of the stresses in the rest of the wing. 21.4.2 Shear Stresses As in the wing bending section, the shear flow in the wing is evaluated at four spanwise stations of the wing at 0%, 27%, 60%, and 75%. The resulting shear flows, spar thicknesses, and margins of safety for the wing stations at 75%, 60%, and 0% are shown in Appendix G. A sample table of results is presented in Table 21.4 for the wing station at 27%. Note that the stringers and spars for the wing were designed around the critical Tresca stresses, as is shown by the low margins of safety for the Tresca stresses given in the next section. Section Thickness

(inches) Shear Flow (lbf/in)

Applied Shear (psi)

Allowable Shear (psi)

M.S.

Leading Edge 0.032 -600.54 18,766 37,000 +0.97 Front Spar 0.032 -299.36 9,355 37,000 +2.95 Rear Spar 0.050 1,303.68 26,073 37,000 +0.41 Wing Skin (greatest)

0.032 -818.62 25,581 37,000 +0.44

Table 21.4: Shear flow information for the wing at the 27% station. To stay within the required margins of safety, the rear spar thickness is 0.050” from 0% of the span to 60% of the span, and 0.032” until the tip of the wing. The forward spar thickness is 0.032” along the entire span. 21.5 Tresca Yield Criterion While the various sections of the wing have passed the set margin of safety of 1.35 without experiencing yielding in both bending and shear flow, the structure needs to be checked to ensure that the combination principle stresses do not exceed the yield stress of the material. This can be checked through use of the Tresca Yield Criterion. 21.5.1 Principle Stresses The principles stresses can be easily found by using Mohr’s Circle after using the plane stress assumption. A plane stress representation of Mohr’s Circle is shown in Figure 21.6, and the relationships that can be derived from it follow.

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Figure 21.6: Mohr’s Circle is a graphical representation for finding the principal stresses given the normal

stresses acting on a body. Note that the diagram shown assumes a plane stress situation, and has been adapted from [14].

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max 2 zxz τ

στ +⎟

⎠⎞

⎜⎝⎛= (Eqn. 21.3)

2maxmax

zn

στσ += (Eqn. 21.4)

maxmin 2τ

σσ −= z

n (Eqn. 21.5)

These three equations give what the principal stresses on the body are given the applied stresses. Note that τmax (the Tresca stress) is equal to half the difference between the maximum stress and the minimum stress. 21.5.2 Tresca Stresses and Margin of Safety From the bending and shear analysis sections, the maximum stresses in each spanwise section are given in Table 21.5. Note that both the maximum tension stresses as well as the maximum compressive stresses are shown. Whichever value has the greater magnitude will be used to calculate the normal stresses and the Tresca stress. The margin of safety for the Tresca stress is then calculated with the 2024 T3 aluminum shear allowable of 37 ksi, as is shown in Figure 21.4. Recall that by using the margin of safety equation given in (Eqn. 21.2), this value in Table 21.5 must be greater than 0.35.

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Spanwise Station 0% 27% 60% 75%Max Shear (psi) 9,471 26,073 21,836 27,159Max Tension (psi) 3,002 2,011 588 29Max Compressive (psi) -5,352 -2,766 -221 -29Sigma_n max (psi) 11,343 24,727 21,727 27,144Sigma_n min (psi) -8,341 -27,493 -21,948 -27,174Tresca Stress (psi) 9,842 26,110 21,838 27,159Minimum Margin of Safety +2.76 +0.42 +0.69 +0.36

Table 21.5: Calculation of principal stresses and Tresca stress

The above margins of safety clearly indicate that the Tresca stress does not exceed the allowable stress at any spanwise station, however the Tresca stresses did prove to be the primary design driver as is evidenced by the low margins of safety in the table above.

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Appendix A: Aircraft Design Comparisons Unmanned aerial vehicles are being widely used for a variety of missions; from reconnaissance and surveillance since 1950s to their recent more advanced combat and artillery co-ordination roles. The UAV we are designing is primarily for long-duration border patrol and surveillance and is further constrained by the requirements stated on page iii. Based on the information provided, four existing UAVs that are similar to our design requirements are briefly described in this section to provide a preliminary idea of our UAV design. A.1 General Atomics RQ-1 Predator The Predator UAV, illustrated in Figure A.1, is a medium-altitude, long-endurance unmanned aerial vehicle that operates on a 914 Rotax pusher propeller engine that provides up to 100 hp. Its WTO is 2300 lbs, which exceeds our maximum WTO of 1000 lbs. Capable of carrying 450 lbs of payload and holding up to 650 lbs of fuel, it has a range of 454 miles, an endurance of up to 40 hrs and a ceiling height of 27,000 ft [17], which satisfy our mission requirements. It has a stall speed of 54 kts, cruise speed of 70-90 kts, and dash speed of 120 kts [18], of which only the cruise speed meets our requirement. The design is characterized by its ability to minimize drag, as the wing is tapered, unswept, and has a high aspect ratio. In addition, the configuration of each Predator UAV aircraft is such that it can be disassembled into six main components and loaded into a container, making it very mobile and operationally-ready for Intelligence, Surveillance, Target Acquisition, and Reconnaissance (ISTAR) missions.

Figure A.1: The Predator UAV in flight.

A.2 General Atomics GNAT-750 The GNAT-750, having served as the first long endurance unmanned reconnaissance aerial vehicle and as the predecessor of the modern Predator and Prowler II, makes for an excellent example of UAV design. This aircraft is illustrated in Figure A.2. With a maximum takeoff weight of 1131 lbs, the GNAT is slightly outside of our required weight class. However, since the GNAT was designed for a loiter endurance of over 30 hours (requiring 426 lbs of fuel) [19], simply reducing the fuel load to meet our 21 hour endurance requirement easily brings the maximum gross take-off weight down to 875 lbs and to within our weight class.

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Figure A.2: General Atomics GNAT-750 during flight.

From a design aspect, the GNAT appears almost identical to its offspring, the Predator. The primary element emphasized in the design appears to be the minimization of drag, as the wing is tapered, unswept, and has a high aspect ratio. In addition, the fuselage is straight and streamlined. In addition, with its inverted V-tail rather than a vertical fin and horizontal tail, drag as well as weight is reduced. Its primary propulsion system is a single Rotax 582 pusher propeller located at the aft-end of the aircraft. However, having a stall speed of 59 kts and a max speed of 115 kts, it is slightly shy of completely fulfilling our required specifications. A.3 Galileo Avionica Falco The Falco, illustrated in Figure A.3, is a medium altitude and endurance UAV system designed to fulfill electronic and optical surveillance roles. Weighing in at 926 lbs maximum at takeoff with a maximum payload weight of 154 lbs, the Falco meets both of the weight requirements for our aircraft design. It also meets our endurance requirements, with a maximum endurance of 14 hrs. The aircraft is powered by a 65 hp engine, giving it a maximum speed of 115 kts and an altitude ceiling of 19,700 ft [20]. Increasing the power of the engine would be necessary for this airframe to achieve our speed and ceiling requirements.

Figure A.3: Galileo Avionica Falco in flight.

The most distinct design features of the Falco are its slightly bent gull wings and its twin tail booms. The wings are mounted high on the fuselage, allowing optional external payloads of up to 55 lbs each to be attached to the external hard point located under each wing. The twin boom design accommodates the pusher prop configuration, which benefits wing efficiency by removing prop wash over the wing which would have been introduced in a tractor configuration. The twin boom configuration also allows the relatively heavy engine to be located near the center of gravity of the aircraft.

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A.4 IAI-MALAT Searcher Mk II Searcher Mk II, pictured in Figure A.4, is a multi-role UAV system used in the Israeli Air Force. Its missions include surveillance, reconnaissance, target-acquisition & artillery adjustment. It has some variants being exported to the Indian Air Force and Singapore Air Force. Searcher Mk II has a gross takeoff weight of 820 lbs, with maximum payload capability of 139 lbs. Its weight category is consistent with our design specifications. Its payload consists of Multi-Mission Optronic Stabilized Payload (MOSP), combined TV and forward looking infrared (FLIR) for both day- and night-time observation, and synthetic aperture radar. It is also equipped with a GPS system for real-time manual mission control. With a fuel capacity of 220 pounds, it can stay in air for up to 14 hours. Searcher Mk II is designed with a slightly swept-back wing and a twin-boom tail configuration. It is powered by a rear-mounted 35hp Sachs piston engine, capable of flying a maximum speed of 110 kts and cruise at 55 kts. It has a design ceiling of 18,500 ft [21]. By switching to a more powerful engine, it is capable of faster speed and higher flight ceiling.

Figure A.4: IAI-MALAT Searcher Mk II in flight.

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Appendix B: Aircraft Configuration History

Third Iteration Aircraft Design Drawings Aircraft Design as of 11/17—End of Engine Selection and Tail Sizing

32 ftCG = 6.09 ft from nose

15 ft

2.5 ft

1:125 Scale

2. ft

1:67 Scale

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Second Iteration Aircraft Design Drawings Aircraft Design as of 10/3—End of Initial Aerodynamic Design Iteration

37.7 ft CG = 5.87 ft from nose

15 ft

3 ft

1:125 Scale

1:67 Scale

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Appendix C: MATLAB Codes Used in Calculations In order to calculate the performance parameters of our UAV, a MATLAB code was implemented. This code was used to assist in calculations of the aircraft center of gravity, lift, drag, pitching moment, and flap effects. The code is presented as follows. Mainm.m % Mainm.m Last changes made 10/02/2006 UAV Team 2 (UAVarsity) % This is the main file which executes other functions This file assumes % that the user created the necessary input parameters. % Load Everythingv1.4m to load all necessary parameters needed. % Angle of Attack range n = 1; inc = 1; a(n,1) = alfamin; % CG.m calculates the CG location as well as xw (Distance between CG and % AC) [mo,y,aa,c,Sw,cwBar,taper,AR,St] = InputParameters(moairfoil,b,cr,ct,a0,agt,vstall,btail,ctail); [WING_W] = wingweight(AR,Sw,mthickwing); [Moment Mass cg_tot AC xw]=CG(WING_W,WING_X,TAIL_W,TAIL_X,POWER_W,POWER_X,FGEAR_W,FGEAR_X,RGEAR_W,RGEAR_X,FUEL_W,FUEL_X,FUS_W,FUS_X,CONTROL_W,CONTROL_X,TWIN_W,TWIN_X,SAR_X,SAR_W,EOI_X,EOI_W,ADDPAY_W,ADDPAY_X,PROP_W,PROP_X,DATA_W,DATA_X); W_TO = Mass; x = TAIL_X - WING_X; qflaps = input('1.Flaps Deployed \n2.Flaps Retracted \n3.Cruise \n4.Dash \n(Select number) : ','s'); if qflaps == '1' Df = input('Flap Deflection Angle (deg) : '); end % Create range of alfas from -10 to 20 degrees for CLmaxac calculation awr=linspace(-10,20,500); % The code is designed such that it will calculate takeoff condition with % stall velocity and sea level density if the flap deflection angle (Df) is % greater than 0. Else, the code will calculate the cruise/dash conditions. if qflaps == '1' [deltaAlphaLo clMaxF cmacF deltaCDflap SF] = flapFX(cfc, mo, Df, clmax, bflap, cmac, Sw, cr, taper, b,InboardFlapLoc); OutboardFlapLoc = InboardFlapLoc + bflap/2; for i = 1:1:101 if abs(y(i))< OutboardFlapLoc & abs(y(i))> InboardFlapLoc aa(i) = aa(i) - deltaAlphaLo; end end [CLFlapt CDiFlapt clflap] = LiftLineP(awr,y,aa,mo,c); dcl=1; J=0; while dcl>0 J=J+1; dcl=min(clMaxF-clflap(:,J)); end awStallFlap = awr(1,J); CLwmaxFlap = CLFlapt(J); runpermission = input('Do you want to generate max. cl plot?(y/n) ','s');

