350

TIIE PRINCIPLES OF THE MARINE ENGINE.

set off the lead of the slide valve, at the same scaleas the lap, on the lower tangent, and from the lapsset off the leads also. From these last points drawlines parallel with the vertical centre line, to intersectwith the circle above and below; connect these inter-sections by angles crossing each other at the centreof the circle. Then with the chord a as a radius, andb as a centre, describe an arc on the circle, in reverselocalities, and each last intersection is the centre of thecrank pin, when the slide valve has closed the supplyports, during the forward and backward strokes of thepiston. The curve seen intersecting with the circle’scentre is described by the connecting-rod when thepiston is at half stroke; and, by a similar process, theposition of the piston can be ascertained at the points ofcut-off, which in this case is a mean of 12-82 inchesfrom the commencement of the stroke. As the top andbottom tangents represent the steam and vacuum sides ofthe slide-valve, the position of the latter, and angle of theeccentric, are also obvious.

Professor Rankine, when treating of the Slide-valveGearing, in his work of “ Rules and Tables,” states:—

By tho angular advance of the eccentric is to be under-stood the angle at which the eccentric radius stands inadvance of that position which would bring the slidevalve to mid-stroke when the crank is at its dead points.

Rule I. Given, the positions of the crank at theinstants of admission and cut-off; to find the properangular advance of the eccentric, and the proportion ofthe lap on the induction-side to the half-travel of theslide.*

In Fig. 235 let A B and A C bo the positions of thecrank at the beginning and end of the forward stroke;let the arrow show the direction of rotation; let X x beperpendicular to B C; let AD be the position of thecrank at the instant of cut-off, and A E its position atthe instant of admission. Draw A F, bisecting theangle E A D; A F will represent the position of thecrank at the instant when the slide is at the forwardend of its stroke; and FAX will be the angular advanceof the eccentric.

Lay off the distance A F to represent the half-travel;and on A F as a diameter describe the circle A H F G,

cutting A D in G and A E in H; then will

’ A F A F

* The method used in this and the following rules is that ofProfessor Dr. Zeuuer of the Swiss Federal Polytechnic School atZurich , published in his treatise on Slide Valve Gearing, entitledDie aJdebersteuerungen.

be the required ratio of lap at the induction-side to half-travel ; and A G = A H will represent that lap, on thosame scale on which A F represents the half-travel.

Fig. 235.

DR. ZEUNER’s GEOMETRICAL DIAGRAM or TUE SLIDE VALVE ANDCRANK.

On the same scale, I K represents the width of openingof the valve at the beginning of the stroke, sometimescalled the “ lead of the slide.” Strictly speaking, this isthe lead of the induction-edge of the slide only; the leadof tho centre of the slide being A K; that is, its distancefrom its middle position at the beginning of the forwardstroke.

Given the data and results of the preceding rule, andthe position A M, of the crank at the instant of release,to find the ratio of lap on the eduction-side to half-travel, and the position of the crank when cushioningbegins. Produce F A to L, making A L = A F; onA L as a diameter draw a circle, cutting A M in N; thenA N

will be the required ratio of lap at eduction-side tohalf-travel.

About A draw the circular arc N P, cutting the circleA L again in P; join A P; then A P will be the re-quired position of the crank at the instant when cushion-ing begins.

Rule III.—Given, the data and results of Rule I., andthe position, A Q, of the crank at the instant of cushion-ing ; to find the ratio of lap at the eduction-side to half-travel, and the position of the crank at the instant ofrelease—produce F A as before; on A L = F A as a

A P

diameter draw a circle cutting A Q in P: -— will

A L

be the required ratio of lap at the eduction-side to half-travel.

About A draw the circular arc P N, cutting the circle