Lift and Drag for Elliptical Loading

The lift coefficient for an aerofoil in terms of the circulation k0 around it, by Equation (8.6a), is:

nbk0

Cl —

The aspect ratio of the aerofoil is:

_ span 2b яі — — —

chord c

2b x 2b c x 2b _ 4b2

— ~y.

ко

4b

Thus, the lift coefficient in terms of constant downwash velocity, at the trailing edge, is:

лЛію

U

By Equation (8.3), w/U = e and by Equation (8.25):

є = (a — a0).

Therefore:

By Equation (8.8), the induced drag coefficient is:

C2

Cl

nJR

The variation of Cl with CDv is called the polar curve of the aerofoil.

Equation (8.8) shows that the polar curve of an elliptically loaded aerofoil is a parabola, provided the only source of the drag is the induced velocity.

The polar curve is as shown in Figure 8.13. The polar curve can be graduated in incidence as indicated in Figure 8.13. Since a is proportional to the lift coefficient Cl, equal increments of incidence gradients of the polar correspond to equal increment of Cl.

For incidence below the stall, the CL verses a curves are straight lines whose slopes increase as the aspect ratio increases, as shown in Figure 8.14.