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if runpermission == 'y' figure plot(y,clflap(:,J),'k-',y,clMaxF,'k:'); xlabel('y (ft)'); ylabel('C_L');title('(C_L_m_a_x)_w Profile'); end CLmaxac=CLwmaxFlap.*(x./(x-xw)) + cmac.*(cwBar./(x-xw)); else [CLr, CDir, clr, cdir, AR1r, mr, AZLr, clbr, clar] = LiftLineP(awr,y, aa, mo, c); clmaxp=clmax*ones(101,1); dcl=2; J=0; while dcl>0 J=J+1; dcl=min(clmaxp-clr(:,J)); end awStall=awr(1,J); CLwmax=CLr(J); runpermission = input('Do you want to generate max. cl plot?(y/n) ','s'); if runpermission == 'y' figure plot(y,clr(:,J),'k-',y,clmax,'k:'); xlabel('y (ft)'); ylabel('C_L');title('(C_L_m_a_x)_w Profile'); end CLmaxac=CLwmax.*(x./(x-xw)) + cmac.*(cwBar./(x-xw)); end % This is the main for-loop which calculates the CL, CD, Lift, Drag at % various angles of attack. Again, when Df is greater than 0, the code will % calculate the cruise condition. Otherwise, it will calculate the takeoff % condition. % Not the best design of code. Code will be revised in the future to omit % unnecessary calculations that are made inside the for-loop. for alfa = alfamin:inc:alfamax aoa = alfa; if n > 1 a(n,1) = a(n-1,1) + inc; end Cmact(n,1) = Cmac_t(cmac,FusLength,FusDiameter,Sw,cwBar,aoa); if qflaps == '1' v = vstall; rho = rhosl; [deltaAlphaLo clMaxF cmacF deltaCDflap] = flapFX(cfc, mo, Df, clmax, bflap, cmac, Sw, cr, taper, b,InboardFlapLoc); Cmact(n,1) = Cmact(n,1) + cmacF; [CLFlap CDi] = LiftLineP(aoa,y,aa,mo,c); CLFlapv(n,1) = CLFlap; CLac = CLFlap.*(x./(x-xw)) + Cmact(n,1).*(cwBar./(x-xw)); [Cdtrim CLt] = trimmed_drag_coefficient (CLFlap,St,TAIL_X,WING_X,cwBar,Sw,clmax,xw,Cmact(n,1),btail,ctail); CLtail(n,1) = CLt; [Cdo a1 a2 a3 a4] = parasite_drag_coefficient(qflaps,rho,v,cwBar,ctail,btail,Sw,xcmwing,mthickwing,sweepwing,FusLength,FusDiameter,BoomLength,BoomDiameter,xcmtail,mthicktail,sweeptail,upsweepangle,propbladearea,PropDiameter,AirbrakeFrontalArea); [Cdtotal] = total_drag_coefficient (Cdo,deltaCDflap,CDi,Cdtrim);

C-3

CLoutput(n,1) = CLac; CDoutput(n,1) = Cdtotal; Lift(n,1) = 0.5*rho*v^2*CLoutput(n,1)*Sw; Drag(n,1) = 0.5*rho*v^2*CDoutput(n,1)*Sw; else [CL,CDi,cl,cdi,AR,m,AZL,clb,cla]=LiftLineP(aoa,y,aa,mo,c); deltaCDflap = 0; if qflaps == '2' rho = rhosl; v = vstall; end if qflaps == '3' rho = rhocr; v = vcruise; end if qflaps == '4' rho = rhodash; v = vdash; end [Cdtrim CLt] = trimmed_drag_coefficient (CL,St,TAIL_X,WING_X,cwBar,Sw,clmax,xw,Cmact(n,1),btail,ctail); CLtail(n,1) = CLt; CLv(n,1) = CL; CLac = CL.*(x./(x-xw)) + Cmact(n,1).*(cwBar./(x-xw)); [Cdo a1 a2 a3 a4] = parasite_drag_coefficient (qflaps,rho,v,cwBar,ctail,btail,Sw,xcmwing,mthickwing,sweepwing,FusLength,FusDiameter,BoomLength,BoomDiameter,xcmtail,mthicktail,sweeptail,upsweepangle,propbladearea,PropDiameter,AirbrakeFrontalArea); [Cdtotal] = total_drag_coefficient (Cdo,deltaCDflap,CDi,Cdtrim); CLoutput(n,1) = CLac; CDoutput(n,1) = Cdtotal; Lift(n,1) = 0.5*rho*v^2*CLoutput(n,1)*Sw; Drag(n,1) = 0.5*rho*v^2*CDoutput(n,1)*Sw; end n = n + 1; end % Calculate K A = ones(size(CLoutput),2); A(:,2) = CLoutput.^2; X = inv(A'*A)*A'*CDoutput; K = X(2,1); % Landing Gear Sizing FrontWheelW = 0.1*W_TO; RearWheelW = 0.9*W_TO/2; ADia = 1.51; BDia = 0.349; AWid = 0.715; BWid = 0.312; FrontWheelDia = ADia*(FrontWheelW^BDia); FrontWheelWid = AWid*(FrontWheelW^BWid); RearWheelDia = ADia*(RearWheelW^BDia); RearWheelWid = AWid*(RearWheelW^BWid); % Plots if qflaps == '1' figure plot(a,Lift)

C-4

hold on plot(awStallFlap,Lift) hold on plot(a,Mass) xlabel('Angle of Attack (Deg)'); ylabel('Lift (lbf)');title('Lift against Angle of Attack (Takeoff, With Flaps)') end if qflaps == '2' figure plot(a,Lift) hold on plot(awStall,Lift) hold on plot(a,Mass) xlabel('Angle of Attack (Deg)'); ylabel('Lift (lbf)');title('Lift against Angle of Attack (Takeoff, With Flaps)') end

InputParameters.m % This function calls the input paramters from the global space. % It assumes that the parameters loaded from Everythingv1.x.m function [mo,y,aa,c,Sw,cwBar,taper,AR,St] = InputParameters(moairfoil,b,cr,ct,a0,agt,vstall,btail,ctail) M = 100; theta = [0:pi/M:pi]'; taper = ct/cr; Sw = b*cr*(1+taper)/2; AR = b^2/Sw; y = -b*cos(theta)/2; c = 2*b*(1-(1-taper)*2*abs(y)/b)/AR/(1+taper); aat = -a0; aa = agt*2*abs(y)/b + aat; cwBar = (cr+ct)/2; mo = moairfoil*ones(101,1); St = btail*ctail;

wingweight.m function [WING_W] = wingweight(AR,Sw,mthickwing) B = (750*3.5*Sw*(1.9*AR-4))/(1+0.11*100*mthickwing); WING_W = 69*(B*10^-6)^0.69;

CG.m % This function calls the input paramters from the global space. % It assumes that the paramters are generated using InputCG.m function [Moment Mass cg_tot AC xw]=CG(WING_W,WING_X,TAIL_W,TAIL_X,POWER_W,POWER_X,FGEAR_W,FGEAR_X,RGEAR_W,RGEAR_X,FUEL_W,FUEL_X,FUS_W,FUS_X,CONTROL_W,CONTROL_X,TWIN_W,TWIN_X,SAR_X,SAR_W,EOI_X,EOI_W,ADDPAY_W,ADDPAY_X,PROP_W,PROP_X,DATA_W,DATA_X) Moment=WING_W*WING_X+TAIL_W*TAIL_X+POWER_W*POWER_X+FGEAR_W*FGEAR_X+RGEAR_W*RGEAR_X+FUEL_W*FUEL_X+FUS_W*FUS_X+CONTROL_W*CONTROL_X+TWIN_W*TWIN_X+SAR_X*SAR_W+EOI_X*EOI_W+ADDPAY_W*ADDPAY_X+PROP_W*PROP_X+DATA_X*DATA_W;

C-5

Mass=WING_W+TAIL_W+POWER_W+FGEAR_W+RGEAR_W+FUEL_W+FUS_W+CONTROL_W+TWIN_W+SAR_W+EOI_W+ADDPAY_W+PROP_W+DATA_W; cg_tot=Moment/Mass; AC=WING_X; xw = cg_tot-AC;

InputCG.m % When launched, it will prompt users to input the necessary parameters to run Main.m % Save the input parameters as filename.mat file such that it is easy to % load the parameters in the future. prompt={'WING_W','WING_X','TAIL_W','TAIL_X','POWER_W','POWER_X','FGEAR_W','FGEAR_X','RGEAR_W','RGEAR_X','FUEL_W','FUEL_X','FUS_W','FUS_X','CONTROL_W','CONTROL_X','TWIN_W','TWIN_X','SAR_W','SAR_X','EO/I_W','EO/I_X','Additional Payload','Additional Payload_X'}; title='Aircraft Properties'; answer=inputdlg(prompt,title); WING_W=sscanf(char(answer(1)),'%f'); WING_X=sscanf(char(answer(2)),'%f'); TAIL_W=sscanf(char(answer(3)),'%f'); TAIL_X=sscanf(char(answer(4)),'%f'); POWER_W=sscanf(char(answer(5)),'%f'); POWER_X=sscanf(char(answer(6)),'%f'); FGEAR_W=sscanf(char(answer(7)),'%f'); FGEAR_X=sscanf(char(answer(8)),'%f'); RGEAR_W=sscanf(char(answer(9)),'%f'); RGEAR_X=sscanf(char(answer(10)),'%f'); FUEL_W=sscanf(char(answer(11)),'%f'); FUEL_X=sscanf(char(answer(12)),'%f'); FUS_W=sscanf(char(answer(13)),'%f'); FUS_X=sscanf(char(answer(14)),'%f'); CONTROL_W=sscanf(char(answer(15)),'%f'); CONTROL_X=sscanf(char(answer(16)),'%f'); TWIN_W=sscanf(char(answer(17)),'%f'); TWIN_X=sscanf(char(answer(18)),'%f'); SAR_W=sscanf(char(answer(19)),'%f'); SAR_X=sscanf(char(answer(20)),'%f'); EOI_W=sscanf(char(answer(21)),'%f'); EOI_X=sscanf(char(answer(22)),'%f'); ADDPAY_W=sscanf(char(answer(23)),'%f'); ADDPAY_X=sscanf(char(answer(24)),'%f'); prompt={'filename desired for .mat file'}; title='File name'; filename=char(inputdlg(prompt,title)); save(filename,'WING_W','WING_X','TAIL_W','TAIL_X','POWER_W','POWER_X','FGEAR_W','FGEAR_X','RGEAR_W','RGEAR_X','FUEL_W','FUEL_X','FUS_W','FUS_X','CONTROL_W','CONTROL_X','TWIN_W','TWIN_X','SAR_W','SAR_X','EOI_W','EOI_X','ADDPAY_W','ADDPAY_X');

flapFX.m % This function calculates the changes in wing properties when flaps are % deployed. Input parameters consists of airfoil properties as well as flap % chord, span and wing surface area. function [deltaAlphaLo clMaxF cmacF deltaCDflap SF] = flapFX(cfc, mo, Df, clmax, bflap, cmac, Sw, cr, taper, b,InboardFlapLoc) %This function calculates the change in sectional properties of a wing with %a flap, given the input parameters of flap geometry and sectional %characteristics. A plain flap is assumed, but equations for split and %slotted flaps are included if the type of flap is to be modified.

