NAVWEPS 00-ROT-80 
HIGH SPEED AERODYNAMICS 
local sonic flow. Actually, the extremely 
low aspect ratios required to produce high 
critical Mach number are not too practical. 
Generally, the advantage of low aspect ratio 
must be combined with sweepback and high 
speed airfoil sections. 
The thin rectangular wing in supersonic 
flow illustrates several important facts. AS 
shown in figure 3.18, Mach cones form at the 
tips of the rectangular wing and affect t~he 
pressure distribution on the area within the 
cone. The vortex develops within the tip 
cone due to the pressure differenti,al and the 
resulting average pressure on the area within 
thecone is approximately one-half the pressure 
between the cones. Three-dimensional flow 
on the wing is then confined to the area within 
the tip cones, while the area between the 
cones experiences pure two-dimensional flow. 
It is important to realize that the three- 
dimensional flow on the rectangular wing in 
supersonic flight differs greatly from that of 
subsonic flight. A wing of finite aspect ratio 
in subsonic flight experiences a three-dimen- 
sional flow which includes the tip vortices, 
downwash behind the wing, upwash ahead of 
the wing, and local induced velocities along 
the span. Recall that the local induced veloc- 
ities along the span of the wing would incline 
the section lift aft relative to the free stream 
and result in “induced drag.” Such a flow 
condition cannot be directly correlated with 
the wing in supersonic flow, ~ The flow pattern 
for the rectangular wing of figure 3.18 dem- 
onstrates that the three-dimensional flow is 
confined to the tip, and pure two-dimensional 
flow exists on the wing area between the tip 
cones. If the wing tips were to be “raked” 
outside the tip cones, the entire wing flow 
would correspond to the two-dimensional (or 
section) conditions. 
Therefore, for the wing in supersonic flow, 
no upwash exists ahead of the wing, three- 
dimensional effects are confined to the tip 
cones, and no local induced velocities occur 
along the span between the tip cones. The 
supersonic drag due to lift is a function of the 
section and angle of attack while the subsonic 
induced drag is a function of lift coefficient 
and aspect ratio. This comparison makes it 
obvious that supersonic flight does not demand 
the use of high aspect ratio planforms typical 
of low speed aircraft. In fact, low aspect 
ratios and high taper are favorable from the 
standpoint of structural considerations if very 
thin sections are used to minimize wave drag. 
If sweepback is applied to the supersonic 
wing, the pressure distribution will be affected 
by the location of the Mach cone with respect 
to the leading edge. Figure 3.19 illustrates the 
pressure distribution for the delta wing plan- 
form in supersonic flight with the leading edge 
behind or ahead of the Mach cone. When the 
leading edge is behind the Mach cone the com- 
ponents of velocity perpendicular to the leading 
edge are still subsonic even though the free 
stream flow is supersonic and the resulting 
pressure distribution will greatly resemble the 
subsonic pressure distribution for such a plan- 
form. Tailoring the leading edge shape and 
camber can minimize the components of the 
high leading edge suction pressure which are 
inclined in the drag direction and the drag due 
to lift can be reduced. If the leading edge 
is ahead of the h4ach cone, the flow over this 
area will correspond to the two-dimensional 
supersonic flow and produce constant pressure 
for that portion of the surface between the 
leading edge and the Mach cone. 
CONTROL SURFACES. The design of con- 
trol surfaces for transonic and supersonic flight 
involves many important considerations. This 
fact is illustrated by the typical transonic and 
supersonic flow patterns of figure 3.19. Trail- 
ing edge control surfaces can be affected ad- 
versely by the shock waves formed in flight 
above critical Mach number. If the airflow