Chapter XV: Part XI: The Valve-Gear (2)

QUESTION 207. _Why is it difficult to admit and maintain steam at the full boiler pressure in the cylinder during admission?_

_Answer._ Because it is necessary to reduce the travel of the slide-valve in order to cut off the steam “_short_,” or soon after the beginning of the stroke of the piston. When the travel is reduced, the valve opens the port only a small distance, so that the area of the opening is not then sufficient to allow the steam to flow into the cylinder with sufficient rapidity to fill it at full boiler pressure, especially if the engine is working at a high speed. Thus, by referring to the table given on page 216 and to the motion curves in fig. 128, it will be seen that when the steam is cut off at from ¹⁄₄ to ¹⁄₂ stroke, the port is opened for the admission of steam only from ¹⁄₄ to ¹⁄₂ inch wide. From the curves it will also be seen that the valve then acquires its maximum travel and the steam-port its greatest width of opening very soon after the piston begins its stroke; after which the port is gradually closed, so that before the steam is entirely cut off the opening is so much reduced in area that the steam cannot flow through it rapidly enough to maintain the steam at full boiler pressure in the cylinder when the engine is working at high speeds.

QUESTION 208. _What means are used to overcome this difficulty and thus admit steam at full boiler pressure when the valve is cutting off short?_

_Answer._ In the first place, the steam-ports are made from ten to twelve times as long as they are wide, so that a narrow opening will have a comparatively large area. In the second place, by giving the valve lead, not only are the clearance space and the steam-way filled with steam when the piston begins its stroke, but the port is then open a distance equal to the lead. With the ordinary link motion, as has already been shown, this lead increases as the travel and period of admission diminish, so that the smaller the total distance that the port is opened, the greater is its opening at the beginning of the stroke. As the steam is usually cut off short when locomotives run at high speeds, it will be seen that the increased lead which is imparted to the valve by the shifting link is an advantage rather than a disadvantage. But while it is often possible in this way to secure a pressure of steam in the cylinder at the beginning of the stroke equal or nearly so to that in the boiler, yet it is almost impossible to maintain this pressure during the whole period of admission, when the steam is cut off short and the engine working at a high speed. To obviate this evil what is called the Allen valve was designed, which is represented in fig. 132. This valve has a channel or supplementary port, _a a_, which passes over the exhaust cavity, and has two openings, _b_, _b′_, in the valve-face. When the valve begins to admit or “_take_” steam at _c_, as shown in fig. 133, it will be seen that it also uncovers the opening _b′_ at _e_ and admits steam at _b′_, which passes through the channel _b′ a a b_ and enters the steam-port _c_ at _b_, and in this way there is a double opening for the admission of steam. The opening _b_ of the supplementary port is closed as the valve advances, but when this takes place the steam-port is uncovered far enough to admit all the steam that is required. This form of valve is very efficient when the travel and point of cut-off are very short. It then gives just twice as much opening as the ordinary valve for the admission of steam. This improved valve has been much used in Europe; but, although it is an American invention, has not received the attention in this country which its merit deserves.

_Fig. 132._

_Fig. 133._

Scale ³⁄₁₆ in. = 1 inch.]

QUESTION 209. _What is meant by the pre-release of steam?_

_Answer._ It is the release of the steam before the piston has completed its stroke. If it is confined until the piston has reached the end of the cylinder, there will not be time nor will it be possible, with a slide valve and link-motion, to secure a sufficiently large opening of the port to permit the steam to escape from the cylinder before the piston begins its return stroke. If there were no pre-release, there would therefore be more or less back pressure on the piston.

QUESTION 210. _Upon what does the amount of pre-release depend?_

_Answer._ First, as has already been explained in answer to Question 51, on the amount of inside lap; and second, on the outside lap of the valve and lead of the eccentrics; and third, on the travel of the valve. The less the inside lap, the greater the outside lap and consequent lead of the eccentrics; and the shorter the travel of the valve, the earlier will be the release. The proper amount of this pre-release depends upon the velocity of the piston and the quantity of steam to be discharged or the degree of expansion. From the motion-curves in fig. 128 it will be seen that it is a marked feature of the shifting-link motion that the pre-release occurs earlier in the stroke as the link approaches mid-gear, or as the travel of the valve diminishes. As the link is usually worked near that position when the engine is run at a high speed, it will be seen that in this respect again the link-motion is well adapted for working the slide-valves of locomotives.