C-6

deltac = 0; % No slotted flaps moF = max(mo); c0 = cfc*cr*(1+2*InboardFlapLoc*(taper-1)/b); cn = cfc*cr*(1+2*(InboardFlapLoc + bflap/2)*(taper-1)/b); SF = bflap*(c0+cn)/2; %Zero-Lift Angle of Attack %(Plain assumed) tau = 4.375E+00*cfc^3 - 6.500E+00*cfc^2 + 3.775E+00*cfc + 9.059E-14; eta = 7.292E-09*Df^5 - 1.581E-06*Df^4 + 1.277E-04*Df^3 - 4.560E-03*Df^2 + 5.759E-02*Df + 5.679E-01; %Plain %eta = 2.7778E-07*Df^3 - 1.4881E-05*Df^2 - 3.6409E-03*Df + 5.7714E-01; %Split %eta = 1.4583E-07*Df^4 - 1.8472E-05*Df^3 + 6.3958E-04*Df^2 - 1.1897E-02*Df + 8.8071E-01; %Slotted deltaAlphaLo = -tau*eta*Df; %Section Maximum Lift Coefficient %(Plain or Split assumed) deltacl = moF*tau*eta*Df; deltaClMaxOdeltaCl = 5.5611*cfc^5-17.817*cfc^4+20.665*cfc^3-9.8256*cfc^2+.4242*cfc+.9924; %Plain or Split %deltaClMaxOdeltaCl = 137.12*cfc^5 - 128.31*cfc^4 + 26.886*cfc^3 - 1.113*cfc^2 - .2078*cfc + 1.003; %Slotted clMaxF = clmax + deltaClMaxOdeltaCl*deltacl; %Section Pitching Moment Coefficient %(Plain, Split, Slotted assumed) deltaCmOdeltaCl = -0.1246*cfc^2+0.3849*cfc-0.2576; %Plain, Split, or Slotted cmacF = deltaCmOdeltaCl*deltacl; %Drag due to Flaps %(Plain or Split assumed) deltaCDflap = 1.7*cfc^1.38*(SF/Sw)*(sin(Df*pi/180))^2; %Plain or Split %deltaCD = 0.9*cfc^1.38*(SF/Sw)*(sin(Df))^2; %Slotted

LiftLineP.m function [CL,CDi,cl,cdi,AR,m,AZL,clb,cla]=LiftLineP(aw,y,aa,mo,c) %LiftLine determines the performance of a wing using Glauert's solution % method of the lifting-line-theory wing equation. %Version: 2.0 %Code: Luis P Bernal %Date: 9/18/05 if nargin~=5 % Check number of input arguments error(['LiftLine input error: Incorrect number',... ' of input arguments']) end; [NMO,MMO]=size(mo);[NC,MC]=size(c); [ny,MY]=size(y);[NAA,MAA]=size(aa); if MY~=1|1~=MMO|1~=MC|1~=MAA|ny~=NMO|ny~=NC|ny~=NAA error(['LiftLine input error: Section input arrays ',... 'must be column vectors of the same length']) end; [MAW,M]=size(aw); if MAW~=1 error(['LeftLine input error: aw must be a row vector']); end; % Require a minimum of 5 sections including the % wing tip sections and the midspan section. if ny<5|mod(ny,2)~=1 error(['LiftLine input error: Section input arrays ',... 'must contain at least 5 elements and the length',...

C-7

' must be an odd numebr']) end; % Verify that the wing planform is symmetric and % includes the symmetry plane ns=fix(ny/2)+1; if y(1:ns)~=-y(ny:-1:ns)|abs(y(ns))>0.00001 error(['LiftLine input error: The y locations must ',... 'be symmetric about the center plane and',... ' include the symmetry plane']) end; if c(1:ns)~=c(ny:-1:ns) error(['LiftLine input error: The c values must ',... 'be symmetric about the center plane']) end; % If chord at wing tips zero make it finite if c(1) < 0.0001*c(ns) c(1)=0.0001*c(ns);c(ny)=c(1); end; if aa(1:ns)~=aa(ny:-1:ns) error(['LiftLine input error: The at values must ',... 'be symmetric about the center plane']) end; %Evaluate constants including the wing Aspect Ratio. aw=aw*pi/180;aa=aa*pi/180;mo=mo*180/pi; mc=mo.*c;b2=abs(y(1));mcs=mc(ns);b=2*b2;P=mcs/4/b; S=abs(trapz(y,c));AR=b^2/S; % Initialize arrays theta=zeros(ny,1);st=theta;snt=zeros(ny,ny);B=snt;BI=snt; clb=theta;cla=theta;Ao=theta;A2=theta;AA=theta; aat=zeros(ny,M);A=aat; CL=zeros(1,M);CDi=CL;cl=zeros(ny,M);cdi=cl; % Evaluate the coefficient matrix, B theta=acos(y/b2);st=sin(theta); for j = 1:ny for n = 1:ny snt(j,n)=sin(theta(j)*n); if theta(j)==0 B(j,n) = n^2*P; elseif theta(j)==pi B(j,n) = n^2*P*(-1)^(n-1); else; B(j,n) = snt(j,n)*(mcs/mc(j)+P*n/st(j)); end; end; end; % Compute the lift and induced drag coefficients % for different wing angles of attack aat=repmat(aw,ny,1)+repmat(aa,1,M); % Construct the absolute angle of attack % array including all cases A=B\aat; %Compute the An coefficients % Find wing lift and induced drag coefficient CL=P*pi*AR*A(1,:); % Find CL CDi=(P^2*pi*AR)*(diag((repmat([1:ny]',1,M).*A)'*A))'; %Find CDi % Find section lift coefficient and induced drag % coefficient distributions cl=mcs*(snt*A)./repmat(c,1,M);cdi=cl.*(aat-cl./repmat(mo,1,M)); % Find the An coefficients for the % 'Basic' and 'Additional' lift coefficient distributions if M==1 Ao=A;aa1=aa+0.1;A2=B\aa1;daa=0.1; else

C-8

Ao=A(:,1);A2=A(:,2);daa=aw(2)-aw(1); end; AA=(A2-Ao)/daa; % Find m, AZL and circulation distributions m=P*pi*AR*AA(1);AZL=aw(1)-Ao(1)/AA(1);Ab=Ao+(AZL-aw(1))*AA; cla=(snt*AA)*mcs/m./c;clb=(snt*Ab)*mcs./c; AZL=AZL*180/pi;m=m*pi/180; % convert to degrees

Cmact_t.m % This function calculates the Cmact % Cmac of the wing is Cmac of the airfoil section as our wing is unswept % and has no taper. % Cmac of fuselage is calculated using the formula described above. % Cmac change due to the flaps are implemented in the flap section. function [Cmact] = Cmac_t(cmac,FusLength,FusDiameter,Sw,cwBar,aoa) KF = 0.045; cmfus = KF*FusDiameter^2*(FusLength)*aoa/(cwBar*Sw); Cmact = cmac + cmfus;

trimmed_drag_coefficient.m % This function calculates the trimmed drag coefficient. function [Cdtrim CLt] = trimmed_drag_coefficient (CL,St,TAIL_X,WING_X,cwBar,Sw,clmax,xw,Cmact,btail,ctail) x = TAIL_X - WING_X; ARt = btail^2/(St); %Tail volume coefficient, should have value around .9 for turboprops vht=(x*St)/(cwBar*Sw); %Lift coefficient of the tail CLt =(CL*xw/cwBar+Cmact)*x/(x-xw)*1/vht; %Oswald efficiency factor for the tail et=1.78*(1-.045*ARt^.68)-.64; %OUTPUT, trimmed drag coefficient Cdtrim=CLt.^2./(pi*et*ARt)*(St/Sw);

parasite_drag_coefficient.m % This function calculates the parasite drag coefficient % Wing, Tail, Fuselage, Boom properties as well as density and velocity % values are necessary to calculate this coefficient. function [Cdo a1 a2 a3 a4] = parasite_drag_coefficient (qflaps,rho,v,cwBar,ctail,btail,Sw,xcmwing,mthickwing,sweepwing,FusLength,FusDiameter,BoomLength,BoomDiameter,xcmtail,mthicktail,sweeptail,upsweepangle,propbladearea,PropDiameter,AirbrakeFrontalArea) mju = 3.62e-7; a = 1116.437; %Wing (the wing is represented as 1) WingRe = Re(rho,v,cwBar,mju);

C-9

if WingRe < 500000 Cfwing = 1.328/sqrt(WingRe); else Cfwing = 0.455/((log10(WingRe)).^2.58*(1+0.144*(v/a).^2).^0.65); end FF1=(1+.6/(xcmwing)*(mthickwing)+100*(mthickwing)^4)*(1.34*(v/a)^.18*cos(sweepwing*pi/180)^.28); Q1 = 1; %Fuselage (the fuselage is represented as 2) FusRe = Re(rho,v,FusLength,mju); if FusRe < 500000 Cffus = 1.328/sqrt(FusRe); else Cffus = 0.455/((log10(FusRe))^2.58*(1+0.144*(v/a)^2)^0.65); end f2=FusLength/FusDiameter; FF2=(1+60/f2^3+f2/400); Q2=1; %Booms (the booms are represented as 3) BoomRe = Re(rho,v,BoomLength,mju); if BoomRe < 500000 Cfboom = 1.328/sqrt(BoomRe); else Cfboom = 0.455/((log10(BoomRe))^2.58*(1+0.144*(v/a)^2)^0.65); end f3=BoomLength/BoomDiameter; FF3=(1+60/f3^3+f3/400); Q3=1; %Tail (the tail is represented as 4) TailRe = Re(rho,v,ctail,mju); if TailRe < 500000 Cftail = 1.328/sqrt(TailRe); else Cftail = 0.455/((log10(TailRe))^2.58*(1+0.144*(v/a)^2)^0.65); end FF4=(1+.6/(xcmtail)*(mthicktail)+100*(mthicktail)^4)*(1.34*(v/a)^.18*cos(sweeptail*pi/180)^.28); Q4=1.08; % Calculating Cdmis, drag contribution of components with large form drag (fuselage % upsweep, propellar and speed brakes) % Fuselage Upsweep (the fuselage upsweep is represented as 5) Dq5=3.83*upsweepangle*(pi/180)*pi*FusDiameter^2/4; % Propellar, feathered (the propellar is represented as 6) % Dq6=0.1*propbladearea*pi*PropDiameter^2/4 % Propellar is assumed to be running at all times Dq6 = 0; %Speed Brakes (the speed brakes are represented as 7) Mlanding = (1.15*v)/a; Dq7=(.139+.419*(Mlanding-.161)^2)*AirbrakeFrontalArea; if qflaps == '1' | qflaps == '2'| qflaps == 1 | qflaps == 2 Cdmis=(1/Sw)*(Dq5+Dq6+Dq7+0.25); else Cdmis=(1/Sw)*(Dq5+Dq6+Dq7); end %Calculating Cdo

C-10

Cdo1=1/Sw*((Cfwing*FF1*Q1*Sw*2)+(Cffus*FF2*Q2*44.7)+(Cfboom*FF3*Q3*22*2)+(Cftail*FF4*Q4*ctail*btail*2))+Cdmis; a1 = (Cfwing*FF1*Q1*Sw*2)/Sw; a2 = (Cffus*FF2*Q2*44.7)/Sw; a3 = (Cfboom*FF3*Q3*22*2)/Sw; a4 = (Cftail*FF4*Q4*ctail*btail*2)/Sw; %Leakage Drag Cdlp=.08*Cdo1; Cdo = Cdo1 + Cdlp;

Re.m % Reynolds Number function. % Inputs are rho(density), v(velocity), l(characteristic length), % mju(coefficient of viscosity) function a = Re(rho,v,l,mju) a = rho*v*l/mju;

total_drag_coefficient.m % Input parameters : % Cdo : Parasite Drag Coefficient % deltaCDflap : Drag increased due to the flap % CDi : Induced Drag % Cdtrim : Trimmed Drag function [Cdtotal] = total_drag_coefficient(Cdo,deltaCDflap,CDi,Cdtrim) Cdtotal = Cdo + deltaCDflap + CDi + Cdtrim;

Density.m %This function takes calculates the air density for a given altitude in %English units. function [rho] = density(h) %Code taken from McClamroch's notes Chp 2 Pg 15 and verified with standard %atmosphere tables in Appendix A and also with online sources. %Variables %h: altitude (ft) %rho: air density (slugs/ft^3) %Prepared by Zhiwei Song %=======predefined constants=========== a0 = -6.5e-3; g = 9.80665; mol = 28.9644; R0 = 8.31432; R = R0/mol*1e3; T0 = 288.15; p0 = 1.01325e5; rho0 = 1.225; %=======================================

C-11

h = h*0.3048/1000; %Converting altitude in ft to km T = T0 + a0*h*1e3; %Calculating temperature at altitude h p = p0.*(T./T0).^(-g/a0/R); %Calculating pressure at altitude h rho = rho0.*(T./T0).^(-g/a0/R-1); %Calculating density at altitude h in kg/m^3 rho = rho*0.00194032; %Converting density to slugs/ft^3 return thrust_levelflight.m function [T, V_minthrust, S_minthrust, CL_minthrust] = thrust_levelflight(V, rho, S, CD_o, W, K) %This function calculates thrust required for steady level flight given %true air speed, air density, wing area, parasitic drag coefficient, %weight, and K. % %Formulas taken from notes Aircraft Performance pg 6 %Input parameters can be row vectors if needed. %Variables: %Inputs: %V: True air Speed (ft/s) %rho: Air Density (slugs/ft^3) %S: Wing Area (ft^2) %CD_o: Parasitic Drag Coefficient %W: Aircraft Weight (lbf) %K: Aerodynamic parameter %Outputs: %T: Thrust (lbf) %V_minthrust: Speed for minimum thrust (ft/s) %S_minthrust: Wing area for minimum thrust (ft^2) %CL_minthrust: Lift coefficient at minimum thrust %Written by Zhiwei Song T = (0.5.*rho.*(V.^2).*S.*CD_o) + ((K.*(W.^2))./(0.5.*rho.*(V.^2).*S)); V_minthrust = ( (2./rho).*(W./S).*((K./CD_o).^0.5)).^0.5; S_minthrust = (2*W./(rho.*(V.^2))).*((K./CD_o)^0.5); CL_minthrust = (CD_o./K).^0.5; return

