NAVWEPS 00-801-80  HIGH SPEED AERODYNAMICS  However, if high speed flight is the primary  consideration, the airfoil must be chosen to  have. the highest practical critical  Mach  number.  Critical Mach number has been defined as  the flight Mach number which produces first  evidence of local sonic flow.  Thus, the air-  foil shape and lift coe&ient-which  determine  the pressure and velocity distribution-will  have a profound effect  on critical Mach number.  Conventional, low speed airfoil shapes have  relatively poor compressibility characteristics  because of the high local velocities near the  leading edge. These high local velocities are  inevitable if both the maximum thickness and  camber are well forward on the chord.  An  improvement of the compressibility character-  istics can be obtained by moving the points of  maximum camber and thickness aft on the  chord. This would distribute the pressure  and  velocity more evenly along the chord and  produce a lower peak velocity for the same  lift coefficient. Fortunately, the airfoil shape  to provide extensive lamiaar flow and low  profile drag in low speed, subsonic flight will  provide a pressure  distribution which is favor-  able for high  speed flight.  Figure 3.12  illustrates  the  pressure distributions  and  variation of critical Mach number with lift  coefficient for a conventional low speed airfoil  and a high speed section.  Figure 3.13 shows the flow patterns for  two basic supersonic airfoil sections and pro-  vides the approximate equations for lift,drag,  and lift curve slope. Since the wave drag is  the only factor of difference between -the two  airfoil sections, notice the configuration fac-  tors which affect the wave drag. For the  same thickness ratio, the circular arc airfoil  would have a larger wedge angle formed  between the upper and lower surfaces  at the  leading edge.  At the same flight Mach num-  ber the larger angle at the leading edge would  form the stronger shock wave at the nose and  cause a greater pressure  change on the circular  arc airfoil.  This same principle applies when  investigating the effect of airfoil thickness.  Notice that the wave drag coefficients for  both airfoils vary as the SQUARE of the  thickness ratio, e.g.,  if the thickness ratio  were doubled, the wave drag coefhcient would  he four times as great.  If the thickness were  increased, the airflow at the leading edge will  experience a greater change in direction and  a stronger shock wave will be formed. This  powerful variation of wave drag with thick-  ness ratio necessitates  the use of very thin air-  foils with sharp leading edges for supersonic  flight.  An additional consideration is that  thin airfoil sections favor the use of low aspect  ratios and high taper to obtain lightweight  structures and preserve stiffness and rigidity.  The parameter JMz-l  appears in  the  denominator of each of the equations for the  aerodynamic coefficients and indicates a de-  crease in each of these coefficients with an  increase in Mach number. Essentially, this  means that any aerodynamic surface becomes  less sensitive to changes in angle of attack at  higher Mach numbers. The decrease  in lift  curve slope with Mach number has tremendous  implications in the stability and control of  high speed aircraft.  The vertical tail becomes  less sensitive to angles of sideslip and the  directional stability of the aircraft will deteri-  orate with  Mach number. The horizontal  tail  of the airplane experiences the same  In order to obtain a high critical Mach  number from an airfoil  at some low  lift  coefficient the section must have:  (u) Low thickness ratio.  The point of  maximum thickness should be aft to smooth  the pressure  distribution.  (6) Low camber. The mean camber line  should be shaped to help minimize the  local velocity peaks.  In  addition,  the higher the required lift  coefficient the lower the critical Mach number  and more camber is required of the airfoil.  If supersonic flight is a possibility the thick-  ness ratio and leading edge radius must be  small to decrease  wave drag. 