S2000 Driver

"Mid-Engine Magic -- Mid-Engine Physics (It's All About Polar Moment of Inertia)"

by Patrick Hong

ROAD & TRACK MAGAZINE, December 2000, Page 81

"Newton's laws of physics govern most of the objects that can be seen and touched. The familiar second law describes and quantifies an object's LINEAR motion as F=ma, where F is the net external force acting on an object having a mass (m), and causing it to accelerate (a). For example, a dragster with minimal weight (mass x Earth's gravity) and lots of horsepower will generate a tremendous amount of straight-line acceleration.

"But when it comes to make an object turn, the rotational analysis T=Ia', is needed. T represents the net torque acting on an object having a moment of inertia (I) causing it to rotate with an angular acceleration (a'). Applying this concept to vehicle dynamics means that a car with the lowest possible moment of inertia will need little torque (or turning force, in this case) to change directions and negotiate a corner quickly. Since a car operates in a three-dimensional world where it rotates about a vertical z-axis, the moment of inertia is referred to as being polar.

"What exactly is polar moment of inertia? Unlike weight, it cannot be easily calculated or measured directly. It depends on both the mass of an object and how that mass is distributed. For example, consider a spinning figure skater. Usually skaters begin to spin very quickly with their arms held close to their chests in a low polar moment of inertia position. To slow down, they extend their arms outward so that the distributed mass is farther away from the axis of rotation, incurring a larger polar moment of inertia. To speed up again, they simply bring in their arms. No additional force is needed to continue the maneuver.

"In automotive engineering, a car with most of its mass concentrated near its vertical axis of rotation (which ideally is near the center) will have a lower polar moment of inertia, as with a mid-engine layout. This allows the vehicle to be more agile, requiring less torque for it to change directions. A front- or a rear-engine car's mass is distributed farther away from the axis of rotation, and thus holds a higher polar moment of inertia, needing more torque to turn.

"So, although a mid-engine layout is ideal for race cars with professional drivers onboard, it may not be as appropriate in road-going cars. Having a lower polar moment of inertia is great for agility, but in the hands of a less skilled driver, it can be dangerous. Because a mid-engine design requires less effort to change directions, it also means the car is more likely to be tail-happy and experience snap-oversteer. For road-going cars, a front-mounted powerplant may be better suited because it will have a slower transition to oversteer, and give plenty of warning before an impending spin.

"Mid-engine means not only having the powerplant behind the driver and in front of the rear axle, but can include having a power unit between the front axle and the cockpit. For everyday use, perhaps a front mid-engine design is the best solution, offering more usable space and more relaxed road manners."

Guess what car has a front mid-engine layout?



[This message has been edited by S2000 Driver (edited November 13, 2000).]

Sev

Interesting.

Although we do have a front-mid engine our weight distribution is 49.4 Front 50.6 Rear.

Which is more like a "rear" mid-engine.

Thanks for thge article.

honda_s2k

Very interesting post. Thanks!

Ldogdotcom

I like chicken.

wirejock

I like the article, but what's the comment about the chicken?

bbsilver

In this case it doesn't matter whether it is front or rear. What matters is how close the mass is to the rotation point (Center of Gravity) of the car.

For those interest the entire inertia equation (Excel Style) is:

sum(I+m*d^2)

The closer to the rotation point to the interia contributed by that component is the squared difference. So what that says in laymans terms is if you bring a part by 30% of the distance cut the inertia generated by that part in half.

That said, it is independant of the location of the center of gravity because it is relative to the center of gravity. Things are a bit different if it is required to spin around a specific axis, like a tire or flywheel does. In that case there is a dynamic balancing aspect (products of inertia); a different ball of wax, but still part of the inertia.

http://www.efunda.com is a good place to get the basics and pictures to accompany my explanation.

Ldogdotcom

Nothing, really. The topic is very technical, so I decided to add to the discussion in the simplest of terms. Completely irrelevant, but nevertheless easy to understand.

I really do like chicken though.

S2WOOOW

I think that this article give just enough info to be dangerous. I think 95% of the readers have the wrong picture in their minds. Using the skater as an illustration is much to simplistic. It

GTRPower

Good call S2WOOOW-

By the way, the last time I drove a 911 it was a 993 GT2 (big turbo version) with an RS Tuning clutchless shifter box. I pretty much early apexed, oversteered the turn initiation, and stomped on the throttle immediately to power out from the oversteer to correct. I don't think it was the right way to drive a 911, but man, it sure was fun!

-Nick

Bieg

I think the figure skater analogy works pretty well to show how the car will spin when you ultimately lose it (zero traction front & rear).

Mid engine cars spin a heck of a lot faster than front engine cars when you lose them just like the figure skater.