# Hi :) new here, to ask an angular velocity question

#### Dave1123

Well, hello everyone.

I will be honest. I basically registered here, to get a question answered which is bothering me a lot lately. Would be really nice if someone could help me a little. So lets cut right to the case

Assuming you have an aircraft with a propellor on each wing.
And lets say, the aircraft as well as the rotors rotate at an angluar velocity (Wx,Wy Wz - for the aircraft & Nx,Ny,Nz - for the rotor).

The rotor can only rotate about its X-axis (so for example Nx=100 rad/s, Ny=0, Nz=0) and the aircraft can rotate freely about all of its 3 axis (I dont know, something like Wx=0 rad/s, Wy=0, Wz=0.5 --> So we are yawing).
Aircraft frame is (X=Roll, Y=Pitch, Z=Yaw)

The time t is set to 1s.

Now... what is the angluar velocity of the propellor center of gravity combining both rotations (aircraft & prop)?

What i found is this general formulation: (R = angular velocity at prop CoG)
Rx = Wx + Nx
Ry = Wy * cos(Nx * t) + Wz * sin(Nx * t)
Rz = -Wy * sin(Nx * t) + Wz * cos(Nx * t)

I think it makes sense, but i dont quite get fully behind the calculation of Ry & Rz. Can someone please help me to fully understand those two lines. I can add some illustrations/visualizations if needed.

Thanks!

#### Osprey

Sounds like you're an expert in aero-engineering ??? A diagram would help ...

studiot

#### Woody

The key, I think, are the axes in which the rotations are defined.
the way you have written your equations, Rx, Ry, Rz and Wx, Wy and Wz are all defined in the initial flight axes.
You are then rotating your prop axes back into the original flight axes as the aircraft yaws pitches and rolls.
Note however that the current flight axes are changing as the aircraft yaws pitches and rolls
So if you chose to define the results in current flight, or aircraft, or prop axes, the result would be different.

topsquark