SUPERSONICSUPERSONICAIRFOILSAIRFOILS

Stacey Huang

COSMOS 2010 [C 3]COSMOS 2010 – [Custer 3]

http://img453.imageshack.us/f/58263535yh1.jpg/

History of Supersonic Flighty p g• 1887: Ernst Mach, shockwaves• Early 1900’s: NACA research• 1940’s: Multiple attempts to travel 

at supersonic speeds, couldn’t “break the sound barrier”

Infinite drag‒ Infinite drag‒ Compressibility – shockwaves

• First supersonic flights:XP 86: In a dive jet propulsion

http://history.nasa.gov/SP‐4219/4219‐065.jpg

– XP‐86: In a dive, jet propulsion• George Welch on October 1 and October 14, 1947

• Couldn’t prove how fast the plane was flyingflying

– Bell X‐1: In level flight, rocket propulsion

• Charles E. Yeager on October 14, 194719 0’ Whi b A l• 1950’s: Whitcomb Area Rule

http://history.nasa.gov/SP‐4219/4219‐060.jpg •http://history.nasa.gov/SP‐4219/4219‐083.jpg

A General Look At Airfoils

Any mechanical or organic structure designed for the purpose of generating lift

In airplanes, usually displayed as cross-section, like here ↓Airfoil geometry:Airfoil geometry:

Leading EdgeCamber (Max, Min)Mean CamberChordTrailing EdgeTrailing Edge

SymmetricalAsymmetrical (cambered)

http://www.allstar.fiu.edu/aero/flight31.htm

y

Generating LiftGenerating Lifthttp://wings.avkids.com/Book/Flight/Images/airfoil.jpgNewton:Bernoulli:

http://virtualskies.arc.nasa.gov/aeronautics/images/airflow.jpg

Image Cropped From:http://www.grc.nasa.gov/WWW/K‐12/airplane/Images/newton3.gif

A l   f A khttp://hyperphysics.phy‐astr.gsu.edu/Hbase/fluids/imgflu/airfoil.gif

http://media.photobucket.com/image/newton%252527s%203rd%20l %20 i f il/l f i /Ai f %2 20 h i %2 20 i i %2• Angle of Attack

– Flying upside down

0law%20airfoil/leftieman/Aircraft%2520Physics%2520Discussion%2520Images/airfoil.jpg

The Speed of SoundThe Speed of Sound

The Mach Number M (with airplane velocity V d d l land sound velocity approximately                *1, 

given a discrete altitude) is given by           .If M > 1  the aircraft is in supersonic flightIf M > 1, the aircraft is in supersonic flight.Gives an indication for how much faster than the speed of sound an aircraft is traveling: p gMach 2 is twice the speed of sound.Critical Mach NumberS d  f  dSpeed of sound:

1,116.4 ft/s or 761.2 mph 340 3 m/s or 1 225 1 km/h 340.3 m/s or 1,225.1 km/h 661.5 knots 

*1 With γ = specific heat ratio; R = specific gas constant;  T = atmospheric temperaturehttp://www.impactlab.com/wp‐content/uploads/2009/06/3‐43563.jpg

CHALLENGES IN SUPERSONIC FLIGHT

The "critical speed" at which these occur decreases as the angle of attack is increased and the airfoil gthickness is increased. Increasingly difficult to maintain lift (lift coefficient decreases)decreases)Apparent infinite drag (drag coefficient increases)Compressibility problems

Changes in air densityFlow chokingExpansion fans

Compressibility burble: uncontrollable divesShockwavesShockwaves

Normal shockBow shock

http://history.nasa.gov/SP‐4219/4219‐064.jpg

http://aero.stanford.edu/Reports/vki_kroo_supersonics.pdf

ConventionalCanardConsiderations:

h b d dMach number: speed constitutes designOptimal altitude

Fuselage: higher volume, greater dragOptimal area distributions

Whitcomb Area RuleHigh overall fineness ratiogLow boomSupersonic Laminar Flow(SLF)(SLF)

http://www.compositesworld.com/cdn/cms/HPC0109_beyondtheconcorde_b.jpg

Supersonic Wing DesignSupersonic Wing Design

• Wing aspect ratioWing aspect ratio• SLF (swept wing)

L – Low sweep– Pressure gradients

http://www.aerospaceweb.org/design/psp/figures/fig07.jpg• Oblique– Elliptic distributions

http://www.aerospaceweb.org/design/waverider/figures/fig18.jpg

– Area Rule– Structural adv.

