in pressure without apparent changes in den-  sity.  Such a condition of airflow is analogous  to the flow of water, hydraulic fluid, or any  other incompressible fluid.  However, at high  flight speeds the pressure changes that take  place are quite large and significant changes  in air density occur. The study of airflow at  high speeds must account for these changes  1 in air density and must consider that the  1 air is compressible and that there will  be  “compressibility effects.”  A factor of great importance in the study of  high speed airflow is the speed of sound.  The speed of sound is the rate at which small  pressure disturbances will  be propagated  through the air and this propagation speed  is solely a function of air temperature.  The  accompanying table illustrates the variation  of the speed of sound in  the standard  atmosphere.  --  D F.  - c.  K?uI,  59.0  15.0  661.7  41.1  5.1  650.3  23.3  -4.8  6%. 6  5.5  -14.7  6X6.7  --12.,  --24.6  614.6  --30.2  -34.5  602.2  -48.0  -44.4  589.6  -65.8  --w.3  516.6  -69.7  -56.5  573:s  -69.1  -56.5  573.8  -69.7  -56.5  573.8  directions. Evidence of this “pressure warn-  ing’ ’  is seeii in the typical subsonic flow  pattern of figure 3.1 where there is upwash  and flow direction change well ahead of the  leading edge. If the object is travelling at  some ,speed  above the speed of sound the air-  flow ahead of the object will not be influenced  by the pressure  field on the object since pres-  -sure disturbances cannot. be propagated ahead  of the object.  Thus, as the flight speed nears  the speed of sound a compression wave will  form at the leading edge and all changes in  velocity and pressure will  take place quite  sharply and suddenly. The airflow, ahead of  the object is not influenced until the air par-  ticles are suddenly forced out .of the way by  the concentrated pressure wave set up by the  object. Evidence of this phenomenon is seen  in the typical supersonic flow pattern of  figure 3.1.  The analogy of surface waves on the water  may help clarify these phenomena. Since a  surface wave is simply the propagation of a  pressure  disturbance, a ship moving at a speed  much less than the wave speed will not form  a “bow  wave.”  As the. ship ’ s speed nears  the wave pro$agation speed the bow wave  will  form and become stronger as speed is  increased beyond the wave speed.  At this point it should become apparent  that all compressibility effects depend upon  the relationship of airspeed to the speed of  sound. The term used to describe this rela-  tionship is the Mach number, M, and this  term is the ratio of the true airspeed to the  speed of sound.  As an object moves through the air mass,  velocity and pressure changes occur which  create pressure disturbances in the airflow sur-  rounding the object. Of course, these pressure  disturbances are propagated through the air  at the speed of sound. If the object is travel-  ling at low speed the pressure  disturbances  are  propagated ahead of the object and the airflow  immediately ahead of the object is influenced  by the pressure  field on the object.  Actually,  these pressure disturbances are transmitted in  all directions and extend indefinitely in all  where  M=Mach number  V= true airspeed, knots  d= speed of sound, knots  =a&  aO=speed of sound at standard sea level  conditions, 661 knots  e= temperature ratio  = T/T,  Revised January 1965  TABLE 3-I. V.r;afIm <  Altitude in  ,I T<  the  -  NAVWEPS 00-601-60  HIGH SPEED AERODYNAMICS  ,-I  M=; 