distribution produces an inclined lift with 
drag due to lift which is in addition to the 
wave drag at zero lift. Part (g) of figure 3.8 
shows the wave pattern for a circular arc air- 
foil. After the airflow traverses the oblique 
shock wave at the leading edge, the airflow 
undergoes a gradual but continual expansion 
until the trailing edge shock wave is en- 
countered. Part (h) of figure 3.8 illustrates 
the wave pattern on a conventional blunt nose 
airfoil in supersonic flow. When the nose is 
blunt the wave must detach and become a 
normal shock wave immediately ahead of the 
leading edge. Of course, this wave form 
produces an area of subsonic airflow at the 
leading edge with very high pressure and 
density behind the detached wave. 
The drawings of figure 3.8 illustrate the 
typical patterns of supersonic flow and point 
out these facts concerning aerodynamic surfaces 
in two dimensional supersonic flow: 
(1) All changes in velocity, pressure, 
density and flow direction will take place 
quite suddenly through the various. wave 
forms. The shape of the object and the 
required flow ,direction change dictate the 
type and strength of the wave formed. 
(2) As always, lift results from the distri- 
bution of pressure on a surface and is the net 
force perpendicular to the free stream direc- 
tion. Any component of the lift in a direc- 
tion parallel to the windstream will be 
drag due to lift. 
(3) In supersonic flight, the zero lift drag 
of an airfoil of some finite thickness will 
include a “wave drag.” The thickness of 
the airfoil will have an extremely powerful 
effect on this wave drag since the wave drag 
varies as the square of the thickness ratio- 
if the thickness is reduced 50 percent, the 
wave drag is reduced 73 percent. The lead- 
ing edges of supersonic shapes must be sharp 
or the wave formed at the leading edge will 
be a strong detached shock wave. 
(4) Once the flow on the airfoil is super- 
sonic, the aerodynamic center of the surface 
NAWEPS 00-80T-80 
HIGH SPEED AERODYNAMICS 
will be located approximately at the SO per- 
cent chord position. As this contrasts with 
the subsonic location for the aerodynamic 
center of the 23 percent chord position, sig- 
nificant changes in aerodynamic trim and 
stability may be encountered in transonic 
flight. 
CONFIGURATION EFFECTS 
TRANSONIC AND SUPERSONIC PLIGHT 
Any object in subsonic flight which has some 
finite thickness or is producing lift will have 
local velocities on the surface which are 
greater than the free stream velocity. Hence, 
compressibility effects can be expected to 
occur at flight speeds less than the speed of 
sound. The transonic regime of flight pro- 
vides the opportunity for mixed subsonic and 
supersonic flow and. accounts for the first 1 
significant effects of compressibility. 
Consider a conventional airfoil shape as 
shown in figure 3.9. If this airfoil is at a 
flight Mach number of 0.50 and a slight posi- 
tive angle of attack, the maximum local 
velocity on the surface will be greater than 
the flight speed but most likely less than 
sonic speed. Assume that an increase in 
flight Mach number to 0.72 would produce 
lfrst cvidmc of local son@ flow. This condition 
of flight would be the highest flight speed 
possible without supersonic flow and would 
be termed the “critical Mach number.” Thus, 
critical Mach number is the bouodary between 
subsonic and transonic flight and is an im- 
portant ~point of reference for all compressi- 1 
bility effects encountered in transonic flight. 
By delinition, critical Mach number is the 
“free stream Mach number which produces 
6rst evidence of local sonic flow.” Therefore, 
shock waves, buffet, airflow separation, etc., 
take place above critical Mach number. 
As critical Mach number is exceeded an 
area of ~uprrronic airflow is created and a normal 
215 
Revised January 1965