I am new! New to this forum and new to aviation (i normally deal with statics) so thanks in advance for beeing patient with me.
Recently i was trying to figure out how much weight a rotor can lift as a function of the rotor diameter.
Therefore I came across this formula.
$$
T_{rotor} =(0.5*P^2*η_{rotor}^2*η_{el}^2*π*d_{rotor}^2*ρ_{Air})^{1/3}
$$
This brings me already quite close to my goal as I now have $ Thrust = f(P^2, d^2)$. Now I tried to relate the engine power to the rotor diameter by using :
$ P=T * {rpm}$
with $ T=I *α=(0.5* m*r^2)*v_{sound}/r $
and $ {rpm}=v_{sound}/(\pi*d)$
Which leads me to $$ P(m)=(v_{sound}^2/(4*π))*m $$
From this calculation a few questions arise:
- Do you think this is a good estimate (within +-15%)?
- Is there a better formula to estimate $I_{rotor}$ than using $I_{zylinder}$?
- Is there any formula to estimate $ m_{rotor} = f(d_{rotor}) $
I want to add that this estimate is for a rough feasability study and not to design a rotor or aircraft. I also know that several of the values in this formulas are a function of altitude and aircraft velocity. Please dont take this into account. At the moment I am only interested in a stationary solution.
Thanks for your help!