perpendicular to both the stream and the foil. The assumed axis of rotation 

 may be displaced into any paraJ-lel position in the plane of the foil without 

 affecting the motion provided an appropriate change is made in v. 



The foil is assumed to be attached to some structure but it is 

 assumed to be so long that disturbance of the lift by the presence of the 

 structure may reasonably be neglected. 



7.1 FOIL ATTACHED ELASTICALLY WITH DAMPING TO AN IMMOBILE BASE 



Let the foil be attached so that it can undergo displacements v and 

 8 as described and, to simplify the formulas, locate the 9 axis so that 

 the lift acts through it. When the foil is displaced, let an elastic 

 force - k,v and a frictional force - c v act on it along the same line as 

 Fy and positive in the same direction. Also let an elastic moment - kpS 

 and a frictional moment - c 6 act on it about the axis and positive in 

 the same direction as 0. 



Let the foil be so positioned that the lift acts at a distance L from 

 the center of mass of the foil, L being positive when the lift is dis- 

 placed from the center of mass toward the approaching stream. Denote by 

 m the foil mass and by I its moment of inertia about an axis drawn 

 throui^ its center of mass and parallel to the 6 axis. See Figure k where 

 directions are shown for positive v, v, 6, 6, F and L. 



* With 9 terms present, no single location for action of Fj^ was con- 

 sidered. In the present case such a location is specified. L here 

 is not the same as in Equation [i+5b]. 



** Note that here the moment of inertia of the foil is denoted by I 

 instead of Iq, to allow use of I^ for a rigid body in Section 7.2. 



72 



