What is the forumula for horsepower over a given distance?

Question

I need to know a formula that can estimate horsepower if given the time it takes to cover a given distance, measured in feet. The formula needs to be for any distance (not just the quarter mile....the distnance needs to be a variable in the equation).

A forumula for the quarter mile is this:

HP=(weight)/((time/5.825)^3)

This formula only needs a weight and a time to estimate horsepower. The number 5.825 has something to do with the fact that the distance covered is a quarter mile (1320 ft). I need to know how this number would change is the distance is changed to something other than 1320 ft.

My equation above is from another site. Basically, it is as follows:(W)/((T/5.825)^3)

Weight is measured in pounds.


Time is in seconds.
This formula is based on a quarter mile (1320ft).

Answer 1

Horsepower is, predictably, a unit of power. Power is the product of force and velocity. If the formula is going to have distance as its only unknown, you need to know the time it took to travel the distance (which you said you do have) and the applied force that caused the displacement (which you did not mention having).

P = F*v = F*x/t, so if you knew F and t, x would be the only variable. To preserve the units of hp, F in lbf needs to be divided by 180, x in feet needs to be divided by 57.6*pi, and t needs to be in minutes. That makes the final formula P' = F*x / (10368*pi*t).

Without providing any units, your additional information is confusing.