A common misunderstanding in the world of motor sports enthusiasts is over the use of the terms “torque” and “horsepower”.  Common statements include, “Torque is low end power and horsepower is high end power”, and “Torque is the grunt ability of an engine and horsepower is the wide open power of an engine”.  However, in the world of physics and engineering, both of these terms have very specific meanings, and distinctive mathematical means of determining them.

While the above quotations of the differences in torque and horsepower have some glimpses of truth within them, the overall statements are both wrong, and very misleading.  When one refers to torque and horsepower, they are referring solely to measurements taken of the work and power done by an engine.  The net production of this work and power is delivered to the output end of the crankshaft, and then mechanically connected to whatever device that is to receive the work and power output.  In the case of automobiles, trucks, motorcycles and other engine driven vehicles, the device receiving the output of the engine is the clutch/transmission combination (in manual transmission applications), the torque converter/transmission combination (in automatic transmission applications) or the hydraulic pump/hydraulic motor (in hydrostatic drive applications) or the belt or chain in small engine direct drive applications.  The transmission then transmits, or transfers, the work and power to the final drive.

To measure the work and power of an engine, it is measured either on an engine dynamometer directly off the crankshaft, or at the rear wheels on a chassis dynamometer.  The engine dynamometer is the preferred method for accurate results of true engine output, since it eliminates all of the inertial and frictional losses between the engine and the final drive.  The rear wheel dynamometer measures the output at the rear wheel, inclusive of frictional and inertial losses between the engine and the rear wheel/dynamometer roller interface.  The losses include inertial losses from the engine having to accelerate the rotating mass of clutches, gears, shafts, torque converters, etc.  There are also frictional losses from the mating of gears, drag in bearings and the viscous effect of the lubricating oils and greases in bearings, gears, etc.  There is also sometimes slippage between the tire and the dynamometer roller.  Although all of these losses can be measured and calculated, one still is left with little more than an accurate estimate of the losses.  The inertia of the components is the easiest to calculate accurately, but the frictional losses are more difficult to pinpoint – they vary with time, temperature and speed.  Oils and greases are thermo-viscous lubricants, where the viscosity of each is temperature dependent.  Further, the acceleration and velocities at which the fluids are displaced from bearing rollers and gears in mesh affects the viscosity and the kinematic viscosity of the lubricating fluid, and, ultimately, the fluid friction.  With all of the above variables, a precise estimation of the drivetrain losses would be quite difficult.  However, there is one true advantage to a chassis dynamometer - measuring the rear wheel work and power is a measure of what actually moves the vehicle down the road – all losses are included.

In the case of measuring actual engine output (the device responsible for producing the work and power delivered to the final drive) an engine is mechanically connected to the engine dynamometer and the dynamometer measures the engine’s output as it operates through its rpm range.  The dynamometer only measures two meaningful pieces of output from the crankshaft’s rotational output.  It measures the work of the crankshaft, or torque, and the rotational speed of the crankshaft, commonly described in revolutions per minute (rpm).  (There is other data recorded, such as air temperature, barometric pressure, etc., but these are for calculating “correction factors” for determining engine output in a “standard” atmosphere.)  In layman’s terms, the dynamometer measures the amount of rotational force the engine produces and how fast it turns.  The terms “work” and “power” have been used in describing the output of an engine.  The dynamometer measures the rotational force of the engine, which is a term of work.  This measurement is simply in units of force at some given distance.  In the United States, the accepted unit of force is the pound (lb.).  The accepted unit of distance is the foot (ft.).  The dynamometer measures that the rotational force of an engine will exert a given force (lbs.) at a given distance of one foot (ft.).  The dynamometer measures the rotational output in lbs.-ft. of torque (often called “ft.-lbs.”).  This is the work of an engine, or the rotational force (torque), in lbs.-ft., it produces. 

The power of an engine refers to how much torque it produces in a given time, usually one second.  In other words, horsepower is work divided by time.  In days long gone, when the horse was the supreme form of pulling force, it was determined that a mature, fully grown “standard” horse could pull a cable over a pulley to lift a load of 550 pounds one foot in one second.  This was then determined as the standard of horsepower, the amount of power required to do 550 lbs.-ft. of work per second.  Another figure used sometimes for the horsepower standard is 33,000 pounds one foot in one minute, which is converting 550 lbs.-ft. per second to the work done in one minute (550 lbs.-ft./sec. x 60 sec./min. = 33,000 lbs.-ft./min.).  Given this standard, once the dynamometer measures the torque of an engine, and the speed at which it rotates, it computes, or calculates, the horsepower.

