How would you calculate horsepower for a windmill without a generator?

Question

I need to find horsepower for mini windmills for a science fair project, and so i need a formula.

Answer 1

Horsepower (hp) is the name of several non-metric units of power. In scientific discourse, the term "horsepower" is rarely used because of its various definitions and the existence of an SI unit for power, the watt (W). However, use of the term "horsepower" persists as a legacy in many languages and industries, particularly in the automotive industry because of their continued advertising of maximum power output of internal-combustion engines in "horsepower" units of measurement.

There are two important factors to consider when evaluating the measurement of "horsepower":

The various definitions of the "horsepower" unit itself
The various standards used in measuring the value of "horsepower"
These factors can be combined in unexpected ways — the power output for an engine rated at "100 horsepower" might not be what a reader expects. For this reason, various groups have attempted to standardize not only the definition of "horsepower" but the measurement of "horsepower." In the interim, more confusion may surface. In contrast, the watt, defined by the International System of Units ("SI"), is not encumbered by varying definitions.

That said, if your intent is to physically test a mechanical windmill device for its horsepower capacity, you are testing mechanical horsepower. Obviously the wind speed will affect your outcome, I'll let you do what you want with that. If you can attach a known weight to the windmill so that it will lift the weight a measurable vertical distance, and you have a reasonably accurate stop-watch, you can calculate the horsepower output of your windmill. One horsepower is defined as power equivalent of lifting 550 pounds a vertical distance of one foot in one second. So if you tied one end of a rope to a 550 pound weight, suspended the rope over a pulley, and tied the other end to a horse, and the horse was able to lift that weight one foot in one second, he would be capable of generating one horsepower. Or if a 220 pound man can run up a 5 foot (vertical) staircase in two seconds he is generating one horsepower.
Here's the formula:
W = weight(pounds), D = distance(feet), T = time(seconds)
Horsepower = WD/(550T)

Answer 2

Power = Torque * rotational speed (in radians/sec)

If you use MKS (SI) units, power is in watts, torque is in newton-meters, and speed is radians/sec.

There are ~746 watts per horsepower.

The windmill supplier should provide engineering data showing the device rated power, speed, and torque.

No generator required!