Transcript Subsonic Airplanes

Subsonic Airplanes
Airfoil & Wing Design
Jiajie Wen
Abstract
O 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 Number
M=
𝑉
𝑎
Mach number is dimensionless. It
varies by the composition of the
V is the velocity of the source relative to the medium
𝑎
temperature and pressure.
is the speed of sound in the medium.
Elevation
Temperature
surrounding medium and also by
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 Airplanes
A 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 engine
O Min. bypass ratio: 2
Turbofan
O Low-bypass turbofan engine
O Max. bypass ratio: 2
Turbojet
O Zero-bypass
Propeller Aircraft
𝑡ℎ𝑟𝑢𝑠𝑡 × 𝑎𝑥𝑖𝑎𝑙 𝑠𝑝𝑒𝑒𝑑
h=
𝑡𝑜𝑟𝑞𝑢𝑒 × 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑠𝑝𝑒𝑒𝑑
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.
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 :
𝐶𝐿 =
𝐶𝐿𝑖
1 − 𝑀∞ 2
O 𝐶𝐿 is the compressible lift coefficient.
O 𝐶𝐿𝑖 is the incompressible lift coefficient.
O 𝑀∞ is the Mach number.
Thin Airfoil Theory
O 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.
𝐶𝐿𝑖 = 2𝜋𝛼
O For symmetrical airfoil, 𝛼 is the angle of attack in radians,
measured relative to the chord line.
O For cambered airfoil, 𝛼 is the angle of attack measured relative to
the zero-lift line.
Prandtl–Glauert Transformation
+ Thin Airfoil Theory
𝐶𝐿 =
2𝜋𝛼
1 − 𝑀∞ 2
O For three-dimensional flows, it is necessary to compute the
𝐶𝐿 and subsequently the pressure. No simple results are
possible, except in special cases:
O For a flat elliptical wing, the lift coefficient is:
𝐶𝐿 =
2𝜋𝛼
1 − 𝑀∞ 2 +
2
𝐴𝑅
Prandtl–Glauert Transformation
O 𝐶𝑝 =
𝐶𝑝0
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
O𝐿 =
1
2
𝜌𝜐 𝐴𝐶𝐿
2
𝐿 is lift force
𝜌 is air density
𝜐 is true airspeed
𝐴 is planform area
𝐶𝐿 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 Clausius
O 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
∆𝑄
∆𝑆 =
𝑇
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
Decrease in entropy
Ice
References
O Professor Mohamed M. Hafez
O
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Anderson Jr., John. The Airplane - A History of Its Technology. Reston, Virginia: AIAA,
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Stinton, Darrol. The Design of the Airplane. Second Edition. Reston, Virginia: AIAA,
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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.
Torenbeek, Egbert. Synthesis of Subsonic Airplane Design. Rotterdam, The Netherlands:
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<http://www.av8n.com/how/htm/airfoils.html>.
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References
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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>.
"Speed of sound, temperature and pressure at various elevations." The Engineering
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Wikipedia contributors. "Lift (force)." Wikipedia, The Free Encyclopedia. Wikipedia, The
Free Encyclopedia, 18 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Turbofan." Wikipedia, The Free Encyclopedia. Wikipedia, The
Free Encyclopedia, 21 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Turbojet." Wikipedia, The Free Encyclopedia. Wikipedia, The
Free Encyclopedia, 13 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Propeller (aircraft)." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 22 May. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Turboprop." Wikipedia, The Free Encyclopedia. Wikipedia, The
Free Encyclopedia, 5 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Planform." Wikipedia, The Free Encyclopedia. Wikipedia, The
Free Encyclopedia, 25 Jun. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Airfoil." Wikipedia, The Free Encyclopedia. Wikipedia, The Free
Encyclopedia, 25 Jun. 2012. Web. 22 Jul. 2012.
References
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Wikipedia contributors. "Heinrich Gustav Magnus." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 25 Jul. 2012. Web. 30 Jul. 2012.
Wikipedia contributors. "Wright Flyer." Wikipedia, The Free Encyclopedia. Wikipedia,
The Free Encyclopedia, 20 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Spirit of St. Louis." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 5 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "North American P-51 Mustang." Wikipedia, The Free
Encyclopedia. Wikipedia, The Free Encyclopedia, 21 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Boeing B-52 Stratofortress." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 17 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Boeing 747." Wikipedia, The Free Encyclopedia. Wikipedia, The
Free Encyclopedia, 22 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Fairchild Republic A-10 Thunderbolt II." Wikipedia, The Free
Encyclopedia. Wikipedia, The Free Encyclopedia, 24 Jun. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Airbus A380." Wikipedia, The Free Encyclopedia. Wikipedia,
The Free Encyclopedia, 20 Jul. 2012. Web. 22 Jul. 2012.
Wikipedia contributors. "Lockheed C-130 Hercules." Wikipedia, The Free Encyclopedia.
Wikipedia, The Free Encyclopedia, 20 Jul. 2012. Web. 23 Jul. 2012.
Thanks for
Listening!