Torque vs. Horsepower

When do you suppose people completely differentiated the terms torque and horsepower in their minds, pretending like each one is mutually exclusive of the other?  This is perhaps one of the most misunderstood basic concepts in the automotive aftermarket.

 In order to fully comprehend the relationship between torque and horsepower, it is important to go back to the basics of what torque and power are, fundamentally speaking that is.  Stated very simply, a torque is a twisting force, or moment and power is a rate of doing work.  Long, long ago it was stated that one horsepower was defined as 550 ft-lbf/second and that was derived from the amount of time it took the horse to lift a predetermined weight a certain height.  It’s important to note that the weight had to be lifted, not just held in place to qualify as power.  Thus power, by definition, is a rate of doing work.  To put it into simple terms, it takes more power to drive carry 100 lbs up a flight of stairs compared to carrying 50 lbs up the same flight of stairs (in the same period of time).

When we begin to talk about shaft power out of an internal combustion engine we are talking about two constituents, torque and speed.  You must have both torque and speed to make shaft power, it’s really that simple.  You could induce a torque of 500 ft-lbs on a shaft and have no rotation on that shaft.  In this scenario there is no power coming off the shaft…it doesn’t matter if we put a million ft-lbs on the shaft, until it rotates, there is no power output!

Sometimes graphical data is better suited to explaining a concept than words can ever be.  Presented here is a torque-speed curve and the corresponding power-speed curve.  As you can see, torque can be falling off but power can still continue to climb and this is common.  If the engine can continue to make enough torque to push hp higher and at the same time can handle higher RPM, then there is no reason to stop turning the engine higher.

If you take the torque (in ft-lbs) and speed (in RPM) at any given point on the chart, multiply them and divide by 5252 you will get the power number in horsepower.  The “cookbook” equation for calculating power is as follows:

 Power=(Torque*Speed)/5252

 Where:      Power is in HP
                  Torque is in ft-lbs
                  Speed is in Rev/Min

Example:  If we have an engine which makes 500 ft-lbs at 6000 RPM, calculate the power the engine is making at this engine speed:
Solution: Power=(Torque*Speed)/5252
Power=(500 ft-lbs*6000 RPM)/5252=571.2HP

For those interested in the “classical” solution using proper engineering units, the following is presented:
Power=Torque*Speed

 
Power= (500 ft-lbs)*(6000 rev/min)*(2pi radians/rev)*(1min/60sec)
Power=314,000 ft-lbf/second
1 HP=550 ft-lbf/second (this is a valid unit for power!), therefore:
 
314,159.2 ft-lbf/second=571.2 HP (314159.2/550=571.2)

From this one can see that the “5252” conversion factor is very simply for the unit conversion.   The magical “crossing” of torque and power at 5252 RPM only applies if torque is expressed in fl-lbs and power in HP because, by definition, “5252” is the conversion factor when calculating power from torque in ft-lbs and engine speed in RPM.  Please note, that rule only applies if both torque and power are expressed n those units and are plotted on the same scale against RPM.  No matter which way you slice it, power is the product of torque and speed…it always has been and always will be!

So which is better, torque or horsepower?  Put simply, with all other factors equal, the vehicle with the wider torque curve will always make more power than one with a narrower and lower torque curve. Provided that torque can be put to the road effectively at high RPM means there is more useable power.  Remember it takes power to do work, not just torque!

In addition to the above points, it is very important to understand that peak power numbers only represent one small area of the engine’s powerband.  The next time you are buzzing your car to the point at which peak power is made, take a look at how long the tachometer stays there, particularly when moving through two or three gears on your way up to speed.  If you look at things objectively, you can see that the engine in a street or race car spends a lot of time at many different engine speeds.  Most piston engines today work over a wide range of engine speeds (typically at least 4,000 RPMs worth of speed range).  Even race cars who favor the top end of the engine speed scale still operate over a wide range of speeds, maybe 2,500 RPM in that scenario.  Remember, when you select a performance enhancing product make certain it is going to do what you want it to do across the speed range you intend to operate the engine.  It’s unfortunate, but a lot of people purchase engine performance enhancing products based simply on a peak HP number.  Heading straight for that number without any consideration for power band width is a foolish endeavor that could cost you a lot of money and result in a big case of cognitive dissonance.

 

 

 

© 2011 Kuhn Performance Technologies.