NAVWEPS 00-ROT-80  HIGH SPEED AERODYNAMICS  local sonic flow.  Actually, the extremely  low aspect ratios required to produce high  critical Mach number are not too practical.  Generally, the advantage of low aspect ratio  must be combined with sweepback and high  speed airfoil sections.  supersonic drag due to lift is a function of the  section and angle of attack while the subsonic  induced drag is a function of lift coefficient  and aspect ratio.  This comparison makes it  obvious that supersonic  flight does not demand  the use of high aspect ratio planforms typical  of low speed aircraft. In fact, low aspect  ratios and high taper are favorable from the  standpoint of structural considerations if very  thin sections are used to minimize wave drag.  The thin rectangular wing in supersonic  flow illustrates several important facts. AS  shown in figure 3.18, Mach cones form at the  tips of the rectangular wing and affect t~he  pressure distribution on the area within the  cone. The vortex develops within  the tip  cone due to the pressure differenti,al and the  resulting average pressure on the area within  thecone is approximately one-half the pressure  between the cones. Three-dimensional flow  on the wing is then confined to the area within  the tip cones, while the area between the  cones experiences  pure two-dimensional flow.  If sweepback is applied to the supersonic  wing, the pressure  distribution will be affected  by the location of the Mach cone with respect  to the leading edge. Figure 3.19 illustrates the  pressure  distribution for the delta wing plan-  form in supersonic flight with the leading edge  behind or ahead of the Mach cone. When the  leading edge is behind the Mach cone the com-  ponents of velocity perpendicular to the leading  edge are still subsonic even though the free  stream flow is supersonic and the resulting  pressure  distribution will greatly resemble the  subsonic pressure distribution for such a plan-  form. Tailoring the leading edge shape and  camber can minimize the components of the  high leading edge suction pressure which are  inclined in the drag direction and the drag due  to lift can be reduced. If the leading edge  is ahead of the h4ach cone, the flow over this  area will correspond to the two-dimensional  supersonic flow and produce constant pressure  for that portion of the surface between the  leading edge and the Mach cone.  It is important to realize that the three-  dimensional flow on the rectangular wing in  supersonic flight differs greatly from that of  subsonic flight.  A wing of finite aspect ratio  in subsonic flight experiences  a three-dimen-  sional flow which includes the tip vortices,  downwash behind the wing, upwash ahead of  the wing, and local induced velocities along  the span. Recall that the local induced veloc-  ities along the span of the wing would incline  the section lift aft relative to the free stream  and result in  “induced drag.”  Such a flow  condition cannot be directly correlated with  the wing in supersonic  flow, ~ The flow pattern  for the rectangular wing of figure 3.18 dem-  onstrates that the three-dimensional flow is  confined to the tip, and pure two-dimensional  flow exists on the wing area between the tip  cones. If the wing tips were to be “raked”  outside the tip cones, the entire wing flow  would correspond to the two-dimensional (or  section) conditions.  CONTROL SURFACES. The design of con-  trol surfaces  for transonic and supersonic  flight  involves many important considerations. This  fact is illustrated by the typical transonic and  supersonic flow patterns of figure 3.19. Trail-  ing edge control surfaces can be affected ad-  versely by the shock waves formed in flight  above critical Mach number. If the airflow  is separated by the shock wave the resulting  buffet of the control surface  can be very objec-  tionable. In addition to the buffet of the sur-  face, the change in the pressure  distribution due  to separation and the shock wave location can  Therefore, for the wing in supersonic flow,  no upwash exists ahead of the wing, three-  dimensional effects are confined to the tip  cones, and no local induced velocities occur  along the span between the tip cones. The  236 