# Pitching moment of inertia

• chris12321232
In summary: Iyy is not the only component, and you don't need to calculate it in order to calculate the other components.

#### chris12321232

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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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

chris12321232 said:

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

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.

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)?

CWatters said:
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)?
No. The Parallel Axis Theorem also can come into play as well.

The Pitching Moment of Inertia is just one of the components of the inertia tensor for the aircraft, and AFAIK, all of these components (pitch, roll, and yaw) are centroidal MMOIs.

## What is the definition of pitching moment of inertia?

The pitching moment of inertia is a measure of an object's resistance to changes in rotation around its pitch axis. It is a physical property that depends on the mass distribution of the object and the location of its pitch axis.

## How is the pitching moment of inertia calculated?

The pitching moment of inertia can be calculated by summing the products of each element's mass and distance from the pitch axis squared. This is represented by the equation: I = ∑(m * r^2), where I is the pitching moment of inertia, m is the mass of each element, and r is the distance from the pitch axis.

## Why is the pitching moment of inertia important in engineering?

The pitching moment of inertia is an important factor in engineering design as it affects an object's stability, maneuverability, and response to external forces. It is crucial in the design of aircraft, ships, and other objects that experience rotational motion.

## How does the pitching moment of inertia differ from other moments of inertia?

The pitching moment of inertia is a specific type of moment of inertia that only considers the object's resistance to changes in rotation around its pitch axis. Other moments of inertia, such as roll and yaw, consider rotation around different axes.

## How can the pitching moment of inertia be altered?

The pitching moment of inertia can be altered by changing the mass distribution of an object or by shifting the location of the pitch axis. This can be achieved through design modifications or by adding external weights to the object.