Figure 124 — Illustrating the construction of an airfoil contour. 



If jS = 0, so that the initial circle is centered on the a;-axis, the skeleton arc becomes 

 a straight line and the contour obtained from the circle is symmetrical about the a; '-axis. Its 

 shape depends on the ratio a/c. If (i ^ 0, the contour is asymmetric. 



For the flow in the surrounding fluid, nothing needs to be changed in the discussion of 

 the last section except that here the velocity can be infinite only at the sharp edge or at 

 3 = - c, and ih is to be replaced by A cos ry + ih sin r; = Ae"?, as in Section 77. With the 

 latter change, Equations [78i] and [78j] for xl\ i)'and g, which are expressed in terms of 

 quantities on the 3-plane, hold as before. 



If r = 4?7af/ sin («+ /3), the velocity is again finite everywhere. Here V is the 

 relative velocity of the airfoil and the fluid at infinity and a is the angle of attack, or the 

 angle between the direction of approach of the fluid and the chord of the skeleton arc, taken 

 positive when the approach is from the concave or less convex side. With this valtie of F, 

 the lift per unit length is again 



L-^TTpaU sin ( a + ^) 



[79e] 



where p is the density of the fluid. 



In any case L = pV U, provided the motion is steady, as for any cylinder. 



The torque about the origin of coordinates on the 2' plane is, from Equation [77g], 

 in which here y = - a, ~ 



186 



