The Effect of Weight Distribution on Steady State Handling

Well since we are in a lull period, lets review something quite fundamental to vehicle handling - weight distribution. For those who know, please bear with me.

The entire weight of a car is carried by its 4 wheels, or more accurately its 4 tire contact patches. Assuming symmetry on the left and right side of the car (which is often not especially if there is a driver but no passenger), the fore-aft weight distribution determines the vehicle's centre of gravity. Weight distribution or centre of gravity location, is a key consideration in car design. It is the reason why manufacturers select different engine layout configurations, and why race teams do their best to create the lightest car as possible to have the freedom in positioning their ballast weight to meet minimum weight regulations.

Why is it important? The two most important considerations for CG location are its fore-aft location (or x-axis in SAE terms), and its vertical location (z-axis). It's lateral or y-axis position is normally assumed to be in the centre.

The fore aft position of the CG primarily influences the steady state stability of the vehicle. By steady state we do not mean 'not moving', but rather when the yaw moment of the vehicle approaches zero, or when the vehicle reaches its maximum lateral acceleration. This is typically when the vehicle is close to the apex of a turn. If we define the position of the CG relative to the front and rear axles in the following diagram, a1 and a2 are the distances between the front and rear axles to the CG respectively.

From the above, we can see that the sum of a1 and a2 is the vehicle's wheelbase. Instead of explaining it in a way such as front weight bias will result in understeer or vice versa, etc. lets look at it from a more quantitative point of view. The steady state stability factor for a vehicle is represented in the following equation:

Where m is the mass of the car, l is the wheelbase, Caf and Car are the tire stiffness of the front and rear tires respectively (or more simply the amount of 'grip' of the tires). The tire stiffness of the front and rear are said to be equal if they are of the same width and construction. From the above, we can see that a front heavy car with a1 being lesser than a2, would result in an understeering car, all things equal. Similarly, we notice that a rear heavy car (eg. rear engined car) would require a higher rear tire stiffness (often with larger rear tires) in order to reduce the second term to reduce the overall value of K.

Should the CG position be central, forward or rearwards of the vehicle with respect to the middle of the vehicle's wheelbase? In other terms, is a 50:50 weight distribution ideal? It may or may not be, depending on the vehicle's design, purpose and capabilities. For a high performance car, eg a formula single seater, it is usually more desirable to have a slightly rearward biased CG, giving a front/rear weight distribution of something like 45/55 or 40/60. This gives a slight oversteer characteristic to the vehicle, allowing for better response for quick transitions such as those seen in autocross. It also allows for better braking performance as weight is shifted to the front, making better use of the capabilities of the rear tires. Also, the slight rear bias gives an advantage grip when the vehicle accelerates.

A sporty or fun car would more likely benefit from a 50:50 weight distribution as much of its driving pleasures come from winding roads in which a car with neutral handling characteristics would be the easiest to drive in. A passenger car rarely sees more than 0.7Gs of lateral or longitudinal acceleration with a maximum seldom more than 1G with street tires, thus there is no need to largely 'offset' this CG location to take advantage of that.

An everyday car for anyone would benefit from a front biased car, eg a front wheel drive with a typical front/rear weight distribution of around 60/40. This gives the car an understeer characteristic, which is easily recognisable and instinctively corrected (reduce speed and increase steering depending on which portion of the tire curve the driver is at). Moreover, safety systems in the car, both passive and active, are most effectively designed for a front on collision than a sideways collision into a tree.

The vertical position of the CG is important as well, but it is not changed by weight distribution. We'll cover it in another post. While we are on the subject of weight distribution, consider the following very simplified car model:

It can be agreed that in both cases, the weight under each wheel would be 200kg excluding the mass of the car obviously. But the location of the weight relative to the car's CG is another important consideration, a term known as Moment of Inertia. The moment of inertia equation varies according to the geometry of an object. For simplicity, we shall assume the car is a giant cylinder with the following equation:

Where 'r' can be taken as a1 or a2 if the CG is exactly in the middle of the wheelbase, and d is the offset distance of the masses. The above equation is what's known as the Parallel Axis Theorem, which suggests that the influence of distance of overhanging masses from the centre of rotation is exponential. In fact all distance related factors are exponential (squared). What this means is that distance of the mass from the centre is a more important consideration than the actual mass itself for reducing the MOI.

Why reduce MOI? Similar reason to why divers tuck themselves in, or why a figure skater brings her arms close to her body, a car with lower MOI would be more agile and respond quicker to direction changes. Another extreme end would be a tightrope walker, who would want a larger MOI for greater stability on the rope. Examples of reducing MOI would be selecting a hatchback over a sedan, choosing a smaller wheelbase and shifting the positions of the engine and driver closer towards the vehicle's centre of rotation.

From the above, we can see that not only is the weight distribution of a vehicle important, but also the location of placement of the masses that greatly influence the steady state handling characteristics of a car. :)