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Polar moment of inertia

What it is and what you can do with it, or without it

Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. Here Mark answers your chassis set up and handling queries. If you have a question to put to him Email: markortizauto@ Tel: +1 704-933-8876 Write: Mark Ortiz 155 Wankel Drive , Kannapolis NC 28083-8200, USA

day. I have heard this expression before, but do Q

a polar moment of inertia in roll and pitch. Yaw is a rotational, or angular,


motion about a vertical axis (ie rotation that changes the direction the car points). To take a turn, we must accelerate the car in yaw in the direction of the turn during entry, then decelerate it in yaw (accelerate it in the direction opposite the turn) during exit. We must start it rotating to make it turn, then stop the rotation to make it go straight again. In this way, the car acts as

A car with a high level of polar moment of inertia in yaw will be more stable, whereas a short wheelbase, mid-engined car with a low yaw inertia will be twitchy

a giant flywheel – its inertia opposing these accelerations. When it’s running straight, it doesn’t want to start rotating but, once it’s rotating, it wants to keep rotating. This effect tightens entry and loosens exit. The polar moment of inertia is the magnitude of this inertial effect. We increase it by moving

he way racers use the term, it means polar moment of inertia in yaw, but a car also has

One of my racing buddies used the term ‘polar moment of inertia’ in a conversation we were having the other

not understand what it is. Could you explain it, and also what effect it has on a racecar. Also, can you measure it somehow? And how does it relate to suspension design and / or coilover placement?

masses away from the c of g. We decrease it by centralising masses. A mid-engine car, like an IndyCar, has a small polar moment of inertia in yaw. A stock car with the engine between the front wheels and 200lb of ballast ie the battery and the fuel load behind the rear axle has a large polar moment of inertia in yaw. So does a VW Beetle, a front- wheel drive Audi or a Porsche 911, all of which have the engine outside the wheelbase.

MEASURING YAW INERTIA Most people don’t try to measure yaw inertia, though GM built a giant turntable fixture to do just that. You can mathematically estimate it by breaking the car down into components, weighing these or calculating their mass, and multiplying the masses by the square of their distance from the c of g. Most of us don’t bother. For a pure racecar, we just try to put all the heavy stuff as close to the middle, or the

expected c of g, as possible. For a production-based car, we

often face the issue as a choice between placing components or ballast toward the rear bumper to get more rear percentage, or more centrally to reduce yaw inertia. In such cases, I usually go for the rear percentage, especially for oval track applications. An exception would be where you can get more than enough rear percentage, and still fall short of legal minimum weight. Then it makes sense to centralise the ballast. On an oval track car, we can

use asymmetrical set ups to make the car enter and exit as loose or tight as we want, even if the car has a lot of yaw inertia. Also, we don’t encounter such abrupt changes of direction on an oval as we see in a chicane or sharp turn on a road course. Consequently, minimising yaw inertia is more important in road racing than on oval tracks. Both large and small polar

moments of inertia are mixed blessings for any car. A car with a small polar moment and a short wheelbase will be twitchy (eg an older Toyota MR2), unless it’s set up very tight (eg a Pontiac Fiero). When such a car encounters a slippery patch in mid-turn, it will do a big wiggle and possibly spin, whereas a car with more yaw inertia will be more stable. Suspension geometry

requirements don’t really change with yaw inertia. Moving coilovers toward the centre of the car reduces yaw inertia, but not a lot since coilovers aren’t very heavy.

February 2012 • 33

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