64 tons; and to obtain the horse-power the boiler will be one of the largest that can be built to the construction gauge. After acceleration to the journey speed of 30 m. per hour the horse-power required is reduced to about one-third of that required for acceleration alone.
§ 10. General expression for total rate of working.—Adding the various rates of working together
(22)
where W_{e} is weight of engine and tender in tons, W_{v} the weight of vehicles in tons, W the weight of train in tons = W_{e} + W_{v}, r_{e}, and r_{v} the respective engine and vehicle resistances taken from the curves fig. 17 at a speed corresponding to the average speed during the acceleration a, G the gradient, g the acceleration due to gravity, and V the velocity of the train in feet per second. In this expression it is assumed that the acceleration is uniform, and this assumption is sufficiently accurate for any practical purpose to which the above formula would be applied in the ordinary working of a locomotive. If a is variable, then the formula must be applied in a series of steps, each step corresponding to a time interval over which the acceleration may be assumed uniform.
Dividing through by V and multiplying through by 550,
(23)
an expression giving the value of R the total tractive resistance. If the draw-bar pull is known to be R_{v}, then applying the same principles to the vehicle alone which above are applied to the whole train,
(24)
This expression may be used to find r_{v} when the total draw-bar pull is observed as well as the speed, the changes of speed and the gradient. The speed held to correspond with the resistance must be the mean speed during the change of speed. The best way of deducing r_{v} is to select portions of the dynamometer record where the speed is constant. Then a disappears from all the above expressions. These expressions indicate what frequent changes in the power are required as the train pursues its journey up and down gradients, against wind resistance, journal friction and perhaps the resistance of a badly laid track; and show how both the potential energy and kinetic energy of the train are continually changing: the first from a change in vertical position due to the gradients, the second from changes in speed. These considerations also indicate what a difficult matter it is to find the exact rate of working against the resistances, because of the difficulty of securing conditions which eliminate the effect both of the gradient and of acceleration.
§ 11. The Boiler.—Maximum Power.—The maximum power which can be developed by a locomotive depends upon the maximum rate of fuel combustion which can be maintained per square foot of grate. This maximum rate depends-upon the kind of coal used, whether small, friable, bituminous or hard, upon the thickness of the fire, and upon the correct design and setting of the blast-pipe. A limit is reached to the rate of combustion when the draught becomes strong enough to carry heavy lighted sparks through the tubes and chimney. This, besides reducing the efficiency of the furnace, introduces the danger of fire to crops and buildings near the line. The maximum rate of combustion may be as much as 150 ℔ of coal per square foot of grate per hour, and in exceptional cases even a, greater rate than this has been maintained. It is not economical to force the boiler to work at too high a rate, because it has been practically demonstrated that the boiler efficiency decreases after a certain point, as the rate of combustion increases. A few experimental results are set forth in Table XX., from which it will be seen that with a relatively low rate of combustion, a rate which denotes very light service, namely 28 ℔ of coal per square foot of grate per hour, the efficiency of the boiler is 82%, which is as good a result as can be obtained with the best class of stationary boiler or marine boiler even when using economizers.
The first group consists of experiments selected from the records of a large number made on the boiler of the locomotive belonging to the Purdue University, Indiana, U.S.A.
The second group consists of experiments made on a boiler belonging to the Great Eastern Railway Company. The first one of the group was made on the boiler fixed in the locomotive yard at Stratford, and the two remaining experiments of the group were made while the engine was working a train between London and March.
The third group consists of experiments selected from the records of a series of trials made on the London & South-Western railway with an express locomotive.
Kind, and calorific value of coal. | Dry coal fired per square foot of grate per hour. ℔ |
Pounds of water evaporated per ℔ of coal from and at 212°F. |
Boiler efficiency. |
Reference. |
Indiana block coal from the neighbourhood of Brazil. Estimated
calorific value, 13,000 B.Th.U. per ℔ |
49 109 181 |
7·83 6·59 5·71 |
0·58 0·49 0·42 |
Prof. Goss (Amer Soc. of Mech. Eng., vol. 22, 1900). |
Nixon’s Navigation. Calorific value 15,560 B.Th.U. per ℔ | 35·5 28·1 31·7 |
13 13·3 13·1 |
0·82 0·82 0·81 |
“Experiments on Steam Boilers,” Donkin and Kennedy, (Engineer, London, 1897). |
Calorific value, 13,903 | 62·5 | 11·15 | 0·77 | Adams and Pettigrew (Proc. Inst. C.E., vol. 125). |
Calorific value, 12840 | 80·9 | 8·86 | 0·66 |
§ 12. Draught.—One pound of coal requires about 20 ℔ of air for its proper combustion in the fire-box of a locomotive, though this quantity of air diminishes as the rate of combustion increases. For instance, an engine having a grate area of 30 sq. ft. and burning 100 ℔ of coal per square foot of grate per hour would require that 60,000 ℔ of air should be drawn through the furnace per hour in order to burn the coal. This large quantity of air is forced though the furnace by means of the difference of pressure established between the external atmospheric pressure in the ash-pan and the pressure in the smoke-box.
Fig. 18.—Smoke-box, L. & N.W.R. four-coupled 6 ft. 6 in. passenger engine.
The exhaust steam passing from the engine through the blast pipe and the chimney produces a diminution of pressure, or