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# Pitching Moment of Inertia

## Pitching Moment of Inertia

(OP)
Hi everyone,

Just wonder if anyone could explain me with an example how to calculate the Pitching Moment of Inertia on aircraft.
Aircraft Details;
Weight 50t
fuselage length 40m
wing span 37m
c.g from nose 20m
Ry 0.38 for 2engine cargo aircraft

Thanks a lot

### RE: Pitching Moment of Inertia

Ry=0.38 looks like a helpful but unexplained number. I suggest that is a non domensional scaling factor for some dimension of the aircraft, hopefully length, otherwise span.

If the former is correct then Iyy=50*(.38*40)^2*1000 kg m^2

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Pitching Moment of Inertia

(OP)
In the text book it says that Ry is nondimensional radii of gyration. Each aircraft has its own specific value whether or not it is a cargo two engine or 4 engine aircraft.
The R value comes in a form of Rx Ry and Rz with a dash above them. As I am only required to find pitch moment therefore I only need Ry.

The formula I found in the text book to calculate moment of inertia is;

Ixx=....

Iyy=(L^2*W*R^2)/(4g) L=fuselage length W=weight

Izz=...

I have only gave the formula for Iyy as I guess its the one that need to be use for pitching moment of inertia.

As I have read few books, I found out that the moment of inertia has to do something with the centre of gravity. However, the equation I gave you above has nothing to do with aircraft centre of gravity.

Please show me the solution with an example if you can.

Thanks a lot

### RE: Pitching Moment of Inertia

Your equation and mine agree except for a factor of 4, which is a matter of convention. If you divide my answer by 4 it should be correct. The assumption for CGX is built into Ry.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Pitching Moment of Inertia

(OP)
Ok,

What if I do not have Ry value. What formula should I use instead or how do I calculate Ry.

Thanks a lot

### RE: Pitching Moment of Inertia

In general the pitching moment of inertia is the integral of dM*r^2 where dM is all the infitiesimal masses of the aircraft, and r is the distance of dM from the centre of gravity in side view.

Then Ry^2=(pitching moment of inertia)/(total mass)/L^2

This is high school physics, are you sure you are in the right course?

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Pitching Moment of Inertia

greg, did you notice his "4g" term (in his 13:20 post) ? i think that's your factor of "4".

is this a student problem ? the numbers are too "round", it's unlikely that the airplane CG would be in the middle of the fuselage.

Ry looks like radius of gyration, as explained by the OP.

why the "4" in "4g" ?

### RE: Pitching Moment of Inertia

beacuse they've effectively scaled Ry using the half length of the fuselage, I used the whole length. Their approach is the better one, but either is valid so long as you state your assumptions.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Pitching Moment of Inertia

oh, i see, i think ...
Ry is the radius of gryration about the CG, but if you assumed it was about the nose, then there'd be a shift squared term (a 4 times factor ... bd^3/12 vs bd^3/3)

### RE: Pitching Moment of Inertia

No, what i meant was that I assumed

Iyy=M*(Ry*L)^2

whereas they have used

Iyy=M*(Ry*L/2)^2

The confusion comes because Ry is not a radius, it is a scale number, and so its values depends on the equation you use. Both are valid but theirs results in bigger numbers for Ry, and it seems more natural to scale radius than diameter I suppose.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Pitching Moment of Inertia

i would have gone with your calc ... Ry is a factor on L, no?

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