QUESTION 211. _What governs the period of release?_

_Answer._ The release like pre-release is dependent upon the amount of inside lap, the outside lap and consequent lead of the eccentrics, and the travel of the valve.

The addition of inside lap has the effect of closing the port earlier than it would be closed without, and thus shortening the period of release and also of reducing the area of the opening of the port. This will be apparent by referring to fig. 128, in which the valve had ¹⁄₁₆ in. lead. The dotted lines which represent the edges of the ports in relation to the exhaust edges of the valve are therefore drawn ¹⁄₁₆ in. from the centre line _a b_. If, however, there had been no inside lap, then the edges of the ports would have conformed to the line _a b_. It will be observed that the first curve crosses the dotted line _g g′_ at 15¹⁄₂ in. of the forward stroke, which is the point at which the port is closed to the exhaust, or where the period of release ends and compression begins. If there had been no lap and the line _g g′_ had therefore occupied the same position as _a b_, then the motion-curve would not have crossed it until the piston had reached 16 in. of its stroke, thus showing that the period of release had been lengthened and compression delayed. As the width of the opening of the port is represented by the distance of the motion-curve from the right hand side of the line _g g′_, which represents the edge of the port, it is obvious that if there had been no lap, so that the position of the line representing the edge of the port had occupied the position of _a b_, then the space between it and the motion-curve would have been greater, thus showing that the port would have been opened wider if there had been no inside lap. The width of the opening of the port to the exhaust is in fact always diminished by an amount equal to the inside lap.

With the same travel, increase of outside lap and lead shortens the period of release, but has no effect on the width of the opening of the port to the exhaust.

Increase of travel, with the same outside lap, lengthens the period of release and also increases the width of the opening of the port to the exhaust.

QUESTION 212. _What governs the period of compression?_

_Answer._ As compression begins when release ends, or when the port is closed to the exhaust, it is controlled by exactly the same causes, and as the two events occur simultaneously, of course whatever shortens the period of release lengthens that of compression.

QUESTION 213. _What effect do the clearance spaces and steam-ways have upon the compression of the confined steam?_

_Answer._ By referring to the motion-curves in fig. 128, it will be seen that the steam-port is closed by the exhaust edge of the valve, or compression begins some time before the piston reaches the end of the stroke. The result is that the remaining portion of the cylinder, through which the piston must move _after_ the port is closed to the exhaust, is filled with steam of atmospheric pressure, or possibly a little above that pressure. As this is confined in the cylinder, it is compressed by the advance of the piston. If there was no room between it and the cylinder at the end of the stroke, then either the cylinder would be burst or the valve would lift so as to allow the compressed steam to flow back into the steam-chest. The clearance and the steam-passages, however, afford considerable room, into which the confined steam can be compressed without danger of bursting the cylinder, or of raising the slide-valve when there is steam in the steam-chest. As the clearance spaces and steam-ways must be filled with high-pressure steam at the beginning of each stroke, it must be obtained either by taking a supply of “_live_”[58] steam from the boiler, or by compressing into the clearance spaces the low-pressure steam that still remained in the cylinder when the port was closed to the exhaust. By the latter process, a certain quantity of steam is saved at the expense of increased back pressure. It should be borne in mind also that the total heat of the compressed steam increases with its pressure, and as this latter approaches that in the boiler, the temperature of the former must have been raised from that due to about atmospheric pressure to nearer the temperature of that in the boiler. These changes of temperature which the steam undergoes will affect the surface of the metal with which the steam is in contact during the period of compression; it follows from this, that the ends of the cylinder principally comprising the clearance spaces must acquire a higher temperature than those parts where expansion only takes place. This is an important consideration, since the fresh steam from the boiler comes first in contact with these spaces, and by touching surfaces which have thus previously been heated, as it were, by the high temperature of the compressed steam, less heat will be abstracted from the fresh steam, and therefore a less amount of water will be deposited in the cylinder.[59]

[58] The term “live” steam means steam taken direct from the boiler
and which has not been used in the cylinder or to do any work.

[59] Bauschinger’s Indicator Experiments on Locomotives, published in
Vol. III. of the RAILROAD GAZETTE.