Power_levelflight.m %This function calculates power required for steady level flight given %a range of true air speeds, altitude, wing area, parasitic drag coefficient, %weight, and K. It also plots the actual available power of the engine %given the power of the engine(ideal) at sea level. function [V_max, P_needed] = power_levelflight(V_initial, V_final, h, P_engine, D_prop, S, CD_o, W, K, plotvariable) % %Formulas taken from notes Propulsion System Design pg 14 %Variables:

C-12

%Inputs: %V_initial & V_final: Provides the bounds of which to iterate V % across (kts) %h: Altitude (ft) %P_engine: Power of the uninstalled engine at sea % level (hp) %D_prop: Diameter of propeller (ft) %S: Wing Area (ft^2) %CD_o: Parasitic Drag Coefficient %W: Aicraft Weight (lbf) %K: Aerodynamic parameter %plotvariable: Boolean Variable that determines whether % function plots the power curves %Outputs: %P_needed: Power required for steady level flight % (hp) %V_max: Maximum airspeed (kts) %Transients: %V: A row vector containing airspeeds %rho: Air density (slugs/ft^3) %A_prop: Area of propeller (ft^2) %T: Thrust (lbf) %CT: Coefficient of thrust %eta_i: Propeller efficiency coefficient %P_engine_i: Ideal power output of the engine in flight at altitude % (hp) %Written by Zhiwei Song V = [V_initial:0.1:V_final]*1.68780986; %Creating a row vector of test airspeeds %in ft/s rho = density(h); A_prop = pi*(D_prop/2); %Calculating the various parameters at each test airspeed for i = 1:size(V,2) T(i) = thrust_levelflight(V(i), rho, S, CD_o, W, K); CT(i) = T(i)/(0.5*rho*(V(i)^2)*A_prop); eta_i(i) = 2/(1+sqrt(1+CT(i))); P_needed(i) = T(i)*V(i)/eta_i(i)*0.001818182; P_engine_i(i) = P_engine*0.85*eta_i(i)*rho/density(0); end %Calculating maximum attainable air speed if P_engine_i(size(V,2)) < P_needed(size(V,2)) %Check that power needed exceeds %power available for j = 1:size(V,2) error(j) = abs(P_needed(j) - P_engine_i(j)); end counter = find(error == min(error)); %Entry where minimum error occurs V_max = V(counter); else display('V_max does not fall within specified air speed range. Please redefine range of V'); V_max = 'not found'; end V = V.*0.592483801; V_max = V_max.*0.592483801; if plotvariable == 1 plot(V,P_needed,V,P_engine_i) xlabel('True Air Speed, V (kts)'); ylabel('Power (hp)'); title('Plot of Airspeed versus Power Needed and Power Output'); legend('Power Needed for Level Flight','Power Provided By Engine'); end

C-13

return

flight_envelope.m %This function plots the flight envelope of the aircraft. function [V_max,V_min,V_stall] = flight_envelope(h, P_engine, D_prop, S, CD_o, W, K,CL_max) %Variables: %Inputs: %h: A row vector of altitudes at which to determine % V_max (ft) %P_engine: Power of the uninstalled engine at sea % level (hp) %D_prop: Diameter of propeller (ft) %S: Wing Area (ft^2) %CD_o: Parasitic Drag Coefficient %W: Aicraft Weight (lbf) %K: Aerodynamic parameter %Outputs: %V_max: Maximum airspeed possible with available power % (kts) %V_min: Minimum airspeed possible with available % power from engine (kts). Note that this is % not the same as the stall speed that is % determined by aerodynamic properties of the % aircraft. %V_stall: Stall airspeed calculated from aerodynamic % parameters of the aircraft (kts) %Written by Zhiwei Song V_initial = 10; %Setting a range of V (kts) to iterate across V_final = 150; if size(CD_o,2) == 1 %Creating a row vector of CD_o if only one value is given CD_o = CD_o*ones(size(h)); end if size(K,2) == 1 %Creating a row vector of K if only one value is given K = K*ones(size(h)); end if size(h,2)~=size(CD_o,2) %Ensuring that sizes of the vectors match up error('Dimensions of altitude vector and CD_o vector do not match') end if size(h,2)~=size(K,2) %Ensuring that sizes of the vectors match up error('Dimensions of altitude vector and K vector do not match') end %Finding the maximum and minimum airspeed attainable at each altitude test case for i=1:size(h,2) [V_max(i),V_min(i)] = power_levelflight(V_initial, V_final, h(i), P_engine, D_prop, S, CD_o(i), W, K(i),0); h(i) end %Calculating stall boundary [V_stall] = stall_boundary(h,W,S,CL_max); %Plotting flight envelope ceiling = 27000; plot(V_max, h,'-k', V_min,h,'-k',V_stall,h,0:1:160,ceiling,'--') xlabel('True Airspeed V (knots)') ylabel('Altitude h (ft)') title('Flight Envelope')

C-14

Stall_boundary.m %This function calculates the stall boundary of the aircraft over a range %of altitudes. This data is required for the stall boundary of the flight %envelope. function [V_stall] = stall_boundary(h,W,S,CL_max) %This function uses the equations for stall boundary from Aircraft %Performance notes pg 13. %Variables %Inputs %h: A row vertor of test altitudes (ft) %W: Weight of aircraft (lbf) %S: Wing Area (ft^2) %CL_max: CL_max of the wing %Output %V_stall: Stall velocity (kts) %Prepared by Zhiwei Song for i = 1:size(h,2) rho(i) = density(h(i)); %calculating density at the respective altitudes V_stall(i) = ((2.*W./(rho(i).*CL_max.*S)).^0.5)*0.592483801; End fuelflowrate.m function [fuel_rate] = fuelflowrate(P_sealevel) %This function determines the fuel flow rate for the AR 801 engine for a given %throttle setting. The equation was obtained from engine data obtained %from the engine manufacturer. %Variables %Input %P_sealevel: Output of engine at sea level %Output %fuel_rate: Fuel mass flow rate (lbs/s) fuel_rate = (0.0036*(P_sealevel^2) + 0.2406*P_sealevel + 2.9915)/3600; Fuel_levelflight.m %This function calculates the total fuel expended during a steady level %flight at a defined altitude and velocity for a defined duration. The %function updates the current weight of the aircraft for every predefined %step in time to account for the fuel burnt during the steady level flight %phase. It outputs both the total fuel consumed and the final weight of %aircraft at the end of the phase.

function [total_fuel_consumed,W_final] = fuel_levelflight(h, V, duration, P_engine, D_prop, S, CD_o, W_initial, K)

C-15

%Variables %Inputs %h: Altitude of flight (ft) %V: Speed of flight (knots) %duration: Duration of phase (seconds) %P_engine: Power generated by the engine at sea level (hp) %D_prop: Diameter of the propeller (ft) %S: Wing Area (ft^2) %CD_o: Parasitic Drag Coefficient %W_inital: Starting weight of the aircraft (lbs) %K: Aerodynamic parameter %Outputs %total_fuel_consumed: Total fuel consumed during the phase (lbs) %W_final: Final weight of the aircraft (lbs) %Transients %W_current: Weight of the aircraft during the current % iteration (lbs) %P_needed: Power required for flight (hp) %P_generated: Sea level power that engine needs to % generate to produced required power for % flight (hp) %Written by Zhiwei Song step = 10; %size of iteration step W_current = W_initial; if mod(duration,step) ~= 0 %if duration entered is not divisible by step duration = duration + (step - mod(duration,step)); %round up end for time = 0:step:duration [P_needed,eta_i] = power_levelflight2(V, h, P_engine, D_prop, S, CD_o, W_current, K); P_generated = P_needed/0.85/eta_i; fuel_consumed = step*fuelflowrate(P_generated); W_current = W_current - fuel_consumed; %subtracting expended fuel %weight from aircraft weight %at the end of each iteration end W_final = W_current; total_fuel_consumed = W_initial - W_final;

Fuel_climb.m %This function calculates the fuel expended during a climb phase. It %assumes that the engine is operated at full throttle during the entire %climb maneuver. It also assumes that the aircraft is flying with maximum %climb speed permissible by the engine. The function is iterative and %recalculates the maximum climb speed and aircraft weight at a predefined %altitude interval.

function [total_fuel_consumed,W_final,hor_dist_covered,total_time_taken] = fuel_climb(h_initial, h_final, P_engine, S, CD_o, W_initial, K, eta_i) %Variables %Input %h_initial: Starting altitude (ft) %h_final: Final altitude (ft) %P_engine: Power generated by the engine at sea level (hp) %D_prop: Diameter of the propeller (ft) %S: Wing area (ft^2) %CD_o: Parasitic drag coefficient %W_inital: Starting weight of the aircraft (lbs) %K: Aerodynamic parameter

C-16

%Output %total_fuel_consumed: Total fuel consumed during the phase (lbs) %W_final: Final weight of the aircraft (lbs) %hor_dist_covered: Horizontal distance covered during climb % (ft) %total_time_taken: Total time taken to complete the climb % phase (s) %Written by Zhiwei Song step = 100; %setting the altitude iteration step size W_current = W_initial; fuelflow = fuelflowrate(P_engine); %calculating fuel consumption at max throttle total_time_taken = 0; hor_dist_covered = 0; for h = h_initial:step:h_final rho = density(h); %calculating density at current altitude P_avail = 550*P_engine*0.85*eta_i*rho/density(0); vclimb_max = P_avail/W_current - (4/3)*sqrt((2*W_current/(rho*S))*sqrt(3*(K^3)*CD_o));%calculating maximum climb speed v_horizontal = sqrt( 2*W_current/(density(h)*S)*sqrt(K/CD_o));%corresponding horizontal speed time_taken = step/vclimb_max;%time taken to complete each iteration

fuel_consumed = time_taken*fuelflowrate(P_engine*rho/density(0)); W_current = W_current - fuel_consumed;

total_time_taken = total_time_taken+time_taken; hor_dist_covered = v_horizontal*time_taken + hor_dist_covered; end W_final = W_current; total_fuel_consumed = W_initial - W_final;

LoadMain.m %This program calculates and compares the load distribution along the span of the wing. choice = 1; i=1; while choice < 8 [wingloads1 y fuel_weight]=LoadFunc(choice); [wingloads2 y fuel_weight2]=LoadFunc(choice+1); VzFuel(:,i)=wingloads1(:,1); VxFuel(:,i)=wingloads1(:,2); MTFuel(:,i)=wingloads1(:,3); MxFuel(:,i)=wingloads1(:,4); MzFuel(:,i)=wingloads1(:,5); VzEmpty(:,i)=wingloads2(:,1); VxEmpty(:,i)=wingloads2(:,2); MTEmpty(:,i)=wingloads2(:,3); MxEmpty(:,i)=wingloads2(:,4); MzEmpty(:,i)=wingloads2(:,5); i=i+1; choice=choice+2; end figure(1) plot(y,VzFuel,y,VzEmpty,':') legend('A Fuelled','D Fuelled','E Fuelled','G Fuelled','A Empty','D Empty','E Empty','G Empty'); xlabel('y (ft)') ylabel('Vz (lbf)') title('Vz') figure(2) plot(y,VxFuel,y,VxEmpty,':') legend('A Fuelled','D Fuelled','E Fuelled','G Fuelled','A Empty','D Empty','E Empty','G Empty'); xlabel('y (ft)') ylabel('Vx (lbf)')

