By placing the generator and motor near each other, assuming no loss in the connecting wires, we get— One hundred per cent. mechanical energy delivered at generator pulley 100 Loss by conversion in dynamo, 10 per cent 10 90 Loss by reconversion in motor, 10 per cent. of 90 9 81 This shows that omit of 100 mechanical horse-power applied to the generator pulley, 81 mechanical horse-power should be recovered at the motor shaft if loss in the conductors could be avoided. This efficiency of a couple of electric machines connected as generator and motor, with practically no loss in the connecting conductors, is often called the " couple efficiency." In practice the generator and motor are so far apart that there is loss of electrical energy in overcoming the resistance of the conductors. This loss depends upon three factors, viz.: distance between generators and motors, electric pressure at generators, and size of copper conductors. For a given case the first factor, distance, is constant; pressure and size of con ductors are variable and may be determined at will: therefore, the loss in the conductors may be any percentage desired. It should be stated that only " complete metallic circuits " are here considered, or, in other words, it is assumed that the generator is connected to the motor by means of two conductors. "Earth returns," which are mainly used in electric railway work, are not considered.
If a "couple efficiency" of 81 per cent. and a loss of say 10 per cent, in the conductors is assumed, there will be: Couple efficiency 81.0 Loss in the wire, 10 per cent. of Si 8.1 72.9 Or the commercial efficiency of the transmission system from generator pulley to motor shaft would be 72.9, or almost 73 per cent.
Table I. (Badt's Transmission. handbook) shows the relations of the different factors cf electrical transmission to each other, assuming an efficiency of generators and motors of 90 per cent. (or a couple efficiency of 81 per cent.), and losses in the conductors varying from 0 per cent. to 50 per cent.
Rules for the Inter-relation of Electromotive Force, Current, Distance, Cross-sertion and Wright of Copper .1. Sprague, in a lecture on the "Transmission of Power by Electricity," delivered before the Franklin Institute, November 12, 18t-.8, lays down the following important Mies on the above relations : With any amount of energy transmitted, the electromotive force and the current will vary inversely.
any given work done, loss on the line, electromotive force at the terminals of the motor and distribution, the weight of the copper will vary as the square of the distance, its cross-seetion, (f course, varying directly as the distance.
With the same conditions, the weight colt vary inversely as the square of the electromotive force used at the motor.
With the same cross-section of conductor, the distance over whirle a given amount of power can be transmitted will vary as the square of the electromotive fiwee.
If the weight of the copper is fixed, with any given amount of power transmitted and given loss in distribution, the distance over which the power can be transmitted will vary directly as the electromotive force.
With any given work done, given loss on the line and electromotive force of motor, the number of circular mils of the conductors will vary directly as the distance. Bence, with given conditions, if we double the distance we must also double the cross-section, or if we treble the distance we must treble the cross-section. The weight of a foot of the conductor of course increases also in direct proportion to its cross-section. If we therefore double both cross-section and distance, the total weight of the conductor will he increased four-fold, or if we treble both cross section and distance, the total weight of the conductor will be increased nine-fold. This shows that, with the conditions given, the weight of the copper will vary as the square of the distance.
The weight and cost of the conductor increase in direct proportion to the current. In order to get the cost of the conductor very low, it is therefore necessary to reduce the current strength to a permissible minimum. As a definite amount of electrical energy depends, how ever, on the product of current and electromotive force, the electromotive force must be increased in the same ratio as the current is reduced, which shows that for least cost of con ductor the electromotive force of the motor must be made as high as permissible.
Conditions of Plant for Least Operating certain percentage of electrical energy must be lost in the conductors; this loss, of course, involves continuous operating expense, as the prime mover (steam, water, etc.) and the electric generator must produce an additional amount of energy which is lost in the conductors. It is a loss in a commercial sense only, as this so-called " lost " energy reappears as heat in the conductor.
This loss can be decreased and power economized by using conductors of greater cross section, which, of course, would involve a greater outlay for copper. On the other hand, to reduce the first cost, we should employ conductors of the :east possible cross-section. Hence, for any gieen ease. the chealyst in the long run will be a certain, size of conductor for which the in terest on its first cost plus annual cost of energy wasted in the conductor, becomes a minimum.
Sir William Thomson's law states that, The most economical area of conductor will be that for which the annual interest on capital outlay equals the annual cost of energy wasted.