Putt-putt go vroom-vroom: A look at torque and horsepower

I’m an unabashed fan of Top Gear UK. Watching those guys whip huge cars around the track in a cloud of tire smoke spouting British witticisms (or building the ridiculous, like turning a Reliant Robin into a space shuttle) is pretty much my favorite thing to do any night of the week. (I also credit the show with my wife’s evolution from “All four-door sedans are the same” to “You know, I really like the lines on Audis.”)

But I have to admit, sheepishly, that I’ve always been confused by one thing — the difference between horsepower and torque. I get that they’re both ways of looking at how powerful a car is, but I’ve never been quite sure what each is actually measuring in physical terms.

Getting all twisted around

A wrench by aplumb on Flickr. Used under Creative Commons license. http://www.flickr.com/photos/aplumb/5228456731/

(aplumb/Flickr)

Let’s start with torque. From an automotive point of view, torque tells you how much power an engine produces to get a car moving.

For engineers and physicists, though, torque means the amount of force put on an object to make that object rotate. Or put another way, it’s the amount of twisting force applied to something.

For instance, imagine for a moment that you’re in your kitchen and you want to make a peanut butter and jelly sandwich. You’re trying to get the jelly jar open, but it’s stuck. You’re grabbing on the lid as tightly as you can and twisting with all your might — you’re applying torque.

According to NASA, the maximum amount of torque a person can exert on an object in a clockwise motion using their hand is, on average, 121.5 pound-inches (lb-in), or 10.125 pound-feet (lb-ft).

(To put that in perspective, the engine in my Subaru Outback produces 169 lb-ft of torque, while the engine in a Bugatti Veyron, one of the fastest road cars in the world, produces 922 lb-ft.)

10.125 what? At this point, we should take a moment to talk about the units by which torque is measured  and how it’s calculated. Here’s the equation:

T = r x F

where F is the amount of force (in pounds here in the US and newtons everywhere else) and r is the distance between the rotational axis of the thing being rotated and the point at which the force is being applied (in feet or inches here, meters or centimeters elsewhere). Put another way, r is the length of the lever you’re using to twist whatever it is you want to twist.

Torque animation by Yawe on Wikimedia Commons. Released to the public domain. http://en.wikipedia.org/wiki/File:Torque_animation.gif

An animation of torque. (Yawe/Wikimedia Commons)

So in our jar lid example above, r would be the distance between the middle of the lid and your fingers (say, an inch and a half). Using those numbers from NASA, we know that your max bare-handed torque is 121.5 lb-in. Assuming a 3-in wide jar lid and calling r half that distance (because you’re gripping the lid with your bare hand), we can calculate the force you’re putting on the lid:

121.5 lb-in = 1.5 in x F

F = 121.5 lb-in / 1.5 in = 81 lb

But even though you’re twisting that lid with all your might, the bugger still won’t budge. So you pick up a jar wrench. Now this won’t change the amount of force you apply, but it does give you a longer lever. Let’s say it’s 6 inches long and see what it does to your torque:

T = (1.5 in + 6 in of lever) x 81 lb = 7.5 in x 81 lb = 607.5 lb-ft.

By extending r, you’ve greatly upped the amount of torque you can apply to the jar lid. Now nothing will stand between you and your sandwich!

“This is all very nice Tom,” you say, “but we were talking about cars, and my car doesn’t rotate when I step on the gas. It goes forward.”

True. But the crankshaft inside your car’s engine does. As each piston fires, it exerts a twisting force on the crankshaft through the connecting rod, forcing the crankshaft to rotate.

Crankshaft animation by NASA. Public domain image. http://en.wikipedia.org/wiki/File:Cshaft.gif

(NASA/Wikimedia Commons)

That amount of  twisting force is what gets recorded on your car’s spec sheet. The more torque = the more twisting force the engine puts on the crankshaft = the more power the engine has available to get the rest of the car moving.

Horsing around

Horsepower infographic from Jalopnik.

(Jalopnik; click through and zoom to see the original enlarged)

Torque took a bit of explaining, but horsepower is a bit simpler: It’s pure straight-line power.

Or put another way: Torque gets you moving, horsepower keeps you moving.

Horsepower is a unit of measure for power, telling you how much work an engine, horse, or person can perform, and how quickly. Now, that’s work in the physics sense, meaning the amount of force needed to move an object, like a car or a cart or a bag of groceries, over a certain distance.

The equation for power looks like this:

P = work / t = (F x d) / t

where F is our old friend force, d is distance, and t is time. And horsepower is merely an arbitrary unit of measure for power, typically defined as 33,000 foot-pounds of work per minute, or roughly 746 watts, with 1 watt being equalling 1 newton-meter per second. So using the equation above, you could express 1 hp this way:

1 hp = 33,000 ft-lb/1 min

(At least as far as cars are concerned. There are actually several different ways of defining horsepower depending on the engine or system you’re measuring and how you’re measuring it. But we won’t go into all that.)

“But Tom,” you say, “you just used pound-feet to talk about torque, and now you’re using foot-pounds for horsepower!”

Yes, but the difference is in the feet. Remember, in torque we were talking about the amount of force applied to a lever to get something to turn, where the feet refer to the length of that lever. Here, we’re talking about the amount of force needed to move something in a straight line, where the feet refer to the distance moved.

The guys at Jalopnik have a handy infographic (look to the right) that explains where horsepower comes from and how it works. And if you read it, you’ll notice a funny thing about horsepower: If you keep the amount of horsepower and the amount of time constant — say, 1 minute — you can either move a really light thing really far or a really heavy thing a short distance and still exert the same amount of work.

Or you can keep the time and force constant, and see what happens when you play with horsepower and distance. So, as Jalopnik says at the bottom of the infographic, a 50 hp Volkswagen Beetle could plausibly pull a big-rig cab 100 feet in 1 minute. But by my math, the above-mentioned Bugatti Veyron, which produces 1,001 hp — or 330,033,000 foot-pounds/min — could pull that same truck cab 2002 feet in the same amount of time.

All of which assumes that the Beetle’s engine could produce enough torque to get moving which hitched to the cab in the first place.

So in real terms, what’s the difference between horsepower and torque? Autotrader says:

“When trying with all your might to open the top of a new jar of mayo, torque is present even if movement isn’t. It’s pure twisting force. Horsepower, on the other hand, requires movement to exist. A hand with lots of horsepower could spin the lid rapidly once it’s loose, but without much torque, that lid might never budge.”

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