Race Car Physics: Mastering Tire Contact Patch for Auto Racing Success

[Ranger Mike]

webmaster, pls move this to applicable forum. I have much respect for members on this website and hope I may show the absolute requirement of good working knowledge of Physics..to compete successfully in Auto Racing...

Many of you have expressed interest in a subject I have tried to master for decades..and still find it tuff. Race car handling.
We could go into a lot of practical Physics like Internal Combustion engine function, volumetric efficiency, thermal dynamics, et al..and I gladly welcome these conversations..but the basic challenge is to make your car win races and it all comes down to Tires, Tires, Tires. Specifically, the tire contact patch.


Just calculating the Gs in a turn is a good start, What you ultimately want to do is have the biggest tire contact patch in contact with the track surface at all times. Suspension settings like camber, toe out, Akerman, bump steer are adjustments that improve tire contact patch area. Springs and shocks , "Sway Bars (anti roll bars) regulate the amount of spring weight transferred to the front / side of the car during cornering, acceleration, deceleration ( braking).

Tire traction- realize the more load placed on a tire, the more traction ..but...the tires coefficient of friction decrease. However, up to the design limit of the tire, its traction capacity ( ability to actually transmit force to the road) as opposed to dimensionless coefficient of friction, increases with vertical load.
simplified - vertical load on a given tire increases, the area of the rolling contact patch remains virtually constant, and so the unit pressure of the footprint increases. As the unit loading rises, the rubber has less resistance to frictional shearing and so the coefficient decreases. However, the curve is so gentle , if you graphed this, that the increase in vertical load overpowers the decrease in coefficient of friction.

longitudinal load transfer which occurs in the longitudinal plane under linear acceleration or deceleration = acceleration (g) x Weight x ch height ( center of gravity) / wheelbase

assume 1760 lb formula car with 100 inch wheelbase, 13 inch center of gravity
704 lb front weight , 1056 rear wheel weight
braking at 1.2 g

crank thur the formula and 275 lbs. is tansfered ..i.e. ft wheel weight is now 979 lbs, rear wheel weight is now 781 lbs.
but...there is also left to right side weight that occurs as well!

this is lateral load transfer (lb) = Lateral accelaeration (g) x weight x cg height / track width

the track width is distance from the center the right rear tire to the center of the left rear tire...just about all race cars have wider rear track width so you use the widest track width on the car

 

[Ranger Mike]

Our Can Am car with total rear wheel load of 1080 lbs. CG of 13 inches, rear track width of 60 inches cornering at 1.4 G

load transfer= (1.4) x 1080 lbs) x (13") / (60") = 328 lbs.
this means under steady state conditions, 328 lbs. of the load of the inside rear tire would be transferred to the outside rear tire giving resultant inside read tire load of 212 lbs. and outside tire load of 868 lbs. We have transferred 61 % of the inside tire vertical load to the outside tire. This is not good. See chart below. We find that we reduced the cornering force of the pair of rear tires from 1512 lbs. to 1400 lbs.

The only way to decrease the magnitude of the lateral transfer for a given lateral acceleration is to decrease the vehicle weight, increase rear track width or lower the center of gravity.

Again.. unsprung weight is bad because you can not control its actions. Sprung weight is what we control with placement, CG, Roll Centers, Springs, Shocks, Sway bars.

 

[Ranger Mike]

Swing Axle Jack - Any one who raced a VW will tell you t he car " jacks itself up" when going around a corner. It is the effect caused by the fact that the reaction force at the tire which balances the centrifugal force of the turn must arc through the ROLL CENTER.If the roll center is above the ground, then the line of action between the tire contact patch and the roll center will be inclined upward toward the vehicle centerline. This being so, the side force developed by the tire will have a vertical component which will tend to lift or " Jack' the unsprung mass. This lifting action, in addition to raising the CG will also move the suspension into droop with tire camber going the wrong way. Bad news.
The higher the roll center ( or narrower the track) the steeper the inclination of the line of action and the greater the jacking force.

 

[Ranger Mike]

Diagonal Load transfer- as a car enters the corner, a portion of the vertical load on the inside rear tire is transferred to the outside rear tire and the same transference takes place between the front tires. If this was all that happened, and if the roll axis were correctly positioned with respect to the mass centroid axis and roll resistance of the springs and sway bars were correctly selected, we would have a slight amount of corner entry understeer and everything is cool...normal longitudinal load transfer due to braking would not cause major concern.

HOWEVER- when we combine turning , or lateral acceleration braking or linear deceleration, some of the load from the inside rear tire is shifted diagonally to the outside front tire and the apple cart is upset..big time!

what actually happens is rear cornering power is lost by transferring load to the front and we lost front cornering power by generating and understeer torque about the vehicles CG. Also further front cornering power is lost by either overloading the outside front tire or we compress its spring to the point the we fall off the tires camber curve.
Exiting the corner, this situation is reversed.

The lesson is-
1. Anytime a race car is accelerated or decelerated, we have complex weight transfer.
2. We can not eliminate chassis roll and still have a working suspension.
3. The track itself introduced variables by bumps. dips, hills ( road race course) corners of varying radius and camber, track friction characteristics and the obvious one, traffic.