Lateral Load Transfer Calculations

The variables needed to calculate lateral load transfer are as follows:

LLT = Lateral Load Transfer (our output)

G = How many lateral "G-Forces" we're pulling in a turn

M = Mass of the of the vehicle†

H = Center of gravity height

T = Track width of the vehicle

The formula for for calculating LLT is as follows:

LLT = G x M x H / T

†This only applies when vehicle weight distribution is 50/50 front/rear, which it often is not. If weight distribution is not 50/50 front/rear, total vehicle weight will be substituted out for just the total weight on the two front tires (or the two rear tires) and the front and rear LLT will be calculated separately. Also this assumes all mass is unsprung.

Here is an example problem:

An F1 vehicle weighs approximately 600kg with a driver. Weight distribution is approximately 40/60 Front/Rear and 50/50 Left/Right. The wheelbase is 3075mm, the front track width is 1457mm and the rear track width is 1416mm. The center of gravity is 300mm high. Assume that all of the mass is unsprung. Determine the load on each of the wheels in a right turn that puts a lateral load of 2.0 G on the car. Assume the car is travelling at a constant rate of speed.

The first step is determining static corner weights at each of the wheels (before we apply a 2.0 G lateral load).

Since we're at a 40/60 front/rear weight bias, the two front wheels carry 40% of the entire weight of the car on them, while the two rear wheels carr the other 60%. Therefore,

Weight on the front wheels = 600kg x .40 = 240 kg Weight on the rear wheels = 600kg x .60 = 360kg

Since the left/right weight bias is 50/50, half of all the weight on the front is on the left wheel and half is on the right. Same goes for the rear wheels. Therefore,

Weight on Front left wheel = 120 kg

Weight on Front right wheel = 120 kg

Weight on Rear left wheel = 180 kg

Weight on Rear right wheel = 180 kg

Now, we will calculate the lateral load transfer between the front right and front left wheels of the car. Setting the variables we established earlier equal to the values established in this scenario, we have:

Front LLT = Unknown

G = 2.0 G

M = 240 kg‡

H = 300 mm

T = 1457 mm §

‡Remember, we are using the total weight on both the front wheels (240 kg), not the weight on just one of the wheels (120 kg).

§ Since we are calculating load transfer in the front, we are using the track width of the front wheels, not that of the rear wheels.

Calculating front LLT:

Front LLT = 2.0 G x 240 kg x 300 mm / 1457 mm

Front LLT = 99 kg

Calculating rear LLT using values established earlier:

Rear LLT = 2.0 G x 360 kg x 300 mm / 1416 mm

Rear LLT = 153 kg

So, front LLT and rear LLT are 99 kg and 153 kg respectively. But what does this mean? Simply, this number is subtracted from the static weight on the inside wheel in and added to the static weight on the outside wheel. In this case, the car is turning right, so naturally the inside wheels will be right side wheels. Determining the load on the front left and front right wheels:

Front left = 120 kg + 99 kg = 219 kg

Front right = 120 kg - 99 kg = 21 kg

And the rears:

Rear left = 180 kg + 153 kg = 333 kg

Rear right = 180 kg -153 kg = 27 kg.

So, in a 2.0 G right-hand turn with this car:

The front left wheel has 219 kg on it.

The front right wheel has 21 kg on it.

The rear left wheel has 333 kg on it.

The rear right wheel has 27 kg on it.

It is important to understand how, when designing a car, we can decrease our potential for lateral load transfer. Fortunately, all we need to do is look at our equation again:

LLT = G x M x H / T

The variables G, M, and H are all in the numerator of this formula. Decreasing the value of any one of these will lower our LLT. Realistically, that only leaves us two variables to mess around with because we cannot lower our lateral G value in a turn since the only way to do that is to drive slower. So, we're left with weight and center of gravity height. If you lower these, your LLT goes down, your grip goes up, and you go faster.