Horsepower vs. Torque



While horsepower is often considered when shopping for a vehicle, what about that "other" engine rating: torque?


Specifically, what are the differences between horsepower and torque? If you flip through the pages of any automotive publication, you'll notice that these two measurements are commonly listed under vehicle specifications. And while the average car enthusiast knows that both horsepower and torque play a role in performance, most of them don't understand exactly how or why.


Let's begin by explaining the technical difference between the two. Horsepower is defined as the amount of energy required to lift 550 pounds, one foot, in one second. From this definition you can see that the components of horsepower are force, distance and time. Distance and time are self-explanatory but force, specifically a twisting force, is what torque is all about.


Remember that the initial energy that moves a car forward starts in the combustion chamber in the form of an explosion. This explosion forces a piston (or group of pistons) down in a straight line, which pushes on a connecting rod and turns the engine's crankshaft. It's this turning crankshaft where the twisting force of torque initiates. From there the force is carried through a flywheel, transmission, driveshaft, axle(s) and wheel(s) before moving the car.


The measurement of torque is stated as pound-feet and represents how much twisting force is at work. If you can imagine a plumber's pipe wrench attached to a rusty drainpipe, torque is the force required to twist that pipe. If the wrench is two feet long, and the plumber pushes with 50 pounds of pressure, he is applying 100 pound-feet of torque (50 pounds x 2 feet) to turn the pipe (depending on the level of rust, this may or may not be enough torque). As you may have noticed, this measurement of torque does not include time. One-hundred pound-feet of torque is always 100 pound-feet torque, whether it is applied for five seconds or five years. So, if you want a quick answer to the difference between horsepower and torque, just keep in mind that horsepower involves the amount of work done in a given time, while torque is simply a measurement of force and is thus a component of horsepower.


To see how torque and horsepower interact, imagine your favorite SUV (everyone has one of those, right?) at the base of a steep hill. The engine is idling and the gear lever is in the "Four-Low" position. As the driver begins to press on the throttle, the engine's rpm increases, force is transmitted from the crankshaft to each wheel, and the SUV begins to climb upward. The twisting force going to each wheel as the vehicle moves up the hill is torque. Let's say the engine is at 3,000 rpm, the gear ratio is 3, and the vehicle is creating 300 pound-feet of torque. Using the following formula, we can calculate horsepower:


Take the torque of 300 multiplied by a shaftspeed of 1000 (3000 rpm divided by a gear ratio of 3) for a total of 300,000. Divide 300,000 by 5,252 and you get 57.1 horsepower that the SUV is making as it begins to ascend the hill. It is interesting to note that, since 5,252 is used to calculate horsepower by way of torque and shaftspeed, it is also the number in the rpm range at which torque and horsepower are always equal. If you were to view the horsepower and torque curves of various engines, you would notice that they always cross at 5,252 rpm.


The horsepower and the torque are related through the following simple equation:



How is this equation obtained? Imagine you are turning a shaft of radius R feet  with a force constant F pounds, so the torque is T = R*F; suppose the shaft turns at a speed of N RPM, so for every second, the shaft turns N/60 times. Therefore, for every second, the amount of work done is W = F*L, where L is the distance that the force F has worked on and is equal to 2p*R*N/60. Since one HP equals 550 pound-feet, the total horsepower is then equal to:


HP = W/550 = F*L/550 = (F*2p*R*N/60)/550 = (F*R*N)/(550*60/2p) = T*N/5252


Use this equation, you can easily explain (see the figure below) why when the engine’s RPM reaches certain speed, although the torque starts to drop (due to (a) too short time for explosion; (b) too short time to suck in fuel mixture in the intake stroke; (c) too much frictional heat due to faster piston’s speed; and others), the horsepower still increases with the RPM. This is because while the torque decreases, increase in RPM will compensate its loss in the above equation, so the overall result is that the horsepower still increases. Only when the torque drops so much (i.e. when RPM is near 6000), the increase of the RPM can no longer compensate its loss, then the horsepower starts to drop.




So now we have a technical understanding of how torque interacts with horsepower, but let's move beyond that to some real-world examples. For instance, we all know that a car moves from a dead stop in 1st or low gear, yet as the car's speed increases, the gears must be moved up through 2nd, 3rd and 4th to maintain acceleration. This is because at low speeds the transmission's gears work to transmit maximum torque from the engine to the wheels. You want this because it takes more force, or torque, to move a vehicle that is at rest than it does to move a vehicle in motion (Newton's 1st Law). At the same time, once a vehicle is underway, you want less torque and more horsepower to maintain a high speed. This is because horsepower is a measurement of work done and includes a time element (such as wheel revolutions per minute necessary to maintain 75 mph).



Horsepower and Torque "At the Wheels"


Now when we're talking about automobiles, the amount of horsepower or torque generated at the flywheel is not very useful when determining acceleration. What is useful, however, is horsepower and torque "at the wheels". The problem here is that drivetrains cannot be perfectly efficient and pass 100% of the power of the engine through its components to the wheels. Some of the power is lost for several reasons. Generally 15-25% of engine power never makes it to the wheels. Different types of drivetrains will have different levels of efficiency. Generally, drivetrains with more weight and those with more components will be less efficient.

Let's use my own car for some sample calculations. In stock form, it has 165 hp @ 5600 RPM and a torque of 166 lb-ft @ 4000 RPM.

Dyno results have shown that the car has around 127 peak hp at the wheels. That's a 23.03% loss. Note that this is higher than most cars because of the heavy and sophisticated all-wheel-drive system.

Here's a chart to show how the power and torque change before they reach the wheels. Although, the efficiency loss is difference for each gear, we'll assume that 127 peak hp is attainable in every gear. At 5600 RPM, the flywheel torque calculates as 154.7 lb-ft. Calculating the same efficiency loss (23.03%) as horsepower, this would come out to 119.1 lb-ft.