add lead-angle, making 124.6. From the second table, for angle between admission and cut-off, 125°, we have ratio of travel to port-opening = 3.72, or for 124.6° 3.74, which, multiplied by port-opening 2.5, gives 9.45 in travel. The ratio of lap to travel, by the table, is .2324, or 9.45 X .2324 = 2.2 in. lap. For exhaust-lap we have, for release at .95, crank-angle : = 151.3; add lead-angle 10° 161.3°. From the second table, by interpolation, ratio of lap to travel.0811, and .0811 x 9.45 0.77 in., the exhaust-lap. Lap-angle = (180° lead-angle crank-angle at cut-off); = (180° 10 114.6) 27.7°. Angular advance lap-angle lead-angle 27.7+10= 37,7°. Exhaust lap-angle crank-angle at release + lap-angle + lead-angle = 151.3+27.7 +10 180° 9o. = Crank-angle at compression measured on return stroke = 180° = 180 lap-angle-lead-angle - exhaust lap-angle; -27.7109 133.3°; corresponding, by table, to a piston position of .81 of the return stroke; or Crank-angle at compression = 180° - (angle at release - angle at cut-off) lead-angle; The positions determined above for cut-off and release are for the forward stroke of the piston. On the return stroke the cut-off will take place at the same angle, 114.6°, corresponding by table to 66.6% of the return stroke, instead of 75%. By a slight adjustment of the angular advance and the length of the eccentric rod the cut-off can be equalized. The width of the bridge should be at least 2.5 +0.25 — 2.2 = 0.55 in. Crank Angles for Connecting-rods of Different Length. FORWARD AND RETURN STROKES. Ratio of Length of Connecting-rod to Length of Stroke. Fraction of Stroke from Commencement. For. Ret For. Ret. For. Ret. For. Ret. For. Ret. For. Ret. or Ret. 11.5 .01 10.3 13.2 10.5 12.8 10.6 12.6 10.7 12.4 10.8 12.3 10.9 12.1 .02 14.6 18.7 14.9 18.1 15.1 17.8 15.2 17.5 15.3 17.4 15.5 17.1 16.3 .03 17.9 22.9 18.2 22.2 18.5 21.8 18.7 21.5 18.8 21.3 19.0 21.0 19.9 .04 20.7 26.5 21.1 25.7 21.4 25.2 21.6 24.9 21.8 24.6 22.0 24.3 23 1 .05 23.2 29.6 23.6 28.7 24.0 28.2 24.2 27.8 24.4 27.5 24.7 27.2 25.8 .10 33.1 41.9 33.8 40.8 34.3 40.1 34 6 39.6 34.9 39.2 35.2 38.7 36.9 .15 41 51.5 41.9 50.2 42.4 49.3 42.9 48.7 43.2 48.3 43.6 47.7 45.6 .20 48 59.6 48.9 58.2 49.6 57.3 50.1 56.6 50.4 56.2 50.9 55.5 53.1 .25 .30 .35 .40 54.3 66.9 55.4 65.4 56.1 64.4 56.6 63.7 57.0 63 3 57.6 62.6 60.0 60.3 73.5 61.5 72.0 62.2 71.0 62.8 70.3 63.3 69.8 63.9 69.1 66.4 66.1 79 8 67.3 78.3 68.1 77.3 68.8 76.6 69 2 76.1 69.9 75.3 72.5 71.7 85.8 73.0 84.3 73.9 83.3 74.5 82.6 75.0 82.0 75.7 81.3 78.5 .45 77.2 91.5 78.6 90.1 79.6 89.1 80.2 88.4 80.7 87.9 81.4 87.1 84.3 .50 82.8 97.2 84.3 95.7 85.2 94.8 85.9 94.11 86.4 93.6 87.1 92.9 90.0 .55 88.5 102.8 89.9 101.4 90.9 100.4 91.6 99.8 92.1 99.3 92.9 98.6 95.7 .60 94.2 108.3 95.7 107.0 96.7106.1 97.4 105.5 98.0 105.0 98.7104.3 101.5 .65 100.2113.9 101.7 112.7 102.7 111.9 103.4 111.2 103.9 110.8 104.7 110.1107.5 .70 106.5 119.7 108.0118.5 109.0 117.8 109.7117.2110.2 116.7110.9 116.1 113.6 .75 113.1125 7114.6 124.6115.6 123.9 116.3 123.4 116.7 123.0117.4122.4 120.0 .80 120.4132 121.8 131.1122.7 130.4123.4 129.9 123.8129.6 124.5 129.1126.9 .85 128.5 139 129.8 138.1 130.7137.6 131.3 137.1 131.7 136.8 132.3 136.4 134.4 .90 138.1 146.9139.2 146.2139.9 145.7 140.4 145.4 140.8 145.1 141.3 144.8 143.1 .95 150.4 156.8 151.3 156.4 151.8156.0 152.2 155.8 152.5 155.6 152.8155.3 154.2 96 153.5 159.3 154.3 158.9 154.8158.6 155.1 158.4 155.4 158.2 155.7 158.0 156 9 .97 157.1 162.1157.8 161.8 158.2 161.5 158.5 161.3 158.7 161.2 159.0 161.0 160.1 .98 161.3165.4 161.9 165.1 162.2 164.9 162.5 164.8 162.6 164.7 162.9 164.5 163.7 .99 166.8 169.7 167.2169.5 167.4 169.4 167.6 169.3 167.7 169.2167.9 169.1 168.5 1.00 180 180 180 180 180 180 180 180 1180 180 180 1180 180 Relative Motions of Cross-head and Crank.