Watts to Horsepower

A good friend of mine recently posed a follow on question to the watts article that appeared here some time ago. He had recently read about a new small car that had an engine power output of 6.5hp. Now, Tom is keen to know if that kind of output could be supplied by pedals and a couple of willing and fit passengers. So this post is for you Tom.
            A good place to start is by looking at the definition of horsepower. Basically the answer is in the name. Back when the steam engine had just been invented there was born a need to be able to measure power. What was this boiler shaped thing, puffing steam capable of? It was all very well turning up at a mine with one in hand but unless you could say to the mine owner that this had the power of something that they already knew, it was always going to be a tough sell. Thus horsepower was born. A guy named Thomas Savery came up with the horse comparison around 1702. He used it to good effect and sold many a steam unit by saying how it did the work of 15 horses. A problem arose quite quickly however, with competing manufacturers adding an extra horse on the figures here and there. All I can fathom is either some out and out monstrous sized horses were around back in the day or the figures were being fudged a little. So along came a standardized measurement of an average horse's potential, devised by Mr. James Watt the Scottish engineer. Using a gathering of fit dray horses, a mill wheel and a measured weight they ended up with the following. It is still the standard today. They fathomed that the average horse could produce 33,000 foot pounds per minute. Anyone that knows horses will tell you that those figures are a little optimistic, especially for a longer, period but those are the numbers.
              So that is the horsepower figure and Toms little car is producing about six and a half cart horses worth. The more astute of you are probably seeing a problem already, but I will continue. How does a human stack up with a horse? And can we fit them all in the car?
              There is a basic conversion for watts into hp., I won’t bore you with it, suffice to say that 1hp is equivalent to roughly 745.5watts, sustained, therefore the 6.5hp car is equivalent to 4845.75 watts. Going back to the original post we can see that a guy of reasonable recreational rider fitness, weighing in around 185lbs will be able to sustain approximately 196.8 watts over a period of an hour or so. Looking at these figures we can see that the car will need to be the size of a school bus to accommodate our human engine. The figures look a lot better if we can convince a dozen or so tour guys to be the engine but even then it is going to get cramped and gas, although expensive, is still cheaper than steroids.
              Tom had already fathomed this out and his main question is. Would it be possible to power batteries by pedal power that in turn powers the car with the necessary wattage and equivalent hp? Answer; yes, hooray. Not so fast, yes it would be possible for pedals to charge the battery bank but it would take a long time.
Using Ohm's law (amps=power divided by voltage) we can see that the average person could quite reasonably produce a 10amp charge rate, requiring about 120watts output, this is about the same as your average car battery charger. So, looking around at some electric motors it seems that the average requirement for a 1hp output motor is around 1000 watts. I know I said that 1hp = 745 watts but there is no such thing as a 100percent efficient motor.  
Watts ÷ volts = amps. Therefore the above example would mean 1000 ÷ 12 =83.3. Your average car battery can supply about 50 to 80 amp hours of capacity each battery would then require 5 to 8 hours of charge time at your pedal power 10 amp charge rate (divide battery capacity in amp hours by the charge rate).
Our 6.5 hp car would need approximately 8 batteries. I will leave you to work out your charge routine… Now I shall go and lay down, all this math has given me a headache.

Posted on November 2, 2012 .