### Horsepower vs Torque

#### What is Torque

Torque is the measure of an objects tendency to rotate about a point. It is a measure of work, or the magnitude of a force acting through a distance. In terms of engine output, it can be described simply as the net twisting force produced at the crankshaft. The greater the torque output, the greater the load that the engine is capable of overcoming.

It's important to understand that torque is not a time dependent variable. Imperial units of torque include inch pounds (in-lbs, lb-in) and foot pounds (ft-lbs, lb-ft, pound feet) while metric units of torque are typically given in Newton meters (N-m). Notice that these units include a force and a distance.

#### What is Horsepower

Horsepower is a measurement of, no surprise, power; the measure of the rate at which work is performed or how much energy is consumed during a process. Horsepower is dependent on time and torque as it is the force generated through a distance per a unit of time. Therefore, power identifies the total work done over a given time interval.

Horsepower is a fictitious concept based on the assumption that a horse can move a 33,000 pound object 1 foot per minute (33,000 lb-ft/min). Horsepower itself is not actually measurable by any instrument; it is calculated by measuring the torque at a particular angular velocity. In the case of reciprocating engines, this would refer to rotations per minute (RPM) of the crankshaft. By measuring the torque and RPM, horsepower is then calculated using the following formula:

Horsepower = (torque x RPM)/5,252

The constant "5,252" is derived from the fact that a circle 1 foot in diameter has a circumference of 6.2832 feet. Dividing 33,000 by 6.2832 results in 5,252 and resolves the units for the equation. Interestingly, but not coincidently, horsepower and torque curves will **always** cross paths at precisely 5,252 RPM (horsepower and torque will be equal at this engine speed).

#### Engine Horsepower & Torque vs Drive Wheel Horsepower & Torque

Automakers and engine manufactures typically advertise peak rated engine horsepower and torque, whereas a vehicle dynamometer measures actual drive wheel horsepower and torque (often referred to as rear wheel horsepower and rear wheel torque). Engine horsepower and torque is generally considerably less than drive wheel horsepower and torque as measured by a dynamometer. This is due to a number of factors that include parasitic losses resulting from friction, heat, and energy consumed in the movement of the reciprocating assembly. Drivetrain losses, energy consumed by the transmission and differential assemblies, also reduce drive wheel horsepower and torque due to the same mechanisms.

There's also torque multiplication through the drivetrain that must be considered. For example, an engine producing 600 lb-ft of torque at a particular RPM through a 2:1 transmission ratio and 3.73:1 rear differential ratio actually produces, disregarding all parasitic losses, 4,476 lb-ft of torque at the drive wheels (600 x 2 x 3.73). Up-shifting the transmission to a 1:1 ratio reduces the torque multiplication and our vehicle now only experiences 2,238 lb-ft of torque at the drive wheels (600 x 1 x 3.73).

Torque multiplication through the drivetrain is a form of mechanical advantage that allows the engine to overcome greater resistive forces, such as those experienced when trying to bring a heavy load up to speed. An important use of a vehicle dynamometer is to identify engine performance characteristics while taking into consideration drivetrain factors. Thus, correction factors are used in order to negate all torque multiplication through the drivetrain and deliver real-world engine horsepower and torque figures.

### Horsepower, Torque, & Acceleration

In classical physics, torque is directly related to the rate of acceleration of a body. More specifically, the net force acting on a moving body is directly related its rate of acceleration. This is expressed mathematically in Newton's second law of motion, which ascertains that the force acting on an object is equal to the object's mass times its rate of acceleration (F=M*A). The formula can be rearranged to A=F/A, or the rate of acceleration is equal to the force acting on an object divided by its mass. Since torque is the measurement of a force through a distance, we can mathematically isolate the force produced by a torque and calculate the rate of acceleration using Newton's equation. In order to do so, we'd need to know the torque that is being produced by the engine at a certain RPM, the final drive ratio, and the tire height. The resultant would be in the form of a net drive force or net propulsive force.