It will thus be seen that the effect of compression is to fill the clearance spaces and steam-ways with compressed steam before pre-admission begins. As already stated, this is done at the expense of back pressure in the cylinder. It must be remembered that all the energy, excepting that part which is wasted by loss of heat, friction, etc., which is consumed in compressing the confined steam, is again given out to the piston by expansion. The confined steam also acts as an elastic cushion to receive the piston, just as the steam which is admitted before the end of the stroke would if there were no compression. Compression, therefore, has the effect of saving the quantity of live steam which it would otherwise be necessary to admit before the end of the stroke to fill the clearance spaces and steam-ways and also to “cushion” the piston. As already stated, the momentum of the piston and other parts depends upon their weight and the speed at which they are working, increasing directly as the square of the speed, from which it follows that the compression should increase rapidly with the speed, and should be the greatest at high speeds. As the ports are prematurely closed to the exhaust with the shifting-link motion, and as the lead increases rapidly as the link approaches mid-gear, and the amount of compression is at the same time correspondingly augmented, it will be seen that the shifting-link motion fulfills these conditions very perfectly.

The pressure to which the confined steam will rise depends of course upon the amount of the period of compression, and also on the size of the clearance spaces. As it is possible to have such an amount of compression that it will exceed the boiler pressure, and thus raise the valve from its seat and be forced back into the steam-chest, some care must be exercised to proportion the one to the other, so that the degree of the confined steam may not be excessive.

QUESTION 214. _How can the effect of the distribution of the steam upon its action in the cylinder be determined by experiment?_

_Answer._ As already explained in answer to Question 55, this can be done by an instrument called a steam indicator.

Scale 3 in. = 1 foot.]

QUESTION 215. _What is the construction of this instrument?_

_Answer._ The indicator now ordinarily used is the Richards indicator, the outside of which is represented in fig. 134 and a section in fig. 135. It consists of a cylinder, _B_, into which a piston, _C_, is accurately fitted, but so that it will move freely in the cylinder. The piston rod is surrounded with a spiral spring, _D_, the lower end of which is attached to the top of the piston, and the upper end to the cylinder cover. When steam is introduced below the piston it pushes it up in the cylinder and the spring is compressed. If there should be a vacuum below the piston, the air above it will press the piston downward and extend the spring. This latter occurs only when the indicator is used on condensing engines. Of course the distance which the piston is forced up by the steam pressure below it depends upon the amount of pressure and also on the tension of the spring; and therefore by attaching a pencil to the piston-rod so that it can mark on a moving card in front of it, a diagram will be drawn which would indicate the steam pressure, as was explained in answer to Question 55. But there are some practical difficulties in the way of doing this. It is found that if the pencil is attached directly to the piston-rod of the indicator, the distance through which they must move, in order to make the scale of the diagram sufficiently large to be clear, is so great that the momentum of the parts carries them further than the pressure of the steam alone would move them. The distance through which the pistons or instruments move, moreover, makes it impossible that the changes of pressure should be indicated simultaneously with the position of the piston; the latter must travel while the action is taking place, and thus the diagram shows changes of pressure later or more gradually than they occur.[60] To overcome these and other difficulties, the piston-rod of the indicator which we have illustrated is attached at _h_ to the short arm of a lever, _F G_, and to the end of the long arm a piece, _F I_, is attached, which carries a pencil, _J_. By this means the piston has only one-fourth of the motion that it imparts to the pencil, so that the momentum of the moving parts is comparatively slight. If the pencil was attached directly to the end of the lever, it is obvious that it would move in the arc of a circle, and that this would be a source of error in the diagram. To avoid this the pencil is attached to what is called a “parallel motion.” This consists of a coupling-rod, _F I_, which connects the ends of two levers, _F G_ and _I H_. The centre of the rod _F I_, to which the pencil is attached, will with this arrangement move in a straight line. The levers and all the parts are of course all made as light as possible, so that their weight will have little effect on the motion of the indicator piston.

[60] Richards’ Steam Indicator, by Charles T. Porter.

The paper or card on which the diagram is drawn is wrapped around a brass cylinder, _A A_. This cylinder is made to revolve part of the way around by a strong twine, _a b_, which is wrapped around a pulley, _b_, at the bottom of the cylinder. The twine is attached to a lever, similar to that shown in fig. 30, which receives a reciprocating motion from the piston of the engine. The twine can of course move the cylinder only in one direction, and therefore a coiled spring similar to a clock spring is placed inside of the cylinder to draw it back when the twine is relaxed. In this way the paper cylinder or drum receives a part of a revolution at each stroke of the piston, and moves simultaneously with it. This drum is used instead of a flat card, on account of the practical difficulties of employing the latter. The motion of the paper on this drum will, however, be exactly the same in relation to the pencil as the motion of a flat card would be.

