# How position of c.g. affects car polar moment of inertia?

How position of c.g. affects polar moment of inertia for car in turn, why all racing cars have engine placed in the middle, has that something with polar moment of inertia?

Using search terms "center of gravity Formula 1 race car" presents a number of useful considerations for placement of the center of gravity (also called center of mass) in the design of a vehicle. Formula 1 cars may be the most analyzed motor vehicle in the racing world (opinion) but the Technical F1 Dictionary does a great job of summarizing things. Image from linked site:

A brief summary is that the COG should be on the centerline, should be as low as possible and also as close as possible to the middle of the vehicle, fore to aft.

Any forces applied to a moving vehicle in a manner as to create an unbalance will tend to instability if the COG is outside of limits created by tire traction, applied power and aerodynamic forces at the moment of application.

The linked article is relatively brief and may lead you to perform your own search to find specifics if you require.

• No, the cg of an F1 car is towards the rear. Commented Oct 25, 2023 at 1:25
• @GregLocock isn't the engine directly behind the driver and the gearbox at the rear so the cg is closer to central than closer to rear? Commented Oct 25, 2023 at 5:19
• No The specified minimum axle weights, equate to a weight distribution ranging between 45.5 - 46.7% on the front axle and 53.3-54.5 on the rear. Aero balance is more like 40/60 Commented Oct 25, 2023 at 20:34
• @GregLocock Why more weight is more toward back, any reason? And why aero force 60% at the back? Commented Oct 26, 2023 at 16:29
• Because the rear tires are bigger. Commented Oct 26, 2023 at 21:37

So you are talking about the polar moment of inertia (PMOI) and cornering. The PMOI is the sum of the masses of each part in the car multiplied by the distance^2 of the part from the centre of rotation (typically taken as being the centre of gravity (CG)) of the car in plan view. The way to reduce it is to put all the heavy parts near the CG. A car with a low PMOI will be able to respond more quickly in yaw, that is it will enter a turn more easily. Taken to extremes it results in a twitchy car.

• "car multiplied by the distance^2 of the part from the centre of rotation " But where is car center of rotation? Why do you think that car pivot around c.g.? Commented Oct 25, 2023 at 5:55
• It doesn't. The car pivots around the centre of its radius of curvature of the path, where PMOI is irrelevant, but for establishing the yaw frequency it pivots more or less around the cg. Commented Oct 25, 2023 at 20:30
• how to find point about what car rotate if we observe only car yaw? Commented Oct 26, 2023 at 8:59
• That's tricky. I attach lateral velocity sensors to the front and rear of the car. Alternatively measure lateral velocity and yaw rate and work it out from that. Commented Oct 26, 2023 at 21:36