In this article we are not only going to learn how to calculate load transfer in a vehicle, but more importantly, learn to visualize how the forces are acting between the car and the tires. Understanding these forces becomes very important when we move on to articles dealing with car balance, roll centers, and almost all things suspension related. If you haven't read our tire science article, make sure to go through that first, particularly the section on load sensitivity, as we will be using those concepts here.
calculating Load Transfer
Calculating the load transfer in a vehicle is fairly straightforward. You divide the center of gravity height by the width of the contact patches, and then multiply that by the acceleration and weight of the vehicle. For example, if our car had a center of gravity 1 foot above the ground and the tires were 4 feet apart, we would divide 1 foot by 4 feet which would give us 1/4. If the car was cornering at 1 g and weighed 1000 lbs, we would then take that 1/4 and multiply it by 1 g and multiply that by 1000 lbs. This would give us a total load transfer of 250 lbs. In that 1 g turn, 250 lbs that had been resting on the inside tires would now be resting on the outside tires.
As we learned previously, due to load sensitivity, the less load transfer we have, the greater the amount of potential grip our car has. You can plug in some different numbers to see why racecars are typically built low and wide as this reduces load transfer. In fact, the CG height and width of a car are the only variables that affect the percentage of total load transfer for a given lateral g. Once a car is built, you typically can only make small changes to total load transfer by changing ride height. Other suspension settings such as springs and anti-roll bars can be used to change how the load transfer differs front to rear (altering balance,) but the total amount of load transfer and therefore maximum potential grip remains the same.
As we learned previously, due to load sensitivity, the less load transfer we have, the greater the amount of potential grip our car has. You can plug in some different numbers to see why racecars are typically built low and wide as this reduces load transfer. In fact, the CG height and width of a car are the only variables that affect the percentage of total load transfer for a given lateral g. Once a car is built, you typically can only make small changes to total load transfer by changing ride height. Other suspension settings such as springs and anti-roll bars can be used to change how the load transfer differs front to rear (altering balance,) but the total amount of load transfer and therefore maximum potential grip remains the same.
The angle Determines the Load transfer
Let's now take a look at the forces acting on the vehicle so we can visualize what actually causes the load transfer. During cornering, a lateral force acts on the car's center of gravity and this is resisted by the tire friction. We can visualize this by drawing arrows from the center of gravity to the tires.
There is one force trying to push the outside tire directly toward the CG as well as one trying to pull the inside tire directly away from the CG. The amount of load transfer is directly related to the angle of those arrows. In the example we are using, the angle is 26.565 degrees. The smaller the angle between the CG and the ground, the lower the amount of load transfer. To understand why, you just need a friend and a sled.
There is one force trying to push the outside tire directly toward the CG as well as one trying to pull the inside tire directly away from the CG. The amount of load transfer is directly related to the angle of those arrows. In the example we are using, the angle is 26.565 degrees. The smaller the angle between the CG and the ground, the lower the amount of load transfer. To understand why, you just need a friend and a sled.
Pushing a sled transfers load
When pushing a friend on a sled, not all the work you are doing is being used to move the sled forward. Part of the force you are applying is moving the sled forward, but part of it is pushing the sled and your friend into the ground.
This causes the friend and sled to effectively weigh more which increases friction and makes it harder to push. Since everything still weighs the same total amount however, this also causes you to effectively weigh less. There is load transfer. This load transfer is unavoidable because the force you are applying is up above the ground and the frictional force from the sled is at ground level.
This works in exactly the same way as the center of gravity of a vehicle being resisted by the tire friction during cornering. The sled acts like the outside tire and your shoes are the inside tire. The point you push on your friend is like the location of the CG as it determines the angle of force. If you wanted to reduce the load transfer to make it easier to push you could do so by ducking down and pushing on the sled instead of the person as this would reduce the ANGLE between the force you are applying and the resisting frictional force at ground level.
There is another solution however. Instead of pushing, you could pull the sled. Pulling a sled causes load to transfer away from the sled and on to you. This reduces the friction experienced by the sled and increases friction in your shoes so they have more grip on slippy surfaces. If you started to slip, you could pull the rope at higher angles to improve your shoes' grip by increasing the load on them.
This causes the friend and sled to effectively weigh more which increases friction and makes it harder to push. Since everything still weighs the same total amount however, this also causes you to effectively weigh less. There is load transfer. This load transfer is unavoidable because the force you are applying is up above the ground and the frictional force from the sled is at ground level.
This works in exactly the same way as the center of gravity of a vehicle being resisted by the tire friction during cornering. The sled acts like the outside tire and your shoes are the inside tire. The point you push on your friend is like the location of the CG as it determines the angle of force. If you wanted to reduce the load transfer to make it easier to push you could do so by ducking down and pushing on the sled instead of the person as this would reduce the ANGLE between the force you are applying and the resisting frictional force at ground level.
There is another solution however. Instead of pushing, you could pull the sled. Pulling a sled causes load to transfer away from the sled and on to you. This reduces the friction experienced by the sled and increases friction in your shoes so they have more grip on slippy surfaces. If you started to slip, you could pull the rope at higher angles to improve your shoes' grip by increasing the load on them.
Force angles & Suspension
It's also important to remember that the CG is acting on all four tires in 3 dimensions. You might think of it as a pyramid with the vehicle CG being the top of the pyramid and each bottom corner of the pyramid representing a tire. For example, during braking the vehicle CG exerts a force downward and angled out toward each front tire and pulls up and in on the rear two tires.
If a vehicle had rigidly mounted tires, most of this would be academic, but since tires are typically mounted on suspension and they each move through an arc as the suspension moves, understanding these force angles can be quite important to take into account. In an upcoming article we'll learn about roll centers and how these force angles interact with the suspension to create jacking forces and alter vehicle balance.
I hope you enjoyed this article. If you are interested in a complete guide to the physics of racing, we also offer The Science of Speed book series, available through our bookstore or at popular retailers such as Amazon.
If a vehicle had rigidly mounted tires, most of this would be academic, but since tires are typically mounted on suspension and they each move through an arc as the suspension moves, understanding these force angles can be quite important to take into account. In an upcoming article we'll learn about roll centers and how these force angles interact with the suspension to create jacking forces and alter vehicle balance.
I hope you enjoyed this article. If you are interested in a complete guide to the physics of racing, we also offer The Science of Speed book series, available through our bookstore or at popular retailers such as Amazon.
