Back Torque and Back Force in Linear Generators

See Lenz's Law.

One of the first experiments I witnessed in Freshman physics (that's as far as I got) was one involving a hand crank generator and a variable load. When there was no load on the generator the crank was pretty easy to turn; but as soon as there was a load placed on the generator the amount of work required to turn the crank increased dramatically.

Making a long story short, it brought me to the understanding that with a generator the efficiency of the generator will require that slightly more mechanical energy be applied to rotate the armature than is applied through the load circuit.

In a perfect machine the Work = Power X Time (electrical output) = Torque X angular displacement (mechanical rotational energy). Because no machine is 100 percent efficient it will require more mechanical energy input than that which can be used (or lost) in the load circuit.

The "force" required to turn the generator is the braking force used in electrical dynamic braking or regenerative braking in automobiles and locomotives. It is well understood by all those smart people who understand that stuff.

Electrical Generators and electrical motors have relatively high efficiency when compared to, lets say, a reciprocating heat engine.

A few decades ago, the primary producer of energy in a mechanical system was called the "prime mover." In an automobile or locomotive that "prime mover" is a reciprocating heat engine. I believe back then a reciprocating heat engine with an efficiency of 20 percent would be considered quite good. That means that for each unit of mechanical energy produced, 5 units of the fuel combustion energy is used. It is for this reason that regenerative braking makes so much sense. For each unit of kinetic energy converted to stored energy during braking and then applied to accelerate the vehicle during the next cycle, 5 units of combustion energy is saved.

The Mechanics of linear and rotational systems are pretty straight forward and easily understood with only a rudimentary background required for extrapolating the relationships between work and displacement in everything from electrical generators to asteroid deflection.

Recapping; I believe that in a rotational system the mechanical input: Torque X Angular Displacement will ≈ eff X Power X time where eff is the efficiency of the generator.

Gavilan