# How to calculate lift for multiple rotors?

So I know that $$L = \frac{1}{2}​ρv^2AC_L$$, but if I want to find the lift for a three-blade helicopter, do I just multiply by 3 or what? Let's say I have a 700mm rotor at 61mm wide, would it be: $$L = 1/2\cdot1.225\cdot73^2\cdot0.0434 = 141.6$$ newtons. If I have 3 blades would it simply be: 141.6 x 3 = 424 newtons?

Side question, what sort of motor would I need for a 700mm 3 prop setup, you can ignore this if you want.

• What is 73 in your calculation? How did you calculate speed? And where is CL in there? Generally, propellers are calculated differently to wings, and there is plenty of literature about it...
– Zeus
Commented Feb 23, 2022 at 8:18
• Literal answer to your title question is easy, provided the rotors don't overlap: 1) calculate the lift (thrust) of one rotor; 2) multiply by the number of rotors. This doesn't quite work for blades though, which you seem to imply in the body. Please clarify.
– Zeus
Commented Feb 23, 2022 at 8:20

That equation is for wings, where the whole wing is moving at the same airspeed. Rotor blades are spinning, so their airspeed changes along their length. To use an equation like that, you need to calculate the speed for any position along the blade and integrate for the whole blade. For multiple blades, you're right, you just multiply by the number of blades.

However, it's generally more useful to consider the momentum flow through a rotor disk. The area of the disk is known, and the blade pitch gives the maximum air speed through the disk. Every second a mass of air is accelerated from stationary to that speed. Force = mass * acceleration, so you can work out the force. You can also work out the kinetic energy input ever second, which is the power.

Some of the equations are here but this was an option in the third year of an aerospace engineering course, so it builds on stuff from the earlier years and I don't remember all of it!

The topic you should look for is actuator disk theory