Newton's second law is F = ma, so acceleration is force divided by mass. A car that makes the same push with less mass accelerates harder, and a car with more power can push harder at speed. Power-to-weight ratio puts both into one number. This post uses it to estimate quarter-mile times with two well-known rules of thumb, then shows why shedding weight pays back less than the percentage suggests. All cars below are invented examples, not data about any car in a game.
Two ways to write the ratio
Power-to-weight can be quoted either way up:
- Horsepower per tonne. A car of 3,000 lb with 300 hp is 3,000 ÷ 2,204.62 = 1.361 tonnes (1 tonne is 1,000 kg, or 2,204.62 lb). That is 300 ÷ 1.361 = 220.5 hp per tonne. Higher is better.
- Pounds per horsepower. The same car is 3,000 ÷ 300 = 10.0 lb per hp. Lower is better.
The two are the same information. Both use mechanical horsepower here, the unit of the 5,252 rule in the dyno chart post, and the weight should include the driver and fuel.
The quarter-mile approximations
Two formulas, usually credited to Hale and Fox, turn the ratio into a quarter-mile estimate. With weight in pounds and power in horsepower:
- Elapsed time (ET) ≈ 5.825 × (weight ÷ hp)1/3 seconds
- Trap speed ≈ 234 × (hp ÷ weight)1/3 mph
These are approximations fitted to real cars, not laws. They assume a well-launched car with enough grip and sensible gearing, and the result depends on whether you feed in flywheel power or wheel power, so quote which one you used. They are good for comparing two setups, and less good for predicting one car's exact slip.
The cube root appears because power, not force, is the fixed quantity. A car holding constant power covers distance in proportion to time to the power of 1.5, which leaves time depending on the cube root of weight ÷ power. The constants then come from fitting real results.
Worked examples
Take a 3,000 lb car with 300 hp as the base. Its weight ÷ power is 10.0 lb per hp, so ET ≈ 5.825 × 101/3 = 5.825 × 2.154 = 12.55 s, and trap speed ≈ 234 × 0.11/3 = 234 × 0.464 = 108.6 mph. Now change one thing at a time:
| Weight | Power | lb per hp | hp per tonne | ET | Trap speed |
|---|---|---|---|---|---|
| 3,000 lb | 300 hp | 10.00 | 220.5 | 12.55 s | 108.6 mph |
| 2,700 lb | 300 hp | 9.00 | 245.0 | 12.12 s | 112.5 mph |
| 3,000 lb | 330 hp | 9.09 | 242.5 | 12.16 s | 112.1 mph |
| 3,000 lb | 400 hp | 7.50 | 293.9 | 11.40 s | 119.5 mph |
| 2,500 lb | 400 hp | 6.25 | 352.7 | 10.73 s | 127.0 mph |
Ten per cent is not ten per cent
Look at the second row. Removing 10% of the weight (3,000 lb to 2,700 lb) gives 9.00 lb per hp instead of 10.00. ET falls from 12.55 s to 12.12 s, a gain of 0.43 s, or 3.45%. The cube root explains it: 0.91/3 = 0.9655, so the time is multiplied by 0.9655, not by 0.9.
Adding 10% power (300 hp to 330 hp) is a little less effective, and it gives 12.16 s, 3.13% quicker. That is because 1.1-1/3 = 0.9687. The two are not equal because removing 10% of the weight raises the ratio by 1 ÷ 0.9 = 11.1%, while adding 10% of the power raises it by exactly 10%.
The trap speed follows the same cube root, in the other direction: the lighter car crosses the line at 112.5 mph against 108.6 mph, 3.6% faster.
Time depends on the cube root of weight ÷ power. To cut ET by 10% you need weight ÷ power to fall to 0.93 = 0.729 of its value, which is 27.1% off the weight or 37.2% more power (1 ÷ 0.729 = 1.372).
What the formulas leave out
- Traction. The estimate assumes the tyres can pass on the force. A powerful car that spins is slower than the figure, as covered in the launch RPM post.
- Gearing. Power is only useful at the wheels in the right ratio. See the gear ratio post and the shift point post.
- Where the weight is. Weight over the driven wheels helps grip, so a lighter car is not always quicker off the line.
- Drag. Air resistance grows with speed, and the formulas do not model it separately.
Use the ratio to rank setups and to see which change is worth chasing. Test the answer against the clock: the time slip post explains the lines to compare.
In the game
Pink Slip Kings lets you upgrade your engine, drivetrain, tires and suspension, compare horsepower and torque on the dyno, and take a setup to Test & Tune, where race time slips show the result. The game is in closed testing, and how it models weight and power is outside this post, so treat the numbers above as real-world arithmetic rather than a prediction of in-game times.
Pink Slip Kings: Drag Racing is a 3D drag racing game with manual launch and shift controls, detailed tuning, a dyno, telemetry and race time slips, and Test & Tune and tuner sandbox modes. It plays offline, has no ads and no in-app purchases, and its in-game cash and cars cannot be bought or exchanged for real money. The game is currently in closed testing.