tension 500 volts, current 35 amperes, total resistance in motor circuit 1.245 ohms, resistance of motor armature and magnets 0.91 ohm, generator current 23.5 amperes.

Using Equation 62, we find at once that the torque losses in the two machines amount to 5,240 watts, or 2,620 watts each. The CR loss in the motor is 1,112 watts. The electrical input of the motor is 17,500, leaving 13,360 watts as useful mechanical output. We can now construct a table of energy expended in the motor.

The total efficiency of the motor is thus 78-2 per cent.

The results of a complete test of a G.E. 800 railway motor by this method are given in Fig. 34. The losses are shown in percentages of the whole input for different currents. The torque losses are divided into core loss, including hysteresis and eddy currents, and friction of gears, by a separate experiment, in which the motor armature was driven by a small motor on open circuit with separately excited magnets.

L

CHAPTER VII

ACCELERATION

LET the vertical and horizontal ordinates in Fig. 37 measure respectively torque in inch-pounds and revolutions per second. Let the curve A represent on the given scales the total torque of a motor at different speeds. At o where the torque is a maximum the speed is nothing. Let the curve B represent on the same scales the torque required to overcome all resistance to motion due to the load, friction of the gearing, hysteresis, &c. At the point h where the curves A and B intercept, draw a vertical line cutting the speed base in g. The speed at which the motor will run when uniform motion has been attained will then be given by og.

For if a curve C be constructed, whose vertical ordinates are the difference between those of curves A and B, the ordinate of the curve C gives the torque available for acceleration at any speed, being the difference between the total torque and that required to overcome resistance to motion. At g this difference is nothing, so that at this point the motor has ceased to accelerate, and is therefore running uniformly. The form of the curve B is determined mainly by the variation of the friction with the speed, since this constitutes the greater proportion of

the whole resistance to motion. Experiment shows that the friction is greatest at the moment of starting, and that after the first few revolutions it diminishes and continues very nearly constant for all speeds.

If the initial retarding torque o is greater than the maximum total torque oa, the motor cannot move. The current that is taken from the line when a motor is started depends simply upon the tension of the line and the resistance in circuit at the moment: if there is a heavy load on the motor, that is, if the resistance to motion is great, the motor will start up slowly, if at all; if the load on the motor is light. the motor will start up quickly. Thus the load on the motor does not affect the current taken from the line at the moment of starting, but only the rate at which the motor speeds up.

The acceleration at any instant is proportional to the accelerating force. If n is the speed of the motor in revolutions per second, the acceleration will be

dn

at

The accelerating force will be proportional to the torque available for acceleration, and if the induction factor remains constant, it will be proportional to the difference between the total current flowing through the motor at any moment, and the current that the motor will take when uniform motion has been attained. If we denote the former by c, and the latter by c, we can write the equation for acceleration thus:

where is a constant depending, as we shall see later, upon the value of the induction factor, the moment of

inertia of the mass to be moved, the velocity ratio, and the resistance of the motor.

If E is the tension of the line, R the total resistance in the circuit, for the present considered constant, and M the induction factor, we can write down the following equation, which we know must hold good at any instant:

Substitute in this equation the value of c obtained from Equation 63 and we have

motor when it has ceased to accelerate. If this is n,, we

then get

n=n, + Ke

kM
Rt

.(67).

and put n=n;

To find the value of the constant K, we know that when t=o, n is the initial speed, if we call this