Of horses, trucks, and horsepower

Horsepower is a unit of work production rate, about 3/4 of a kW, for those who like standard international units. It is also the pulling force of a work horse of the 1700s times its speed when pulling, perhaps 5 mph. A standard truck will develop 200 hp but only while accelerating at about 60 mph; to develop those same 200 horsepower at 1 mph it would have to pull with 200 times more force. That is impossible for a truck, both because of traction limitations and because of the nature of a gasoline engine when attached to typical gearing. At low speed, 1 mph, a truck will barely develop as much force as 4-5 horses, suggesting a work output about 1 hp. This is especially true for a truck pulling in the snow, as shown in the video below.

Here, a semi-truck (of milk) is being pulled out of the snow by a team of horses going perhaps 1 mph. The majority of work is done by the horse on the left — the others seem to be slipping. Assuming that the four horses manage to develop 1 hp each (4 hp total), the pull force is four times a truck at 1 mph, or as great as a 200 hp truck accelerating at 50 mph. That’s why the horse succeed where the truck does not.

You will find other videos on the internet showing that horses produce more force or hp than trucks or tractors. They always do so at low speeds. A horse will also beat a truck or car in acceleration to about the 1/4 mile mark. That’s because acceleration =force /mass: a = F/m.

I should mention that DC electric motors also, like horses, produce their highest force at very low speeds, but unlike horses, their efficiency is very low there. Electric engine efficiency is high only at speeds quite near the maximum and their horse-power output (force times speed) is at a maximum at about 1/2 the maximum speed.

Steam engines (I like steam engines) produce about the same force at all speeds, and more-or-less the same efficiency at all speeds. That efficiency is typically only about 20%, about that of a horse, but the feed cost and maintenance cost is far lower. A steam engine will eat coal, while a horse must eat oats.

March 4, 2016. Robert Buxbaum, an engineer, runs REB Research, and is running for water commissioner.

2 thoughts on “Of horses, trucks, and horsepower

  1. R.E. Buxbaum Post author

    Ronnie, any decent car or truck will have more horsepower than a horse at normal car speeds, but at low speeds it’s otherwise because of mechanics. Another way you can see this is to watch the first second or two of competition between a horse and a racer starting from dead stop. You will notice that the horse accelerates faster at low speed. Assuming that the horse and the racer weigh about the same, we conclude that the horse has more horsepower. hp = f•v = m•a•v. If m is the same, and a is greater at the same v, then the hp is greater. Here’s a video you can watch. https://www.youtube.com/watch?v=0Yb6XEGpUdw

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  2. Ronnie Schreiber

    Robert, I’d like to republish this at The Truth About Cars with some revisions. A typical semi truck will have a bit more horsepower than 200 these days. I believe that most are in the 400 to 500 hp range. Also, you mentioned that horsepower is a figure derived from horses in the 18th century. I’m sure that a horse might have been able to accelerate faster than a Model T but I doubt that even the fastest horse can run the 1/4 mile as fast as a modern supercar. The McLaren 675LT I drove can do 0-60 mph in 2.9 seconds and the 1/4 mile in 10.45 seconds with a trap speed of 142 mph. American Pharaoh can do a 1/4 mile in about 24 seconds. A V6 Camry can do it in 14.4.

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