# How do I get the horsepower rating for other animals? (Elephants, Oxen, Mice, etc.)

…in the off chance that someone else has already done the calculations, or at least knows how they could be made, I thought I’d check here. How many horses does a hamster produce, anyway? And how good would my chances be of figuring it out for extinct animals, such as mammoths? (Too ambitious?)

Hopefully it won’t involve me renting a force meter and trying to sweet-talk a zookeeper, but hey, all in the name of science, right?

Note that a horse does not produce “one horsepower”.

wiki sez: *Horsepower from a horse

R. D. Stevenson and R. J. Wassersug published an article in Nature 364, 195-195 (15 July 1993) calculating the upper limit to an animal’s power output. The peak power over a few seconds has been measured to be as high as 14.9 hp. However, for longer periods, an average horse produces less than one horsepower.*
http://en.wikipedia.org/wiki/Horsepower

The Master weighs in:

*How did we end up with the “horse” in horsepower? The term was coined by James Watt (1736-1819), the British inventor best known for his improved steam engines, who used the term to relate steam engine performance to that of horses. At the time horses were the primary energy source for applications ranging from pumping water from mines and turning grinding mill wheels to pulling carts and loads. Although sources differ on exactly how Watt arrived at the number, it’s generally thought that in 1782, he noted how quickly a brewery horse could turn a mill wheel of a certain radius, estimated the amount of force the horse needed to exert to turn the wheel, did the math, and came up with a value of 32,400 ft-lbf/min, later rounded to 33,000 ft-lbf/min. Comparing the power output of a steam engine to an equivalent number of horses was an easy way for prospective engine purchasers to compare power ratings, so the term stuck.

What type of horse was a brewery horse? In England at the time a work horse most likely would have been one of the three British “heavy breeds” – the Suffolk punch, the shire horse, and the Clydesdale. The Clydesdale is said to have originated in the latter 1700s, perhaps too late to be a common work horse at the time Watt was doing his horsepower calculations. So it seems likely the horse in question was either a Suffolk punch or a shire horse. *

Then it wouldn’t be horsepower, it’d be elephant-power, just like any of the other power sources of modern energy. Like hydro power from water, thermo power from the Earth, and the Allspark from transformers, currently residing in the body of Megatron, at least according to the 2007 film…

Mistress, and I only weigh 9 stone 4…

Per this experiment, about 1/2072 hp.

I would expect that total muscle power would be more or less proportional to body mass. A Clydesdale weighs about a ton, plus or minus 20%, while an African elephant is about 8 tons, so offhand, I’d estimate that an elephant can put out about 8 times as much power as a Clydesdale (which, as mentioned, isn’t exactly a horsepower anyway).

Here is an article that discusses draft animal power.

It contains a table denoting the sustainable power of individual animals in good condition and gives, among other details, the standard horsepower generated by a draft horse (0.864) an ox (0.576) a mule (0.432) a donkey (0.216) and a man (0.090). Despite hamsters legendarily providing the power for a computer installation not a million miles from Chicago, they are excluded from the list of animals compared therein.

Mice also fail to feature in the comparison, either because the author thought nobody would ask the question raised by the OP, or because it’s unusual to find a working mouse-powered mechanism in any viable industrial or agricultural environment.

I am not presenting this as an authoritative cite, but I’ll try some calculations for an estimate of mouse horsepower.

According to this cite (page 2), 1 liter of oxygen consumed is about 5 kcal. http://www.uta.edu/faculty/blevinsj/Metabolic%20Calculations.pdf

According to this paper (http://www.eurodiabesity.org/pubs/faldt.pdf) mice were running on treadmills at a fixed angle of 20 degrees for an hour (after resting for an hour first), and their average oxygen use over that hour of running was about 3.0-3.25 ml/min/mouse (see Figure 4). Rounding up, we have 3.25 ml/min * (5 kcal/1000 ml) = 0.01625 kcal/min. Converting this to horsepower, we get 0.00152 horsepower.

You’ve got to be careful with that, though: That’ll tell you the total energy consumption of the mouse, but especially for a small animal like that, a lot of that will be lost as heat, rather than being used for useful work.

Why should a mouse’s muscles be less efficient than a horse’s?
The mouse has a larger surface area/volume ratio (compared to an elephant or human), so it loses heat faster, but I don’t see a reason to think that it produces more heat per gram than anything else.

I hope the aeroplane didn’t squash them!

There were two things wrong with my quick calculation - the problem was I thinking along the lines of boiler horsepower, rather than turbine horsepower - or in this case total power to maintain the system versus the productive power of the system. Of course it’s more correct to think of the productive power, which means I have the following two differences:

1. I did not subtract out the base metabolic rate energy of the mouse, which was given in the paper but which I just skimmed over.

2. What Chronos says - how efficiently the mouse converts the food to energy (how much of that 5 kcal was output energy of the mouse). I’m going to guess, given a half-remembered cite from a journal I cannot remember at a time which I do not remember that the mouse may be 50% efficient in total energy conversion.

So if we take the base metabolic oxygen consumption rate as being somewhere around 2.0 ml/min, we get:

(3.25 - 2.0) ml/min * (5 kcal/1000 ml) = 0.00625 kcal/min of total differential metabolic energy use.

Assume that during the exercise only 50% of the differential energy goes into usable work, so we get 0.003125 kcal/min of usable work. Converting this to horsepower, we get a new value of 0.000292 horsepower, or 1/3424 horsepower. This is not too far from YamatoTwinkie’s cite of a hamster putting out 1/2072 horsepower.

Hmmm, let’s figure a hamster at 1/4 lb, and a draft horse at a ton. A hamster weighs 1/8000 what the horse does, but produces (1/2072)/.864 as much power, using figures quoted above, which comes out to about 0.00056. Times 8000 is about 4.5, so a hamster produces 4.5 times as much power for its weight as the horse. Doesn’t surprise me - I would expect smaller animals to produce more power for their weights in general, due to their faster metabolisms.

Question - which animal produces the most absolute horsepower (an elephant? a water buffalo?), and which the most power for its weight (a shrew? a hummingbird?).

(I just want to see that 16000 hamster team pulling the Budweiser wagon in place of the 8 Clydesdales.)

How could it lose heat faster per gram without producing more heat per gram, if it’s keeping its temperature constant?