**Brian Beckman’s – The Physics of Racing.**

Introduction to the Physics of Racing article series

#### PhOR - Introduction

I have been interested in racing since the age of three, and Physics since I learned about it in high school. There was once upon a time when I was ...

#### PhOR - Part 1 - Weight Transfer

Weight Transfer Most autocrossers and race drivers learn early in their careers the importance of balancing a car. Learning to do it consistently and automatically is one essential part of ...

#### PhOR - Part 2 - Keeping your Tyres Stuck to the Ground

Keeping Your Tyres Stuck to the Ground In last month’s article, we explained the physics behind weight transfer. That is, we explained why braking shifts weight to the front of ...

#### PhOR - Part 3 - Basic Calculations

Basic Calculations In the last two articles, we plunged right into some relatively complex issues, namely weight transfer and tyre adhesion. This month, we regroup and review some of the ...

#### PhOR - Part 4 - There is no such thing as Centrifugal Force

There Is No Such Thing as Centrifugal Force One often hears of “centrifugal force.” This is the apparent force that throws you to the outside of a turn during cornering. ...

#### PhOR - Part 5 - Introduction to the Racing Line

Introduction to the Racing Line This month, we analyse the best way to go through a corner. “Best” means in the least time, at the greatest average speed. We ask ...

#### PhOR - Part 6 - Speed and Horsepower

Speed and Horsepower The title of this month’s article consists of two words dear to every racer’s heart. This month, we do some “back of the envelope” calculations to investigate ...

#### PhOR - Part 7 - The Traction Budget

The Traction Budget This month, we introduce the traction budget. This is a way of thinking about the traction available for car control under various conditions. It can help you ...

#### PhOR - Part 8 - Simulating Car Dynamics with a Computer Program

Simulating Car Dynamics with a Computer Program This month, we begin writing a computer program to simulate the physics of racing. Such a program is quite an ambitious one. A ...

#### PhOR - Part 9 - Straights

Straights We found in part 5 of this series, “Introduction to the Racing Line,” that a driver can lose a shocking amount of time by taking a bad line in ...

#### PhOR - Part 10 - Grip Angle

Grip Angle In many ways, tyre mechanics is an unpleasant topic. It is shrouded in uncertainty, controversy, and trade secrecy. Both theoretical and experimental studies are extremely difficult and expensive. ...

#### PhOR - Part 11 - Braking

Braking I was recently helping to crew Mark Thornton’s effort at the Silver State Grand Prix in Nevada. Mark had built a beautiful car with a theoretical top speed of ...

#### PhOR - Part 12 - CyberCar

CyberCar, Every Racer’s DWIM Car? The cybernetic DWIM car is coming. DWIM stands for “Do What I Mean.”2 It is a commonplace term in the field of Human-machine Interfaces, and ...

#### PhOR - Part 13 - Transients

Transients Obviously, handling is extremely important in any racing car. In an autocross car, it is critical. A poorly handling car with lots of power will not do well at ...

#### PhOR - Part 14 - Why Smoothness?

Why Smoothness? I’m back after a hiatus of nine years. Time does fly, doesn’t it? For those counting articles, the last one published was part 12; there is no Part ...

#### PhOR - Part 15 - Bumps in the Road

Bumps In The Road Brian Beckman PhD, and Jerry Kuch This month, we investigate how the effects of road bumps vary with speed. Everyone has experienced that bumps are more ...

#### PhOR - Part 16 - RARS A Simple Racing Simulator

RARS, A Simple Racing Simulator If you’ve been following this series, you know that I’ve been moving inexorably toward a computer simulation of racing. I’ve repeatedly debated with myself writing ...

#### PhOR - Part 17 - Slow In Fast Out

You may remember way back in part 5 that we did some simple calculations by hand to show that the classic racing line through a 90-degree right-hander is better than ...

#### PhOR - Part 18 - Slow In, Fast Out Continued

Physics of Racing, Part 18: “Slow In, Fast Out!” or, Advanced Racing Line, Continued In the previous instalment, we did exact calculations for a dummy line down a 650-foot entry ...

#### PhOR - Part 19 - Space, Time and Rubber

Space, Time, and Rubber In part 16, we introduced RARS, the Robot Auto Racing Simulator. We talked about the clever and simple tyre-friction model in RARS and gave a terse ...

#### PhOR - Part 20 - Four Point Statics

Four-Point Statics In this instalment, we analyse the stability of a single wheel, a bicycle, tricycle, and, finally, of a four-wheeled vehicle. In the offing, we introduce force moments, vector ...

#### PhOR - Part 21 - The Magic Formula: Longitudinal Version

The Magic Formula: Longitudinal Version Driving a car is a classic problem in control. Here, we mean control in the technical sense of control theory, an established branch of engineering ...

#### PhOR - Part 22 - The Magic Formula: Lateral Version

The Magic Formula: Lateral Version In this installment, we review the other side of the magic formula: the one that computes lateral or cornering forces from slip angles (or ...

#### PhOR - Part 23 - Trail Braking

Trail Braking Trail-braking is a subtle driving technique that allows for later braking and increased corner entry speed. The classical technique is to complete braking before turn-in. This is ...

#### PhOR - Part 24 - Combination Slip

Combination Slip The goal in this and the next instalment of the Physics of Racing is to combine the magic formulae of parts 21 and 22, so that we ...

#### PhOR - Part 25 - Combination Grip

Combination Grip In this instalment of the Physics of Racing, we complete the program begun last time to combine the magic formulae of parts 21 and 22, so that ...

#### PhOR - Part 26 - The Driving Wheel Chapter 1

The Driving Wheel, Chapter I Imagine 400 ft-lbs of torque measured on a chassis dynamometer like a DynoJet (see references at the end). This is a very nice number ...

#### PhOR - Part 27 - Four Wheel Weight Transfer

Four-Wheel Weight Transfer In this installment, we revisit the four-wheel statics of Part 20, solving the statics problem for level ground, which is very common in simulation. The problem ...

#### PhOR - Part 28 - Hazards of Integration

Hazards of Integration The equations of motion are differential equations. Such equations tell us how to calculate “what’s happening now” from “what happened a little while ago.” They’re called ...

#### Physics of Racing - Part 29

The Physics of Racing, Part 29: A Magical Trick Brian Beckman, PhD ©Copyright February 2002 The Magic Formulae (Physics of Racing parts 21, 22, 24, 25) for grip versus slip ...

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