Curved performance characteristics

Even though an energy target might depend on a single driving factor, it does not follow that the relationship is a straight line. This is particularly true in cases of continuous production machinery whose output is varied by changing speed. Since the frictional and windage losses in the machinery increase according to a power law, the predicted electrical energy requirement for the drive motors will increase more steeply as speed and output are increased.

If D were the driving factor, it would be possible to express the energy target E mathematically as:

E = k₀ + k₁Dⁿ

(k₀ and k₁ being the customary targeting parameters) and indeed this could be represented graphically, although the target line would be curved rather than straight. This is not a major problem, expect that not many M&T software systems would have provision to accommodate such a target. A straight line is preferable in that respect. To force the graph to look like a straight line, one can manipulate D, and create a 'massaged' version of the driving factor, D', thus:

D' = Dⁿ

which transforms equation (1) into the familiar straight-line model:

E = k₀ + k₁D'

It is not just simple clean curves which can be transormed in this fashion. Quite complex discontinuous functions could also be tamed in an analogous way.

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