C-17

title('Vx') figure(3) plot(y,MTFuel,y,MTEmpty,':') legend('A Fuelled','D Fuelled','E Fuelled','G Fuelled','A Empty','D Empty','E Empty','G Empty'); xlabel('y (ft)') ylabel('MT (lbf)') title('MT') figure(4) plot(y,MxFuel,y,MxEmpty,':') legend('A Fuelled','D Fuelled','E Fuelled','G Fuelled','A Empty','D Empty','E Empty','G Empty'); xlabel('y (ft)') ylabel('Mx (lbf)') title('Mx') figure(5) plot(y,MzFuel,y,MzEmpty,':') legend('A Fuelled','D Fuelled','E Fuelled','G Fuelled','A Empty','D Empty','E Empty','G Empty'); xlabel('y (ft)') ylabel('Mz (lbf)') title('Mz')

LoadFunc.m %This programme calculates the load on the wing function [wingloads,yp, fuel_weight] = LoadFunc(choice) %-----------------Aircraft weight--------------------- W_full=644.8; %lbf W_empty=461.4; %lbf %----------------------------------------------------- if choice == 1; V=107.3;nz=3.5; %DesignPoint A, Fully fuelled W=W_full; TrimMain2; elseif choice == 2; V=91;nz=3.5; %DesignPoint A, Empty fuel W=W_empty; TrimMain2; elseif choice == 3; V=194;nz=3.5; %DesignPoint D, Fully fuelled W=W_full; TrimMain2; elseif choice == 4; V=194;nz=3.5; %DesignPoint D, Empty Fuel W=W_empty; TrimMain2; elseif choice == 5; V=194;nz=-1; %DesignPoint E, Fully fuelled W=W_full; TrimMain2; elseif choice == 6; V=194;nz=-1; %DesignPoint E, Empty Fuel W=W_empty; TrimMain2; elseif choice == 7; V=103.3;nz=-1.9; %DesignPoint G, Fully fuelled W=W_full; TrimMain2; elseif choice == 8; V=87.7;nz=-1.9; %DesignPoint G, Empty fuel W=W_empty; TrimMain2; else display('You have entered an invalid choice'); end

C-18

load aircraftCza.mat %--------------------- %User Input Parameters %--------------------- cdo=0.0077; %Profile drag coefficient M=100; %Number of spanwise stations rho_f = 44.988; %fuel density, lbs/ft^3 Sw=74.25; %wing area b = 27; %wing span w_w=68.8/b; %weight of wing/ft a0=-4; %zero lift AoA cr = 3.1; %root chord ct = 2.4; %tip chord Cmo=-0.1008*ones(M+1,1);%sectional moment coefficient rho=0.00237; %sea level %rho=0.001266; %cruise %rho=0.0023423; %dash %--------------------- %================================================================= %This part of the code needs updating when the stall angles change %================================================================= Czabar=nz.*W./(0.5.*rho.*V.^2.*Sw); %Total normal force coefficient aw=16+33*(Czabar-Cza(end))./(Cza(end)-Cza(1)) %Finding aw from Trim Curve alfa=aw+a0; q=0.5*rho*V.^2; %Freestream dynamic pressure %================================================================= %Generate sectional cl and cd of wing [cl,cd,c,y]=sectionalCLCDi(aw,cdo); %Begin Iteration for i=1:M+1 dLwdy(i)=q.*c(i).*cl(i); %lift/ft dDwdy(i)=q.*c(i).*cd(i); %drag/ft dNwdy(i)=dLwdy(i).*cosd(alfa); %normalForce/ft dCwdy(i)=dDwdy(i).*cosd(alfa)-dLwdy(i).*sind(alfa); %chordwiseForce/ft dMacdy(i)=-q.*(c(i)).^2.*Cmo(i); %pitching moment/ft dFIGzdy(i)=-nz.*w_w; w_f(i) = -0.5*c(i)*0.45*0.17*c(i)*rho_f; %fuel weight end %boom consideration for j=1:M Dy(j)=abs(y(j)-y(j+1)); %spanwise lengths of stations DNw(j)=(dNwdy(j)+dNwdy(j+1)).*Dy(j)./2; DCw(j)=(dCwdy(j)+dCwdy(j+1)).*Dy(j)./2; DMac(j)=(dMacdy(j)+dMacdy(j+1)).*Dy(j)./2; %======= account for twin booms ========= if y(j)<-2.33 & y(j)>-3.67 B(j) = -60.225; %boom weight per ft else B(j) = 0; end %====== fuel weight ======= %fuel weight concentrated near to the wing root if y(j) > -7 fuel(j) = (w_f(j) + w_f(j+1))/2; fuel_tot(j) = fuel(j)*Dy(j); else fuel_tot(j)=0; end if choice == 2 || choice == 4 || choice == 6 || choice == 8 fuel_tot(j) = 0; end DFIGZ(j)=(dFIGzdy(j)+dFIGzdy(j+1))*Dy(j)./2 + fuel_tot(j);

C-19

DFIGZ(j) = DFIGZ(j) + B(j)*Dy(j); Dxcg(j)=(c(j)/12+c(j+1)/12)/2; end fuel_weight = sum(fuel_tot); Vz(1)=0; Vx(1)=0; Mz(1)=0; Mx(1)=0; MT(1)=0; for J=1:M-1 Vz(J+1)=Vz(J)+DNw(J)+DFIGZ(J); Vx(J+1)=Vx(J)+DCw(J); Mz(J+1)=Mz(1)-(Vx(J).*Dy(J))-(DCw(J).*Dy(J)./2); Mx(J+1)=Mx(J) + (Vz(J).*Dy(J)) + (DNw(J).*Dy(J)./2) + (DFIGZ(J).*Dy(J)./2); MT(J+1)=MT(J)+DMac(J)+(DFIGZ(J).*Dxcg(J)); end wingloads=[Vz' Vx' MT' Mx' Mz']; for H=1:M yp(H)=(y(H)+y(H+1))/2; %y location of each spanwise station end end

TrimMain2.m %TrimMain2.m Last changes made 11/29/06 UAV Team 2 (UAVarsity) %This program calculates the trimmed forces acting on the wing. if choice == 1 load UAVspecs.mat; load Afull.mat; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3); [Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); elseif choice == 2 load UAVspecsNoFuel.mat; load Aempty.mat; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3); [Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); elseif choice == 3 load UAVspecs.mat; load Dfull.mat; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3); [Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); elseif choice == 4 load UAVspecsNoFuel.mat; load Dempty.mat; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3); [Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); elseif choice == 5 load UAVspecs.mat; load Efull; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3);

C-20

[Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); elseif choice == 6 load UAVspecsNoFuel.mat; load Eempty; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3); [Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); elseif choice == 7 load UAVspecs.mat; load Gfull; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3); [Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); elseif choice == 8 load UAVspecsNoFuel.mat; load Gempty; CDoutput=CDCLCmact(:,1); CLoutput=CDCLCmact(:,2); Cmact=CDCLCmact(:,3); [Cza,Cz,Cx,Czt] = trimanalysis(a0,alfamin,alfamax,AR,CLoutput,CDoutput,Cmact,xcg_t,xcg_w,Sw,St,cwBar,at0,ARt); else display('You have entered an invalid choice.') break end

D-1

Appendix D: Aerodynamic Performance Calculations D.1 Aerodynamic parameter changes due to flaps

fflappedl mc τηδ)( 0=Δ (Eqn. D.1)

where τ - is the flap effectiveness η - is the viscous correction factor

The aerodynamic pitching moment is changed as well, given by the following equation.

ll

mm c

ccc Δ⋅ΔΔ

=Δ (Eqn. D.2)

where Δcm / Δcl – is given in Figure D.1.

Figure D.1: Δcm / Δcl vs. flap chord ratio.

D.2 Aircraft Pitching Moment Coefficient (without Tail) The aircraft pitching moment coefficient without the tail is given by the following equation.

( ) ( ) ( ) ( )AC ACM M M Mac t fusw flapsC C C C

−= + + Δ (Eqn. D.3)

The wing pitching moment ( ( )ACM w

C ) is equivalent to the pitching moment of the airfoil since

the wing has no sweep. The airfoil pitching moment is -0.13 for the NASA GA(W)1. The change in pitching moment due to the flaps calculation can be found in the flap section. Lastly, the pitching moment due to the fuselage is given by the following.

D-2

( )2

f fus fusM fus

K l DC

cSα= (Eqn. D.4)

Kf is an empirical pitching moment factor, which can be obtained by looking up the tabulated Kf value for different wing AC location on the fuselage. For our design, the wing is located approximately at 42% of the fuselage and the corresponding Kf value is 0.018. D.3 Parasite Drag Coefficient The parasite drag coefficient (CD0) during takeoff, cruise and dash were calculated using Eqn. D.5.

( )&0

1mis L PD fc c c wetc D DC C FF Q S C C

S= + +∑ (Eqn. D.5)

The subscript c denotes component c. A total of 4 components were considered for the calculation: wing, fuselage, twin booms and tail. Cfc is the friction coefficient, FFc is the form factor, Qc is the interference factor and Swetc is the wetted area. CDmis is drag contribution of aircraft components with large form drag, such as non-retracted landing gear and fuselage upsweep. CDL&P is the drag associated with air leakages and protuberance, which is usually 8% of the CD0. To calculate Cfc, Eqn D.6 was used.

( ) ( )0.652.58 210

0.455

log Re 1 0.144fC

M=

+ (Eqn. D.6)

This equation assumes that the Re is above 500,000. Given the dimensions of each component, even at stall conditions, the Re was above 500,000. Fuselage length and boom length were used as characteristic length while the mean aerodynamic chord was used for wing and tail. Form factors for wing and tail used the formula shown in Eqn D.7.

( ) ( )4

0.280.180.61 100 1.34 cos/ m

m

t tFF Mx c c c

⎡ ⎤⎛ ⎞ ⎡ ⎤= + + Λ⎢ ⎥⎜ ⎟ ⎣ ⎦⎝ ⎠⎢ ⎥⎣ ⎦ (Eqn. D.7)

The variable (x/c)m represents the chordwise location of the airfoil maximum thickness while (t/c) is the airfoil maximum thickness. The sweep angle ( mΛ ) was set to 0 since the swept wing only benefits flight as transonic speeds. For fuselage and booms, slightly different equation was used to calculate the form factor.

D-3

3

601 ,400

f lFF ff d

⎛ ⎞= + + =⎜ ⎟⎝ ⎠

(Eqn. D.8)

As shown from Eqn D.8, only length and diameter of fuselage and boom were required to calculate the form factor. The interference factor, Q, was set to 1 for all components except the tail, which was set at 1.08 due to the H-shape of the tail. The surface wet area for each component was simple to calculate since the dimensions of geometry were specified from the beginning. The miscellaneous drag mainly comes from the fuselage upsweep. In addition, the fuselage upsweep, windmilling propellers, and speedbrakes add to the miscellaneous drag. However, we assumed that the propeller does not stop and no speed brakes are applied. Eqn D.9 shows the drag contribution due to the fuselage upsweep.

3.83DmisC Aθ= (Eqn. D.9) θ is the upsweep angle in radians and A denotes the fuselage cross-sectional area. A MATLAB code was created to calculate the CD0 of the aircraft (Appendix C) D.4 Trim Drag Coefficient The trim drag is the induced drag of the tail.

2Lt t

Dtrimt t

C SCe AR Sπ

= (Eqn. D.10)

Eqn D.10 was used to calculate the trim drag. e is the Oswald efficiency factor while the coefficient of lift of tail was calculated from obtaining CL of the wing and the aircraft pitching moment without the tail.

E-1

Appendix E: Takeoff and Landing Calculations E.1 Take off The ground roll can be computed with the following equations, where μ is the friction coefficient of the ground, Vi is zero, and Vf is 1.1 times stall speed.

2

2

1 ln2

T A fG

A T A i

K K VS

gK K K V⎧ ⎫+⎛ ⎞ ⎪ ⎪= ⎨ ⎬⎜ ⎟ +⎪ ⎪⎝ ⎠ ⎩ ⎭

(Eqn. E.1)

TTKW

μ⎛ ⎞= −⎜ ⎟⎝ ⎠

(Eqn. E.2)

( )0

2

2( / )A L D LK C C KCW Sρ μ= − − (Eqn. E.3)

The rotation distance can be computed next, where VTO is 1.1 times the stall speed of 35 knots. The rotate time, trotate, is 1 second.

