NAVWEPS 00-8OT-80 
HIGH SPEED AERODYNAMICS 
shock wave forms as the boundary between 
the supersonic flow and the subsonic flow on 
the aft portion of the airfoil surface. The 
acceleration of the airflow from subsonic to 
supersonic is smooth and unaccompanied by 
shock waves if the surface is smooth and the 
transition gradual. However, the transition 
of airflow from supersonic to subsonic is 
always accompanied by a shock wave and, 
when there is no change in direction of the 
airflow, the wave form is a normal shock 
wave. 
Recall that one of the principal effects of 
th,e normal shock wave is to produce a large 
increase in the static pressure of the airstream 
behind the wave. If the shock wave is 
strong, the boundary layer may not have 
sufficient kinetic energy to withstand the 
large, adverse pressure gradient and separation 
will occur. At speeds only slightly beyond 
critical Mach number the shock wave formed 
is not strong enough to cause spearation or 
any noticeable change in the aerodynamic 
force coefficients. However, an increase in 
speed above critical Mach number sufhcient 
to form a strong shock wave can cause sepa- 
ration of the boundary layer and produce 
sudden changes in the aerodynamic force 
coefficients. Such a flow condition is shown 
in figure 3.9 by the flow pattern for M=O.n. 
Notice that a further increase in Mach number 
to 0.82 can enlarge the supersonic area on the 
upper surface and form an additional area of 
supersonic flow and normal shock wave on the 
lower surface. 
As the flight speed approaches the speed of 
sound the areas of supersonic flow enlarge and 
the shock waves move nearer the trailing 
edge. The boundary layer may remain sepa- 
rated or may reattach depending much upon 
the airfoil shape and angle of attack. When 
the flight speed exceeds the speed of sound 
the “bow” wave forms at the leading edge and 
this typical flow pattern is illustrated in 
figure 3.9 by the drawing for M= 1.05. If the 
speed is increased to some higher supersonic 
value all oblique portions of the waves incline 
more greatly and the detached normal shock 
portion of the bow wave moves closer to the 
leading edge. 
Of course, all components of the aircraft 
are affected by compressibility in a manner 
somewhat similar to that of basic airfoil. 
The tail, fuselage, nacelles, canopy, etc. and 
the efkct of the interference between the 
various surfaces of the aircraft must be 
considered. 
FORCE DIVERGENCE. The airflow sepa- 
ration induced by shock wave formation can 
create significant variations in the aerody- 
namic force coefficients. When the free stream 
speed is greater than critical Mach number some 
typical effects on an airfoil section are as 
follows : 
(1) An increase in the section drag coeffi- 
cient for a given section lift coe5cient. 
(2) A decrease in section lift coefficient 
for a given section angle of attack. 
(3) A change in section pitching moment 
coe5cient. 
A reference point is usually taken by a plot 
of drag coe5cient versus Mach number for 
a constant lift coefficient. Such a graph is 
shown in figure 3.10. The Mach number 
which produces a sharp change in the drag 
coe5cient is termed the “force divergence” 
Mach number and, for most airfoils, usually 
exceeds the critical Mach number at least 5 
to 10 percent. This condition is also referred 
to as the “drag divergence” or “drag rise.” 
PHENOMENA OF TRANSONIC FLIGHT. 
Associated with the “drag rise” are buffet, 
trim and stability changes, and a decrease 
in control surface effectiveness. Conventional 
aileron, rudder, and elevator surfaces sub 
jetted to this high frequency buffet may 
“buzz,” and changes in hinge moments may 
produce undesirable control forces. Of course, 
if the buffet is quite severe and prolonged, 
structural damage may occur if this operation 
is in violation of operating limitations. When 
airflow separation occurs on the wing due to 
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