THE RACING LINE

Introduction

The purpose of the Tire Grip Calculator is to demonstrate the effects of the basic characteristics of the car, the g force generating during a left turn, and the wieght transfer on the amount of grip produced by the tires. By comparing the g force generated during the turn with the g force rating of the front and rear tires, we can determine if the car has sufficient grip to complete the corner, and if the car will have nuetral, oversteer or understeer characteristics.

The Tire Grip Calculator summarizes the first three lessons in a simple manner to help the sim-racer set up his NASCAR, IndyCar or Grand Prix vehicle. By adjusting the basic parameters of the car, the changes in the cornering characteristics can be quickly seen.

As mentioned in the previous PITS lessons, the amount of grip produced is a function of the vertical load on the tire, i.e. the greater the vertical load the more grip the tire can produce. The graph of the vertical load vs tire grip is not a straight line as can be seen in the chart included as the second worksheet of the Excel spreadsheet. As the vertical load exceeds about 1000 lbs, the amount of tire grip increases but not as quickly.

The g rating of a tire is defined as the traction of the tire divided by the vertical load of a tire. For example, if the wieght (vertical load) is 630 lbs, the traction available is 784 lbs, therefore the g rating of the tire is 1.24 (784lbs/630lbs). If the car is attempting a 1 g turn, then this tire has sufficient grip.

The calculator determines the front g which is the g rating of the front tires and the rear g which is the rating of the rear tires. If the front or rear g rating, or both, is less than the corner g the car won’t make the corner. If both are above the corner g then the car will get around the corner. In this case, if the front g is greater than the rear g, the front tires have more grip and the car will tend to oversteer. The larger the difference then the larger amount of oversteer. The front tires will follow the curve that the driver is trying to follow but rear wheels with less grip will tend to go straight and the back end will tend to cause the car to spin out.

The converse is also true, if the rear g is greater than the front g, the car will tend to understeer as the rear wheels have more grip than the fronts. As the rears have more grip they will tend to overpower the fronts and the car will be forced to go in a straight line.

Neutral steering occurs when the front and rear g ratings are approximately equal.

Description of the Tire Grip Calculator

Cell A5: Weight of the car is the static weight of the car, at rest.

Cell A6: Weight distribution (F/R) is the front to rear weight ratio, expressed as percentage. Set the distribution to 50 if the car weight is balanced over the four tires. A distribution greater than 50 indicates that more weight is over the front tires. The results of static weight are shown in cells B24 to B27. The sum of the static weight will equal cell A5.

Cell A7: Left bias is just for you Good Old Boys who race the ovals in NASCAR and add ballast on the left side of the car to help with the left turns. It will help illustrate the effect of ballasting. Grand Prix types and road racers should leave this cell set to zero.

Cell A8: Height of the C. of G. has quite a large effect on the amount of weight transfer as can be seen by adjusting this figure.

Cell A9: Track width is the distance between the tires from one side of the car to the other.

Cell A10: Wheelbase is the distance between the front and rear axles.

Cell A11: Accelerating Force is the g force generated by the car during acceleration. The effect of the acceleration is shown in cells A18 and A19, and cells D24 to D27. For the effect of braking use a negative number. For no acceleration or braking use zero (0).

Cells A12: Corner g force is the force required to go through the corner as discussed in the first three lessons. I have set the spreadsheet to perform the calculations based on a left turn, see note regarding the Good Old Boys, y’all. I have set the default to one (1) as the calculator has been designed to look at the basic principles. This is a good figure for a street car, and I think the tire graph, taken from the book Chassis Engineering by Herb Adams, is based on very good street tires. For the mathematically inclined, try multiplying the tire grip by 5 to simulate Grand Prix tires. I haven’t had a chance to try this yet.

Cells A13 and A14: Rollbar Transfer (Ft) Front and Rr (Rear) allow the sim-racer to input values for the front and rear rollbars. Increasing the amount of rear roll bar decreases the amount of tire grip at the rear of the car. What is the advantage of reducing tire grip in a racing situation? Remember the definition of understeer, that the rear wheels have more grip than the rears and are, therefore, to use the American term for understeer, “pushing” the car. Increasing the rear roll bar reduces the rear tires nearer to the grip of the fronts, thereby reducing the understeering effect. Conversely increasing the front roll bar reduces the oversteer effect by bring the grip of the front tires closer to the value of the rears.

Cells A16 and A17: Lateral Weight Transfer indicates the total weight transfer to the left and right side of the car due to the cornering force. Cells C24 to C27 show the weight transfer to each tire and also takes into account the weight distribution of the car.

Cells A18 and A19: Accel. Weight Transfer indicates the total weight transfer to the front and rear of the car due to acceleration (positive g’s in Cell A11) or braking (negative g’s in Cell A12). Cells D24 to D27 show the weight transfer to each tire.

Cells B24 to B27: Indicate the static weight on each tire taking into account the weight distribution of the car. Cell B28 is the sum of the four cells and will equal the total static weight of the car as defined in Cell A5.

Cells C24 to C27: Indicate the Lateral Weight Transfer on each tire taking into account the weight distribution of the car.

Cells D24 to D27: Indicate the Accel. Weight Transfer on each tire.

Cells E24 to E27: Indicate the Weight Transfer due to the Front Roll bar on each tire.

Cells F24 to F27: Indicate the Weight Transfer due to the Rear Roll bar on each tire.

Cells G24 to G27: Indicate the Weight on the Tire during Cornering and is calculated by taking the sum of Cells B24 + C24+D24+E24+F24 for row 24 for example. Cell G28 is the sum of Cells G24 to G27 and will equal the static weight of the car, as the weight is being transferred between the tires during cornering and/or accelerating. Weight is not be added or subtracted from the car.

Cells H24 to H27: Traction Available is calculated from the relationship between the vertical load of the tire and the traction available. The sum of the cells is total traction of the car.

Cell I23: Corner g is taken from Cell A12.

Cell I24: front g is calculated by dividing the total traction of the front tires by the vertical load on the front tires, i.e. (H23 + H24 ) / (G23 + H23)

Cell J24: front g is calculated by dividing the total traction of the rear tires by the vertical load on the rear tires, i.e. (H25 + H26 ) / (G25 + H26)

Cell J28: total g is calculated by dividing the total traction of the car by the total vertical load, i.e. (H28 / G28)

Cells E6 to H12: Tire Grip Graph data is used to calculate the traction available as a function of the Weight on the Tire.

The object of the exercise is to adjust the rollbar at the front or rear of the car so that the traction at the front and rear are approximately equal and also exceed the g force required to complete the corner.

It is also worth emphasizing that we are setting the car for one of many corners if we are racing on a road course. Try setting the car up for a 1.2 g corner and then change the corner to a .75 g corner and determine the effect on oversteer or understeer.

If you are looking for accurate data on a car such as wheelbase, track and weight distribution try Road and Track road tests.

The next version will have the forces generated by the front and rear wings, but I will leave that for another session. Have fun with the Tire Grip Calculator and if you have any comments or suggestions, please free to contact me at rduncan@unix.infoserve.net