high speed aerodynamics

04/11/23 Author: Harry L. Whitehead 1

Compressibility EffectsImportance of the Speed of SoundRealms of FlightSupersonic Flow Patterns

High Speed AirfoilsCritical Mach NumberAerodynamic Heating

V. High Speed Aerodynamics


V. High Speed Aerodynamics

Compressibility EffectsImportance of the Speed of SoundRealms of FlightSupersonic Flow Patterns

High Speed AirfoilsCritical Mach NumberAerodynamic Heating


High Speed Aerodynamics

As WWII progressed, aircraft flew faster and faster. By mid-war, P51s, Spitfires, and other types were reaching speeds close to that of sound, especially in dives. Pilots began to report control difficulties and unexpected problems which experts determined were due to flying too close to the speed of sound.

Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingHistory and Introduction



In 1940, NACA commissioned the Bell Aircraft Company to build a special research aircraft for the purpose of exploring the speed range near and beyond the speed of sound. It was considered better to do the research using an actual aircraft because the USA had no wind tunnels capable of operating at supersonic speed. Of course, the Germans did.




The research aircraft Bell built was designated the X1. Two operational aircraft were finally built, although they did not fly until the war was over.




By the time the war was over, the German research data had been captured and several of the questions the X1 was intended to answer were already known. Nevertheless, the X1 became the first aircraft to exceed the speed of sound in October 1947 when Chuck Yeager flew it to Mach 1.1 .





X1 movie



At subsonic speed (less than Mach 1) air acts as if it’s an incompressible fluid– Can change it’s velocity and pressure but not

density– As long as it can still move, the space between

molecules will effectively not change = density remains constant

Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingCompressibility Effects




Bernoulli’s Principle:–Subsonic:

•In CONVERGING portion of venturi (Inlet)–Air must travel faster to get to other side at same time as bypass air–Velocity goes up–Pressure goes down



Bernoulli’s Principle:– Subsonic:

• In DIVERGING portion of venturi (Exit)– Pressure and Velocity return to original

– Based on Total Energy being constant throughout• Pressure = Potential Energy• Velocity = Kinetic Energy




At supersonic speed (more than Mach 1) air can be compressed and it’s density increased– Space between molecules can and is reduced


Link to venturi simulation




Link to venturi simulation

Bernoulli’s Principle:•Opposite effects as compared to subsonic

•Converging: Pressure goes up and Velocity goes down•Diverging: Pressure down, Velocity up



Sound is pressure disturbances radiating in all directions from the source

Travels @ 661.7 knots (1,116.9 fps, 761.5 mph) under Standard Conditions– Speed is directly proportional to temperature

(goes down as temp. goes down)

– Can be calculated (CS = Local Speed of Sound):

• CS in kts = 29.04 oR

• CS in fps = 49.022 oR

• CS in mph = 33.42 oR

Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingImportance of the Speed of Sound

Note: oR = oF + 460



Note that at 36,089 feet the temperature stabilizes at –69.7 and the Speed of Sound also stabilizes at 573.8 kts

Also note that above 80,000 feet the temp starts to rise and the Speed of Sound also rises




In subsonic flight– Sound waves radiate from all points of airframe– Can go in all directions as are faster than aircraft




In supersonic flight– Airplane faster so

sound waves “pile up” at nose of airfoil

– Creates Shock Wave(s) = changes in pressure and velocity of airflow


Pressure Waves Link(Hide Shockwaves)

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Mach # = ratio of True Airspeed of an aircraft to the Speed of Sound at that temperature

Subsonic:– .75 Mach or less– All airflow over aircraft is < Mach 1

Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingRealms of Flight



Transonic:– .75 to 1.2 Mach– Mixture of sonic airflow speeds

• Some < Mach 1, some >= Mach 1– Aerodynamic center of lift moves to about 50% of

chord– Shock waves form and move around = large

changes in trim & stability (control buffeting)




