Supersonic Airfoils

7/18/2019 Supersonic Airfoils

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Stacey Huang

– uster

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



Histor of Su ersonic Fli h• 1887: Ernst Mach, shockwaves• Early 1900’s: NACA research• 1940’s: Multiple attempts to travel

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

‒ Compressibility – shockwaves

• First supersonic flights:

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

– ‐ , • George Welch on October 1 and October

14, 1947• Couldn’t prove how fast the plane was

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

• Charles E. Yeager on October 14, 1947

• 1950 s: W itcom Area Ru e

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 ↓

Leading Edge

Camber (Max, Min) Mean Camber

Chord

Trailin Ed e

Symmetrical

Asymmetrical (cambered)

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



http://wings.avkids.

com/Book/Flight/I

mages/airfoil.jpgNewton:Bernoulli:http://virtualskies.arc.nasa.gov/a

eronautics/images/airflow.jpg

Image Cropped From:

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

http://hyperphysics.phy‐astr.gsu.edu/Hbase/fluids/imgflu/airfoil.gif

http://media.photobucket.com/image/newton%252527s%203rd%2

• ng e

o

ttac

– Flying

upside

down

0law%20airfoil leftieman Aircraft%2520Physics%2520Discussion%2

520Images/airfoil.jpg



The Mach Number M (with airplane velocity V

an

soun

ve ocity

approximate y *1

,

given a discrete

altitude)

is

given

by

.

, . Gives an indication for how much faster than

the s eed

of

sound

an

aircraft

is

travelin :

Mach 2 is twice the speed of sound. Critical Mach Number

pee

o

soun :

1,116.4 ft/s or 761.2 mph

. , .

661.5

knots

*1 With γ = specific heat ratio; R = specific gas constant; T = atmospheric temperature

http://www.impactlab.com/wp‐content/uploads/2009/06/3‐43563.jpg



CHALLENGES IN SUPERSONIC FLIGHT

The "critical speed" at which these occur decreases asthe an le of attack is increased and the airfoil

thickness is increased. Increasingly difficult to maintain lift (lift coefficient

Apparent infinite drag (drag coefficient increases)

Compressibility problems Changes in air density

Flow choking

Expansion fans

Compressibility burble:uncontrollable dives

Normal shock

Bow shockhttp://history.nasa.gov/SP‐4219/4219‐064.jpg



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



Conventional

Canard Considerations: Mac num er: spee constitutes esign

Optimal altitude

Fuselage:

higher

volume,

greater

drag Optimal area distributions

Whitcomb

Area

Rule

Hi h

overall

fineness

ratio

Low

boom

Supersonic Laminar Flow

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



•

• SLF (swept wing)

– ow sweep

– Pressure gradientshttp://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.pdf http://www.aviation‐history.com/convair/b58‐3.jpg



• Military aircraft

– Fighter aircraft

• Stealth aircraft

• Space shuttle re‐http://www.seorf.ohiou.edu/~af641/sr71001.jpg

• 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





Konstantin Eduardovitch Tsiolkovsky

Константин Эдуардович Циолковский

"Men are weak now, and yet they transform

' .

might will increase to the extent that they will

change the surface of the Earth, its oceans, the

atmosphere, and themselves. They will control the 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 ener instead

of 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/



Became deaf at a young age due to illness◦ -

Attended university in Moscow

Then worked as schoolteacher in Kalu a

Started to publish works about space, butinitially little recognized

After Bolshevik Revolution, he earnedgovernmental support and died famous foris wor





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



urther Studies in Rocket lighturther Studies in Rocket light

Rocket ro ellantshttp://www.audacity.org/images/fe

atures/A‐photo‐Apollo‐11/Apollo‐

11‐mission‐launch‐16‐July‐1969.jpg

Liquid propellants: Hydrogen, oxygen Hi h exhaust velocit

Space shuttle designs

Combustion chambers

Pressurized cabins

G rosco es

Etc.

