When we compare the energy expended by the two methods, we see that the results of the test give a much greater expenditure than that indicated as necessary by the calculations. The maximum speed attained in the test was 35 feet per second, the kinetic energy is thus 380 × 101 foot-pounds. The train resistance is 900 pounds, giving an expenditure of energy of 174 x 10' foot-pounds throughout the distance of 1,930 feet. Hence the total energy expended as work is 554 × 101 foot-pounds. The area of the dotted current curve in the figure represents the total expenditure of energy in the experiment; this area measured with a planimeter is found to represent 963 × 10 foot-pounds. The difference between the work done and the observed expenditure of energy, amounting to 409 x 10' foot-pounds, is mainly represented by the energy lost in heating the resistances. If we allow a mechanical efficiency averaging 85 per cent., the heat loss amounts to 311 x 10' foot-pounds. The maximum speed for the calculated curve is 33.5 feet per second, giving 350 x 10 foot-pounds of kinetic energy; the energy required to overcome the train resistance is 174 × 104 foot-pounds, giving a total of 524x101 foot-pounds of work done. Assuming an average efficiency of 85 per cent. we get a total torque loss of 92 x 10 foot-pounds. We have already seen how to estimate the heat loss, and know that it is represented, within a small error, by the area of the current curve above the line oa in the figure; this area is 67 × 101 foot-pounds, hence the total energy required, as obtained by calculation, is 683 x 101 foot-pounds, as compared with 963 x 104 obtained with the existing motors. The area of the calculated current curve in Fig. 63 gives 675 x 10 foot-pounds, or about 3 per cent. less than that estimated. These results are represented below in tabular form. The difference in the energy expended is almost wholly accounted for by the difference in the heat loss. The existing motors require 40 per cent. more energy to operate the train under the given conditions than those whose induction curves have been calculated, and the maximum current from the line is 28 per cent., and the maximum current per motor 48 per cent. higher than appears necessary. The force factor required to start is, by calculation, 257 × 72 or 18.5 kilodynes. If a hyperbola be drawn in Fig. 61 having MC=18·5 kd., it will cut curve A at c=257, and curve B at c=385 amperes. We thus see why the existing motors have to take nearly 50 per cent. more current to start than is necessary. We have supposed that the limit of weight fixes the maximum induction factor at 72, for 257 amperes. The motors in use have a maximum induction factor of 48. For this value of M the best economy is obtained when v=9.75, the induction curve is then straight. Suppose that the consideration of clearance limits the value of v to 4.78, the induction curve must then be of the form Cin Fig. 61, whose vertical ordinates bear to those of curve A the ratio of 4.78 to 3.18. The expenditure of energy I will then be the same as for the motors with induction curve A. The economy of working may be expressed in terms of the energy required to move the given weight through the given distance. This may be stated in terms of watt-hours per ton mile. Thus in the previous example, the trains can be worked at the required speed with an expenditure of 60.5 watt-hours per ton mile; the distance, of course, includes that in which the brakes are on. The actual energy expenditure is 85.5 watt-hours per ton mile. The results of our investigation may be summed up as follows:-There are three forms of expenditure of energy involved in carrying a train of given weight through a given distance in a given time. (1) The work done in overcoming train resistance. This depends on the distance, and can only be reduced by increasing the mechanical efficiency of the motors. (2) The work done in producing kinetic energy. This increases as the square of the final speed. Equation 103 gives us the least possible final speed for the given conditions, and thus the least possible expenditure of energy in accelerating. (3) The energy expended in heat. Equation 111 shows that this increases as the square of 103 gives us the least possible value of d d Mv Mv' Equation if M is to be constant. If, however, series winding is used, the heat loss may be reduced to any desired extent by increasing M, but at the expense of an increase in the weight of the motor. 259 CHAPTER XII ARMATURE REACTION THE magnetisation curves of a dynamo can be found by substituting for the ordinary brushes a pair of thin steel brushes insulated from one another and touching the commutator at a small angular distance apart. If these brushes are connected to the terminals of a voltmeter, and the armature rotated at a uniform speed when the magnets are excited, the reading on the voltmeter will measure the rate at which the conductors on the armature, included between the two exploring brushes, are cutting lines of force. If the brush holder is moved round the commutator, the voltmeter reading will vary with the intensity of the magnetisation measured across the surface in which the conductors on the armature are moving. If the readings observed are plotted vertically on a line along which distances represent successive positions of the exploring brushes, we shall obtain a curve whose ordinates represent the intensity of magnetisation round the armature. The curve in Fig. 64 marked 'magnets only' is such a curve. The magnetisation is nothing at points a and b, and is uniform under the poles, the sign of the curve being different under adjacent poles. The actual values of the voltmeter readings will depend upon the angular width of the exploring brushes; hence |