http://aero.stanford.edu/Reports/vki_kroo_supersonics.pdfhttp://www.aviation‐history.com/convair/b58‐3.jpg

ApplicationsApplications• Military aircraft

– Fighter aircraft• Stealth aircraft• Space shuttle re‐entry

http://www.seorf.ohiou.edu/~af641/sr71001.jpg

entry• Business aircraft

http://psipunk.com/wp‐content/uploads/2010/01/supersonic‐business‐jet‐futuristic‐aircraft‐01.jpg

http://www.nasa.gov/centers/ames/images/content/146600main_sts1anniv‐AC76‐1713.jpg

Bibliography: Supersonic Airfoils

“Aeronautics – Principles of Flight (AIRFOILS) – Level 2”. ALLSTAR. Florida International University. 23 December 2008. Web. 22 July 2010. <http://www.allstar.fiu.edu/aero/flight31.htm>“Airfoil History” Aircraft Aerodynamics and Design Group Stanford University N d Web 21 July 2010 Airfoil History . Aircraft Aerodynamics and Design Group. Stanford University. N.d. Web. 21 July 2010. <http://adg.stanford.edu/aa241/airfoils/airfoils.html>“Airfoils and Lift”. The Aviation History Online Museum. 13 December 2009. Web. 22 July 2010. <http://www.aviation-history.com/theory/airfoil.htm>“Airfoils, Bernoulli, and Newton”. HyperPhysics. Georgia State University. N.d. Web. 23 July 2010. <http://hyperphysics.phy-astr.gsu.edu/Hbase/fluids/airfoil.html>Alexander, Greg. “Speed of Sound, Mach Number, and Sound Barrier”. Aerospaceweb.org. 1 June 2003. Web. 23 July 2010.

htt // b / ti / t h / 6 ht l<http://www.aerospaceweb.org/question/atmosphere/q0126.shtml>Anderson, Clarence E. “The Problem”. N.d. Web. 23 July 2010. <http://www.cebudanderson.com/problem.htm>Anderson, John D., Jr. “Research in Supersonic Flight and the Breaking of the Sound Barrier”. From Engineering Science to Big Science. NASA. N.d. Web. 21 July 2010. <http://history.nasa.gov/SP-4219/Chapter3.html>“Angle of Attack for Airfoil”. HyperPhysics. Georgia State University. N.d. Web. 23 July 2010. <http://hyperphysics.phy-astr.gsu.edu/Hbase/fluids/angatt.html>Colon Raul “The Area Rule” Century of Flight N d Web 25 July 2010 <http://www century-of-Colon, Raul. The Area Rule . Century of Flight. N.d. Web. 25 July 2010. <http://www.century-of-flight.net/Aviation%20history/evolution%20of%20technology/area_rule.htm>Heintz, Chris. “Aircraft Airfoils”. Official Guide to Experimental Aircraft. N.d. Web. 23 July 2010. <http://exp-aircraft.com/library/heintz/airfoils.html> Kroo, I. “Unconventional Configurations for Efficient Supersonic Flight”. Innovative Configurations and Advanced Concepts for Future Civil Aircraft. Stanford University. 6-10 June 2005. Web. 23 July 2010. <http://aero.stanford.edu/Reports/vki_kroo_supersonics.pdf>“Obli Sh k ” S l 8 b l h // / / / i l / bli h l“Oblique Shock Waves”. NASA. 11 July 2008. Web. 25 July 2010. <http://www.grc.nasa.gov/WWW/K-12/airplane/oblique.html>“Puget Sound Airship Society: Glossary”. Puget Sound Airship Society. N.d. Web. 25 July 2010. <http://www.pugetairship.org/glossary/index.html>“Similarity Parameters”. NASA. 11 July 2008. Web. 25 July 2010. <http://www.grc.nasa.gov/WWW/K-12/airplane/airsim.html>“Supersonic Aircraft Fuselage Design”. Aircraft Aerodynamics and Design Group. Stanford University. N.d. Web. 24 July 2010. <http://adg.stanford.edu/aa241/fuselayout/sstfuse.html>“Supersonic Aircraft” NASA 11 July 2008 Web 25 July 2010 <http://www grc nasa gov/WWW/K 12/airplane/lowsup html>Supersonic Aircraft . NASA. 11 July 2008. Web. 25 July 2010. <http://www.grc.nasa.gov/WWW/K-12/airplane/lowsup.html>Yoon, Joe. “First Supersonic Jet”. Aerospaceweb.org. 2 March 2003. Web. 23 July 2010. <http://www.aerospaceweb.org/question/history/q0113.shtml>

