# How do you calculate the moment of inertia of a Quadcopter?

I'm building a quadcopter for my final year project. I have a set of equations describing attitude and altitude but they involve $I_{xx}$, $I_{yy}$ and $I_{zz}$. None of the papers I have read describe how these are calculated. they simply choose it before their simulation. Can anyone help?

• First you need to know where the center of gravity is. With a decent design this should be in the middle of the quadrotor. Then take every component of the quadrotor, simplify them to a basic body, you can find in a table (engr.colostate.edu/~dga/mech324/Labs/Lab%2010/images/…) . At the end just use Steiner's theorem in all three dimensions and sum them up. Commented Jan 8, 2015 at 10:03
• @TobiasK Link is broken Commented Sep 14, 2023 at 11:26

## 1 Answer

You can calculate the moment of inertia of a pendulum by measuring the period of oscillation for small amplitudes. Suspend the quad by one arm and give it a little push and time the period. It does work better for larger aircraft, measuring the period of a quad-pendulum will be tricky. Maybe get a video of the aircraft with a high framerate so you can get a more accurate measurement than just a stopwatch.

https://www.boundless.com/physics/textbooks/boundless-physics-textbook/waves-and-vibrations-15/periodic-motion-123/the-physical-pendulum-432-1488/

Also having an accurate solidworks model or cad model should have the moments of inertial in some properties list.

• I really like the idea with the penduluum, but I guess he need a real calculation for his thesis. Still the idea is nice. Commented Jan 8, 2015 at 18:37
• Thanks. Though this approach may not be pretty, it is effective. It is how we check moments of inertia for small rc aircraft in our lab to double check the calculated values. Commented Jan 8, 2015 at 18:44
• What do you think of reducing the quadcopter to a spheric point mass with 4 point masses located distance l from the centre. So basically Ixx=(2m(r^2)/5)+2m(l^2),Iyy=(2m(r^2)/5)+2m(l^2) and Izz=(2m(r^2)/5)+4m(l^2). I was suggested a paper written by Randal Beard. This is how he calculates its. I cant actually do it experimentally because I need to simulate it before building. Commented Jan 8, 2015 at 22:07
• That would work perfectly if you're just doing a simulation. Commented Jan 8, 2015 at 22:14
• Thank you. I have to actually build one in the end so I am going to use the experimental method of determining the inertial moment and see how it affects the real thing compared to the simplified calculation. Thanks for your suggestions. Hopefully this will answer peoples questions on the matter. Dr beards paper was the only one that actually stated how the inertial moment was calculated. Commented Jan 8, 2015 at 22:17