-It Z= length of connecting-rod, R = length of crank, = angle of crank with centre line of engine, D = displacement of cross-head from the beginning of its stroke, = R(1 cos 0) + L - VI - R2 sin2 0. PERIODS OF ADMISSION, OR CUT-OFF, FOR VARIOUS LAPS AND TRAVELS OF SLIDE-VALVES. The two following tables are from Clark on the Steam-engine. In the first table are given the periods of admission corresponding to travels of valve of from 12 in. to 2 in., and laps of from 2 in. to 3% in., with 14 in. and in. of lead. With greater leads than those tabulated, the steam would be cut off earlier than as shown in the table. The influence of a lead of 5/16 in. for travels of from 15% in to 6 in., and laps of from in. to 11⁄2 in., as calculated for in the second table, is exhibited by comparison of the periods of admission in the table, for the same lap and travel. The greater lead shortens the period of admission, and increases the range for expansive working. Periods of Admission, or Points of Cut-off, for Given Travels and Laps of Slide-valves. Periods of Admission, or Points of Cut-off, for the following Periods of Admission, or Points of Cut-off, for given Travels and Laps of Slide-valves. Diagram for Port-opening, Cut-off, and Lap.—The diagram on the opposite page was published in Power, Aug., 1893. It shows at a glance the relations existing between the outside lap, steam port-opening, and cut-off in slide valve engines. In order to use the diagram to find the lap, having given the cut-off and maximum port-opening, follow the ordinate representing the latter, taken on the horizontal scale, until it meets the oblique line representing the given cut-off. Then read off this height on the vertical lap scale. Thus, with a port-opening of 114 inch and a cut-off of .50, the intersection of the two lines occurs on the horizontal 3. The required lap is therefore 3 in. If the cut off and lap are given, follow the horizontal representing the latter until it meets the oblique line representing the cut-off. Then vertically below this read the corresponding port-opening on the horizontal scale. If the lap and port-opening are given, the resulting cut-off may be ascertained by finding the point of intersection of the ordinate representing the port-opening with the horizontal representing the lap. The oblique line passing through the point of intersection will give the cut-off. If it is desired to take lead into account, multiply the lead in inches by the numbers in the following table corresponding to the cut-off, and deduct the result from the lap as obtained from the diagram: Piston-valve.-The piston-valve is a modified form of the slide-valva The lap, lead, etc., are calculated in the same manner as for the common slide-valve. The diameter of valve and amount of port-opening are calculated on the basis that the most contracted portion of the steam-passage between the valve and the cylinder should have an area such that the velocity of steam through it will not exceed 6000 ft. per minute. The area of the opening around the circumference of the valve should be about double the area of the steam-passage, since that portion of the opening that is opposite from the steam-passage is of little effect. Setting the Valves of an Engine.-The principles discussed above are applicable not only to the designing of valves, but also to adjustment of valves that have been improperly set; but the final adjustment of the eccentric and of the length of the rod depend upon the amount of lost motion, temperature, etc., and can be effected only after trial. After the valve has been set as accurately as possible when cold, the lead and lap for the forward and return strokes being equalized, indicator diagrams should be taken and the length of the eccentric-rod adjusted, if necessary, to cor rect slight irregularities. To Put an Engine on its Centre.