discussion that the center of mass of the foil does not lie on the axis 

 of rotation; hence, that L / and that, consequently, the v and 9 motions 

 are mechanically coupled together. Furthermore, some elastic attachment 

 to the base is necessary, hence, either kp > or k > ; if k = , it is 

 also necessary that the rotational motion be damped (cp > 0) to keep v from 

 wandering off. 



7.2 FOIL ELASTICALLY MOUNTED WITH DAMPING ON A FREE RIGID BODY 



Let the foil be attached to a free rigid body so that it will turn 

 about an axis fixed in the body, drawn parallel to the foil axis and 

 perpendicular to the stream. Let the center of mass of the foil lie on the 

 axis , and denote the distances from the axis to the center of mass of the 

 body and to the center of lift on the foil by h^ and L, respectively. 

 These three points are assumed to lie on a line that is parallel to the 

 stream in the undisplaced position of the system, and h and L are 

 positive toward the approaching stream. Positive directions are shown in 

 Fi gure 5 . 



Let the body have a principal axis of inertia at its center of mass 

 parallel to the axis of rotation, and denote the masses of foil and body 

 by m and m and their moments of inertia about their center of mass by I 

 and I , respectively. Assume that motion of the axis of rotation in the 

 direction of the stream is somehow prevented. 



* h^ and m^ refer now to the rigid body, not the foil; hence the change 

 of notation from h and m used in previous sections for the foil. 



80 