Konstantin Eduardovitch TsiolkovskyКонстантин Эдуардович Циолковский

"Men are weak now, and yet they transform the Earth's surface In millions of years theirthe Earth s surface. In millions of years their might will increase to the extent that they will change the surface of the Earth, its oceans, the atmosphere, and themselves. They will control h l d h l hthe climate and the Solar System just as they control the Earth. They will travel beyond the limits of our planetary system; they will reach other Suns, and use their fresh energy instead , gyof the energy of their dying luminary.”

http://www.informatics.org/museum/tsiol.htmlhttp://www.informatics.org/museum/portoftsiolkovsky.jpg

1857‐1935Name in Russian script obtained from: http://www.peoples.ru/technics/designer/tsiolkovsky/

Background: Background: TsiolkovskyTsiolkovskyBackground: Background: TsiolkovskyTsiolkovsky

Fifth of eighteen childrenFifth of eighteen childrenBecame deaf at a young age due to illness◦ No formal education; self-taught from booksNo formal education; self taught from booksAttended university in MoscowThen worked as schoolteacher in KalugaThen worked as schoolteacher in KalugaStarted to publish works about space, but initially little recognizedAfter Bolshevik Revolution, he earned governmental support and died famous for hi khis work

Aka the “Ideal Rocket Equation”Derived 1895, published 1903Derived using Newton’s Laws http://blogs.discovermagazine.

com/sciencenotfiction/files/20

Conservation of momentum◦ Rocket provides thrust for itselfMaximize rocket velocity

08/08/eq1.jpg

Δv = change in velocity

ve = effective exhaust l iMaximize rocket velocity

Large mass change to obtain a large velocity

velocity

mi = initial rocket mass

mf = final rocket masslarge velocityEffective exhaust velocity◦ Payload ratio

http://exploration.grc.nasa.gov/education/rocket/Images/rktpow.gif

Further Studies in Rocket FlightFurther Studies in Rocket Flight

Rocket propellantshttp://www.audacity.org/images/features/A‐photo‐Apollo‐11/Apollo‐11‐mission‐launch‐16‐July‐1969.jpgp p

Liquid propellants: Hydrogen, oxygenHigh exhaust velocityg y

Space shuttle designsCombustion chambersCombustion chambersPressurized cabinsGyroscopesy pEtc.

Multi-stage rockets

http://www.informatics.org/museum/graphics/rockets.gif

Multi stage rocketsOnly way to attain escape velocity into Earth orbit

Humans in Spacehttp://www.informatics.org/museum/russianscan%20folder/drawing3 jpgHumans in Space

Necessities for space travel:

ng3.jpg

Necessities for space travel:Eating, sleeping in zero‐gravitySolar energySolar energyFood and oxygen for colonies

Extraterrestrial lifeExtraterrestrial lifeBelieved:

Mankind’s destiny to expand into the universehttp://www.daviddarling.info/images/Tsiolkovsky_spaceship.jpg

Mankind s destiny to expand into the universeHumans must traverse beyond Earth in order to evolveevolve

Major Publicationsj

Exploration of Space by Means of Reactive Exploration of Space by Means of Reactive Apparatus (1896): space flight“Exploration of the Universe with Reaction Exploration of the Universe with Reaction Machines” (1903): rocket equation"Investigating Space with Rocket Devices" in Investigating Space with Rocket Devices in Nauchnoye Obozreniye (Science Review) (1903)

http://www.informatics.org/museum/postcard%20folder/book.jpg

LEGACYLEGACY

Considered the “father of cosmonautics and http://orig.thestarpress.com/blogs/gadgetguy/images/Rocket.jpg