-Place the engine in a position where the piston will have nearly completed its outward stroke, and opposite some point on the cross-head, such as a corner, make a mark upon the guide. Against the rim of the pulley or crank-disk place a pointer and mark a line with it on the pulley. Then turn the engine over the centre until the cross-head is again in the same position on its inward stroke. This will bring the crank as much below the centre as it was above it before. With the pointer in the same position as before make a second mark on the pulleyrim. Divide the distance between the marks in two and mark the middle point. Turn the engine until the pointer is opposite this middle point, and it will then be on its centre. To avoid the error that may arise from the looseness of crank-pin and wrist-pin bearings, the engine should be turned a little above the centre and then be brought up to it, so that the crank pin will press against the same brass that it does when the first two marks åre made. Link-motion.-Link-motions, of which the Stephenson link is the most commonly used, are designed for two purposes: first, for reversing the motion of the engine, and second, for varying the point of cut-off by varying the travel of the valve. The Stephenson link-motion is a combination of two eccentrics, called forward and back eccentrics, with a link connecting the extremities of the eccentric-rods; so that by varying the position of the link the valve-rod may be put in direct connection with either eccentric, or may be given a movement controlled in part by one and in part by the other eccentric. When the link is moved by the reversing lever into a position such that the block to which the valve-rod is attached is at either end of the link, the valve receives its maximum travel, and when the link is in mid-gear the travel is the least and cut-off takes place early in the stroke. In the ordinary shifting-link with open rods, that is, not crossed, the lead of the valve increases as the link is moved from full to mid-gear, that is, as the period of steam admission is shortened. The variation of lead is equalized for the front and back strokes by curving the link to the radius of the eccentric-rods concavely to the axles. With crossed eccentric-rods the lead decreases as the link is moved from full to mid-gear. In a valve-motion with stationary link the lead is constant. (For illustration see Clark's Steamengine, vol. ii. p. 22.) The linear advance of each eccentric is equal to that of the valve in full gear, that is, to lap+ lead of the valve, when the eccentric-rods are attached to the link in such position as to cause the half-travel of the valve to equal the eccentricity of the eccentric. The angle between the two eccentric radii, that is, between lines drawn from the centre of the eccentric disks to the centre of the shaft equals 180° less twice the angular advance. Buel, in Appleton's Cyclopedia of Mechanics, vol. ii. p. 316, discusses the Stephenson link as follows: "The Stephenson link does not give a perfectly correct distribution of steam; the lead varies for different points of cut-off The period of admission and the beginning of exhaust are not alike for both ends of the cylinder, and the forward motion varies from the backward. "The correctness of the distribution of steam by Stephenson's link-motion depends upon conditions which, as much as the circumstances will permit, ought to be fulfilled, namely: 1. The link should be curved in the arc of a circle whose radius is equal to the length of the eccentric-rod. 2 The |