## Polar Moment of Inertia [Kg m ^2]Calculation

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But non-sense never gets old, that's for certain.
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xpensive
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Joined: 22 Nov 2008

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Does he want the polar MOI in yaw, pitch, or in roll? With a full fuel load or on empty tanks?
"Q: How do you make a small fortune in racing?
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riff_raff
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Joined: 24 Dec 2004

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Dear Ciro

First of all thank for answer but I was asking to compute a polar moment of Inertia regarding masses and I think that the other guys undertood the same I wanted to mean how the inside masses of the car afect his stabilty I ´m not interested to compute Polar moment of area like you correctly explain before
Thank you Again and I hope you consider your mistake or my mistake because I made a question without regarding specifically to what I wanted to compute

Kind regards
Alfoncito
Alfoncito
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Joined: 23 Jul 2009

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Punctuation...
Grip is a four letter word.

2 is the new #1.
Jersey Tom
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Joined: 29 May 2006
Location: Huntersville, NC

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Thanks for your kind words, Alfoncito.

I'll try to be practical, then. Check this:

I draw a sphere, 2 m radius and then I click on Tools/Inquiry/ and then in Region/Mass Properties.

I get a moment of inertia of 53.6165.

I check against the formula, assuming that the density is equal to 1 (water). m is the mass, R is the radius:

$I = 2*m*R^2/5$

$I = 2*4/3*pi*2^3*2^2/5 = 53.6165$

Check.

Now, for a car (sorry, is solid as the sphere, I made a mess of myself trying to use the SHELL command, to produce a hollow car, but perhaps you know or can consult how to do it):

I first took a sideview of a car that is interred somewhere in the Design Center (you can use your own drawing).

Then I exploded the block (command EXPLODE), converted the edge to a polyline (PEDIT and then Yes).

Then I copied the polyline to create two separate images of the car (COPY, using a frontal view).

I separate them by the width of the car. If you're sophisticated, you can draw a "path" that joins the two copies, but I kept it simple. Then I used the LOFT command to create the volume of the car (LOFT and then click on each polyline).

I use MASSPROP again. Here you have the answer for the three axes (yaw, etc.).

If you wish you can do the same with the engine or other components, by density.

Simply "apply" a material, including density, to each part of the car. Select them all. Use MASSPROP. Voilá.

BORING NOTE: notice AutoCAD uses the terminology of "Moment of inertia" for the Second Moment of Inertia (the one that is used to calculate bendings), while it calls "Principal Moment of Inertia" to the Mass Moment of Inertia (the one used to calculate rotations, the one you need).
Ciro
Ciro Pabón
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Joined: 10 May 2005

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Good good.. never tried it in AutoCAD before.
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n smikle
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Joined: 12 Jun 2008

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Belatti
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Joined: 10 Jul 2007
Location: Argentina

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I'd suggest that whilst a CAD program is the quickest way to get a value once you have a model that is accurate, it is beneficial to know the theory behind what you're doing - at least then if you get obviously silly numbers you realise and try to solve it! For example, are the origin of the axes in your model in the right place? Translating an axis about which you're finding the moment of inertia will change its value...

As JTom said, effectively all you need is Mr^2. For a set of discreet masses it is simply the sum of the massese multiplied by their (perpendicular) distance from the axis squared. As this number tends to infinity (for example with a continuous shape such as a disc spinning around it's 'axle') integration becomes your friend - but all you are doing is still summing lots of masses and squared distances.

So do this with your car. knock up a quick spreadsheet listing the various parts you have and their distance from the axis of choice (in the plane normal to the axis). You can either estimate their masses as point masses (really simple), or represent each part as a simplified version of the part (a cude, a sphere) and calculate MOIs for each part using formulae (or integration) before applying the parallel axis theorem, or you can break each part up into various point masses (or even shapes!) before using the above method for each part then the same method for the whole car.

So it can be as complicated as you like. The most accurate method will be to have a top notch CAD model, with appropriate densities etc. but I'd question how long this model would take compared to a detailed spreadsheet, and whether you could trust the numbers without doing a simple spreadsheet anyway!
bazanaius
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Joined: 8 Feb 2008

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I'm digging up this old thread because I want to get my head around something. I'm currently a novice in vehicle dynamics and trying to understand some of the basic principles.
I have a question regarding the moment of inertia around the vertical axis, I believe some call it yaw moment of inertia. Does a higher MOI only have a higher resistance to the rate of change in vehicle direction, or does it also have a higher resistance to the change in direction alone?

So i.e. having two cars, same mass, same CoG, but car A having a high MOI and car B low MOI. I can understand car B having an advantage in a tight and twisty chicane section, but could it also lead to car A having more understeer in long, medium-speed corners?

o/t:
A second slightly offtopic question: I'm particularly interested in understanding off-road vehicle dynamics (rally). From my experience of reading and searching through various internet cummunities, most of the available information is focused on tarmac circuit racing. I'm saving up to buy the Milliken's RCVD, but does this focus on tarmac racing examples as well and would I be better off buying a similar book that concentrates on some of the different approaches that off-road vehicle dynamics bring along?
spacer
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Joined: 1 Nov 2009

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MOI is the resistance to the angular acceleration. In exactly the same way as mass is a resistance to straight line acceleration. Nothing directly to do with the yawing speed.

RCVD is definately worth it. I dont think there is such a detailed treatment of the dynamics of rally cars, but its not required since the fundamentals are exactly the same. A 4-wheel land vehicle running on pneumatic tyres is still goverened by the same basic physical laws regardless of what surface it runs on. Just the emphasis on certain details are different.

Tim
Tim.Wright
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Joined: 13 Feb 2009

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Tim's right on both counts.

If it helps at all, pitch inertia (without the unsprung masses) is probably best thought of as a mass multiplied by the square of the pitch radius of gyration (k), where value of k will vary with the distrbution of mass. For example, a typical unballasted mid engined open wheeler is likely to have a (k/wheel_base) of between 2.5 (full) & 2.9 (empty) - a little bit shy of (wheel_base/3).
DaveW
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Joined: 14 Apr 2009

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Apologies for the off topic post, but it's really good to hear from you again DaveW...and thanks for the info regarding MOI.
WilO
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Joined: 1 Jan 2010

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