NAVWEPS OO-SOT-~O  BASIC AERODYNAMICS  (3) The induced angle of attack can be  derived as:  quence of developing lift with a finite wing  and is termed INDUCED DRAG, D+  In-  duced drag is separate from the drag due to  form and friction and is due simply to the de-  velopment of lift.  By inspection of the force diagram of figure  1.30, a relationship between induced drag, lift,  and induced angle of attack is apparent. The  induced drag coeficient, CDi, will vary directly  with the wing lift coefficient, C,, and the in-  duced angle of attack, as. The effective lift  is the vertical component of the actual lift and,  if the induced angle of attack is small, will be  essentially the same as the actual lift.  The  J horizontal and vertical component of drag is  insignificant under the same conditions.  By a  detailed study of the factors involved, the fol-  lowing relationships can be derived for a wing  with an elliptical lift distribution:  (NOTE:  the derivation of these relationships  may be found in any of the standard engi-  neering aerodynamics textbooks.)  These relationships facilitate an understanding  and appreciation of induced drag.  The induced angle of attack Eli= 18.~4$~  (  >  depends on the lift coefficient and aspect ratio.  Flight at high lift conditions such as low speed  or maneuvering flight will create high induced  angles of attack while high speed, low lift  flight will create very small induced angles .of  attack. The inference is that high lift coefli-  cients require large downwash and result in  large ,induced angles of attack. The effect of  aspect ratio is significant since a very high  aspect  ratio would produce a negligible induced  angle of attack. If the aspect ratio were in-  finite, the induced angle of attack would be  zero and the aerodynamic characteristics  of the  wing would be identical with the airfoil sec-  tion properties. On the other hand, if the  wing aspect ratio is low, the induced angle of  attack will be large and the low aspect ratio  airplane must operate at high angles of attack  at maximum lift.  Essentially, the low aspect  ratio wing affects a relatively small mass of  air and consequently must provide a large de-  flection (downwash) to produce lift.  EFFECT OF LIFT.  The induced drag co-  e&cient  (  C&l  CDi=0.31E -  shows somewhat sim-  ,I  AR  ilar effects  of lift coefficient and aspect ratio.  Because  of the power of variation of induced drag  coefficient with lift coefficient, high lift coefli-  cients provide very high induced drag and low  lift coefficients  very low induced drag. The di-  rect effect  of C, can be best appreciated  by assum-  ing an airplane is flying at a givenweight, alti-  tude, and airspeed. If the airplane is maneuvered  from steady level flight to a load factor of two,  where  C,= lift coefficient  sin ai=natural sine of the induced angle  of attack, Eli, degrees  r=3.1416, constant  AR= wing aspect ratio  or  CD,-C, sin ai  CD&  c,P  =0.318 -Jjj  (  )  (1) The induced drag equation follows the  same form as applied to any other aerody-  namic force.  where  Di=CDigS  Di=induced drag, lbs.  4= :Vymic pressures;  psf  =295  Cni= induced drag coefficient  S=wing area, sq. ft.  (2) The induced drag coefficient can be  derived as :  68  hWd  Jonua~ 1965  a~= 18.24 &  (degrees)  (  ) 