# Pitching moment of inertia

Hi everyone,

I have a question which requires me to calculate aircraft pitching moment of inertia.
I looked everywhere and can't find much about it, just the basis "what is inertia etc".

Can anyone give an example on how to calculate pitching moment of inertia.

Thanks a lot

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SteamKing
Staff Emeritus
Homework Helper
Vehicles like aircraft and ships are capable of motion in six degrees of freedom: 3 translational (surge, sway, and heave) and 3 rotational (roll, pitch, and yaw).
As with all bodies undergoing rotational motion, this motion is resisted by the vehicle's mass moment of inertia, calculated about the particular axis of rotation.

Since pitching is the rotation of the aircraft such that the nose and tail go up and down, then the pitching moment of inertia is the property of the aircraft and how its mass is distributed which tends to resist pitching.

The details of how to make mass moment of inertia calculations are typically included in texts dealing with dynamics, or the dynamics of vehicles. What you have to do is either perform a mass take-off of the aircraft in question, i.e. tabulate the mass and centers of mass of all its components, or know the radius of gyration in pitch and the total aircraft mass. It's not clear what information you have about this aircraft, so I'll let you digest these comments for now.

If you have any additional questions, please feel free to post them.

Let say my aircraft parameters are listed below;
cargo aircraft, weighting 200t
fuselage length 40m
wing span 36m
c.g. 20m from nose on x axis
Ry=0.38 for 2 engine cargo aircraft
other data you can just make up.

Would you be able to show an example how would you calculate the pitching moment of inertia. I went through many resources and all I found is that I need to calculate Iyy which is not the moment of inertia.

Thank you

SteamKing
Staff Emeritus
Homework Helper

Let say my aircraft parameters are listed below;
cargo aircraft, weighting 200t
fuselage length 40m
wing span 36m
c.g. 20m from nose on x axis
Ry=0.38 for 2 engine cargo aircraft
other data you can just make up.

Would you be able to show an example how would you calculate the pitching moment of inertia. I went through many resources and all I found is that I need to calculate Iyy which is not the moment of inertia.

Thank you
Why do you think Iyy is not a moment of inertia?

Im confused now,

Iyy- I guess is the mass moment of inertia, and it has nothing to do with c.g. Whereas Pitching Moment of Inertia should have something to do with gravity and if it is "Moment" therefore the equation should start with M=... or Mcg=...

I have no idea now.
thanks

SteamKing
Staff Emeritus
Homework Helper
You seem to be a little hazy on the concept of moment of inertia and the dynamics of moving bodies.

The mass moment of inertia of a body is going to be calculated using the c.g. of the body as a reference and will have units of mass * length2. The moment of inertia is not like the moment of a force, for example.

If you have a question requiring the calculation of the pitching moment of inertia, why don't you post the entire question, like the rules for PF state?

Unfortunately, PF is the wrong place to learn dynamics. You'll have to get a text for that yourself and start reading it.

CWatters
Homework Helper
Gold Member
Not my field but google suggest Iyy is the pitching moment of inertia. Is there any reason why this isn't calculated the same way any moment of inertia is calculated (eg sum the moments of inertia for the parts)?

SteamKing
Staff Emeritus