R TO rotateS V t= ⋅ (Eqn. E.4) R is the radius of the arc about which the aircraft rotates during transition, as shown in Figure 14.1.

Climb

TRV

T DS RW−⎛ ⎞= ⎜ ⎟

⎝ ⎠ (Eqn. E.5)

The vertical distance traveled as UAV transitions to steady climb is a function of R and the flight path angle, γclimb.

(1 cos( ))TR climbh R γ= − (Eqn. E.6) The horizontal distance traveled as UAV climbs to avoid the obstacle is computed last.

tan( )obstacle TR

Cclimb

h hSγ−

= (Eqn. E.7)

E.2 Landing The total horizontal distance traveled as the UAV clears obstacle and approaches the runway depends on the obstacle height, the flare height, hF, and the flight path angle.

E-2

tan( )obstacle F

aa

h hSγ−

= (Eqn. E.8)

The horizontal distance traveled as the UAV flares up and prepares to land depends on the radius, R, of the arc that the aircraft makes as it transitions to flare.

( )sinF aS R γ= (Eqn. E.9) The vertical distance traveled during the flare maneuver depends on the flight path angle and the radius.

(1 cos )F ah R γ= − (Eqn. E.10) The distance traveled on the runway after touchdown and before brakes are applied depends on the touchdown velocity, VTD, and the time, td, before the brakes are applied. The touchdown velocity is 1.15 times the stall speed, and td will be 1 second.

FR TD dS V t= ⋅ (Eqn. E.11) Finally, the distance traveled while the brakes are applied until the UAV comes to rest is calculated by the following equations.

2

1 ln2

TB

A T A TD

KSgK K K V

⎛ ⎞ ⎧ ⎫= ⎨ ⎬⎜ ⎟ +⎝ ⎠ ⎩ ⎭

(Eqn. E.12)

TTKW

μ⎛ ⎞= −⎜ ⎟⎝ ⎠

(Eqn. E.13)

( )0

2

2( / )A L D LK C C KCW Sρ μ= − − (Eqn. E.14)

F-1

Appendix F: Tail Sizing Calculations and History F.1. Vertical Tail The equations and intermediate values obtained in the vertical tail calculation are presented in this section. The initial estimate of the vertical tail volume coefficient, CVT, is based on existing aircraft designs. The coefficient is selected s 0.04, which is typical for small single-engine aircraft. The vertical tail area, SVT, is related to the vertical tail volume coefficient by:

VT

WVTVT L

bSCS = (Eqn F.1)

Where b is the wing span, SW is the wing planform area and LVT is the distance from the aerodynamic center of the wing to the aerodynamic center of the tail. Given that SW = 74.25 ft2, b = 27 ft and LVT = 7.7 ft; our initial estimate of vertical tail area is:

24.107.7

25.742704.0 ftSVT =××

= (Eqn. F.2)

Next, an estimate of the directional stability of the aircraft, (Cnψ)ac, is obtained using the following equation: ( ) ( ) ( ) ( ) ( ) ψψψψψψψ nnvnpropnfusnWnacn CCCCCCC 21 Δ+Δ++++= (Eqn. F.3)

Where W, fus, prop and v denote the contributions to directional stability by the wing, the fuselage, the propeller and the vertical tail respectively. The last two terms are correction factors that compensate for the wing geometry and sidewash and interference due to wing-fuselage combination. The wing contribution to directional stability, (Cnψ)W, is obtained from equation (108) from the aforementioned lecture notes, given by: ( ) ( ) 5.005106 Λ×−= −

WnC ψ (Eqn. F.4) Where Λ0 is the sweep angle of the wing at quarter chord. Since our wing is un-swept, the wing contribution to directional stability is 0. The fuselage contribution to direction stability, (Cnψ)fus, is given by equation (109):

( ) ( )127.28KK

bSV

CW

fusfusn −=ψ (Eqn. F.5)

Where Vfus is the fuselage volume and (K2 – K1) is a function of the fineness (length to diameter) ratio of the fuselage. Given the nature of our aircraft design, the fuselage volume, Vfus, is taken as the combined volume of the fuselage and the twin boom. For simplification, the fuselage is viewed as a 6-ft cylinder with diameter 2 ft having a 2-ft tall cone attached to each end. The twin booms are simplified as two cylinders with a diameter of 6 inches and length of 8.1 ft. Therefore, Vfus is calculated to be:

F-2

2222

2.2625.01.82

25.22

312

2262 ftVVVV boomconecylfus =

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛×+⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛××+⎟

⎠⎞

⎜⎝⎛×=++= π (Eqn. F.6)

Our aircraft has a fineness ratio of 5. Reading off the Fig 10 of the lecture notes, the correlation factor (K2 – K1) is 0.8. Therefore, the fuselage contribution to directional stability is:

( ) 41065.38.02725.747.28

2.26 −×=×××

=fusnC ψ (Eqn. F.7)

The propeller contribution on directional stability, (Cnψ)prop, is given the following equation:

( )

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

=bS

Nd

dClD

CW

pYp

pp

propn 45.1

2

ψπ

ψ (Eqn. F.8)

Where Dp is the diameter of the propeller, lp is the distance from the propeller to the center of gravity of the aircraft, Np is the number of propellers, and dCYp/dψ is the rate of change of the yawing moment coefficient due to the side force of the propeller with respect to ψ. For the design of our UAV, we are using a single twin-bladed propeller of diameter 5 ft for the aircraft. The propeller is located 3.76 ft behind the center of gravity of the aircraft. dCYp/dψ is estimated to be 0.00165 based on the lecture notes. The contribution of propeller to directional stability is:

( ) ( ) 52

1011.92725.744

100165.076.355.1 −×−=⎥⎦

⎤⎢⎣

⎡××

××−××=

πψ propnC (Eqn. F.9)

The tail contribution, (Cnψ)v, is given by:

( ) vVT

W

VTvvn b

LSS

aC ηψ ⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−= (Eqn. F.10)

Where av is lift curve slope of the vertical tail, given in Fig 35 as a function of the aspect ratio of the tail, and ηv is the vertical tail efficiency. The initial tail has an effective aspect ratio of 2.5 and this gives us a lift curve slope of 0.05. The vertical tail efficiency is assumed to be 1. Therefore, the tail contribution is:

( ) 0019.0127

7.725.7441.1005.0 −=⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛−=

vnC ψ (Eqn. F.11)

The first correction factor, Δ1Cnψ, is determined by the wing geometry. The wing of our aircraft is mounted on top of the fuselage, and the correction factor is: 0002.01 −=Δ ψnC (Eqn. F.12) The second correction factor, Δ2Cnψ, is to account for the contribution to directional stability due to sidewash and interference flow from the fuselage-wing combination. Given the high wing geometry, 0006.02 =Δ ψnC (Eqn. F.13)

F-3

Now that we have all the terms that contribute to directional stability, the estimate for the aircraft can be obtained:

( ) ( ) ( ) ( ) ( )( ) 00125.00006.000002.00002.01011.9000238.00 5

21

−=+−−+×−+=

Δ+Δ++++=−

acn

nnvnpropnfusnWnacn

C

CCCCCCC

ψ

ψψψψψψψ (Eqn. F.14)

An estimate for the desired directional stability is provided in equation (127) of the notes:

( )5.0

20005.0 ⎟⎠⎞

⎜⎝⎛−=

bS

C Wdesirablenψ (Eqn. F.15)

For our aircraft, the desired directional stability is:

( ) 45.0

2 1060.127

25.740005.0 −×−=⎟⎠⎞

⎜⎝⎛−=

desirablenC ψ (Eqn. F.16)

The desired directional stability is only about 1/10 of the actual aircraft stability, and therefore the initial estimate of the tail area is not good enough to provide a desired directional stability. The vertical tail area has to be altered to match the desired directional stability. Therefore, the new tail contribution should be: ( )[ ] ( ) ( ) ( ) ( )[ ] 4

21 103.8 −×−=Δ+Δ++++−= ψψψψψψψ nnpropnfusnWndesirablennewvn CCCCCCC (Eqn. F.17)

Using the new Cnψ value and equation (123), the new vertical tail area is:

( )[ ]

24

52.47,705.01

2725.74103.8 ftS

LabSC

S

VT

VTvv

WvnVT

=××

×××=

−=

−

ηψ

(Eqn. F.18)

The calculated vertical tail area is 4.52 ft2, or 6% of the wing area. While the vertical tail area of 4.34 ft2 may be able to provide directional stability to the aircraft, it does not guarantee that the aircraft will have sufficient maneuverability. F.2 Horizontal Tail The first iteration of the horizontal tail sizing is presented in this section. Iterations will be performed until the tail area at the end of iteration is within 1% of the tail area at the beginning of the iteration. The horizontal tail size of BBXL was begun with a simplified calculation using the following equation where we assumed the volume coefficient of the horizontal tail to be the same as that for a typical small single-engine aircraft.

HT

wwHTHT L

ScCS

⋅= (Eqn. F.19)

Where:

wc = 2.75 ft wS = 74.25 ft2 HTC = 0.7 HTL = 7.7 ft

F-4

22.75 74.250.7 18.567.7HTft ftS ft

ft⋅

= = (Eqn. F.20)

By assuming the horizontal tail volume coefficient to be 0.7 and using previously calculated values for the wing mean chord, wing area, and the moment arm between the horizontal tail and the aerodynamic center, we estimated the horizontal tail are to be 18.56 ft2. This value was a good start to our horizontal tail sizing iterations which includes more aerodynamic parameters for the desired horizontal tail performance. Note, we began our calculations with the value of 0.7 for the horizontal tail volume coefficient but it will change with each iteration using the below equation.

ww

HTnewHTnewHT Sc

LSC

⋅

⋅= ,

, (Eqn. F.21)

Before using iterations key parameters that affect the performance of the horizontal tail must first be calculated. These parameters include the volume of the fuselage, twin booms, and the lift curve slopes of the wing and horizontal tail. The total volume of the fuselage and the twin boom is given by:

( )222

22

24

234

⎟⎠⎞

⎜⎝⎛⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛= tb

tbf

ff

fD

LD

LD

V πππ (Eqn. F.22)

The lift curve slopes of the wing and the horizontal tail are obtained from the following equations:

57.31W

o

o

aa r aARπ

=⋅ ⋅

+ (Eqn. F.23)

,

,57.31

o HTT

o HT

HT

aa r a

ARπ

=⋅ ⋅

+ (Eqn. F.24)

Where: Df = 2 ft (fuselage diameter) Lf = 10 ft (fuselage length) Ltb= 8.1 ft (twin boom length) ao= 0.11 (lift curve slope of 2D wing) ao,HT = 0.12 (lift curve slope of 2D horizontal tail) r = 1 (correction factor of end plates) Dtb= 0.5 ft (twin boom diameter)

( )22

2

279.82

74.25w

ftbARS ft

= = = (Eqn. F.25)

( ) ( )2 2

2

6.282.10

18.7HT

HTHT

b ftAR

S ft= = = (Eqn. F.26)

F-5

Using these values we find:

( )2 2 2

34 2 2 0.510 4 2 8.1 26.223 2 2 2fft ft ft ftV ft ft ft ftπ π π⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + − + ⋅ =⎜ ⎟ ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (Eqn. F.27)

0.11 0.091357.3 1 0.111

9.82

Wa

π

= =⋅ ⋅

+⋅

(Eqn. F.28)

0.12 0.05957.3 1 0.1212.10

Ta

π

= =⋅ ⋅

+⋅

(Eqn. F.29)

After we found these values we can apply them to find the rate of change of moment coefficients with respect to lift coefficient of the fuselage. Because the primary function of the horizontal tail is to counter the moments created by the fuselage and wings this term is essential to the calculation of the desired horizontal tail area. Using the values calculated above, we are able to obtain:

www

fus

fusL

m

acSKV

CC

⋅⋅⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛7.28

(Eqn. F.30)

0392.00913.075.225.74

8.07.28

22.262

3

=⋅⋅

⋅=⎟⎟⎠

⎞⎜⎜⎝

⎛ftft

ftCC

fusL

m (Eqn. F.31)

Where K is an empirical factor based on experimental results and can be found by reading from Figure 10 in the Static Stability for Aircraft and Trim Curves Lecture Notes. This value was interpolated to be 0.8 for a fuselage fineness ratio of 5. The average angle of downwash at the tail is given by ε. This downwash of a horizontal tail causes a reduction in the angle of attack and therefore the lift. It is also important in our analysis to include the changes of the angle of attack as it is related to the downwash angle. This is given below:

114.6w

d ad ARεα π= ⋅ (Eqn. F.32)

3393.00913.082.96.114

=⋅⋅

=πα

εdd (Eqn. F.33)

After finding the values of these parameters, they are used to find the stability derivative of the aircraft without the effects of the propellers using equation (52):

1cg acm m tHT t

L L wac fus

x xC C a dCC C a dc

εηα

−⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + − ⋅ ⋅ −⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

(Eqn. F.34)

( ) 281.03393.0117.00913.0059.00392.0

75.23.624.6

−=−⋅⋅⋅−+−

=⎟⎟⎠

⎞⎜⎜⎝

⎛ft

ftftCC

acL

m (Eqn. F.35)

We then use these values to find the neutral point, the most aft location of the CG before the aircraft becomes unstable by applying the following equation:

F-6

1ac m to HT t

L wfus

x C a dN CC a dc

εηα

⎛ ⎞ ⎛ ⎞= − + ⋅ ⋅ −⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

(Eqn. F.36)

( ) 55.23393.0117.00913.0059.00392.0

75.23.6

=−⋅⋅⋅+−=ft

ftNo (Eqn. F.37)

The stick fixed neutral point with wind milling propellers is calculated at the point where

L

mdC

dC is zero, and the aircraft is stable. This stick fixed neutral fixed point comes as a result

of the CG moving further aft.

