Resistance of the train in lbs. ={6 +0·3 (V—10) — 2240 i} T;................................ Resistance of the engine and tender in lbs. ={12+0·6 (V—10)±2240 i; E;...................... Total resistance in lbs. ..(1.) ..(2.) ={6+0·3 (V-10)} (T+2 E)=2240 i (T+E)....(3.) At velocities less than ten miles an hour the term containing V-10 is to be omitted: the resistance being sensibly constant below that speed. Mr. D. K. Clark prefers to such formula as the above, another set of formulæ in which the resistance is treated as consisting of a constant part, and a part increasing as the square of the speed; as follows: Resistance in lbs. per ton of engine and train; road and carriages in smooth running condition; weather calm; Road and carriages not in smooth running condition; side wind, The resistance on a curve exceeds that on a straight line, according to experiments by different authors, to the amount of from 0.6 lb. to 1.4 lb. per ton radius of curve in miles (6.) To allow for the resistance of the mechanism of the engine, Mr. Clark adds one-third to the resistance, as calculated above. The mean effective effort of the steam on the pistons required to overcome a given total resistance of engine and train is given by the following equation, in which A is the total area of both pistons, and Pm-P3 the mean effective pressure. Total resistance x circumference of driving wheel A (P-P3)= ...(8.) 386. The Balancing of Engines, both as to centrifugal forces and centrifugal couples, is of great importance as a means of preventing dangerous oscillations. The principle according to which it is effected is, to conceive the mass of the pistons, piston rods, and connecting rods, and a weight having the same statical moment as the crank, as concentrated at the crank pins, and to insert between the spokes of the driving wheels counterpoises whose weights and positions are regulated by the principles explained in Articles 21 and 22, pages 27 to 30. : The following are the formulæ to which these principles lead :DATA W, total weight conceived to be concentrated at one crank pin. c, length of the crank, measured from the axis of the axle to the centre of the crank pin. a, distance of the centre of the crank pin, measured parallel to the axle, from the middle of the length of the axle. b, distance of the centre of a wheel from the middle of the length of the axle. r, radius-vector of each counterpoise; being the distance of its centre of gravity from the axis of the axle. REQUIRED i, angle which that radius-vector makes with a plane traversing the axis in a direction midway between the directions of the two cranks, and pointing the opposite way to those directions. The cranks being at right angles to each other, make angles of 135° with the plane in question. w, weight of each counterpoise. In practice, those formulæ may be used to find a first approximation to the required position and weight of the counterpoises; but the final adjustment is always performed by trial; the engine being hung up by chains attached to the four corners of its frame, and the machinery set in motion: a pencil attached to the frame near one angle, marks, on a horizontal card, the form of the oscillations, being usually an oval; and the counterpoises are adjusted until the orbit described by the pencil is reduced to the least possible magnitude. When the adjustment is successful, the diameter of that orbit is reduced to about of an inch. 387. The Blast Pipe has the effect of adjusting the draught of the furnace, and consequently the rate of consumption of fuel, to the work to be performed by the engine with very different loads, and at very different speeds; and is on that account perhaps the most important of the peculiar parts of the locomotive engine. Its effect upon the back pressure in the cylinder has already been considered in Article 280, pages 382, 383. The effect of the blast pipe in producing a draught depends upon its own diameter and position, on the diameter of the chimney, and on the dimensions of the fire-box, tubes, and smoke-box. Mr. D. K. Clark has investigated the influence of these circumstances from his own experiments, and from those of Messrs. Ramsbottom, Poloncean, and others, and has shown that the vacuum in the smoke-box is about 07 of the blast pressure: that the vacuum in the fire-box is from toof that in the smoke-box: that the rate of evaporation varies nearly as the square root of the vacuum in the smoke-box: that the best proportions of the chimney and other parts are those which enable a given draught to be produced with the greatest diameter of blast pipe, because the greater that diameter, the less is the back pressure produced by the resistance of the orifice that the same proportions are best at all rates of expansion and at all speeds: and that the following proportions are about the best known:— Sectional area of tubes within ferules,......= Sectional area of chimney, 1 area of grate. 5 Area of blast orifice (which should be somewhat below the throat of the chimney,)....... Capacity of smoke-box,. Length of chimney,.... ....its diameter × 4. If the tubes are smaller, the blast orifice must be made smaller also; for example, if Sectional area of tubes within ferules...... 1 = area of grate, 10 Then area of blast orifice 1 = area of grate. 90 388. Examples of Locomotive Engines.-The examples here given are from two locomotive engines by Messrs. Neilson & Co., which are selected, like the screw marine engines of Article 382, because they are good and efficient specimens of the class of engines to which they belong, and have nothing unusual in their proportions and arrangements. (See plate; also page 587.) Fig. 169 is a side view copied from a photograph of a six-wheeled engine, with two pairs of wheels coupled. Its scale is about of the real dimensions. Fig. 170 is a longitudinal section of an engine of the same class with the preceding, but with somewhat larger driving wheels, being intended for a less steep line and higher speeds. The scale is of the real dimensions. The details of the valve gearing are omitted. Fig. 171 shows, at the left-hand side, a cross-section through half the fire-box, and at the right-hand side, a cross-section through half the smoke-box, of the same engine. Fig. 172 is an elevation of the valve gearing of one cylinder, with the cover taken off the valve chest to show the slide valve and ports. Fig. 173 shows a plan of the valve gearing of one cylinder, and a longitudinal section of the cylinder and valve chest. The scale of figs. 171, 172, and 173, is of the real dimensions. A is the ash-pan; B, the grate; C, the fire-box. In fig. 170, the heads of the bolts which tie the outer and inner shells of the fire-box together are irregularly placed; but that is an oversight in the engraving; they ought to be ranged in vertical and horizontal lines. D is the fire-door. E are the tubes, extending from the fire-box to the smoke-box F. G is the lower end of the chimney. I is one of the horizontal feed pumps, worked by a link from one of the eccentrics. H is the supply pipe from the water tank of the tender; K, the feed pipe, leading to the boiler. L is the water space round the fire-box; M, the water space and steam space above it. N are longitudinal ribs, to which the crown of the fire-box is stayed, as explained in Article 312, page 459. The crown receives |