The method of attaching an indicator to a locomotive is represented in fig. 136a. It will be seen from this that it is placed over the center of the steam chest and connected to each end of the cylinder with ³⁄₄-inch pipes. A globe valve was in the case represented placed on each side of the indicator, so that it could be put into communication with either end of the cylinder, or could be completely shut off from both. A better plan, however, is to have a three-way cock at the point where the horizontal pipe connects with the vertical one leading to the indicator, as the passages in a three-way cock are more direct than those in globe valves. The arrangement of the levers for giving motion to the indicator drum, and of the seat, which is very requisite for the experimenter, will be readily understood from the engraving without further explanation. It is thought by some engineers that the indicator should be applied as near to each end of the cylinder as possible. It is believed, however, that if the pipes, cocks, and their connections are made large enough so as not to impede the motion of the steam, no appreciable error will arise from the method illustrated in fig. 136a.

QUESTION 216. _What should be the form of an indicator diagram, if the steam is distributed by a link motion so as to produce the best practicable action in the cylinders?_

_Answer._ It should approximate to that shown in fig. 136b. In this diagram the vertical lines represent inches of the stroke, and the scale on the left the steam pressure in pounds per square inch. The atmospheric and vacuum lines are also indicated, as already explained in answer to Question 55. The points at which the different periods of the distribution begin are indicated by the letters _a_, _b_, _c_, _d_, _e_ and _f_. These are in the order in which they occur: _a_, pre-admission; _b_, admission; _c_, expansion; _d_, pre-release; _e_, release; and _f_, compression. The lines forming the outline of the diagram will be designated for convenience of description as follows:

The line from _a_ to _b_, the _admission line_.
The line from _b_ to _c_, the _steam line_.
The line from _c_ to _d_, the _line or curve of expansion_.
The line from _d_ to _e_, the _exhaust line_.
The line from _e_ to _f_, the _line of back pressure_.
The line from _f_ to _a_, the _line or curve of compression_.

_Fig. 136b._]

The diagram represents a distribution of steam produced by a valve having ⁷⁄₈ in. outside and ¹⁄₁₆ inside lap, and operated by the link motion represented in fig. 103. The eccentrics have 5 in. throw, and the steam-ports are 1¹⁄₄ and the exhaust 2³⁄₄ in. wide. The valve as shown by the diagram is cutting off at 8 in., or one-third of the stroke. Pre-admission begins when the piston still has ¹⁄₂ in. to move before reaching the end of its stroke. Admission of course begins with the stroke, expansion at 8 in., pre-release at 18¹⁄₂ in., release at the end of the stroke, and compression at 17¹⁄₂ in. of the return stroke. The valve is supposed to be set without any lead, or “_line and line_,”[61] as it is called at full stroke. When the steam is cut off at 8 in. of the stroke, the valve has 2⁵⁄₈ in. travel and ³⁄₁₆ in. lead. The steam pressure in the boiler is supposed to be 100 pounds above the atmosphere. Of course, when the valve cuts off at different points of the stroke, the periods of distribution will be somewhat changed; but from the above diagram the principal features of a good distribution can be explained.

[61] That is, the steam edges of the valve correspond with the steam
edges of the port at the beginning of the stroke.

