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Tech Topic - Horsepower and Torque

Which one should you care about?

The topics of horsepower and torque can be confusing. We use these yardsticks to compare engines but what do they really mean, how are they related and which one is more important?  An old saying is "torque wins races, horsepower sells cars". It implies the uninformed public is incorrectly focused on horsepower.  Is that so?

In fact horsepower and torque are entirely different things and are measured using different units.

Torque - Torque is a measure of twisting force, pure and simple. Torque includes no concept of motion or time.  This is easily understood by anyone who has used a torque wrench. A torque wrench can measure twisting force on a bolt that is stationary or turning. In the US torque is normally expressed in foot pounds.

Torque is created any time opposing forces are applied at different points along a lever arm. Imagine a weightless one foot long lever arm connected at one end to a stationary pivot point. If we apply a one pound force at the other end of that lever arm a one foot pound twisting force will be exerted (one foot pound of torque).  If we apply a two pound force then a two foot pound twisting force will be exerted.

Engines exert torque at the crankshaft. That torque is coupled through the transmission, driveline and ultimately to the drive axle. The twisting force at the drive axle is converted to a linear force where the tire tread meets the road surface. The linear force is measured in pounds and pushes the car forward. 

We can easily calculate the linear force that accelerates the car knowing only the torque at the drive axle and the diameter of the tires.

Linear force = Axle Torque / Tire Diameter / 2

The torque exerted by the engine varies with rpm and is typically expressed as a curve. The curve is the collection of instantaneous torque measurements at each rpm point.

Neglecting driveline losses, the axle torque and linear force that pushes the car are directly proportional to the crankshaft torque for a given gear. That means that, for a given gear and neglecting air resistance, the car will always accelerate at the same rate whenever the engine is producing a given torque.  It doesn't matter what RPM the engine is turning or the speed of the vehicle.  A perfectly flat torque curve would allow the car to accelerate the same at any RPM.  

In the real world torque curves are not flat, they build to peak and then taper off at high RPM.  A car will accelerate hardest in a given gear when the engine is operating at its torque peak.

Notice that we can figure out how hard the car is accelerating and horsepower doesn't even enter into the discussion.

Horsepower - Horsepower is a measure of the rate at which work can be performed. Motion and time are integral to horsepower which is typically expressed as foot pounds per minute in the US.

In this case work has nothing to do with your boss. Work means moving an object in opposition to a force (that may remind some of their boss).  Raising one pound a distance of one foot is one foot pound of work.  Raising one pound a distance of two feet is two foot pounds of work.

Horsepower combines the concept of work with time. In the 1700s James Watt of steam engine fame took some measurements and concluded that an average horse could lift a 550 pound weight one foot in one second.  Watt defined one horsepower as 550 foot pounds per second or 33,000 foot pounds per minute.

We can show a direct relationship between torque and horsepower.  Remember our one foot lever arm with the pivot at one end and one pound force at the other?  If it rotates about the pivot one full revolution in one minute it will move that one pound 2*pi*r or 6.28 feet per minute (think about a point on a tire tread rotating about its axle). If it rotates at 5252 RPM it will move that one pound 6.28 * 5252 or 33,000 feet per minute, exactly one horsepower.  Hence the relationship between horsepower and torque is defined as follows:

Horsepower = torque * RPM / 5252

This is a linear relationship and says that horsepower will rise in lockstep with RPM and torque. The horsepower produced by an engine varies with rpm and is typically expressed as a curve. The curve is simply the collection of instantaneous horsepower calculations at each rpm point.

To review we know that a) axle torque converted to linear force accelerates the car b) for a given gear the acceleration will be greatest at the engine torque peak and has nothing to do with RPM or speed c) horsepower is a calculated function of torque and RPM. 

So horsepower doesn't matter, right?  Wrong!  Read on.

Torque multiplication - The transmission is a torque multiplier. Reduction gears are employed to make the drive shaft rotate at a slower RPM than the crank shaft (ignoring overdrive). These reduction gears cause a similar increase in the drive shaft torque.

As an example a hypothetical two-speed transmission might have a first gear with a 2:1 reduction gears and a second gear with 1:1 gears. Let's connect that transmission to a an engine that can produce 100 foot pounds of torque at the crank shaft throughout the RPM range.

The 1:1 second gear rotates the drive shaft at the same speed as the crankshaft and it will exert exactly the same 100 foot pounds of torque (neglecting frictional losses).  However the 2:1 first gear rotates the drive shaft at half the speed of the crankshaft but it will exert 200 foot lbs of torque, twice the torque of the crank shaft!  That means first gear will accelerate the car twice as hard as second gear.

Therein lies the key to why we care about horsepower. Through reduction gears maximum drive axle torque for a given vehicle speed is generated when the engine is operating at its horsepower peak and not its torque peak (they are rarely the same).

As an example recall our car with two speeds, flat torque curve, 100 foot pound engine.  Imagine it has a 1:1 final drive ratio that propels the car at 107 mph (makes the math simple) at 1500 RPM in second gear using 24 inch diameter tires. We can also drive the car 107 mph at 3000 RPM in first gear.  The engine is producing 100 foot pounds of torque in both cases.  Which one accelerates the car faster? 

The answer of course is first gear. The following table uses the formulae presented above and illustrates the value of torque multiplication.

As a result of torque multiplication a car will accelerate fastest at any given MPH when a gear is selected that puts the engine at its horsepower peak and not its torque peak. This is one reason why small high-revving engines can often beat large low-revving engines. Despite a lower crankshaft torque, the high-revving engine can deliver greater drive axle torque through torque multiplication.

So there it is, torque and horsepower. It seems that horsepower is good for selling cars AND winning races.

Chuck Moreland - May 2002

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