Considered the father of cosmonautics and human space flight”Unrecognized for his work for majority of life Unrecognized for his work for majority of life, but glorified by USSR1957 S t ik 1 1957 - Sputnik 1 1961 – Yuri Gagarin

http://astroprofspage.com/wp‐content/uploads/2007/07/Sputnik_teck.jpg

Influenced work of subsequent scientistsLunar crater bearing his name

jpg

Lunar crater bearing his name

Bibliography: Tsiolkovsky

“Relativity Calculator – Rocket Equations and Newton’s 3rd Law of Motion”. Relativity Calculator. N.d. Web. 22 July 2010. of Motion . Relativity Calculator. N.d. Web. 22 July 2010. <http://www.relativitycalculator.com/rocket_equations.shtml>“Rocket Equation”. The Internet Encyclopedia of Science. N.d. Web. 19 Jul 2010.

htt // d idd li i f / l di /R/ k t ti<http://www.daviddarling.info/encyclopedia/R/rocket_equation.html>“Tsiolkovsky, Konstantin Eduardovich (1857–1935)”. The Internet Encyclopedia of Science N d Web 19 Jul 2010 Internet Encyclopedia of Science. N.d. Web. 19 Jul 2010. <http://www.daviddarling.info/encyclopedia/T/Tsiolkovsky.html>“Tsiolkovsky”. Konstantin E. Tsiolkovsky State Museum of the y y fHistory of Cosmonautics. Informatics International, Inc. N.d. Web. 22 July 2010. <http://www.informatics.org/museum/tsiol.html>“Tsiolkovsky” Russianspaceweb com N d Web 19 July 2010 Tsiolkovsky . Russianspaceweb.com. N.d. Web. 19 July 2010. <http://www.russianspaceweb.com/tsiolkovsky.html>

http://www.profcardy.com/matematicos/bKutta.jpg

1867-1944Mathematician, Scientist, Historian, ,

One older brotherParents died when young and brought up by 

lan uncleStudied Mathematics in Munich, but had 

d fwide range of interestsFamous for work in mathematics, aerodynamics, 

fglaciers, and history of mathematicsLater taught as a professor in multiple 

i iti   d Guniversities around Germany

Runge Kutta MethodsRunge-Kutta Methods

http://farside.ph.utexas.edu/teaching/329/lectures/node35.html

Alternate method of solving differential equationsUsed instead of Euler’s method in scientific computationsSymmetric integration method (smaller truncation

)error)Estimation to midpoint to obtain true point

h d l nth order requires n evaluations per step

Discovered independentlyLift   t d b     t ti   li dLift  created by a rotating cylinderAir molecules entrain flow in direction of rotation and create a 

http://www‐mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/poten/img324.png direction of rotation and create a 

vortex flowStreamlines distorted from 

L = lift per unit length

ρ = density of the gas

U∞ = velocity of the air

spinning and creates forcey

Γ = circulation

(strength of rotation)

http://www‐hm.ma.tum.de/geschichte/kutta2.gif

http://hyperphysics.phy‐astr.gsu.edu/hbase/fluids/imgflu/kuttajou.gif

Miscellaneous Work

Measurement of glaciersMeasurement of glaciersEast AlpsMapping of locations of glaciersMapping of locations of glaciers

History of mathematicsGeometric constructionsGeometric constructionsEllipses

http://www.hickerphoto.com/data/media/152/southern‐alps_17456.jpghttp://cxc.harvard.edu/csc/why/imgs/JD_err_ellipses.jpg

Bibliography: Kutta

“Kutta Biography”. School of Mathematics and Statistics: University of St Andrews Scotland August 2006 Web 23 Jul 2010 of St. Andrews, Scotland. August 2006. Web. 23 Jul 2010. <http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Kutta.html>Bulirsch, R., and M. Breitner. “Wilhelm Martin Kutta 1867-1944”. T h i h U i i ä Mü h F k l ä fü M h ik Technische Universität München, Fakultät für Mathematik. <http://www-hm.ma.tum.de/geschichte/node21.html> [translated with Google Translate]Fitzpatrick, Richard. “Rune-Kutta Methods”. The University of Fitzpatrick, Richard. Rune Kutta Methods . The University of Texas at Austin. 29 March 2006. Web. 22 July 2010. <http://farside.ph.utexas.edu/teaching/329/lectures/node35.html>“K tt J k ki Lift Th ” H Ph i G i St t “Kutta-Joukowski Lift Theorem”. HyperPhysics. Georgia State University. N.d. Web. 22 July 2010. <http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/kutta.html>“Lift of a Rotating Cylinder”. NASA. 11 July 2008. Web. 25 July g y y 5 y2010. <http://www.grc.nasa.gov/WWW/K-12/airplane/cyl.html>