These are: First, that the steam pressure should rise rapidly during the period of pre-admission, so that there will be full boiler pressure in the cylinder at the beginning of the stroke. When this occurs, the pre-admission line will rise from _a_ to _b_, to such a point at _b_ which will indicate full boiler pressure in the cylinder. The same pressure should then be maintained in the cylinder during the whole period of admission, and the admission line from _b_ to _c_ should therefore be a straight horizontal line, as shown in fig. 136b. When expansion begins, the pressure will fall, as was explained in answer to Question 55. The expansion line should approximate a hyperbolic curve, but if there is much loss of heat by radiation or other causes, the diagram will fall considerably below the theoretical curve. With cylinders well protected and with dry steam the expansion line will fall slightly below a hyperbolic curve at the beginning of the period of expansion, and rise above it during the latter part of the same period. The reason of this is that the cylinder is heated by the admission of live steam of comparatively high pressure and temperature, so that, when the pressure becomes reduced by expansion, a part of the water which is condensed in the cylinder will be re-evaporated by the heat in the latter. From the point of the pre-release, _d_, to the end of the stroke, _e_, the exhaust line should fall rapidly, so that there will be no pressure behind the piston during its return stroke. To explain the theoretical form of the exhaust line would lead us into a very abstruse discussion, which would be out of place here. It will be sufficient for our purpose to call attention to the fact that the pre-release should allow all the steam in the cylinder to escape before the piston reaches the end of the stroke, so that the back pressure during the return stroke may be as low as possible. It is, however, only at comparatively slow speeds that the steam in locomotive cylinders escapes during the period of pre-release, so that the back pressure is reduced to that of the atmosphere. It is necessary in locomotives, as has already been explained, to contract the area of the blast orifices or exhaust nozzles, in order to stimulate the draft through the fire, so that the steam cannot escape with sufficient rapidity to reduce the back pressure to that of the atmosphere if the engine is running fast. Of course every pound of back pressure on the piston is so much loss of energy, and a reduction of the amount of work done by the engine; but it is a sacrifice which must be made in order to be able to generate the requisite quantity of steam. In studying the distribution of steam, however, every effort should be made to reduce the back pressure as much as is practicable, and yet maintain a sufficient supply of steam, and therefore the line of back pressure should conform as closely as possible to the atmospheric line. The compression line should be a hyperbolic curve, beginning with the period of compression. In calculating both the compression and expansion, allowance must be made for the clearance space and steam-way. In a cylinder like that illustrated in fig. 92, their contents would be about equal to that of two inches of the cylinder. Therefore, when steam is cut off at 8 in. of the stroke, instead of having a quantity of steam which will fill a cylinder 16 in. diameter and 8 in. long, we have as much as would fill a cylinder of that diameter and 10 in. long. The same thing is true of the compression. This must occur in the above example when the piston has 6¹⁄₂ in. more to move before completing its stroke. There is therefore a quantity of steam in front of it sufficient to fill a cylinder 8¹⁄₂ in. in diameter. This steam is of course compressed by the advance of the piston, and if its pressure when compression begins is the same as that of the atmosphere, then it will be 0.9 lbs. above it when the piston has only 6 in. to move and 3.2, 6.2, 10.5, 16.9, and 27.5 lbs. effective pressure when the piston has 5, 4, 3, 2 and 1 inches to move respectively, and when pre-admission begins, the pressure will have risen to 48.7 lbs. If the back pressure is above that of the atmosphere, of course the compression will be correspondingly increased. It will also be seen that, without any or with very little clearance space, the compression would at the end of each stroke rise above the boiler pressure. It being a peculiarity of the ordinary shifting-link motion that as the period of admission is reduced that of compression is lengthened, the latter becomes very excessive when the steam is cut off at less than one-third or one-fourth of the stroke.

QUESTION 217. _In what respect would a diagram made by an indicator differ from the theoretical form represented in fig. 136b?_

_Answer._ It would be drawn with less exactness; that is, the corners instead of being sharply defined, as in fig. 136b, would be more or less rounded, as in fig. 137, and the curves and straight lines would vary somewhat from the exact mathematical form indicated in fig. 136b. The higher the speed at which the engine is working when the diagrams are taken, the greater will be the variation from the theoretical form.

_Fig. 137._]

QUESTION 218. _If the amount of pre-admission is insufficient, how will it be shown in the indicator diagram?_

_Answer._ The effect of too little pre-admission is to lower the pressure of the steam at the beginning of the stroke, and at high speeds there will not be time enough nor sufficient opening of the steam-port to supply the deficiency after the stroke has commenced. The corner of the diagram at _b_ will then be very much rounded, as shown in fig. 138. This is apt to be the case when steam is admitted during a considerable part of the stroke, as a shifting-link motion then gives less lead than when it is worked nearer mid-gear. If the steam is cut off short, then the pressure in the cylinder during admission is very much below boiler pressure, and is apt to fall rapidly after the commencement of the stroke, as shown in fig. 138.

_Fig. 138._]

QUESTION 219. _If the opening of the steam-ports during admission is too small, what will be the form of the diagram?_

_Answer._ The effect will be very much the same as that produced by too little pre-admission or lead; that is, the pressure in the cylinder will be much lower than in the boiler and will fall rapidly during the periods of admission, as shown in fig. 138.