( )0

00.07

Np p

pT t HT t NoWind o p

pTw w w

dC d l Sd d a C dCdN N NS c a a d d

βα α η β

α α=

=

⎛ ⎞⎜ ⎟⎝ ⎠ ⎛ ⎞= − − ⎜ ⎟⋅ ⎝ ⎠

(Eqn. F.38)

Where: Np= 1 (number of propellers)

0

N

pT

dCdα

=

⎛ ⎞⎜ ⎟⎝ ⎠

= 0.00165 (attained from approximate empirical data)

( )dd

βα =1.5·1.2 = 1.8 (approximately ( )1 d

dε

α+ increased by 20% for maneuverability)

NOTE: ( )dd

βα values of 1.35 and 1.85 were used, and resulted in

minimal effects of less that 0.1ft2 in the final SHT. It was decided to average these values to 1.5.

lp = -3.76 ft (length of the propeller relative to the CG) Sp= 19.635 ft2 (area of our 5ft diameter propeller)

( )( )( ) ( )( ) 544.200165.08.107.0

17.00913.0059.0

0913.075.225.74635.1976.38.100165.01562.2 22

2

=⋅

⋅−⋅⋅

−⋅−=

ftftftftNoWind

We then found the CG location due to ground effects from the wind milling propellers.

gecg oWindx N c= ⋅ (Eqn. F.39)

ftftxgecg 02.775.25546.2 =⋅= (Eqn. F.40)

We then found the value that represents the shift in the stick-fixed neutral point from propeller wind milling to critical power on flight configuration. This shift was taken from empirical data determined for a single engine. 0.00oNΔ = (Eqn. F.41) To find the neutral point with power on we sum the shift in the stick fixed neutral point with the shift associated with the wind milling of the propellers. oPower oWind oN N N= + Δ (Eqn. F.42)

F-7

544.2)00.0(544.2 =+=oPowerN (Eqn. F.43) This result comes from the requirement that the aircraft must have a stick-fixed longitudinal stability with power on. We then found the CG location when the power in the below expression.

gecg power oPowerx c N= ⋅ (Eqn. F.44)

ftftx powercgge00.7544.275.2 =⋅= (Eqn. F.45)

The deflection angle when the lift coefficient is equal to zero is found below. Where: Cmac = -0.1 (wing pitching moment coefficient at aerodynamic center) αo= -4° (zero lift angle of attack) τ = 0.59 (elevator effectiveness given the elevator area = 0.4 SHT)

mac oeo

t HT t

Ca C

αδητ τ

−= −

⋅ (Eqn. F.46)

( )°=

−−

⋅⋅⋅−−

= 87.1059.04

59.017.0059.01.0

eoδ (Eqn. F.47)

The most forward location of the CG is used to find the change in the moment coefficient as it related to the change in the lift coefficient. The most forward location of CG is assumed to be 6 ft from the nose.

fwcgmoWind

L fwd

xdC NdC c

⎛ ⎞= −⎜ ⎟

⎝ ⎠ (Eqn. F.48)

362.0544.275.26

−=−=⎟⎟⎠

⎞⎜⎜⎝

⎛ft

ftdCdC

fwdL

m (Eqn. F.49)

Because the most aft location of the CG corresponds to CLmax, we then found the maximum change of the elevator angle below.

,max 0

maxmax

e ee

L L

ddC C

δ δδ −⎛ ⎞=⎜ ⎟

⎝ ⎠ (Eqn. F.50)

91.1594.1

87.1020

max

−=−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛

L

e

dCdδ

(Eqn. F.51)

Using the above value, we then found the new horizontal tail volume coefficient in the below expression.

,

max

m

L fwdHT new

et t

L

dCdC

Cda dCδη τ

⎛ ⎞⎜ ⎟⎝ ⎠

=⎛ ⎞⎜ ⎟⎝ ⎠

(Eqn. F.52)

653.091.1559.01059.0

362.0, =

−⋅⋅⋅−

=newHTC (Eqn. F.53)

We then use this new volume coefficient to calculate a new horizontal tail area.

F-8

,HT new wHT

HT

C S cS

L= (Eqn. F.54)

22

, 32.177.7

75.225.74653.0 ftft

ftftS newHT =⋅⋅

= (Eqn. F.55)

The first iterated horizontal tail area is 18.6 ft2, and this value is about 7% different from the tail area at the beginning of the iteration. Therefore, further iteration is required until the tail area convergence is less than 1%. F.3 Tail Configuration History The relaxed design requirements for the unmanned aircraft left us substantial freedom in its design. After reviewing various proven designs, many different types of tail configurations were considered before we came to our baseline design. Three tail configurations were considered; V-tail, boom-tail, and tailless (flying wing). Below provides a detailed analysis of the pros and cons of the three designs. F.3.1 V-Tail Configuration The inverted V-tailed configuration was considered because it is a characteristic feature of many of the US-manufactured UAVs. Theoretically, the V-tail reduces wetted area and will benefit the aircraft design by reducing the aircraft weight. Also, the interference drag and spiraling tendencies are significantly reduced when using a V-tail design. However, extensive NACA research suggests that the V surfaces need to be enlarged so that they have the equivalent wetted area as a conventional design in order to provide good stability and control [6]. Also, because of the inverted V arrangement, the aircraft’s landing gear will need to be significantly longer, and it will require more stringent ground clearance for landing and take-off. For these reasons, we decided not to include an inverted V tail design into our baseline design. F.3.2 Twin Boom Tail Configuration A twin boom configuration was considered because such a configuration can accommodate a pusher prop layout while allowing the heavy engine to be located near the center of gravity of the aircraft. The long slender booms also allow the tail of the aircraft to be positioned farther aft of the wing, maximizing the moment arm of the tail surfaces without having to incur the full weight penalty of building an equivalently long fuselage. The twin boom tail configuration however could force the wing structure to be more robust than a traditional design, because the booms are usually fixed to the wing. Also, the booms could create additional wetted area, which could increase the drag on the aircraft. Figure illustrates the twin boom tail configuration. Based on our aircraft specification, we decided that the twin boom tail configuration is the best to suit our mission requirements.

F-9

Figure F.1: A typical UAV twin boom configuration [7].

F.3.3 Flying Wing Configuration A flying wing design was considered because of its inherent efficiency. The flying wing configuration eliminates the fuselage and all tail surfaces—reducing the wetted area and drag. Eliminating these components would also improve the structural efficiency of the aircraft. Reducing the drag and the structural mass of the aircraft would mean that it could have longer endurance and require less fuel. However, a problem with this design is that the wing must be designed very carefully so that the wing can be stable with limited control moments. Because of this restriction, compromises usually need to be made in the design that could counteract the structural and aerodynamic advantages that the flying wing has. Even with these compromises, many flying wing designs suffer from stability problems [8]. The flying wing would be a risky design to pursue because many other flying wing designs have had stability problems [9]. Because of the complexity of the flying wing design, we decided not to incorporate this design in our UAV.

G-1

Appendix G: Structures Calculations This appendix outlines the procedure to calculate the bending margins of safety present on the stiffeners of the wing, as was introduced in Section 20: Wing Structure. Also noted are the stringer areas present at each spanwise section of the wing, as well as the margin of safety for each stringer. For reference, the diagram below shows the location of each stringer at an arbitrary spanwise station. Additionally, the stringer numbering scheme is also shown.

G.1 Stringer Areas and Margin of Safety To reduce the weight of the wing skeletal structure, the cross sectional area of each stringer has been tailored to the stresses at its particular location. The table below presents the stringer areas:

1 (in2) 2 (in2) 3 (in2) 4 (in2) 5 (in2) 6 (in2) 7 (in2) 8 (in2) 75% 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 60% 0.01 0.015 0.015 0.01 0.01 0.02 0.02 0.02 27% 0.15 0.15 0.25 0.15 0.05 0.1 0.1 0.1 0% 0.30 0.30 0.45 0.30 0.10 0.20 0.20 0.20

Associated with each stringer is a margin of safety for the bending loads present on the wing. As is noted in the Wing Structure section, some of the margins present are vastly in excess of what they need to be. However practical considerations dictate how small the stringer can reasonably be machined. Also note that due to coupling between the load carrying stringers, it would be almost impossible to ensure that all the stringers were at the design margin of safety of +0.35 without a highly detailed analysis, that would be impractical to conduct at this early stage of development for the Big Brother 4000XL. The margin of safety for each stringer at each station is:

1 (in2) 2 (in2) 3 (in2) 4 (in2) 5 (in2) 6 (in2) 7 (in2) 8 (in2) 75% +8.91 +6.66 +6.06 +7.13 +31.09 +12.74 +9.11 +8.70 60% +0.56 +0.36 +0.36 +0.61 +18.41 +4.01 +2.69 +2.87 27% +0.90 +0.50 +0.43 +0.75 +2.75 +1.11 +0.69 +0.69 0% +0.91 +0.47 +0.40 +0.75 +1.73 +0.66 +0.37 +0.36

G-2

G.2 Bending Calculations As stated previously, the method for calculating the bending margins of safety on the wing are outlined in Chapter 19 of Reference 22. The spreadsheet below summarizes what was calculated. Note that a program was set up to iteratively calculate the effective width of skin included with each stiffening member, and the resulting stress and margin of safety present in that member. The full spreadsheet for the calculations at 27% of the span is shown below.

