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.

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