QUESTION 220. _What defects will be indicated by the expansion curve of indicator diagrams?_

_Answer._ If the cylinders are not well protected, and there is much loss of heat from radiation, there will be a rapid fall of pressure during the period of expansion, which will be shown by the expansion curve falling below the theoretical curve shown in fig. 136b. If, on the contrary, the indicator curve is much above the theoretical curve, it may be caused by a leak in the valve. As steam is quite as likely to leak from the steam-port into the exhaust as from the steam-chest into the steam-port, a valve which is not tight may produce just the contrary effect upon the indicator diagram. As it is usually quite easy to detect a leak in the valve by other means, the use of the indicator for this purpose is unnecessary. Attention is called to it, however, to show the impossibility of getting results of any value with the indicator if the valves are not steam-tight.

QUESTION 221. _What should be observed regarding the exhaust line of the indicator diagram?_

_Answer._ The most important point to be observed is, whether the pressure at the end of the stroke is reduced as low as possible, as at high speeds it is usually much more difficult to exhaust the steam from than to admit it into the cylinder. As already stated, the blast in the chimney makes it almost impossible to exhaust the steam to atmospheric pressure when the locomotive is running fast. If the steam is released too late in the stroke, as already explained, there will not be time enough nor sufficient opening of the port to allow the confined steam to escape from the cylinder before the end of the stroke, and this will be indicated on the diagram by the space between the line of back pressure and the atmospheric line during the commencement of the return stroke, as shown in fig. 138.

QUESTION 222. _What should be observed regarding the line of back pressure?_

_Answer._ The most important point is, that it should approximate as closely as possible to the atmospheric line, as all the back pressure not only diminishes the efficiency of the engine, but is a total loss of energy. Too much inside lap will increase the amount of back pressure, but generally it is more influenced by the area of the blast orifices than by any other cause. Every effort should be made, therefore, to have them as large as possible and yet have the boiler make as much steam as is needed.

When only one blast orifice is used for both cylinders, it often happens that when the steam is exhausted from the one cylinder it “blows” over into the other, and thus produces an additional amount of back pressure. This is shown by a rise or “hump” in the line of back pressure, as indicated in fig. 138.

QUESTION 223. _Can the amount of compression which is needed be determined by calculation?_

_Answer._ Yes; but it involves more abstruse principles of mathematics than it is thought best to introduce here. Some of the reasons can, however, be given, which will make the subject clearer, and enable the reader, if he has sufficient knowledge of mathematics, to investigate the subject still further.

_Fig. 140._]

In the first place it is a well-known fact that the motion of a piston in the cylinder of a steam engine is not a uniform one, but increases in speed from the beginning of the stroke to the middle, and diminishes in speed from the middle to the opposite end. The cause of this is that the crank revolves at a uniform speed during the entire revolution, but the piston moves much less at the beginning of the stroke, with a given amount of revolution of the crank, than it does at the middle. This is shown in fig. 140, in which _A_ is a cylinder and _B_ the piston and _a b c d_ the path of the crank. Now while the crank moves from _a_ to 1, or ¹⁄₁₂ of a revolution, the piston has moved 1³⁄₈ in., or a distance equal to that from _a_ to 1′ or to the base of a perpendicular drawn from 1 to the centre line _a c_. While the crank moves from 1 to 2, or through the second twelfth of a revolution, the piston has moved from 1′ to 2′, or 4³⁄₈ in., or 2³⁄₄ in. further than during the first twelfth of the crank’s revolution. During the third twelfth of the revolution the piston moves from 2′ to 3′, or 6 in., thus showing that it continues to increase in the distance moved during each period of the revolution of the crank until the latter has made a quarter revolution. The speed of the piston then begins to diminish until it reaches the end of the stroke. It is slightly affected by the angularity of the connecting-rod, as already explained, but for the present this is disregarded. It is obvious now that if the momentum, or actual energy stored up in the piston and other reciprocating parts after they have passed the middle of the stroke, added to the pressure behind the piston, is greater than the resistance offered by the crank, the motion of the latter will then be accelerated and thus conveyed to the moving engine and train. If, however, there is any momentum in the piston when it reaches the end of the stroke, evidently it can exert no power to cause the crank to revolve, but must be expended by producing a pressure on the crank-pin and thus on the axle-boxes. Not only will such a pressure not cause the crank to revolve, but it will be more difficult to turn the crank with such a pressure against it than it would be without. The momentum of the piston and other reciprocating parts at the dead point therefore creates a resistance to the movement of the crank instead of helping to turn it. It will also be observed that after the crank has moved slightly from the dead point, any pressure on the piston will exert very little force which will tend to turn the crank. In fact the nearer the piston is to the end of the stroke the greater is the proportion which the friction of the crank-pin and axle bears to the useful effect of the strain in causing the crank to turn. Calculation shows that for about three degrees on either side of the dead points the effect of pressure on the crank-pin is actually to retard the engine. If now the piston reaches the end of the stroke with a certain amount of unexpended momentum stored up in it, if this energy is expended by producing pressure on the crank, then it will not only be a waste of energy but a double waste by retarding the motion of the crank. If, however, this energy can be absorbed by compressing steam which will fill the clearance spaces, it will not only prevent the retarding effect referred to, but the energy in the piston and other parts will be converted into steam pressure, which will be given out in useful work during the next stroke. It would, of course, be impossible to arrest the motion of the piston instantly, and therefore its momentum is gradually absorbed from the time compression begins until it reaches the end of the stroke. As the energy of a moving body is equal to its weight multiplied by the square of its speed, it is obvious that to overcome this a different amount of compression would be required for each speed, and also that it must be adjusted to the weight of the moving parts. Such exact adaptation is not practicable on locomotives, nor does the link motion enable us to alter the amount of compression with so much exactness: but the explanation shows the value of increasing the amount of compression with the speed, which fortunately the peculiarities of the shifting-link motion enable us to do without difficulty.

