Quarter Mile

Over a standing quarter mile, elapsed time and trap speed are governed almost entirely by one number: how many kilograms (or pounds) each unit of power has to move. Decades of time slips have been boiled down into cube-root rules of thumb.

with weight $W$ in pounds, power $P$ in horsepower, time in seconds and speed in mph. The constants depend on whose data you trust:

• Hale: $k_1 = 5.825,\ k_2 = 234$. Optimistic; suits well set-up cars on sticky tires.
• Fox: $k_1 = 6.269,\ k_2 = 230$. Fitted to production road cars.
• Huntington: $k_1 = 6.290,\ k_2 = 224$. The classic 1960s magazine formula.

Where the cube root comes from

If an engine delivered constant power $P$ to a mass $m$ with no losses, kinetic energy would grow linearly with time: $\tfrac{1}{2} m v^{2} = P t$. Integrating speed gives distance $d \propto t^{3/2}$, and solving for the time to cover a fixed distance leaves

The animation uses that same $d \propto t^{3/2}$ curve, which is why the car covers the second half of the strip much faster than the first.