Horsepower is the amount of work an engine can do over a set amount of time. One horsepower is 550 foot pounds of torque per second. A foot pound is the ability to apply one pound of force one foot away from the center of the area the work is being applied to.
Older calculations were off, so one horse can actually produce 5-12 horsepower. So it’s not a good reference for “x” amount of horses pulling your car.
In a modern engine, the horsepower is calculated by running the engine, and seeing how much torque it makes then applying a formula to that result. Torque x RPM (of the engine)/5252 = HP
5252 is a constant so any engine that revs to 5,252 rpm with have even torque and HP figures at this engine speed.
EDIT: fixed a typo, point – pound
To understand horsepower, you need to understand torque. All an engine’s torque is is how much turning power the engine can transmit to the wheels. Applying torque over a certain period of time over a certain distance on the circumference of the wheel equates to a certain amount of work being performed, which we measure in horsepower (usually) because a long time ago some dude’s horse could lift a bucket a certain distance in a certain time which was then defined as 1 horsepower.
To oversimplify, horsepower is a measure of how fast torque happens. Torque is what you want when you’re pulling a stump or getting off the line at the dragstrip. Horsepower (and aerodynamics) are what you want when you’re Bugatti or Hennessey trying to just go as fast as you can at the top end. You can make relatively little torque but still make decent horsepower if your engine redlines at a really high RPM, and conversely you can be a diesel semi-truck and make mountains of torque but make less horsepower than my SUV because those engines only rev to a fraction of what most cars will.
It’s the rate at which work is produced. Torque is the twisting force of an engine and horsepower is how fast this twisting force is applied. The reason why it’s relevant to cars is because torque numbers alone tell us little about how they perform on the road, but horsepower figures give us a good idea of the car’s overall performance.
Horsepower is a measure of power. All else being equal, more power means that the engine can accelerate the car faster.
Pretty much any street-legal car can drive “fast”, e.g., 60 MPH… but while my mom’s little old Toyota Echo takes almost 10 seconds to get going that fast, a Mustang can do it in less than half that.
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