#### What Does Horsepower Actually Tell us About an Engine?

Unlike torque, horsepower builds in a comparatively linear fashion and only begins to drop in the higher RPM ranges (relatively speaking). Low engine speeds produce low horsepower, while higher engine speeds produce higher horsepower. High horsepower engines are typically associated with racing applications and thus many assume that more horsepower denotes a faster vehicle. There may be some truth to this statement, however it is extremely misleading. As previously outlined, torque is directly related to the rate of acceleration of a vehicle. However, one must not forget the *relationship between horsepower and torque*. Horsepower is the rate at which torque is being produced, and it provides some useful insight into the practical application of an engine

To some extent horsepower can be used to compensate for an engine's relatively low torque output. Likewise, torque can be used to compensate for an engine's relatively low horsepower rating. If this seems confusing, recall that an engine is only one piece of an otherwise complex drivetrain system and the mechanical advantage provided by gear reduction in the transmission and differential can also compensate for lower engine torque and horsepower output, albeit to a limited extent.

#### Horsepower and Torque in Diesel Engines

The horsepower vs torque debate surfaces often with regard to diesel engines, which produce a relatively large amount of torque but generally exhibit low horsepower ratings (350 horsepower/750 lb-ft of torque, for example). Recalling that horsepower is time dependent and torque is not, a diesel engine's ratings are primarily limited by engine speed. A typical light duty diesel has a maximum engine speed in the 3,500 rpm range while a typical heavy duty diesel has a maximum engine speed in the 1,800 to 2,200 rpm range. If we were to recalculate the horsepower of these engines at a much higher engine speed, power would be proportionately greater.

Diesel engines are speed limited for several reasons. Torque drops off sharply at higher engine speeds do to frictional losses and the fact that diesel fuel burns at a relatively slow rate. Thus, the combustion process becomes inefficient at high engine speeds as the time of each power stroke theoretically "out-paces" the rate of combustion (piston returns to BDC without ample time for all energy to be extracted). Furthermore, there is the concern that the high compression ratio and long stroke length of a diesel engine may cause excessive wear at high engine speeds. Diesel engines are therefore not well suited for high rpm applications, and this is reflected in their torque-biased output ratings.

#### Horsepower and Torque in Gasoline Engines

Gasoline engines may exhibit horsepower ratings that are lower, equal to, or greater than the respective peak torque rating. As previously discussed with regard to low horsepower in diesel engines, this is indicative of operating range. It is generally acceptable to assume that a high horsepower, low torque (600 hp/400 lb-ft, for example) rated engine has a relatively high maximum engine speed while an engine that has a similar horsepower and torque rating (500 hp/500 lb-ft, for example) has an average maximum engine speed (recall that horsepower and torque always equal each other at 5,252 rpm). An engine that was limited to a much lower engine speed (such as that found in diesel engines) would have a significantly higher torque rating than horsepower (300 hp/400 lb-ft, for example).

Torque is no greater nor no less important in gasoline engines than in diesel engines, however we typically seem to rank gasoline engines by their horsepower ratings as it provides insight into certain performance characteristics. Higher engine speeds are often desirable in high performance applications because shifting at high rpm allows an engine to hold a lower transmission gear longer, thus [theoretically] producing more drive wheel torque for longer periods of time (recall that torque is multiplied through the transmission and rear axle gear ratios, so with each transmission upshift drive wheel torque is reduced).

#### Horsepower and Torque in Electric Motors

Idealistically, electric motors begin to produce peak torque at zero rpm and total torque output remains fixed through the entire operating range. The theoretical torque curve for an electric motor is therefore a perfectly level horizontal line through the max operating speed. In practice, there are various loss factors that cause small imperfections in the torque curve, but the curve is extremely flat and peak torque is generated the moment it is demanded. This is possible because torque is not dependent on movement, and thus you can produce a torque without actually having any rotational speed. Since an electric motor does not require constant rotational motion (i.e. a reciprocating engine must remaining running), full torque can be applied from a complete stop.