Mathematically, it breaks down as follows.  If an engine produces 100 lbs.-ft. of torque at 2,500 rpm, it has produced a force of 100 lbs. at a one foot radius from the center of the crankshaft.  A radius of one foot from the center of the crankshaft produces a circular path with a diameter of two feet.  The distance around this path is the diameter times PI (π) (3.1416).  Therefore, the distance that the force followed around this circular motion is 2 feet x 3.1416 or 6.2832 feet.  Multiplying the force times the distance yields 628.32 lbs.-ft.  It produced this force (100 lbs.), for this distance (6.2832 feet), 2,500 times in one minute, giving a power value of 1,570,800 lbs.-ft. per minute (628.32 lbs.-ft x 2,500 rpm).  Dividing this value by 60 (seconds per minute) converts to 26,180 lbs.-ft. per second. Since there are 550 lbs.-ft. per second in one horsepower, divide the 26,180 lbs.-ft./sec. by 550 lbs.-ft./sec/horsepower, and obtain 47.6 horsepower.  This can be verified by the common conversion formula, “HP = (Torque (lbs.-ft.) x rpm)/5252”, which yields the same result.

How does this math relate to the real world?  The torque value of the engine reveals the maximum rotational force an engine can produce.  The horsepower figure reveals how much work an engine can do in a given time.  Torque is a measure of the strength, rotational force or work capability, of an engine; horsepower is a measure of the rate of work production of an engine.

Illustration one, suppose there are two engines, both of which have two foot diameter pulleys connected to the crankshaft (one foot radius).  A cable is connected to each pulley with a 100 lb. load on the cable. The engines both produce 100 lbs.-ft. of peak torque, although engine “A” produces 100 lbs.-ft. at 2,000 rpm (38.1 hp), and engine “B” produces 100 lbs.-ft. at twice that speed, or 4,000 rpm (76.2 hp).  Although they each will pull the same load, engine “B” will pull the load twice as fast as engine “A”.  It has twice the horsepower, but the same torque, so it will produce twice the quantity of work in the same given time frame with the same load.

Illustration two, the two engines have two foot diameter (one foot radius) pulleys connected to the crankshaft.   A cable is connected to each pulley with a 100 lb. load on the cable.  Engine “A” produces 100 lbs.-ft. of torque at 2,000 rpm (38.1 hp), and engine “B” produces 80 lbs.-ft. of torque at 3000 rpm (45.7 hp).  In this example, engine “A” will pull the load, whereas engine “B” will stall, since the load exceeds the torque.  However, if a gear reduction of 1.25:1 is used between engine “B” and the pulley, this will increase the torque to the pulley to 100 lbs.-ft., but reduce the speed to 2,400 rpm.  Engine “B” still produces 45.7 hp (although the speed is slower, the torque is inversely proportionately higher).  Engine “B” now pulls the 100 lb. load 20% faster than engine “A” (2,400 rpm versus 2,000 rpm).  The engine with the most power, engine “B”, does more work in a given time frame than engine “A”, although engine “B” has less torque.  Also note that engine “B” has 20% more power than engine “A” (38.1 x 1.20 = 45.7).

The two illustrations above are simple illustrations to explain the importance and differences of torque and horsepower.  The only points illustrated are the peak torque positions on the work/power curves.  In real life, as they say, engines seldom operate only at one rpm level, but must operate over some defined range of operating speed.  Therefore, the average torque and average horsepower numbers over the intended operating range are much more meaningful to the overall performance of the engine than a simple peak torque or peak horsepower number.

Torque is directly measurable; it is a measure of work or rotational force.  In physics, work is measured independent of time.  It is measured simply by the formula “work equals force times distance” (W = f x d).  Horsepower is dependent upon the amount of work done in a period of time.  It is a calculated term, calculated from the measured torque.  The formula for horsepower is actually a first order differential equation stating that power (P) equals the change in work (dW) divided by the change in time (dt) (P = dW / dt).  The work must first be measured, and the time taken to accomplish the work is recorded.  The quantity of work done during the time increment is then divided by the time increment taken to accomplish the work.  Torque is a work measurement only; it measures the “strength” of an engine.  Horsepower is a power measurement; it measures how much torque an engine produces in a period of time. 

A common example is of two men loading bales of hay onto a truck.  The work to load each bale is the same.  However, if man one loads one bale per minute and the man two loads two bales per minute, man one has exhibited no greater strength than man two, but man two has produced a greater volume of work in the same time period.  Man two would have the same “torque” as man one, but man two would have produced twice the “horsepower”.

Another example would be if man one could load 150 pound bales on the truck at a rate of one bale per minute and man two could only lift 100 pound bales but could load two per minute.  Man one has produced a greater "torque" in that he can lift 50% more weight than man two (150 pounds vs. 100 pounds), but man two has produced more "horsepower" because he loads 33% more hay (200 pounds per minute vs. 150 pounds per minute).  This is a greater production of work per time.

The bottom line is this, if gear ratios are fixed, and the absolute strongest engine must be chosen, with no regard to operating range and/or speed, choose the engine with the highest peak torque measurement.  It will move the greatest load at a given gear ratio at the engine’s peak torque rpm.  If, on the other hand, gear ratios are to be chosen, and acceleration and/or speed are concerns, choose the engine with the highest peak horsepower and gear the vehicle to operate the engine at peak horsepower rpm; you’ll produce the most work in the shortest period of time.