Weight distribution on tires

[yanna]

Hello there!

I am Yanna and I am building a racing car. I am now trying to calculate the tire drag of this car when cornering, but I'm stuck on something.

In order to find the tire drag, I need the normal load on each wheel. To find this, I made some equations:
1) the sum of the normal load over all four wheels equals the total gravity force;
2) the sum of the momenta around the Center of Gravity in pitch direction is zero;
3) the sum of the momenta around the Center of Gravity in roll direction is zero.
However, I now have 3 equations and 4 unknowns, so I cannot calculate the normal load on each wheel. What should the fourth equation be? I have some ideas:
a) The sum of the momenta around the Center of Gravity in yaw direction is zero;
b) Some equation regarding the torsion of the car being zero. (I would not know how to make this equation)

Is any of these ideas correct or is it another equation that I should use?

Thank you in advance for your help!

[charlyfierros]

Yanna.
The equation b is what you would need but don't worry about that.
If you need only drag for linear motion or acceleration suppose the car simetric wheel load on right equal to the left..
Regards

[Tim.Wright]

With 4 wheels the vertical equilibrium is over constrained so you need to know a lot of info about the suspension and tyres to calculate the vertical loads.

Are you trying to calculate lateral slip induced drag? How accurate does it need to be?

[Greg Locock]

As Tim says. It's the 4 legged stool problem, there is no solution in simple statics. If you have trouble imagining why imagine fitting adjustable spring seats to each wheel. Wind FL and RR down until one or both of the other wheels lifts off the ground. The sum (FL+RR)-(FR+RL) tells you how much diagonal weighting you have.

[DiogoBrand]

It's probably a similar problem to what we have on Civil Engineering with Hyperstatic structures. You won't solve it by analyzing the car as a perfect solid, you need to have the elastic characteristics of each contact point in mind, like spring rates, tyre compression rates and even chassis stiffness if possible.