wave also occurs when a wedge or cone angle 
exceeds some critical value. Whenever the 
shock wave forms perpendicular to the up- 
stream flow, the shock wave is termed a 
“normal” shock wave and the flow immediately 
behind the wave is subsonic. Any relatively 
blunt object in a supersonic airstream will form 
a normal shock wave immediately ahead of the 
leading edge slowing the airstream to subsonic 
SO the airstream may feel the presence of the 
blunt nose and flow around it. Once past the 
blunt nose the airstream may remain subsonic 
or accelerate back to supersonic depending on 
the shape of the nose and the Mach number of 
the free stream. 
In addition to the formation of normal 
shock waves described above, this same type 
of wave may be formed in an entirely different 
manner when there is no object in the super- 
sonic airstream. It is particular that whenever 
a supersonic airscream is slowed to subsonic 
without a change in direction a normal shock 
wave will form as a boundary between the 
supersonic and subsonic regions. This is an 
important fact since aircraft usually encounter 
some “compressibility effects” before the flight 
speed is sonic. Figure 3.6 illustrates the man- 
ner in which an airfoil at high subsonic speeds 
has local flow velocities which are supersonic. 
As the local supersonic flow moves aft, a 
normal shock wave forms slowing the flow 
to subsonic. The transition of flow from 
subsonic to supersonic is smooth and is not 
accompanied by shock waves if the transition 
is made gradually with a smooth surface. The 
transition of flow from supersonic to subsonic 
without direction change always forms a 
normal shock wave. 
A supersonic airstream passing through a 
normal shock wave will experience these 
changes: 
(1) The airstream is slowed to subsonic; 
the local Mach number behind the wave is 
approximately equal to the reciprocal of the 
Mach number ahead of the wave-e.g., if 
NAVWEPS OD-EOT-80 
HIGH SPEED AERODYNAMICS 
Mach number ahead of the wave is 1.25, 
the Mach number of the flow behind the 
wave is approximately 0.80. 
(2) The airflow direction immediately 
behind the wave is unchanged. 
(3) The static pressure of the airstream 
behind the wave is increased greatly. 
(4) The density of the airstream behind 
the wave is increased greatly. 
(5) The energy of the airstream (indi- 
cated by total pressure-dynamic plus static) 
is greatly reduced. The normal shock wave 
is very wasteful of energy. 
EXPANSION WAVE. If a supersonic air- 
stream were turned away from the preceding 
flow an expansion wave would form. The 
flow “around a corner” shown in figure 3.7 
will not cause sharp, sudden changes in the 
airflow except at the corner itself and thus is 
not actually a “shock” wave. A supersonic 
airstream passing through an expansion wave 
will experience these changes: 
(1) The airstream is accelerated; the ve- 
locity and Mach number behind the wave 
are greater. 
(2) The flow direction is changed to 
flow along the surface-provided separa- 
tion does not occur. 
(3) The static pressure of the airstream 
behind the wave is decreased. 
(4) The density of -the airstream behind 
the wave is decreased. 
(5) Since the flow changes in a rather 
gradual manner there is no “shock” and 
no loss of energy in the airstream. The 
expansion wave does not dissipate air- 
stream energy. 
The expansion wave in three dimensions is 
a slightly different case and the principal 
difference is the tendency for the static pres- 
sure to continue to increase past the wave. 
The following table is provided to summa- 
rize the characteristics of the three principal 
wave forms encountered with supersonic flow. 
21’1