The basics of Weight Transfer

Weight transfer is one of the more commonly misunderstood terms in vehicle dynamics. In reality, this topic gets pretty complicated once we factor in more physics, kinematics, considerations for sprung and unsprung masses, geometric and elastic differences, damping, tire characteristics including slip angles, etc. The whole story gets a little too long. Today, we will try to cover the basics and the common misconceptions with weight transfer.

One of the first things to clarify is that weight transfer is not related to what the driver feels, but rather what the tires feel. The opposing forces we feel in the car pushing us in the opposite direction of the turn, throwing us forward as we brake, and pushing us into the seat as we accelerate, are primarily due to inertia and other references or feedback such as roll angle and forward dive. However what eventually connects the car to the road are the tires, or more accurately the 4 tire contact patches.

Most of us would be familiar with the classical friction theory which shows that the amount of friction (or sideways resisting force) is directly proportional to the vertical load as follows:

Where the friction coefficient (mju) is static assuming a no slip condition between both surfaces. What this suggests, is that the larger the vertical load, the larger the amount of sideways force that would be generated. This sounds pretty good, especially since rubber is one of the few materials to have a friction coefficient much greater than 1. Right? Except not. When something sounds too good to be true, there is always a catch. Sure, it's difficult to push a stationary car from the side into a parallel lot for example. The key difference between the stationary 'tire model' block above and a real tire is that real tires rotate.

The mechanisms in which a tire generates grip is quite complex as well, but is generally thought to be the result of 3 main factors: molecular adhesion, deformation and wear/tear. A whole book could be written on tires alone (Hans B. Pacejka), but what we can take from this is that a tire needs a slip angle to generate grip. We'll leave it at there now and get back to weight transfer.

Weight transfer is the transfer of weight from the inside to the outside tires of the car (for example from the left to the right of a car that is turning left), from the rear tires to the front when the car brakes, and from the front to the rear as the car accelerates. The following describes in general (without consideration of suspension geometry and sprung/unsprung mass), a simplified 2 dimensional illustration of the factors that affect weight transfer:

In the car above (without suspension apparently, jacking up the inside wheel as it turns to its left), weight is transferred to the outside tire (Fz), which is responsible for generating the resultant grip or Fy required to keep the car in its intended path. The weight transferred to the outside wheel is a function of the CG height and track of the car in 2 dimensions, which leads to a common misconception that stiffer springs allow you to transfer more weight. The spring rate is not part of this equation, thus does not influence the steady state weight transfer during a corner.

But some of what stiffer springs offer are:
- Reduced time for the load to be transferred, thus increasing the response of the car.
- Reduced body roll, dive and pitch giving the driver more confidence in the car's capabilities.
- Reduced height (usually), which lowers the CG height and reduces weight transfer.
- For custom springs, the ability to adjust the front/rear distribution of roll stiffness

wait, reduce weight transfer?

Another misconception about weight transfer is that it is good, that stiffer springs transfer more weight so we get more grip. We've seen from the above that the Fy (what we are ultimately interested in), is a linear function of Fz, which means the greater the amount of weight transfer, the greater the amount of Fy or sideways grip we get. However, due to the visco-elastic properties of the rubber compound in the tire, the increase in sideways grip is not linearly proportional to the increase in downward force or weight transfer (Fz), a property known as 'Tire Load Sensitivity'. If we revisit the 3 mechanisms that contribute to tire grip, a major contributor would be the deformation of a tire as the rubber tries to 'wrap around' the irregularities in the road (which are vast valleys under a magnifying glass). As the load is increased past a certain limit, the valleys in the road would be pretty much filled up, leaving only 2 mechanisms left for grip.

Source: Milliken & Milliken

We can non-dimensionalize the sideways grip with the vertical load or weight transfer by removing the effect of the weight of the car for different kinds of cars and setup to give the term 'lateral force coefficient'. What is then seen, is a reduction of maximum sideways grip as the amount of vertical load increases. The slip angle required to achieve the maximum is also increased.

If we consider the fact that the inside wheel sees a reduction in vertical load, and hence a reduction in sideways grip, then what Tire Load Sensitivity suggests is that we lose more grip than we gain with weight transfer.


To reduce sideways weight transfer, here are some options:
- Reduce the mass of the vehicle
- Lower the centre of gravity height
- Increase the track of the vehicle (via wheel spacers or wider tires in production cars)

This pretty much sums up the basics of weight transfer. Note that the above was a simplified 2 dimensional explanation without the considerations for suspension kinematics, sprung/unsprung masses and transient effects. Hope it was useful. :)

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. :)