NAVWEPS 0040240  BASIC AERODYNAMICS  air density requires a greater deflection of the  airstream to produce the same lift.  However,  if the airplane is flown at the same EAS, the  dynamic pressure  will be the same and induced  drag will not vary.  In this case, the TAS  would be higher at altitude to provide the  same EAS.  EFFECT OF SPEED.  The general effect of  speed on induced drag is unusual since low air-  speeds  are ’ associated with high lift coefficients  and high lift coefficients create high induced  drag coefficients. The immediate implication  is that induced  drag inmaw with decreasing  air  J@.  If all other factors are held constant to  single out the effect of airspeed, a rearrange-  ment of the previous equations would predict  that “induced drag varies inversely as ,the  square of the airspeed.”  the lift coefficient is doubled and the induced  drag is four times 0.1 grsat. If the flight load  factor is changed from one to five, the induced  drag is twenty-five times as great.  If all other  factors are held constant to single out this  effect, it could be stated that “induced drag  varies as the square of the lift”  where  Di,= induced drag corresponding to  some original lift, L1  Di,= induced drag corresponding to  some new lift, Lp  (and q (or EAS), S, AR are constant)  Di,  ’  0  L!  Di,=  L1  This expression defines the effect of gross  weight, maneuvers, and steep turns on the  induced drag, e.g., 10 percent higher gross  weight increases  induced drag 21 percent, 4G  maneuvers cause 16 times as much induced  drag, a turn with 4s0 bank requires a load  factor of 1.41 and this doubles the induced  drag.  EFFECT OF ALTITUDE.  The effect of  altitude on induced drag can be appreciated by  holding all other factors constant. The gen-  eral effect of altitude is expressed  by:  where  Dil= induced drag corresponding to some orig-  inal speed, Vi  Di,= induced drag corresponding to some new  speed, Vs  (and L, S, AR, ,J are constant)  Such an effect would imply that a given air-  plane in steady flight would incur one-fourth  as great an induced drag at twice as great a  speed or four times as great an induced drag at  half the original speed. This variation may  be illustrated by assuming that an airplane in  steady level flight is slowed from 300 to 150  knots. The dynamic pressure at 1% knots is  one-fourth the dynamic pressure  at 300 knots  and the wing must deflect the airstream four  times as greatly to create the same lift.  The  same lift force is then slanted aft four times  as greatly and the induced drag is four times  as great.  where  Dil= induced drag corresponding to some orig-  inal altitude density ratio, 0,  D&= induced drag corresponding to some new  altitude density ratio, q  (and L, S, AR, V are constant)  This relationship implies that induced drag  would increase with altitude, e.g., a given  airplane flying in level flight at a given TAS  at 40,000 ft. (u=O.25) would have four times  as much induced drag than when at sea level  (u= 1.00). This effect results when the lower  The expressed  variation of induced drag with  speed points out that induced drag will be of 