Subsonic AirplanesAirfoil & Wing Design

Jiajie Wen

AbstractO This PowerPoint Presentation looks on Mach

number, the definition of subsonic airplanes and the propulsion choices for them.

O I will also talk about Prandtl–Glauert Transformation, Thin Airfoil Theory and how to calculate the lift generated by an subsonic airfoil.

O Scientists: Gustav Magnus & Rudolf Clausius.

Mach NumberMV is the velocity of the source relative to the medium

is the speed of sound in the medium.

Mach number is dimensionless.

It varies by the composition of

the surrounding medium and

also by temperature and

pressure.Elevation Temperatu

re Pressure Speed of Sound

(meters)

(feet) (oF) (kPa) (psi) (m/s) (ft/s)

0 0 59.0 101.4 14.7 340.3 1116

2000 6562 35.6 79.5 11.5 332.5 1091

4000 13123 12.2 61.6 9.0 324.6 1065

6000 19685 -11.1 47.2 6.9 316.5 1038

8000 26247 -34.5 35.7 5.2 308.1 1011

10000 32808 -57.8 26.5 3.8 299.5 982

12000 39370 -69.5 19.4 2.8 295.1 968

14000 45932 -69.5 14.2 2.1 295.1 968

Subsonic AirplanesA subsonic aircraft is an aircraft with a maximum speed less than the speed of sound (Mach 1).

Popular Propulsion Choices: O Propeller. At low speeds, propellers provide a very

fuel efficient propulsion system. Lighter and cheaper.

O Turbine. Turbine engine is a type of internal combustion engine. It’s usually heavier and much more expensive.

Wing Geometry (Planform) Choices:O Straight wing. A wing planform favored for low

subsonic planes.

O Swept wing. A wing planform favored for high subsonic planes.

Some Famous Subsonic Aircrafts

Wright Flyer Spirit of St.Louis P-51

B-52 1903 1927 1942

1952

C-130 Boeing 747 A-10

Airbus A380 1954 1969 1972

2005

Propulsion

Turbofan

O  High-bypass turbofan engineO Min. bypass ratio: 2

Turbofan

O  Low-bypass turbofan engineO Max. bypass ratio: 2

Turbojet

O  Zero-bypass

Propeller Aircraft

O Compared to a turbojet (which can fly at high altitude for enhanced speed and fuel consumption), a propeller aircraft has a much lower ceiling.

O A propeller's performance suffers as the blade speed nears the transonic.

h= h𝑡 𝑟𝑢𝑠𝑡×𝑎𝑥𝑖𝑎𝑙 𝑠𝑝𝑒𝑒𝑑

𝑡𝑜𝑟𝑞𝑢𝑒×𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑠𝑝𝑒𝑒𝑑

Turboprop

Airfoil & Wing

Design

Prandtl–Glauert Transformation

O The Prandtl–Glauert transformation allows the comparison of aerodynamical processes occurring at different Mach numbers.

O For two-dimensional flow :

O is the compressible lift coefficient.O is the incompressible lift coefficient.O is the Mach number.

Thin Airfoil TheoryO Thin airfoil theory is a simple theory

that relates angle of attack to lift for incompressible, inviscid flows. 

O It can be imagined as addressing an airfoil of zero thickness and infinite wingspan.

O For symmetrical airfoil,  is the angle of attack in radians, measured relative to the chord line.

O For cambered airfoil,  is the angle of attack measured relative to the zero-lift line.

Prandtl–Glauert Transformation+ Thin Airfoil Theory

O For three-dimensional flows, it is necessary to compute the  and subsequently the pressure. No simple results are possible, except in special cases:

O For a flat elliptical wing, the lift coefficient is:

Prandtl–Glauert Transformation

𝐶𝑝=𝐶𝑝 0

√|1−𝑀∞2|

Airfoil Nomenclature

Leading edge is the point at the front of the airfoil that has maximum curvature.Camber line is the locus of points midway between the upper and lower surfaces.Chord line is a straight line connecting the leading and trailing edges of the airfoil.

