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# Moments of inertia

## Moments of inertia

(OP)
Hello all,

Im putting together a simulation and will need some values of the moments of inertia about each axis. My thoughts were that a BMW 3 series, Ford mustang and a wrx may have a similar radius of gyration about the longitudinal axis (call this the x-axis). A corvette, 911, F430 and an nsx may also be similar about this axis being particularly lower slung. About the vertical, z-axis, in yaw these are going to have pretty differing radii. In this case a 928 and a C5 vette may be similar due to the front engine rear transaxle in both cars. All axis are of importance, but anything is helpful.

My point is that I am mainly looking for typical reasonably accurate radii of gyration so that I can correlate similar cars and make a good initial guess which can be investigated later. If you are willing I would appreciate how you came to your conclusions.

Thanks
Chris

### RE: Moments of inertia

Chris,

I can give you a few rules of thumb for Yaw Inertia. Yaw and Pitch Inertia are any very close.

1) On average the radius of giration for yaw of a car is around 45% of the wheelbase - my own database of vehicle measured.

2) I once found an ancient german formula to estimate yaw intertia:

(0,1269 to 0,1468) * Wheelbase * Total Length * Mass

Cheers

dynatune, www.dynatune-xl.com

### RE: Moments of inertia

On one hand, the more things change, the more they stay the same:

"Typical Vehicle Parameters for Dynamics Studies Revised for the 1980's" SAE Paper #840561

There are several inertia estimation techniques; some to avoid, too. If you are attempting to get inertia's by using just the masses of major structures in the vehicle (engine, transmission, fuel, passengers, glass, etc, the results will be poor because the omitted unknown inertia's of the elements themselves can be substantial (as in the powertrain).

If you need yaw inertia(s) [yes very related to pitch), consider a tri-filar pendulum to measure a real vehicle. Or, consider this: if you need this for handling comparisons, the yaw inertia isn't really a huge player in the yaw plane dynamic characteristics. What IS important and maybe relevant to your analysis is a useful term that represents the departure from one (1.00) of the yaw radius of gyration [in meters]. Lets call this term k (as in kappa). so, Izz = M[1+kk]^2. That being said, classes of vehicles can be produced from inertia measurements where k can range from +.25 to -.25. Plus term vehicles tend to be big motor front wheel drives with the powertrain way out in front, 0.0 vehicles are either front or rear drive with small motors and more favorable (lets say) powertrain packaging, and -.20 vehicles are small motor front or rear drivers with really 'good' mass distributions.

As you might already detect, the negative valued vehicles tend to produce 'better' handling characteristics and the + termed vehicles tend to produce 'worse' handling vehicles. This is because the goals for the car are defined in terms of fixed system response characteristics (gain, damping, bandwidth, response time, etc), regardless of the mass distribution. When the inertia to mass ratio is poor (+ kappa) the front and rear tire and chassis characteristics necessary to produce the handling requirement goals are more severe (and more often than not unattainable).

Meanwhile, keep in mind that the yaw dynamics are NOT that of a spring mass damper system, so that traditional thinking related to this mechanical analogy is just plain wrong. And, tires are not springs in that analogy, either.

You can easily prove this with frequency response analysis tools. Change the yaw inertia by 50% and watch the yawrate peak frequency shift only a small amount.

Roll on the otherhand requires the sprung mass Ixs values. Because of the Federal rollover standards, measurements of many different types of vehicles has been published by NHTSA. Most automakers use the same exact brand of machinery and procedures to measure vehicle inertias because of Federal compliance certification issues. Note that there are now estimation formulae for even unsprung masses of trucks and cars. The NHSTA database can be found online I believe.

You just have to locate them (or use a SWAG and proceed with your life) ! Getting the tire properties and elastic and geometric chassis compliances correct is the only sure way of doing vehicle comparisons. Otherwise, we call it sandbox play.

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