Hi,

I'm trying to find out how to obtain propulsive efficiency, n for a pitching, heaving and sweeping airfoil.

From some references, I managed to get these formulas:

n = power input / power output ( p(out) / p(in) )

p(out) = thrust (T) * u velocity

p(in) = -Lift (L)(t)*dh/dt - Moment (M)(t)*d(theta)/dt

There's something which I don't understand.

h in dh/dt in the reference is given as the heaving height. If there is sweeping (moving the airfoil in the x-direction) involved, will the definition change?

Given the point of pitching, how should the moment be calculated?

Is it given by

M = L*x-T*y where x,y are the horizontal and vertical distance of the airfoil's CG from the point of pitching respectively?

Thank you

Oh ya,

do I need to modify for a case which includes sweeping to become

p(in) = -Lift (L)(t)*dh(y)/dt - Moment (M)(t)*d(theta)/dt - Thrust (T)(t)*dh(x)/dt

where h(x) is the horizontal sweeping displacement and h(y) is the vertical one.