# What Inertial effects should be considered to achieve blade stability on a Variable Pitch Propeller tailoredby aerodynamic loads?

I am developing a self adjusting variable pitch propeller tailored by its pitching moments due to aerodynamic loads setting the blade rotation axis in an offset from the aerodynamic center as shown below.

At the moment i am trying to attain static and dynamic stability of the blade due to mass/Inertial effects. I have created a sketch as shown on the following figure, based on my so far understanding on inertial effects which represents a blade airfoil section and the centrifugal force (OR NOT??) acting on a mass particle.

Mass: ρdxdy*dr

Offset from Pitch Axis x

Offset from longitudinal Axis y

Force: (ρdxdy*dr)*rω^2

Component along the x-axis: (x/r)*Force

Pitch Moment: y*(x/r)*Force

And now comes the difficult part. I suppose that here i need to consider the theory of three dimensional kinetics of a rigid body and angular momentum, however i am confused on defining the coordinate systems on the blade as well as which exact moments and products of Inertia have to take into account. If i am not wrong, here a fixed coordinate reference system and one that rotates with the twisting of the blade have to be defined. The question is where the coordinate reference system has to be defined; on the blade axis of rotation, C.G, or somewhere else?

Finally i have informed that to compute the blade's dynamic stability, i will need also to consider blade flapping (i.e., motion of the blade out of plane with the rotation of the propeller), and pitching (or twisting) and this is another part i am struggling too!

• @mins Actually i have managed to compute twist and chord distributions but i suppose that this is not an issue for the current situation (It is just a sum up on the overall pitch angle (twist) and a variation on the coordinates(chord length)). This is a propeller for small UAVs but i assume theory is similar with heli's tail rotor yes! Commented Aug 24, 2017 at 10:36