How Much Horsepower is a Horse? [video]
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Like humans or any other animals, horses can sustain much higher powers for short times, than for long times. Few horses, if any, could sustain a power of "1 hp" for hours.
A known mass descending down say an old vertical mine shaft would allow potential energy to be converted into Joule/seconds (watts). As the force on the rope/cable is known with good precision an accurate empirical measurement of the dynamometer and its total frictional losses could be accurately determined.
Why calculate those losses at the risk of errors when one can measure them directly?
Such a unit was originally and predominantly used as a marketing tool for early industrial engines
My point is the actual power of a real horse in agreed horsepower units cannot be accurately determined if the conversion of 'pulling' force isn't accurate, so the only issue is calibration.
Even in the metric-phobic US the rest of the dynamometer would likely be designed around SI units simply because that's how most engineering measurement is done nowadays. That means all calculations would be done in SI and converted into legacy hp units.
Fortunately, Imperial measurements in science/engineering has all but died so the interest here is only academic. Another similar anachronistic measurement is the illumination unit candlepower, again a conversion factor to SI was agreed but in this instance (unlike hp) there was a defined physical standard—the international candle (or it was so some 80 years ago until the standard was updated).
(I say 'fortunately' above as I had to learn both Imperial and metric and I'm damn glad Imperial has all but gone. Dealing with foot-poundals, PSI, etc. is for the birds.)