Auto Math Handbook: Easy Calculations for Engine Builders, Racers, Students, and more

• Displacement
• Bore
• Stroke
• Air Capacity
• Volumetric Efficiency
• Center of Gravity
• Weight Distribution
• g Force
• ... and much more!

If you're seriously interested in automobiles and how they perform, sooner or later you'll have to deal with mathematics. Virtually all aspects of motorsports, from bore and stroke, through power and torque, to time and speed, involve mathematical calculations.

I recognized this as a young auto enthusiast in the 1950s, and was pleased when I discovered a booklet called Mechanics of Vehicles by Jaroslav J. Taborek. It was a collection of 14 articles about the mathematics of motor vehicle behavior, originally published by Machine Design magazine in 1957.

Taborek was a professional engineer and he wrote for his colleagues, not for enthusiasts. Much of his work involved more complex mathematics and for many of us was simply too complex.

Then in 1961, an article called "Math and Formulas for Hot Rodders" by Don Francisco appeared in Hot Rod Magazine Yearbook Number One. It was only five pages long, but it provided some genuinely useful mathematics for the aspiring hot rodder, and none of it required more than a grade school background in math. To the best of my knowledge, it was the first such compilation especially for car enthusiasts.

In the years leading up to the publication of the first edition of Auto Math Handbook, there had been numerous magazine articles and book chapters dealing with various aspects of auto math, but they all had been at one or the other of the extremes represented by Taborek's and Francisco's pioneering and long out-of-print efforts.

They've been either ponderous professional tomes or frankly sketchy popular works. There had been no book lengthy collection of practical, elementary math for auto enthusiasts of average education.

That's a gap I sought to fill with this work by concentrating on math of genuine interest to the enthusiast, and avoiding anything too specialized. That dictated a particular emphasis on the engine and drivetrain, which are the core of true hot rodding.

A vehicle has resistance to rolling that comes from a variety of places. For our needs, these can be best quantified by looking at the tires, gearing, brake drag, wheel alignment and bearing loading.

These forces typically rise with increasing vehicular weight. For comparison, let's look at a child's roller skate. It has hard wheels, oversize ball bearings, no gear train and non-steerable axles.

In addition it has only the weight of a small child supported by four hard wheels. It stands to reason that the rolling resistance of a roller skate is very low. An 18-wheeler loaded to 120,000 lb. with a few underinflated tires could have huge rolling resistance.

In order to put a measured number on this resistance, we could tow the vehicle with very sophisticated instruments and measure what is called the force to maintain velocity. In its basic form, this involves towing the subject vehicle and measuring the forces required to maintain various speeds.

Once you look deeper, you realize that in order to eliminate the aerodynamic factors, a really long tow rope is required. This becomes very impractical as well as downright dangerous. Do not try this! A much simpler method is to measure coast down.

• Displacement, Stroke and Bore
• Compression Ratio
• Piston Speed
• Brake Horsepower and Torque
• Indicated Horsepower and Torque
• Air Capacity and Volumetric Efficiency
• Weight Distribution
• Center of Gravity
• g Force and Weight Transfer
• Moment of Inertia
• Aerodynamics
• Rolling Resistance
• Shift Points
• Quarter-Mile E.T. and MPH
• Computer Programs
• Instrument Error and Calibration
• MPH, RPM, Gear and Tires
• Tire Sizes and Their Effects
• Average MPH and MPG
• Fuel Economy and Cost of Ownership
• Crankshaft Balancing
• Conversion Factors
• Bibliography