Formula
Both formulas use the cube root of the pounds-per-horsepower ratio. Hale’s constants are 5.825 for elapsed time and 234 for trap speed. Fox’s 2001 constants are 6.269 and 230. Weight is pounds with the driver. Horsepower is peak power at the clutch.
Hale ET = 5.825 × (weight / hp)1/3
Hale mph = 234 × (hp / weight)1/3
Fox ET = 6.269 × (weight / hp)1/3
Fox mph = 230 × (hp / weight)1/3
The inverses use the same constants. Horsepower from an elapsed time is weight ÷ (ET ÷ constant)3. Horsepower from a trap speed is weight × (mph ÷ constant)3. Each formula then fills in the other number, so a Hale ET produces a Hale trap, and a Fox trap produces a Fox ET. They are not averaged.
A 3,500 lb car at 400 hp is 8.75 lb/hp. The cube root of 8.75 is about 2.0606. Hale is 12.00 seconds and 113.6 mph. Fox is 12.92 seconds and 111.6 mph. Jeff Lucius’s comparison of road tests put Hale toward the quicker cars and Fox closer to ordinary street cars. That is his comparison, not a promise about the car in front of you.
Elapsed time scatters more than trap speed because the launch, the tires, and the shifts move the clock. Trap speed is the steadier of the two horsepower estimates, and it is still an estimate. This page is the quarter mile. It does not apply an eighth-mile factor. Roger Huntington’s 1958 constants, 6.290 and 224, are not used.
Worked examples
3,500 lb, 400 hp. Hale 12.00 s and 113.6 mph. Fox 12.92 s and 111.6 mph. Pounds per horsepower 8.75.
The same weight at the Hale elapsed time. Hale returns 400 hp. Fox, given that same elapsed time, returns a higher horsepower, because Fox’s ET constant is larger. The two trap speeds then follow from those two horsepower figures.
The same weight at the Fox trap speed. Fox returns 400 hp. Hale, given that same trap speed, returns a lower horsepower, because Hale’s trap constant is larger.
Reference
Constants used on this page. The horsepower column is the input when you start from weight and power, and the output when you start from a time or a trap speed.
| Formula | ET constant | Trap constant | Year cited |
|---|---|---|---|
| Hale | 5.825 | 234 | 1986 |
| Fox | 6.269 | 230 | 2001 |
Questions
How long is a quarter mile for this weight and horsepower?
Both answers are estimates. At 3,500 lb and 400 hp, Hale’s constants give 12.00 seconds and 113.6 mph. Fox’s 2001 constants give 12.92 seconds and 111.6 mph. The car, the launch, and the track decide which one is closer.
Which horsepower does the formula want?
Peak horsepower at the clutch, the flywheel number, with the driver in the weight. A chassis-dyno figure is wheel horsepower. These constants were not fit to wheel horsepower.
Why do the ET and the trap speed disagree about horsepower?
Traction, gearing, and the launch move the elapsed time more than they move the trap speed. Geoffrey Fox treated weight and power as the main drivers of trap speed, and the rest of the car as the reason ET is harder to predict. Read both. The gap is often the launch, not a second engine.
Is this a time slip?
No. It is two published curve fits. It is not a prediction of one car, and it is not a tuning recommendation.
Sources
- Jeff Lucius, “Formulas for 1/4 mile ET & mph vs. hp & wgt,” stealth316.com/2-calc-hp-et-mph.htm. Hale’s pair is ET = 5.825 × (weight/hp)1/3 and mph = 234 × (hp/weight)1/3, from the simple estimates Patrick Hale published in 1986 with his Quarter programs. Fox’s 2001 empirical pair on that page is ET = 6.269 × (weight/hp)1/3 and mph = 230 × (hp/weight)1/3. Weight includes the driver. Horsepower is peak power at the clutch.
- Geoffrey T. Fox, “On the Physics of Drag Racing,” American Journal of Physics, vol. 41, 1973, pp. 311–313. That paper is the physics behind a constant-power approximation. The 6.269 and 230 constants are the later empirical pair Lucius attributes to Fox, not a formula copied out of the 1973 article.
- Roger Huntington, “Horsepower at the Drag Strip,” Rod & Custom, December 1958, pp. 50–53. His constants were 6.290 and 224. This page does not calculate them. Lucius also published his own Road & Track fit. This page does not use that fit either.
- Related pages: fuel injector size, turbo size, displacement, gear ratio, and the power-to-weight calculator. None of those is a quarter-mile estimate.