-

http://www.informatic

s.org/museum/graphic

s/rockets.gif

Only way to attain escape velocity into Earth orbit



http://www.info

rmatics.org/mus

eum/russianscan

%20folder/drawi

.

Eating, sleeping

in

zero

‐gravity

Food and oxygen for colonies

Believed:

’

http://www.daviddarling.info/images/Tsiolkovsky_spaceship.jpg

Humans must traverse beyond Earth in order to

evolve



Ma or Publications

Apparatus (1896): space flight“

Machines” (1903): rocket equation

" "

Nauchnoye Obozreniye (Science Review) (1903)

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



“

http://orig.thestarpress.com/blogs/gadgetguy/images/Rocket.jpg

human space flight”

,

but glorified by USSR

- pu n

1961 – Yuri Gagarin

http://astroprofsp

age.com/wp‐

content/uploads/

2007/07/Sputnik_

teck.

Influenced work of subsequent scientists



Bibliography: Tsiolkovsky

“Relativity Calculator – Rocket Equations and Newton’s 3rd Lawof Motion”. elativit Calculator. N.d. Web. 22 Jul 2010.<http://www.relativitycalculator.com/rocket_equations.shtml>

“Rocket Equation”. The Internet Encyclopedia of Science. N.d. Web. 19 Jul 2010.< p: www. av ar ng. n o encyc ope a roc e _equa on.html>

“Tsiolkovsky, Konstantin Eduardovich (1857–1935)”. The. . . . .<http://www.daviddarling.info/encyclopedia/T/Tsiolkovsky.html>

“Tsiolkovsky”. Konstantin E. Tsiolkovsky State Museum of the

History of Cosmonautics. Informatics International, Inc. N.d. Web. 22 July 2010.<http://www.informatics.org/museum/tsiol.html>“ ”. . . . . . .<http://www.russianspaceweb.com/tsiolkovsky.html>



http://www.profcardy.com/matematicos/bK

utta.jpg

1867-1944

Mathematician Scientist Historian



One

older

brother Parents died when young and brought up by

an uncle

Studied Mathematics

in

Munich,

but

had

wide range o interests

Famous for work in mathematics, aerodynamics,

glaciers, and

history

o

mathematics

Later taught as a professor in multiple

un vers t es aroun ermany



-

http://farside.ph.utexas.edu/teac

hing/329/lectures/node35.html

Alternate method of solving differential equations

Used instead of Euler’s method in scientificcomputations

Symmetric integration method (smaller truncation

error Estimation to midpoint to obtain true point

nt or er requires n eva uations per step



Discovered independently

crea e y a ro a ng cy n er

Air

molecules

entrain

flow

in

http://www‐

mdp.eng.cam.ac.uk/web/library/enginfo/aerotherm

al_dvd_only/aero/fprops/poten/img324.png

vortex flow

Streamlines

distorted

from

L = lift per unit length

ρ = density of the gas

U∞ = velocit of the air

spinning and creates forceΓ = 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

East Alps

History of mathematics

Ellipses

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. , . . . .

<http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Kutta.html>

Bulirsch, R., and M. Breitner. “Wilhelm Martin Kutta 1867-1944”.Tec n sc e Un vers t t M nc en, Fa u t t r Mat emat .<http://www-hm.ma.tum.de/geschichte/node21.html> [translated with Google Translate]

“ - ”Texas at Austin. 29 March 2006. Web. 22 July 2010.<http://farside.ph.utexas.edu/teaching/329/lectures/node35.html>

“ ”

u a- ou ows eorem . yper ys cs. eorg a a eUniversity. N.d. Web. 22 July 2010. <http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/kutta.html>

“Lift of a Rotatin C linder”. NASA. 11 Jul 2008. Web. 2 Jul2010. <http://www.grc.nasa.gov/WWW/K-12/airplane/cyl.html>

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Supersonic Airfoils