Supersonic:– 1.2 to 5.0 Mach– All airflow is > Mach 1– Smooth & efficient flight





Hypersonic:– > 5.0 Mach




Hypersonic:– > 5.0 Mach–Leads to Aerodynamic Heating & other flight problems



Shock waves form when the aircraft (or parts of it) are exceeding Mach 1 in speed– Sound waves slower than aircraft speed– Air “piles up” in Compression Wave = large

changes in pressure, velocity, and density of airflow

Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingSupersonic Flow Patterns

(Shock Waves)



Shock waves form when the aircraft (or parts of it) are exceeding Mach 1 in speed– Sound waves slower

than aircraft speed– Air “piles up” in

Compression Wave = large changes in pressure, velocity, and density of airflow


(Shock Waves)




(Shock Waves)

F18 flyby movieF14 flyby movie



3 kinds of Shock Waves:– Oblique– Normal– Expansion


(Shock Waves)

Pressure Waves LinkShow Shockwaves



Oblique Shock Waves


(Shock Waves)

•Forms on sharp edges with surface changing into the direction of the airflow

•commonly on Leading and Trailing Edges of airfoil•Shock wave forms Oblique Angle with surface and “points” downstream in airflow

•Angle gets less as speed goes up•“flattens out”



Oblique Shock Waves


(Shock Waves)

•@ wave:•Flow direction is deflected along surface•Velocity decreases but STAYS ABOVE MACH 1•Pressure increases•Temperature increases•Density increases•Total energy goes down

•Energy loss comes from loss of temperature (Heat of Compression) to atmosphere



Normal Shock Waves


(Shock Waves)

•Forms in front of or on blunt object or one with large included angle



Normal Shock Waves


(Shock Waves)

•In front:•Molecules pile up and create wave detached and in front of the object

•= “Bow Wave”



Normal Shock Waves


(Shock Waves)

•On:•Attaches to curved portion where airflow speed is just above Mach 1•In Transonic range = form on upper airfoil surface first (at about .75 Mach) then lower surface (at about .85 Mach)

•NOTE: the indicated Mach numbers vary depending on the airfoil



Normal Shock Waves

Supersonic Flow Patterns (Shock Waves)

•@ wave:•Flow direction doesn’t change•Velocity decreases TO BELOW MACH 1

•Subsonic speed inversely proportional to Mach # entering wave (higher CS going in = lower subsonic speed coming out)

•Large Pressure, Density, and Temperature increase•Large Total Energy decrease (from temp. radiation into air)



Expansion Shock Waves


(Shock Waves)

•Form where surface turns away from airflow direction•Middle of airfoil

•Velocity increases•Pressure and Density both decrease•Temperature remains relatively constant = little or no Total Energy change (is not a compression wave)



Subsonic Airfoils

Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingHigh Speed Airfoils and

Critical Mach Number

•Below about .75 Mach = all flow is subsonic



Subsonic Airfoils



•In Transonic speed range:•At some airspeed ( = Critical Mach Number or MCR) some airflow will reach or exceed Mach 1



Subsonic Airfoils



•In Transonic speed range:

•Normal shock wave forms on upper surface where max airfoil thickness is ( = greatest velocity)

•Causes large increase in drag



Subsonic Airfoils



•In Transonic speed range:•Pressure rise through shock wave reduces strength of low pressure area on wing

•Low pressure usually “sucks” air against airfoil for smooth flow•Loss of low pressure = air isn’t sucked down smoothly and SHOCK INDUCED SEPARATION occurs on upper surface

•= loss of lift and reduced control effectiveness from turbulence



Subsonic Airfoils



•In Transonic speed range:•As speed increases closer to Mach 1:

•Normal wave forms on lower surface and upper wave moves further back towards trailing edge

•= shock induced separation on bottom, too



Subsonic Airfoils



•In Transonic speed range:•At Mach 1:

•Top and bottom normal waves have moved to trailing edge and form oblique waves there

•Entire surfaces have supersonic flow = smooth flow

•Leading edge now has normal wave forming in front of it

•Known as BOW WAVE•Like wave at bow of boat



Subsonic Airfoils



•In Transonic speed range:•At Mach 1:

