How to Calculate Quarter Mile ET and Trap Speed

Quarter Mile ET and MPH - Trap Speed

Back in 1985 a fellow by the name of Patrick Hale, with his combined Mechanical engineering, software skills and his interest in drag racing, developed software to calculate how a car should perform in the quarter mile. The program predicts elapsed times and trap speeds very accurately as it takes every mathematical variable that affects acceleration into consideration. These variables include the commonly known power to weight ratio to more advanced calculations like gearshift points, drag coefficient and polar moment of inertia, etc. It also shows what modifications will help performance and what will hurt it.

For most racers this software was too precise. It required gathering data that those on a limited budget didn’t have or couldn’t get. So a year later he introduced a simpler program called Quarter Master Jr. This program focuses on readily available specs and provides it’s own built-in estimates of the unknown details.

The two most important variables are horsepower and vehicle weight. The higher the horsepower and/or the lower the weight, the faster the car will go. Here are some math excerpts from Hale’s early works that take only power and weight into consideration. This is great math for the weekend warier who’s not after winning the NHRA Championship or any highly competitive drag race for that matter.

ELAPSED TIME vs. TRAP SPEED (mph): 

The formula for ET involves the cube root of the weight-to-power ratio multiplied by a constant of 5.825, while the formula for Terminal MPH calls for the cube root of the power-to-weight ratio multiplied by a constant of 234. Note the important distinction here: For ET, you want weight-to-power, i.e., pounds per horsepower. For MPH, you want power-to-weight, i.e., horsepower per pound.

Formula for ET:

$ET=\sqrt[3]\frac{WEIGHT}{HP}\times{5.825}$

Here is an example of a BMW E36 M3 that weighs 3200 pounds making 500HP:

$ET=\sqrt[3]\frac{3200}{500}\times{5.825}\Rightarrow\sqrt[3]{6.4}\times{5.825}\Rightarrow{1.856636}\times{5.825}\approx{10.815\,seconds}$

This is a perfect world ET. Although it is obtainable, there are several factors that will reduce the ET. Some of which have to do with reaction time, traction off the line, driver skill, tires, suspension setup, gear ratios etc. The best times we’ve seen on street driven cars are in the high 11’s to low 12’s.

Formula for Trap Speed (mph):

$MPH=\sqrt[3]\frac{HP}{WEIGHT}\times{234}$

Here is an example of a BMW E36 M3 that weighs 3200 pounds making 500HP:

$MPH=\sqrt[3]\frac{500}{3200}\times{234}\Rightarrow\sqrt[3]{0.15625}\times{234}\Rightarrow{0.58609}\times{234}\approx{127\,MPH}$

More about Patrick Hale:

Patrick Hale has held three NHRA National Records in Competition Eliminator and was awarded the "Best Engineered" vehicle in May 1999 for his record holding K/Altered… an all aluminum, electronic fuel injected, 4 cylinder Ford powered Bantam roadster. He is also a Member of the Society of Automotive Engineers (SAE) and has authored numerous technical articles for several automotive magazines; including National Dragster, Hot Rod and Bracket Racing USA.

All contents of this technical document were derived from published data in John Lawler’s book Automath that are based on Patrick Hale’s Quarter Mile Jr.

Automath can be purchased from many sellers ex. HP Books. PN# HP Books 1020

Quarter Jr. Software can be purchased from http://quarterjr.com

Document Prepared by Osh Minelian, Race Marque Systems.