NAVWEPS 00-8OT-80  BASIC AERODYNAMICS  age relative wind which is different from the  remote free stream wind.  Since the aerody-  namic forces created by the airfoil sections of a  wing depend upon the immediate airstream in  which they operate, consideration must be  given to the effect of the inclined average rela-  tive wind.  vortex filaments which consist of the tip or  trailing vortices coupled with the bound or  line vortex. The tip vortices are coupled with  the bound vortex when circulation is induced  with lift.  The effect of this vortex system is  to create certain vertical velocity components  in the vicinity of the wing.  The illustration  of these vertical velocities shows that ahead  of the wing the bound vortex induces an up-  wash.  Behind the wing, the coupled action  of the bound vortex and the tip vortices in-  duces a downwash.  With the action of tip  and bound vortices coupled, a final vertical  velocity (220) is imparted to the airstream by  the wing producing lift.  This result is an  inevitable consequence  of a finite wing pro-  ducing lift.  The wing Producing lift applies  the equal and opposite force to the airstream  and deflects it downward. One of the impor-  tant factors in this system is that a downward  velocity is created at the aerodynamic center  (w) which is one half the final downward  velocity imparted to the airstream (2~).  To create a certain lift coefficient with the  airfoil section, a certain angle must exist be-  tween the airfoil chord line and the avcragc  relative wind.  This angle of attack is a,,, the  section angle of attack.  However, as this lift  is developed on the wing, downwash is in-  curred and the average relative wind is in-  clined.  Thus, the wing must be given some  angle attack greater than the required section  angle of attack to account for the inclination of  the average relative wind.  Since the wing  must be given this additional angle of attack  because  of the induced flow, the angle between  the average reiative wind arid tlie remote fiCC  stream is termed the induced angle of attack,  ai.  From this influence, the wing angle of  attack is the sum of the section and induced  angles of attack.  The effect of the vertical velocities in the  vicinity of the wing is best appreciated when  they are added vectorially to the airstream  velocity.  The remote free stream well ahead  of the wing is unaffected and its direction is  opposite the flight path of the airplane.  ‘ Aft  of the wing, the vertical velocity (2~) adds to  the airstream velocity to produce the down-  wash angle e (epsilon).  At the aerodynamic  center of the wing, the vertical,velocity (w)  adds to the airstream velocity to produce a  downward deflection of the airstream one-half  that of the downwash angle. In other words,  the wing producing lift by the deflection of an  airstream incurs a downward slant co the wind  in the immediate vicinity of the wing.  Hence,  the JeCtionJ  of the wing operate  in an average rela-  tive wind which is inclined downward  one-half  the  final dowraw& angle. This is one important  feature which distinguishes the aerodynamic  properties of a wing from the aerodynamic  properties of an airfoil section.  Another important influence of the induced  flow is the orientation of the actual lift on a  wing.  Figure 1.30 illustrates the fact that the  lift produced by the wing sections is perpen-  dicular to the average relative wind.  Since  the average relative wind is inclined down-  ward, the section lift is inclined aft, by the  same amount-the  induced angle of attack,  ai.  The lift and drag of a wing must continue  to be referred perpendicular and parallel to the  remote free stream ahead of the wing.  In this  respect, the lift on the wing has a component  of force parallel to the remote free stream.  This component of lift in the drag direction  is the undesirable-but  unavoidable-conse-  a=ul)+a;  where  a= wing angle of attack  OLD=  section angle of attack  OI;= induced angle of attack  The induced velocities existing at the aero-  dynamic center of a finite wing create an aver-  INDUCED DRAG  66 