In this spreadsheet, the area of the stringer is entered into the first column. Note that if the skin around the stiffener is in tension, this area includes the effective area of the skin. The number of rivet rows attaching each stiffener to the sheet is needed to take into account the effective width of the skin. There is only one rivet row for each stiffener since the stiffeners are all angle extrusions more than one is not necessary. The total area of the stiffener is the sum of the stringer area as well as the area of the effective skin. The z location Z’ (height above the chord line) of the stringer is entered as well as the x location X’ (distance back from the leading edge

G-3

of the section). Also calculated is the area of the stiffener multiplied with Z’, and then with X’; these values are used in computing the c.g. location of the section, which is noted as Zbar and Xbar in the chart. The equation for Zbar is:

∑∑=

str

str

AZA

Zbar'* (Eqn. G.1)

The equation for Xbar is similar. Next in the table are the products A*X’*Z’, A*Z’2, and A*X’2, which are used in calculating the moments of inertia Ixx, Izz, and Ixz. Note that the calculation of these values make use of the parallel axis theorem. The values of the area moments of inertia are noted on the table. Their equations are shown below: ( ) ( ) 22 *'* ZbarAZAIxx strstr ∑∑ −= (Eqn. G.2) ( ) ( ) 22 *'* XbarAXAIzz strstr ∑∑ −= (Eqn. G.3) ( ) ( ) XbarZbarAXZAIxz strstr **''** ∑∑ −= (Eqn. G.4) In the table, the values of Z and X with respect to the c.g. of the section are computed. To find the stress present in the stiffener, the design moments Mx and Mz must be specified. The stress due to the bending moments present at a location in the cross section is then given by the equation:

ZMzKMxKXMxKMzKb *)**(*)**( 1213 −−−−=σ (Eqn. G.5) Where the constants K1, K2, and K3 are defined as:

21 * IxzIzIxIxzK−

= (Eqn. G.6)

22 * IxzIzIxIzK−

= (Eqn. G.7)

23 * IxzIzIxIxK−

= (Eqn. G.8)

The stress present in each stiffener is then noted in the table. The force P in the stiffener can then be computed as the product of the stiffener area and the stiffener stress. The calculation of this value acts as a check on the computation, since in order for the structure to be in static equilibrium, the sum of P over all the stiffeners should be zero. We can see from the spreadsheet that it is very close. The margin of safety in the stringer can then be found using the compressive yield allowable Fcy and the tension yield allowable Fty. Finally, for a given margin of safety,

G-4

the spreadsheet indicates whether the margin in that particular stringer exceeds the desired margin. G.3 Shear Flow Calculation Results Below are the critical results from the shear flow Matlab code that was provided. Recall that for margins of safety higher than +3.00, +HIGH is shown. 75% of the span: Section Thickness

(inches) Shear Flow (lbf/in)

Applied Shear (psi)

Allowable Shear (psi)

M.S.

Leading Edge 0.032 -421.46 13,170 37,000 +1.80 Front Spar 0.032 -208.40 6,512 37,000 +HIGH Rear Spar 0.032 896.45 27,159 37,000 +0.36 Wing Skin (greatest)

0.032 -610.83 19,088 37,000 +0.93

60% of the span: Section Thickness

(inches) Shear Flow (lbf/in)

Applied Shear (psi)

Allowable Shear (psi)

M.S.

Leading Edge 0.032 -312.07 9,752 37,000 +2.79 Front Spar 0.032 -173.72 5,428 37,000 +HIGH Rear Spar 0.032 698.76 21,836 37,000 +0.69 Wing Skin (greatest)

0.032 -442.97 13,842 37,000 +1.67

0% of the span: Section Thickness

(inches) Shear Flow (lbf/in)

Applied Shear (psi)

Allowable Shear (psi)

M.S.

Leading Edge 0.032 -174.42 5,450 37,000 +HIGH Front Spar 0.032 -136.85 4,276 37,000 +HIGH Rear Spar 0.050 473.58 9,471 37,000 +2.90 Wing Skin (greatest)

0.032 -212.09 6,627 37,000 +HIGH

H-1

Appendix H: Detailed Fuel Requirement Calculations The fuel requirement calculations were made based on the mission profile outlined in Section 2: Mission Description and Analysis. H.1 Fuel Consumption Data

Table H.1: AR801 manufacture’s data.

Horsepower vs. Fuel Comsumption

y = 0.0036x2 + 0.2406x + 2.9915

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Horsepower

Fuel

Com

sum

ptio

n (lb

/hr)

Figure H.2: Constructed fuel consumption curve.

H-2

H.2 Climb During climb, the engine is assumed to be operated at full throttle and is assumed to be climbing at the maximum climb rate. The fuel required for each climb maneuver can be calculated with the following equations, which are calculated in steps of 100 ft to account for the changing ambient air density and the reduction in weight of the aircraft due to fuel consumption. These calculations are performed via a MATLAB code (fuel_climb.m). Firstly, the power available is calculated via the following equation where the altitude is taken to be the altitude at the beginning of each step:

altitudeavailable sea level

sea level

0.85 ( )i shpP Pρηρ

= (Eqn. H.1)

Thus maximum climb rate and the corresponding horizontal velocity are given by:

max 0

3available currentclimb

current

24 33 D

P WV K CW Sρ

= − (Eqn. H.2)

0

current23 D

W KVS Cρ

= (Eqn. H.3)

The time taken to complete each 100 ft step can thus be calculated by:

maxclimb

100stept

V=

(Eqn. H.4) Therefore the fuel consumed and aircraft weight after each step is given by:

availablefuel step 0.85 i

PW t cη

= (Eqn. H.5)

new current fuelW W W= − (Eqn. H.6) where c is the specific fuel consumption of the engine given in units of lbs-hp-s. Also, the horizontal distance covered per step is given by: stepdistance Vt= (Eqn. H.7) The above calculations are then repeated until the required climb altitude is attained, with the fuel weight and horizontal distance of each climb step being summed up.

H-3

H.3 Steady Level Flight During the steady level flight phases of our mission profile, namely cruise, dash and loiter. During these phases, the phase duration and flight speed are defined. The fuel required for each steady level flight phase is calculated via the following equations, which are performed in steps of 1s to account for the changing weight due to fuel consumption during flight. These calculations are performed via a MATLAB code (fuel_levelflight.m). Firstly, the thrust and power required to fly at the defined speed is calculated by the following equations:

0

22 current

altitude2

altitude

1122

DKWT V SC

V Sρ

ρ= + (Eqn. H.8)

2

altitude12 p

T

D

TCV Aρ

= (Eqn. H.9)

21 1i

TCη =

+ + (Eqn. H.10)

requiredP TV= (Eqn. H.11) Thus the fuel consumed per 1s time step and aircraft weight after each time step is given by:

requiredfuel 0.85 i

PW c

η= (Eqn. H.12)

new current fuelW W W= − (Eqn. H.13) where c is the specific fuel consumption of the engine given in units of lbs-hp-s. The above calculations are then repeated until the required flight duration is attained, with the fuel weight and horizontal distance of each time step being summed up.

I-1

Appendix I: V-n Diagram Calculations This appendix outlines the steps and procedures taken to calculate the flight maneuver envelope and gust-loading envelope and display the results in the form of V-n diagrams. This calculation was performed using Professor Friedmann’s lecture notes on Flight Envelope and V-n Diagrams. I.1 Maneuver Envelope The non-dimensional load factor is the ratio of the projection of the aerodynamic and propulsive loading in the aircraft z-axis and the weight of the aircraft. The equation for the load factor is listed below in Equation G.1.

(Eqn. I.1)

Since our pusher-propeller engine is aligned parallel with the aircraft x-axis, we assume that the propulsion system has no net loading in the z-axis direction.

(Eqn. I.2)

The aerodynamic loading of the aircraft in the z-direction can be represented by a coefficient (Cza). This was previously determined by the trim curves and is represented by the equation below.

(Eqn. I.3)

From convention, the maximum positive normal loading coefficient is multiplied by a factor 1.25 to determine the dynamic normal force coefficient, shown below.

(Eqn. I.4)

I.2 Loading From Flaps When the flaps are deployed, it changes the net aerodynamic forces acting on the z-axis of the aircraft. In most cases, the loading from flaps deployed will increase and will thus require separate analysis.

(Eqn. I.5)

The load factor for the flaps deployed case is quite similar to Equation G.1 except the normal aerodynamic force coefficient is determined with the set of aerodynamic data determined for the flaps down case. The maneuver envelope in the case of flaps deployed must extend up to a maximum design velocity expected for operation with flaps deployed. This velocity is determined by the equation below. The flaps design velocity must not be less than 1.4 times the stall speed with flaps retracted or 1.8 times the stall speed with flaps deployed (whichever is greater).

(Eqn. I.6)

I-2

I.3 Gust Loading Envelope The effect of a sharp gust may be very devastating to an aircraft, particularly if the load factor due to the gust loading exceeds that of the limit loads specified by FAR and by the specifications. The gust load factor begins at a n=1 and extends linearly and equally in the positive and negative direction as can be seen in Equation G.7.

(Eqn. I.7)

This can be rewritten as the equation shown below. (Eqn. I.8)

The variable a is the partial derivative of the coefficient of normal force with respect to the angle of attack and is shown in Equation G.9.

(Eqn. I.9)

The variable is the airplane mass ratio is represented by the following equation.

(Eqn. I.10)

The variable is the gust alleviation factor and is displayed below.

(Eqn. I.11)

I.4 Compilation of Load Factors and Plotting From the steps, the load factors due to maneuver, flaps, and gust could be plotted as a function of flight velocity. The design velocities from which to base the wing loading calculations were predetermined by FAR Part 23 and are listed in Section 18 of the body. All the analysis and plotting were performed using Microsoft Excel.

J-1

Appendix J: References [1] “What is Synthetic Aperture Radar.” Sandia National Laboratories. Katelyn M.

Mileshosky. <http://www.sandia.gov/RADAR/whatis.html> [2] “Advanced EO/IR/LD for TUAV.” APM UAV Payloads.

<https://peoiewswebinfo.monmouth.army.mil/portal_sites/IEWS_Public/rus/eoir.htm> [3] “Mini UAV Data Link.” L3 Communications. 15 Feb. 2005 <http://www.l-

3com.com/csw/Product/docs/31-Mini%20UAV%20Data%20Link%20-MUDL%20gen2.pdf>

[4] “AR801R – 51 BHP – Rotary Engine for UAVs.” UAV Engines Ltd. 2004.

<http://www.uavenginesltd.co.uk/index.php?id=403> [5] “AR801-50BHP Rotary Engine for Drones and UAVs” .UAV Engines. Lynn Lane

Shenstone. <http://www.uavenginesltd.co.uk/fileadmin/datapack/AR801.pdf>. [6] Raymer, Daniel P. Aircraft Design: A Conceptual Approach Third Edition. Reston, VA:

American Institute of Aeronautics and Astronautics, Inc. ,2006. [7] Bernal, Luis P. LiftLine.m. Version 2.0. 18 Aug 05. MATLAB® [8] “2 Stroke Rotax Aircraft Engines” Kodiak Research. 16 Sept 06

<http://www.kodiakbs.com/2intro.htm>. [9] “HKS 700E” .HKS Aviation. 17 Sept 06. <http://www.hks-

power.co.jp/hks_aviation/english.htm>. [10] “Powerfin Composite Propellers”. Aircraft Spruce & Specialty Company .Airframe Parts

– Propellers. <http://www.aircraftspruce.com/catalog/appages/powerfin.php>. [11] “Prince Aircraft Company P-tip Props”. Aircraft Spruce & Specialty Company .Airframe

Parts – Propellers. <http://www.aircraftspruce.com/catalog/appages/princeprops.php>. [12] “Aluminum Racing Products [Radiators]”.Aluminum Racing Products. Bohuslav

Pejznoch. <http://aluminiumracing.com/index_e.htm#Radiators>. [13] “Part 23 - AIRWORTHINESS STANDARDS: NORMAL, UTILITY, ACROBATIC,

AND COMMUTER CATEGORY AIRPLANES” .Federal Aviation Administration. Regulatory and Guidance Library. 04 Nov 06 <http://www.airweb.faa.gov/Regulatory_and_Guidance_Library/rgFAR.nsf/MainFrame?OpenFrameSet>.

J-2

[14] Military Handbook - MIL-HDBK-5H: Metallic Materials and Elements for Aerospace

Vehicle Structures (Knovel Interactive Edition). U.S. Department of Defense.

[15] Bruhn, E.F. Analysis and Design of Flight Vehicle Structures. Carmel, Indiana: Jacobs Publishing, Inc., 1973.

[16] Banavara, Nagaraj. Shear Flow and Shear Stress Calculation. 01 Nov 06. MATLAB® [17] “Predator – Unmanned Aerial Vehicle UAV” Airforce-Technology. 17 Sept 06.

<http://www.airforce-technology.com/projects/predator>. [18] “RQ-1 Predator Medium Altitude Endurance (MAE) UAV” GlobalSecurity. 17 Sept 06.

<http://www.globalsecurity.org/intell/systems/predator-specs.htm>. [19] “Vehicles | Production | Gnat 750” UAV Forum. 17 Sept 06.

<http://www.uavforum.com/vehicles/production/gnat750.htm>. [20] “FALCO – Surveillance UAV System” SELEX. 17 Sept 2006. <http://www.selex-

sas.com/datasheets_ga/FALCO.pdf>. [21] “UAV Operations in the Indian Air Force.” Indian Air Force. 17 Sept 06

<http://www.bharat-rakshak.com/IAF/Images/main.php?g2_itemId=2885>.