This article can be found here from Tom Barber

http://www.fjr1300.info/misc/torque-power.html Torque and Power

Five Popular Urban Myths about Torque and Power Debunked

by Tom Barber

Anyone who spends much time on motorcycle and car related Web forums knows that there is a fair amount of debate on whether the torque or the power of an engine is the true indicator of the vehicle's maximum acceleration. Numerous Web sites offer genuine information on the subject, but there are also a few that offer misinformation and that propagate a few popular myths. This article endeavors to clear up some of the misunderstandings and debunk a few of the myths. Along the way, this article will give a usefully complete theoretical treatment of torque, work, and power, and will offer insight into the metrics of torque, work and power. It will present a theoretical perspective of how dynamometers work and will explain how the two basic types differ. It will even explain precisely how torque and power each relate to acceleration.

Myth #1: Dynamometers only actually measure torque. Power is an abstract quantity that can't be measured, and must be calculated from the torque.

This belief is false and it will not be hard to show that. However, it involves a discussion of how dynamometers actually work, and before we can go there, we have to begin with a brief review of some fundamental physics. I'll try to avoid equations as much as possible, and instead I'll try to instill an intuitive understanding of the basic concepts, which is something that classroom lectures and textbooks often fail to accomplish for many people.

Isaac Newton taught us that any object having a mass M, has an intrinsic resistance to changes in its present momentum when external force is applied. The acceleration of the object is proportional to the strength of the external force, and is inversely proportional to the mass of the object. These observations are summed up succinctly by the infamous equation: F = M x A. The true essence of force, mass and acceleration is embodied in this equation, and this equation tells us how force or mass can be detected and measured. When an object's momentum is not constant, this indicates the existence of an external force, and the strength and direction of that force can be determined by investigating the acceleration. Conversely, if an object is accelerated under the influence of a well-known force, its mass can be determined.

Whenever the aggregate force acting on an object is not directed through the object's center of mass, the object is caused to rotate, and this rotation will continue to accelerate as long as this condition persists. The laws governing rotational motion parallel the laws governing straight-line motion. Torque replaces force, the moment of inertia replaces the mass, and the angular acceleration replaces straight-line acceleration. Whereas velocity is measured in terms of absolute distance in straight-line motion, in angular motion we measure velocity in terms of degrees of rotation per unit of time, which we may call angular distance. Angular velocity is the instantaneous rate at which angular distance is covered. Angular acceleration is the instantaneous rate at which the angular velocity is changing, and is proportional to the applied torque, and inversely proportional to the moment of inertia. The torque that is associated with an applied force is equal to the force (magnitude) multiplied by the distance from the center of mass of the object to the line of force (measured at right angles to the line of force). For an object that is constrained to rotate about a fixed axis of rotation, i.e., a wheel, the distance is measured from the axis of rotation to the line of force. Two objects with identical mass will not in general have the same moment of inertia. For example, if two perfect spheres of identical mass are made of different materials having different densities such that they are not the same size, the larger one will have the greater moment of inertia. In the case of objects having fixed axis of rotation, if two such objects have the same overall diameter and density but differ in the radial distribution of the mass, the one with the mass concentrated closer to the axis of rotation will have a lower moment of inertia.

Work, in the case of linear motion, is the force multiplied by the distance through which the force was exerted and the object was moved. Work and energy are equivalent; it takes a specific quantity of energy to move an object a given distance in opposition to a given resistive force, and that amount of energy is the same no matter how quickly the movement is performed. Power is simply the instantaneous rate at which work is performed (or energy is expended), and is therefore equal to the product of the force and the velocity. If you measure the force required to move an object, the distance that it moves, and the time interval required to move it that distance, then you can calculate the average power that was applied throughout that motion and over that interval of time. Note, though, that average power is no more equivalent to power than average speed is equivalent to speed.

In the case of rotational motion, work is the torque multiplied by the angular distance through which the object is rotated. The parallel with linear motion is again applicable: it takes a specific quantity of energy to rotate an object a given angular distance, and that quantity of energy is the same no matter how quickly the rotation is performed. Each time an object undergoes one complete rotation, a fixed amount of work will have been performed. It follows that the amount of work performed in a given interval of time will depend on the angular distance covered in that time interval, and the rate at which the work is performed will therefore depend on the angular velocity. In rotational motion, power is equal to the product of the torque and the angular velocity, which may be measured in revolutions per minute or rpm.

Let's reiterate the important rules discussed thus far:

Straight-line motion:

Force = Mass x Acceleration

Work = Force x Distance

Power = Force x Velocity

Rotational motion:

Torque is measured by taking the right-angle distance from the line of force to the axis of rotation, and multiplying the force by that distance.

Torque = Moment of Inertia x Angular Acceleration

Work = Torque x Angular Distance

Power = Torque x Angular Velocity

We should note that these equations are of the type of equation known as "identities". As opposed to stating conditions on the value of a variable, they simply state that the quantities on the two sides of the equal sign are identical quantities.

Torque Multiplication

There is one more important theoretical concept that we have to discuss, that being an important consequence of the relationship among power, torque, and angular velocity as given in the last equation above.

If you use a gearbox to achieve a different rotational rate at the wheel as compared to the engine, the torque at the wheel will not be the same as the torque at the engine crankshaft, even if there are no frictional losses. The reason that this is so is that the rate at which work is done must be constant throughout the system (excepting only for the loss of energy within the system due to friction), and because power is the product of the torque and the angular velocity.

Analogies between mechanical systems and electrical systems are often insightful, so I'll ask you to indulge me for a moment while I digress and talk about electrical transformers. The voltage transformer is the electrical equivalent of the mechanical gearbox. A voltage transformer (which, by the way, only works for alternating current) takes advantage of the inductive coupling between the primary and secondary windings to transform the voltage. In electricity, power is the product of the voltage and the current. Because the rate at which work is performed must be constant throughout the system, the product of the voltage and the current in the secondary must be the same as the product of the voltage and the current in the primary – at least in the case of an ideal transformer where there is no loss to heat. If the voltage is reduced or increased by a factor of N, the current will be inversely changed in that same proportion.

Okay, back to mechanics. Because power is the product of the torque and the rotational speed, and because the power must be constant throughout the system, the transmission increases the torque in the same proportion by which it reduces the rotational speed. If you measure the torque at the rear wheel, you have to use the overall reduction ratio to calculate the engine torque. At a given engine speed, the rear-wheel torque will depend on what gear is selected. Any dynamometer chart that shows torque must be engine torque or else it would be applicable only to a specific gear and the chart would have to specify the gear, which would not be especially useful. Note, however, that if the torque is measured at the rear wheel and then the overall reduction ratio is used to calculate the engine torque, the result will not be the same as the result that you would get if you rigged the dynamometer directly to the crankshaft, because the measured rear-wheel torque is subject to power train losses. Nevertheless, any dynamometer chart that shows torque and that does not specify the gear is most definitely the engine torque, albeit adjusted for drive train losses.