NAVWEPS OD-EOT-80  HIGH SPEED AERODYNAMICS  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.  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.  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.  (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.  A supersonic airstream passing through a  normal shock wave will  experience these  changes:  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.  (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  21 ’ 1 