_Fig. 139._]

QUESTION 224. _What cause produces the form of diagram represented by Fig. 139?_

_Answer._ It is produced by excessive compression, which causes the pressure in the cylinder to rise above boiler pressure before pre-admission begins. As soon as the port is opened, part of the steam in the cylinder flows back into the steam-chest, and thus the pressure is reduced, as shown by the diagram.

QUESTION 225. _How can we determine whether the steam is distributed in the cylinders to the best advantage, and how can we discover the fault, if there is one, in the link motion?_

_Answer._ The indicator will show the action of the steam in the cylinder, and motion-curves drawn with the instrument described in answer to Question 192 will show the exact movement of the valve. By comparing the indicator diagram with the motion-curves, the one will show the defects in the other.[62]

[62] See description of Richards’ Improved Steam Engine Indicator,
with directions for its use, by Charles T. Porter, London.

QUESTION 226. _To what extent can the movement of the valve be modified by alterations in the proportions of the link motion?_

_Answer._ The motion of the valve is susceptible of an almost infinite number of changes, by different variations and combinations of proportions of the working parts of the link motion. These changes are, however, limited by the general laws which govern the motion of eccentrics, and therefore cannot influence the motion of the valve beyond certain limits. Hardly any variation can be made either in the proportions or arrangement of the working parts which will not have some influence upon the movement of the valve. Aside from the proportions of the valve itself, which have already been discussed, the throw of the eccentrics, the length of the rods and of the link, the point of connection of the rods with the link, the point of suspension, the position of the lifting shaft, the length of the arms, the length and position of the rocker arms will each of them effect the distribution of steam. The number of combinations of all these different proportions is of course almost infinite, and therefore any full discussion of them will be impossible here.

QUESTION 227. _What are the most important points which require attention in designing a link motion?_

_Answer._ It should be proportioned so that--

First, the lead and the period of admission should be the same for each end of the cylinder, for each point of cut-off, and, if possible, in back as well as forward gear.

Second, the width of opening for both admission and exhaust should be as large as possible when steam is cut off short.

Third, the exhaust or pre-release should occur early enough and be maintained long enough to reduce back-pressure as low as possible.

QUESTION 228. _How can the lead and period of admission be equalized?_

_Answer._ It is impossible to make the periods of admission absolutely alike for every point of cut-off in both fore and back gear. It is therefore customary to disregard the back gear, as engines are worked but little with the link in that position. Even for forward gear the periods of admission cannot be made exactly alike for each end of the cylinder and for each point of cut-off, and therefore it is usual to make the periods of admission alike for half-gear forward, in which position the link is worked most.