Lift Generated by an Airfoil

is lift force is air density

 is true airspeed is planform area

 is the section lift coefficient

Flaps

Wing Design (Planform)

Straight Wing Swept Wing

Scientists

Gustav Magnus

O Magnus was a notable experimental scientist.

O His training was mostly in chemistry but his later research was mostly in physics.

O Magnus's laboratory was one of the best equipped in the world during the years when he was professor in Berlin.

May 2 1802 – April 4 1870

Magnus effect

O The Magnus effect: a spinning object flying in a fluid experiences a force perpendicular to the line of motion.

O The effect was described by Magnus. However, Isaac Newton correctly inferred the cause.

O The Magnus effect is responsible for the curved motion of a spinning ball.

Applications

Rotor Ship in the 1920s

Applications

Rudolf ClausiusO He’s a German physicist

and mathematician and is considered one of the founders of the science of thermodynamics.

O On the mechanical theory of heat, published in 1850, he stated the basic ideas of the second law of thermodynamics.

O In 1865 he introduced the concept of entropy.

Jan 2 1822 – Aug 24 1888

Entropy

O Entropy provides a measure of the amount of the energy that cannot be used to do work.

O The entropy of an isolated system always increases or remains constant.

Steam Water IceDecrease in entropy

ReferencesO Professor Mohamed M. HafezO Anderson Jr., John. The Airplane - A History of Its Technology. Reston,

Virginia: AIAA, 2002. 364. Print.O Stinton, Darrol. The Design of the Airplane. Second Edition. Reston,

Virginia: AIAA, 2001. 704. Print.O Cropper, William. Great Physicists: the Life and Times of Leading

Physicists from Galileo to Hawking. New York, New York: Oxford University Press, 2001. 500. Print.

O Torenbeek, Egbert. Synthesis of Subsonic Airplane Design. Rotterdam, The Netherlands: Delft University Press, 1976. 598. Print.

O Lower, Stephen. "Entropy rules! What is entropy?." Thermodynamics of Chemical Equilibrium. N.p., Feb 22 2010. Web. 1 Aug 2012. <http://www.chem1.com/acad/webtext/thermeq/TE2.html>.

O "jet engine." Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc., 2012. Web. 01 Aug. 2012. <http://www.britannica.com/EBchecked/topic/303238/jet-engine>.

O Denker, John. "Airfoils and Airflow." See How It Flies. N.p., n.d. Web. 1 Aug 2012. <http://www.av8n.com/how/htm/airfoils.html>.

O Ackerman, Evan. "First manned FanWing aircraft planned for 2013." Dvice. Dvice, Jul 19, 2012. Web. 1 Aug 2012. <http://dvice.com/archives/2012/07/first-manned-fa.php>.

O Benson, Tom . "Mach Number." NASA Glenn Research Center. N.p., Sep 10 2010. Web. 22 Jul 2012. <http://www.grc.nasa.gov/WWW/k-12/airplane/mach.html>.

O "Speed of sound, temperature and pressure at various elevations." The Engineering Toolbox. N.p., n.d. Web. 22 Jul 2012. <http://www.engineeringtoolbox.com/elevation-speed-sound-air-d_1534.html>.

O Wikipedia contributors. "Lift (force)." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 18 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Turbofan." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 21 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Turbojet." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 13 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Propeller (aircraft)." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 22 May. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Turboprop." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 5 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Planform." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 25 Jun. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Airfoil." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 25 Jun. 2012. Web. 22 Jul. 2012.

References

O Wikipedia contributors. "Heinrich Gustav Magnus." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 25 Jul. 2012. Web. 30 Jul. 2012.

O Wikipedia contributors. "Wright Flyer." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 20 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Spirit of St. Louis." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 5 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "North American P-51 Mustang." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 21 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Boeing B-52 Stratofortress." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 17 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Boeing 747." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 22 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Fairchild Republic A-10 Thunderbolt II." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 24 Jun. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Airbus A380." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 20 Jul. 2012. Web. 22 Jul. 2012.

O Wikipedia contributors. "Lockheed C-130 Hercules." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 20 Jul. 2012. Web. 23 Jul. 2012.

References

Thanks for Listening!