Chapter 1

Introduction

The goal of this guide is to explain, in easy-to-understand terms, the basic car dynamics that take place while the car is in motion. This guide will allow you to grasp the main reasons of why a car does what it does. You should come away with an understanding of what the compromises you will need to make to your setup. More precisely, you will understand how and why tire loads (the key to handling) change! Although there is no one best way, the KISS (Keep It Simple, Stupid) principal is a good foundation.

Many different combinations of springs rates, roll centers, etc., can yield the same results mathematically, but there are many intangibles that make one setup better than another for particular circumstances. This guide was written with the understanding that there is no one best way to set up your car. Many different combinations of the parameters used in this guide could yield the same track performance and even the same theoretical output numbers. So who is to say which set of combinations of the parameters would be best? There are subtleties in the numbers and data that the diligent drivers find and use to their advantage. 

Preface

Keep these thoughts in mind as you study this information:

• This car handling theory must be taken as a whole. At first, you may not understand some part of it, or how some part fits in with the whole. All the details must be known before the whole concept can be seen. It will not help to understand just part of it. It may take you weeks to read and understand this little guide.
• Any setup problem may not have a single solution. It may have layers of solutions. If you think solution "A" should solve your problem, but it does not, maybe it will be the second layer down which, once adjusted, makes solution "A" work. You cannot discard an idea just because it did not work the first time. 
• Understanding the theory and applying it practically are two different disciplines. This is a very complex set of ideas and theories. 

About the Author, Marc

I've raced go-karts for five years and radio controlled cars for eight years--five years on dirt and three years of asphalt. I have a high school education, went through an electronic correspondence course, and have worked in electronic research and development labs for 25 years. My jobs required that I learn software programming and software tools, including this desktop publishing software. To make the learning more fun and interesting, I studied the math for real cars and race cars and applied the information into programs and this guide.

Notation

This section acquaints you with the notations used in this guide.

• In Equations, the multiplication sign is a small period (·) where the multiplication sign (x) would normally be.
• This guide is not meant to be a reference manual of the subject, but will present just the basic facts and formulas. All of the math is at the high school algebra level or less. There are no opinions expressed here.
• The terms "traction," "grip," and "Ct" ( Coefficient of Traction), popularly understood, may be interchanged, but Ct enables a quantity to be associated with it and is used in equations.
• Asphalt in this book is a generic term for a hard racing surface. A dirt track can become very hard packed and take on the characteristics of an asphalt track.

Some Basic Physics

To better understand the dynamics of race cars, knowledge of some of basic physics is needed. Momentum, inertia, and acceleration (both cornering and straight line) are the three main forces. These combined forces define the race car's performance and handling every moment.

Centrifugal Force

When an object is traveling in a circular path, its direction is constantly changing. The object is being accelerated inward because of this constant change of direction. This acceleration is calculated with this formula. Acceleration (a c ) is equal to Centrifugal force. v is speed or velocity. r is the radius of the corner in feet (ft) and Sec is time in seconds.

Equation 1: Centrifugal Force

As an example, if a car was going 110 feet per second (about 75 miles per hour) in a circle with a radius of 400 feet, it would be accelerating at a rate of 30.25 feet per second toward the center of the circle. See Equation 1 .

This rate of acceleration, 30.25 feet per second squared, can be expressed in Gs by dividing by 32 feet per second squared (which is the rate of acceleration of the earth's gravity). The overall acceleration equation looks like this. a g is the acceleration due to gravity. This equation shows the centrifugal force expressed in Gs. Centrifugal force is the force that pushes you to the outside of the car when you are turning a corner.

Equation 2: Centrifugal Force in Gs

This graph shows some examples of Equation 2 . As the Corner Radius increases the G Force decreases. As the Mph increases the G Force increases. Note: The Mph was converted to ft/sec, 1 Mph = 1.467 ft/sec, then applied to the equations.

Graph 1: Centrifugal Force examples

Inertia and Momentum

Inertia is a property of mass whereby it remains at rest or continues in motion until acted upon by some outside force.

Momentum is a indication of how much force it will take to stop a moving object. There are many kinds of momentum, but in this book, only two of them will be discussed, simple and rotational. Simple momentum is mass times velocity. Example, a 3500 lb car traveling at 100 mph would have a momentum of 350000 lb-mph. Rotational momentum is mass times velocity times a radius, this is simplified, but serves to explain. In other words, it is simple momentum around some center point. Example, a person swinging a baseball bat. There is a mass with some velocity pivoting around the person's hands.

Figure 1: Rotational Momentum

Simple momentum is pretty self-evident when your car is sitting helplessly at the end of a straight when it gets hit by a car traveling at a very high speed. Rotational momentum in car racing is a bit more complicated. When the car goes around a corner, it usually has body roll. In fact it has body roll in all three directions (planes).

• The normal body roll to the side. This is mass rotating around some center point.
• The front of the car may drop relative to the rear as the car brakes. This also is mass rotating around some center point.

And, as a car navigates around a corner, it is rotating around some center point that is traveling around the corner with the car. At some point, entering and exiting the corner, this rotational momentum must be started and stopped, just like when you are swinging a bat. To minimize the force needed to start and stop rotational momentum, you can centralize the car's components, thus minimizing the radius of the car's components in the rotational momentum math. This is like choking up on the bat, which provides a lot more control over the bat.

Figure 2: Car traveling around a corner

The point of all of this is that once the car is put into some particular motion, which results in a momentum, it takes a force to stop the motion. These are some of the forces that must be considered when setting up a race car.

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