28. A railway generator is being tested by the electrical method described on p. 87. The line tension is 550 volts, the speed is 400 r.p.m., the generator output is 500 amperes, the resistance of the generator is 0.04 ohm, and that of the motor 0.03 ohm. If the current from the line is 48 amperes, and the torque losses are equal in the two machines, find the torque loss in the generator. 782 inch-pounds.

29. A motor is tested by Hopkinson's method. The total mechanical output is 45 horse-power when running at 900 r.p.m. on a tension of 125 volts. The resistance of the motor and of the generator used in the test are both equal to 0.015 ohm. The torque input measured on the belt is 600 inch-pounds. What is the torque loss in the motor? 191 inch-pounds.

30. A generator is being tested by the method described on p. 87. The terminal tension is 250 volts, the current output 800 amperes, and the current from the line 92 amperes. The resistance of each armature is 0.0058 ohm. If the power used in magnetising the magnets of the generator is 5.2 k.w., find its total efficiency. 92.5 per cent.

31. A railway motor is tested by the method described on p. 144. The terminal tension on the motor is 500 volts, the current 44 amperes, the resistance of the motor magnets and armature 0.72 ohm. The generator current is 34 amperes, and the resistance of the generator magnets in series with the motor circuit 0.43 ohm. Find the efficiency of the motor. 83 per cent.

32. A motor generator runs at 550 r.p.m. on a tension of 588 volts. The current in the motor is 64 amperes, and that in the generator 280 amperes. The motor resistance is 0.175 ohm. The induction factor of the motor is five times that of the generator. Find the total frictional losses in the two machines. 705 inch-pounds.

33. A motor has an induction factor equal to 6, an internal resistance of 0.08 ohm, and torque losses amounting to 76

U 2

inch-pounds. Find the most efficient current and the efficiency for that current. 116 amperes and 85 per cent. 34. The armature of an eight-pole motor contains 646,000 cubic centimetres of iron. If the hysteresis loss is 8,600 ergs per cubic centimetre per cycle, find the current required to turn the armature against the hysteresis torque, the induction factor being 68. 33.2 amperes.

35. A train weighing 40 tons is driven by two gearless motors designed to run at 20 miles an hour in parallel on a tension of 500 volts when the resistance to motion is 495 inch-pounds of torque per ton. The driving wheels are 33 inches in diameter. The resistance of the motors is 03 ohm each. The maximum current per motor is to be 200 amperes. If the acceleration is uniform up to full speed, how many seconds will be spent in covering the first 200 yards from rest? Assume M to be constant and the parallel method of control. 31.5 seconds.

36. A train weighing 600 tons is drawn by four gearless motors at 10 miles an hour up a grade of 0.7 per cent., the frictional resistance being 12 lbs. per ton and the tension of the line 500 volts. Find the total current required to start up on the grade with an acceleration of 0.5 f.p.s. per second, if the motors are connected permanently in series and Mis constant. 1,845 amperes.

37. A motor has M = 8.1, R2.4 ohms. The armature, with an attached fly-wheel, weighs 1,500 lbs., the radius of gyration being 9.2 inches. The frictional and other resistance to motion amounts to 280 inch-pounds, and is constant. The motor is switched on to a line of 100 volts tension and left to run. How many revolutions will it make in two

minutes ?

365.

38. A motor is running on a line of constant tension with a constant load. The speed has to be varied by varying M with a rheostat in the magnet circuit, which is a shunt on the main circuit. Show that the change of speed for any

given change of M decreases as the resistance in the armature circuit increases.

39. A crane has to lift a weight of 5 tons from rest through a distance of 22 feet. M is constant, and equal to 16·4; R = 1.3 ohm. The diameter of the rope drum is 36 inches, and v 65. The friction amounts to 380 inchpounds of torque on the motor shaft. The tension of the line is 225 volts. Find the time required to cover the given distance if the maximum current is limited to 160 amperes. 86 seconds.

40. A weight of 2 tons has to be lifted by a motor working on the principle described in p. 157. E 120.volts, R=0·15 ohm, M = 18, v = 95, and d = 24 inches. The torque due to friction is 254 inch-pounds on the motor shaft. Find the weight of a fly-wheel, of radius of gyration 6 inches, that must be placed on the motor shaft, so that on connecting the clutch the current drawn shall not exceed 50 amperes. 18.1 pounds.

41. Same data as in Problem 40. Find the weight of the fly-wheel, of radius of gyration equal to 6 inches, so that the speed shall not fall below that at which the motor runs when raising the weight at a uniform speed. 36 lbs.

42. A crane has to lift a weight of 20 tons through 15 feet in 35 seconds from rest. E = 500, v = 80, M = 62 and is constant. The drop at full speed is to be 20 volts. The frictional resistances amount to 10 per cent. of the load. Find the diameter of the chain drum and the resistance of the motor. 25.4 inches and 0.228 ohm.

43. A motor with an induction factor of 75 and an internal resistance of 0·02 ohm is running at full speed on a 500-volt line, with a torque on the shaft equal to 63,500 inchpounds. A fly-wheel weighing 1.6 ton, with radius of gyration 8 feet, is mounted on the motor shaft. If the tension of the line drops 10 per cent., find in how many seconds the speed will have dropped the same per cent. Neglect the moment of inertia of the armature. 4.1 seconds.

44. A turret weighing 20 tons, with a radius of gyration of 7 feet 6 inches, is rotated by a motor with a gear ratio of 300, the induction factor being constant and equal to 8, and the resistance being 0-2 ohm. The frictional torque is 338 inch-pounds on the motor shaft. The tension of the line is 80 volts. What is the shortest time in which the turret can be turned through 240 degrees if the maximum current does not exceed 40 amperes? 24.4 seconds. 45. The bascules of the Tower Bridge each weigh 1,070 tons, and have a radius of gyration of 40 feet. The arc of rotation is 82 degrees, and the time 90 seconds. Motion is derived from a motor shaft with a velocity ratio of 360. The friction may be estimated at 200 inch-pounds of torque per ton on the main bearings. The motion can be stopped in 12 degrees in twenty seconds. If the tension of the line is 100 volts, and the drop at full speed 4 volts, find the value of M and the maximum current, the motor being shunt wound. M = 64 and C = 31·4 amperes.

46. The trains on the Central London Railway weigh 145 tons, and are each hauled by a locomotive equipped with four gearless motors, with driving wheels 42 inches in diameter. The tension of the line is 500 volts. The frictional retardation may be taken at 7.5 lbs. per 1,000. The drop at full speed is not to exceed 5 volts, and the mechanical efficiency is to average 95 per cent. The motors are started two in parallel, and changed over to four in parallel for full speed. The time schedule requires that 2,000 feet shall be covered in 75 seconds from rest. Find the current and induction factor at full speed, and the force factor required to start.

Each motor must have M=136 for 70 amperes, and a maximum force factor of 40-8 kilodynes.

INDEX

The numbers refer to the pages