•Area behind bow wave is relatively slow and called STAGNATION AREA

•Large energy loss through normal wave creates significant drag

Shockwave LinkNormal and Oblique Shockwaves



Subsonic Airfoils



•In Transonic speed range:•Above Mach 1:

•Stagnation area gets smaller but energy loss increases

•Greater change in velocity and pressure through normal wave

•= greater drag (proportional to speed)



Subsonic Airfoils

High Speed Airfoils and Critical Mach Number

•To increase Critical Mach Number (or delay Shock Induced Separation occurrence):

•Can use Vortex Generators or Swept Wings



Subsonic Airfoils



•Vortex Generators•Small, low Aspect Ratio airfoils mounted in pairs at 90o on wing surfaces•Produces strong vortex around end = pulls air back onto wing surface•= delays airflow separation •Pair mounting = pairs work together for greater effectiveness

Author: Harry L. Whitehead 45


Subsonic Airfoils



•Swept Wings•Swept wings change the THICKNESS RATIO of the wing (also known as Fineness Ratio)

•Ratio of max. thickness of airfoil to chord•Lower Thickness Ratio = thinner wing = less velocity change across wing = higher MCR



Subsonic Airfoils



•Swept Wings•Unfortunately, this also causes more flow of air in a spanwise direction = stronger wingtip vortices = increased drag overall•Also, aft swept wings generally cause the tip to stall first (= potentially loose aileron control)



Subsonic Airfoils



•Swept Wings•Forward swept wings (I.e. Grumman X-29) have same MCR advantages as aft swept + roots stall first

•= can do more extreme high angle of attack maneuvers without losing control•But needs computer to control as is inherently very unstable



Subsonic Airfoils



•Swept Wings•Also, at higher speeds the wing will twist due to aerodynamic loading and will tend to wash in

•Increase angle of incidence = increased lift and drag = increased loads to failure•Composite materials make wings light and stiff enough to withstand these forces



Subsonic Airfoils



•Movable Hor. Stab.•Horizontal Stablizer will also tend to loose effectiveness at Critical Mach Number•Can keep it effective by making it’s Angle of Incidence adjustable

•F86 used this to allow supersonic speeds while maintaining control•Was first one to do so



Supersonic Airfoils



•To eliminate Shock Induced Separation in Transonic range = airfoils with max. thickness @ 50% of chord

•Double Wedge or Biconvex



Supersonic Airfoils



•Thin airfoil = no normal shock forms•Sharp edges form obliques with tiny bow wave and expansion wave in middle



Supersonic Airfoils



•All lead to practically zero subsonic airflow (= zero turbulence and drag from energy change)•Problem: not good subsonic characteristics



Supersonic Aircraft Configuration



•Wing Planform•Low Aspect Ratio & tapered

•Good strength and weight•Sweptback

•For transonic and low supersonic•Straight

•For high supersonic (Mach 2 +)






•Airfoil•Low Thickness (Fineness) Ratio•Gradual change in thickness (airfoil shape)•Max. thickness @ 50% of chord•Sharp leading and trailing edges






•Fuselage & Nacelles•Long•Slender•Fuselage “Wasp Waisted”

•Decreases overall Form and Interference Drags from interaction of shock waves on various structure areas






•Tail Surfaces•Planform and airfoil similar to wings•Generally all movable horizontal surfaces•Powered irreversible systems



Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingAerodynamic Heating

•As speeds increase above Mach 1, the Stagnation Area sees great temperature rises

•Faster = greater temp rise•Less affect at higher altitudes



Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingAerodynamic Heating

•Increased temps = decreased metal strengths•As we near Hypersonic speeds the temps are so high that normal materials will melt•Research today is in this area with ceramics and composite materials



Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingFuture?

•Lockheed is working on this design slated to fly by 2010•Supposed to disperse the shock waves to allow supersonic flight over populated areas



Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingFuture?

•Also, right now•“Quiet Spike”



Compressibility Effects Importance of the Speed of Sound Realms of Flight Supersonic Flow Patterns High Speed Airfoils Critical Mach Number Aerodynamic HeatingFuture? Flew at Mach 9.6

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