Sometimes understanding the moments of inertia of a model airplane can help you make it fly better.
The moments of inertia in an airplane predict how quickly it will rotate. They play the same role that the weight does when it comes to linear acceleration. You see, the more an airplane weighs, the longer it takes the airplane’s motor to accelerate it forward. There are three moments of inertia, one along each major axis (roll, pitch, and yaw).
The higher the moment of inertia along a given axis, the longer it takes the airplane to gain in angular acceleration. How high the moment of inertia is along a given axis is mainly determined by the distribution of weights along that axis.
For example, in the roll moment of inertia, if the airplane has heavy wing tips, then it will roll more slowly. That means it has a higher roll moment of inertia than normal. This might be due, for example, by having wing tip mounted fuel tanks.
Another situation where an airplane might have a higher roll moment of inertia is when the wing has no taper. This is also called having a constant chord wing. There is a lot more mass (or weight) towards the wing tips. It makes rolling the airplane harder.
There is also a lot more wing area towards the wing tips, which also will cause a slower roll rate.
In the most part, you can just ignore the moments of inertia in your model airplane. Airplanes tend to be built alike. Motor in the front, long skinny fuselage, long flat wing, etc. The moments of inertia are pretty predictable.
That is good news. Computing the moments of inertia is complicated. You would need to take into account the distribution of weights along the entire airplane. It is similar to conducting a balance computation, but along three axes.
When it Matters
Having an understanding of how the moments of inertia work comes in handy when the configuration of the airplane is unusual.
For example, what if the motor is mounted over the wing center section instead of the nose? That will tend to make the pitch and yaw moments of inertia smaller. In an airplane like this, you may notice that the elevator is more effective (works better) than in an airplane with the motor on the nose.
If you are designing an unusual looking model airplane, keep the moments of inertia in mind. You might need to adjust the sizes of the control surfaces to compensate.