Techniques to Reduce Wave Drag

AE 164

Drag Divergence

Mcr = Critical Mach number. The freestream Mach number where sonic flow is first obtained at some point on the surface of a body. MDD = Drag-divergence Mach number. The freestream Mach number where the drag coefficient begins to rise dramatically.

Critical Mach Number

Drag Divergence

Some people used to believe the speed of sound could not be exceeded because it appeared that drag would increase to infinity at the speed of sound, hence the term “sound barrier.” Airliners fly at the drag-divergence Mach number for fuel economy reasons.

Low Mach Number Airfoil Shape

Supersonic Airfoil Shape

• Biconvex airfoil

• For supersonic flight, we want airfoils to have:

• Sharp leading edge (weaker shocks)

• Thin maximum thickness (weaker shocks)

Supersonic Airfoil Shape

http://www.dept.aoe.vt.edu/~devenpor/aoe3114/16%20-%20Airfoil%20Analysis.pdf

Thickness

Bell X-1

Wing airfoil thickness = 8% Tail airfoil thickness = 6% Tail airfoil delayed center of pressure shift due to shocks, providing more control up to higher Mach numbers.

Fuselage modeled after a 0.50 caliber bullet

Supercritical Airfoil

Supercritical Airfoil

As far as I am aware, all aircraft have a maximum CD at Mach 1, and CD decreases after Mach 1.

Area Rule The area rule for Mach 1: The cross-sectional area distribution should be as smooth as possible along the longitudinal axis of the body.

Area Rule

Sears-Hack Body

The Sears-Hack body has the ideal area distribution for Mach 1

Area Rule

F-102 F-102A

Area Rule

X-3 Stiletto

X-3 Stiletto

X-3 Stiletto

Supersonic Area Rule

The area rule is different for different Mach numbers. The cross-sectional areas must be cut at an angle equal to the Mach angle ( = sin-1 (1/M) ). If the Mach angle is NOT 90 degrees, the area distribution will be different at different roll angles of the aircraft. This means the area distribution must be calculated over 360 degrees of roll and averaged.

Forward Swept Wing (X-29)

Oblique Wing

Oblique Wing

Oblique Wing

F-104 (or how to go fast without using wing sweep)

F-104

F-104 is outlier using thin wing with little sweep

Swept Wing

Swept Wing

Mnormal = M cos LE

Swept Wing

The wing cross section (airfoil) perpendicular to the leading edge of a swept wing is what matters for the aerodynamics of the wing, not the streamwise cross section.

LE

Swept Wing

Swept Wing

Swept Wing

Swept Wing

Compression Lift Compression lift uses the shocks produced by the body to enhance lift. At high Mach numbers (3+), the shocks are close to the body. The pressure is higher behind the shocks, so increasing the bottom surface area downstream of the shocks increases lift. This is the principle behind waveriders.

B-70 Valkyrie

B-70 Wingtip Folding

B-70 Inlet

B-70 Nose

B-70 Inlet

B-70 Valkyrie

Summary

• Can reduce wave drag by:

– Thinner Airfoil

– Sharp Leading Edge

– Supercritical Airfoil (0.75 < M < 0.95)

– Area Ruling Entire Airplane

– Sweep Wing Leading Edge

– Combinations of the above

– Compression lift (if high Mach > 3)

• There are major tradeoffs for each of these choices