# Measuring the moment of inertia tensor about the principle axes of a RC helicopter.

1. Aug 25, 2008

### williamshipman

Hi guys.

I am trying to measure the moment of inertia of a remote controlled helicopter about its 3 principle axes at the centre of gravity. In all of the literature I have read relating to this project, everyone just glosses over this part. What I need to figure out is an experimental setup and method.

I have the following 3 equations that relate the moment about each axis and the 3 angular velocities to the angular accelerations. All of these equations are with respect a fixed axis system centred at the centre of gravity.
p_dot=M_x/I_xx -rq/I_xx (I_zz-I_yy )
q_dot=M_y/I_yy -rp/I_yy (I_xx-I_zz )
r_dot=M_z/I_zz -pq/I_zz (I_yy-I_xx )

p_dot, q_dot and r_dot are the angular accelerations. The angular velocities are p (roll), q (pitch) and r (yaw). The moments about each axis are M_x, M_y and M_z and the moments of inertia are I_xx, I_yy and I_zz.

So far, I have thought of putting the helicopter on a table and rotating it about one axis, then repeating the procedure for the other 2 axes. This has the small problem that, if the table rotates at a constant rate, the dot terms are zero. If the table is accelerating, then this could work but how would I know what the torque applied to the helicopter is?

I forgot to mention, the helicopter will be fitted with gyros to measure the orientation and accelerometers for the linear and angular accelerations. Thanks for your help.

2. Aug 25, 2008

### FredGarvin

Re: Measuring the moment of inertia tensor about the principle axes of a RC helicopte

It's not the easiest way to do things, but it is definitely doable. I guess it all boils down to how accurate you want to get. You can measure the principal axes via the method in the attached article. The off diagonal elements you can then calculate.

Go to this thread for the article:

3. Aug 25, 2008

### williamshipman

Re: Measuring the moment of inertia tensor about the principle axes of a RC helicopte

Thanks very much for the info Fred, that was exactly what I was looking for.

4. Jun 7, 2009

### williamshipman

Re: Measuring the moment of inertia tensor about the principle axes of a RC helicopte

Its now a few months later and I thought I'd post this. FredGarvin gave a paper from Space Electronics in the other thread he links to. Space Electronics has published a number of other papers on their website that explain how to measure various properties, like the moment of inertia and center of gravity. Anyone who is struggling with such work should look at their website http://www.space-electronics.com" [Broken].

Last edited by a moderator: May 4, 2017