# Advance ratio formula for drone propeller in vertical climb

According to this wikipedia article. There are two expressions for advance ratio:

• For propellers: $$J = {V_\infty \over nD} \tag{1}$$

• For helicopters:

$$\mu = {V_\infty \over \Omega r} \tag{2}$$

We know that: $$\Omega = 2\pi n$$, so by substitution in (2):

$$\mu = {V_\infty \over {2\pi nr}}= {V_\infty \over \pi n D} = {J \over \pi}$$

So $$\mu \neq J$$

My question: In case of a helicopter in a vertical climb (no forward velocity) with constant velocity $$\vec v = (0, 0, u_z)$$, which expression should I use for advance ratio? $$J$$ or $$\mu$$?

• The advance ratio, since it is not dimensional, is just an intermediate term on your way to something else. For example, for a prop you'd have a chart of coefficient of thrust versus advance ratio. You'd just scale the chart appropriately based on which ratio you were using. – MikeY Mar 24 '19 at 13:53