# Lift of Half Cylinder

It is instructive to compute the lift of a half cylinder (of unit radius) glued to a half plane:

By symmetry the pressure is the same as for a full cylinder, that is on the cylinder surface the pressure $P$ is given by

• $P = -\frac{1}{2} + \cos (2\theta )$ for $0\le \theta\le \pi$,

and thus the lift force $L$ is given by

• $L = \int_0^\pi (-\frac{1}{2}+\cos(2\theta ))\sin (\theta )\, d\theta$ = 1.67,

which gives a lift coefficient $C_L = 1.67$ since the planform width of the cylinder is 2.

We compare with the maximal $C_L$ about 1.5  from measurements:

Not so bad!! You may think of the half cylinder as a sort of wing:

for which you have just computed the lift to be L = 1.67.