SCIENCE. 



103 



ELECTRO-MOTORS. 



THEIR POWER AND RETURN. 

 J. HOSPITALIER. 



The transmission of force from a distance, electric 

 ploughing, the electric railroad, etc., have made electric 

 motors and the conditions of maximum work and maxi- 

 mum return, quite the order of the day. In a previous art- 

 icle on the available force in batteries, we have determined, 

 for the most usual forms, the quantity of energy that could 

 be furnished by a certain number of elements in an external 

 circuit of proper resistance, supposing no polarization and 

 without variation of the internal resistance. 



Is this maximum of available work entirely convertible 

 into effective work ? It is not, and we will show how this 

 maximum should be reduced when a given electric energy is 

 to be transformed into mechanical force. 



Let us suppose, for instance, in numbers, which always 

 strike the attention more than formulas, that we have a 

 source of electricity of 100 volts, with an internal resistance 

 of 1 ohm. It would be easy to realize the conditions by 

 employing an electro-dynamic machine, separately excited, 

 or 100 very large Bunsen cups, arranged for tension in 2 

 parallel series of 50 each. Putting into the circuit an ex 

 ternal resistance equal to the internal, and supposing no 

 polarization to exist and no change in the internal resist- 

 ance, we obtain as elements for the electric circulation : 

 E. — Electro motive force = 100 volts. 



r. — Internal resistance = 1 ohm. 



R. — Exterior resistance = 1 ohm. 



(r + R) — Total resistance = 2 ohms. 



Q.— Quantity = — — = 50 webers. 



v v r+R 1 + 1 



In these conditions we know that we have in the external 

 circuit the maximum of available work, as deduced from 

 the formula of Joule : 



W = 10 Q' 3 R meg-ergs (a) 



2 R 

 or W = ^ — kilogram-meters (6) 

 q.81 

 In the case before us we have : 



W = 10 X 50 2 X 1 = 25,000 meg-ergs (1) 

 What can we do with this available electric work ? If we 

 make it traverse an inert wire it will heat it. All the elec- 

 tric energy will be transformed into heat, and in this wire 

 will be developed a certain number of calorics C, per sec- 

 ond : 



9.81 A 

 A being the mechanical equivalent of heat 424. 



Let us substitute for the inert resistance of a wire, an 

 electro-motor of equal resistance with the wire, say 1 ohm 

 in this particular case. Let us suppose this motor to 

 be one of Gramme's magneto-electric machines, and that 

 the resistance of the armature is equal to 1 ohm. If we 

 put a break on the armature to prevent it turning under 

 the influence of the passing current, we will not have any 

 of the original conditions changed ; the wire of the armature 

 will be heated by the current, and a number of calorics C 

 will be produced equal to that developed in the wire. Now 

 let us make the armature turn under the action of the elec- 

 tric current. The rotary motion of this armature will de- 

 velop a certain electro-motive force E', inverse to that 

 emanating from the source of electricity E, varying with 

 the speed of the motor. It results in a diminution of the 

 current, and can be expressed at each instant by the form- 

 ula : 



Q> = ^-f. (d) 

 r+R 

 Hence the rotation of the motor diminishes the intensity 

 of the current (and consequently the work of the motor) if 

 a machine is employed as a source of electricity, or the 

 consumption of zinc, if you employ a battery. The diagram 

 shows how the different elements vary when the speed of 

 the motor varies from zero (where the work developed is 

 null) to a velocity such that the opposing electro-motive 

 force E, which it develops, becomes equal to the electro- 

 motive force of the source. It is seen that the energy ex- 

 pended by the source of electricity diminishes from the 



time the motor begins to turn (curve I.) ; similarly, the in- 

 tensity of the current (curve V.) diminishes to zero when 

 E and E' become equal. Curve II. represents the work 

 developed by the motor at different speeds. Let us sup- 

 pose these speeds are proportional to the electro-motive 

 forces — a hypothesis easily verified in a well constructed 

 magneto-electric machine — then we see, by the diagram, an 

 augmentation of the work produced, up to a point where 

 the speed of the motor becomes 50. At this moment the 

 work done is at a maximum, and represents but 50 per 

 cent, of the work expended by the source of electricity. 

 The energy converted into work (curve III.) is equal to 

 what is unconverted (curve II.). If the speed augments 

 beyond this point the work produced (curve II.) dimin- 

 ishes, but the return augments (curve IV.). 



30 40 50 co 70 00 90 ICO 



The work produced and the return are hence perfect- 

 ly distinct things which are too often confounded. 

 There is no impossibility in making the motor return 80 

 per cent, of the work expended by the source of electricity, 

 on condition you do not make this source produce all the 

 work which it can furnish. When, at the limit, the work 

 produced becomes null, the return becomes equal to 1. 

 The same conclusion is arrived at on comparing curves I. 

 and II. It is thus seen that energy not converted into 

 work, diminishes more rapidly than the total energy ex- 

 pended by the source of electricity. When the motor is at 

 rest, the work is zero, all energy being transformed into 



E 



heat. When E' = _, the diagram shows that the work is 



2 

 equal to the loss ; curves II. and III. cut each other at B 

 and the return is 50 per cent. Several consequences re- 

 sult from this. If you wish to obtain the greatest results 

 irom any given source of electricity, the electro-motor, 

 turning at normal speed, must be so arranged as to de- 

 velop a counter electro-motive force equal to the half of the 

 original source. If the best results are wanted greater 

 speed is required, by which a return in work is gained 

 with a corresponding loss in the quantity of work pro- 

 duced. 



Curves III. and IV. show why an electro-motor heats 

 more when stopped than when turning at a certain speed ; 

 the intensity of the current is greater in the first case than 