The periods of admission for the front and back ends of the cylinder can be changed most in relation to each other by altering the position of the point of suspension on the link. This can be done either by moving this point up or down, or horizontally. Usually links are suspended from a point halfway between the points of connection of the eccentric-rods and from ¹⁄₄ to ³⁄₄ in. back of the centre line of the slot in the link. A somewhat better distribution can be secured by suspending it about 3 in. above the centre, but the suspending link must then be made so short that it is subjected to very great strains by the motion of the link, and this evil is usually considered much greater than the advantage which is gained thereby in the more equal distribution. The point at which the upper end of the suspension link is hung also influences the relative amount of admission front and back. This point, of course, varies as the end of the lifting arm is raised or lowered. In designing valve gear it is usually tested by a full-sized model, which will show the exact motion of all the parts. The best position for the lifting shaft and the length of its arm can be determined perhaps most satisfactorily by placing the link in full gear forward, then moving the point of suspension of the upper end of the link-hanger horizontally so that the front and back admission will be alike, and then marking this position. The same process should then be repeated for half gear and for the shortest point of cut-off. If the position of the lifting shaft and the length of its arm are then so arranged that the end of the latter will move through the three points which have been thus determined, the admission will be very nearly equal for each end of the cylinder. Usually, however, it is impossible to arrange the shaft and arm so that they will conform exactly to these conditions, and therefore an approximation is made which will come as near as possible to what is required. It may be stated, however, that the lifting shaft should be kept as low as possible, so as not to interfere with the eccentric-rods. In some cases the shaft has been suspended from the boiler, so that the outside eccentric-rod would work past or over the end of the lifting shaft, thus allowing the latter to be located lower than would otherwise be possible.

QUESTION 229. _Which parts of the link-motion have the greatest influence on the distribution of steam?_

_Answer._ The lap of the valve and the throw of the eccentrics. The effect of any change of these upon the distribution is very similar to that produced if a single eccentric is used, which was explained in the answers to Questions 49, 50 and 52.

_Fig. 141._]

QUESTION 230. _What is the effect upon the admission of increasing the throw of the eccentrics with the same lap?_

_Answer._ As already explained, the effect is to increase the period of admission, or in other words to cut off later in the stroke, and also to increase the width of the opening of the steam-port or the distance which the valve throws over the port. This has an important influence upon the admission, when the link-motion is used.

QUESTION 231. _What is meant by the angular advance of the eccentrics?_

_Answer._ It is the angle which a line, _e f_, fig. 141, drawn through the centre of the axle and the centre of the eccentric makes with a vertical line _a b_, when the crank is on one of the dead-points or centres. Thus in fig. 141 the crank _A_ is represented on the front centre. In order to give the valve the necessary lead the eccentric must be moved ahead of the vertical line _a b_. The angle _c_ which the line _e f_ (drawn through the centre of _g_ of the eccentric and _f_ of the axle) makes with the vertical line is called the _angular advance_.

QUESTION 232. _What is meant by linear advance?_

_Answer._ By linear advance is meant the distance which the valve has moved from its middle position at the beginning of the stroke of the piston. This, when the two rocker arms are the same length, is the same as the distance of the centre of the eccentric _g_ from the vertical line _a b_, fig. 141.

QUESTION 233. _Why does the cut-off occur earlier with an eccentric having a short throw than with one which gives more travel to the valve?_

_Answer._ Because it is necessary to give the eccentric with the short throw more angular advance in order to give the valve the required lead. This is illustrated in fig. 142, in which a section of a valve, _V_, and ports _c_, _g_, and _d_, are represented. In order to simplify the diagram as much as possible the rocker is left out and the valve is supposed to be moved by the rod _R_ directly from the centre _a_ of the eccentric.[63] The effect of the angularity of the connecting rod and eccentric rod is also neglected. The circle _a b e f_ represents the path of the centre of an eccentric having 5 in. throw, and _h i j_ the path of one having 3¹⁄₂ in. throw. In order to give the valve the required lead, which is supposed to be just line-and-line at the beginning of the stroke, the linear advance of the valve must be equal to the lap, or ⁷⁄₈ in. If therefore we draw a line, _p a_, parallel to the vertical centre line, _e k_, and ⁷⁄₈ in. from it, the intersection of _p a_ at _a_ and _h_ with the paths of the eccentric will be the centres of the eccentrics. If through these centres and the centre of the circle, lines, _o a_ and _o p_, be drawn, the angles which they make with the vertical _e k_ will be the angular advance. It will be seen from these lines that in order to give the valve the required lead it is necessary to give the eccentric with the small travel more angular advance than is necessary for the one with the larger throw. It is obvious, too, that when the centre of the larger eccentric has reached the point _b_ the valve will have received its greatest travel, and that when it reaches _p_ the steam-port _c_ will again be closed or the steam cut off. If the small eccentric is employed, the valve will then have its maximum travel when the centre _h_ reaches _s_, and the port will be closed when it reaches _i_. By drawing lines, _o p_ and _o n_, through _i_ and _p_, it will be seen that from the beginning of the stroke until the steam is cut off, if the large eccentric is employed, it, and consequently the shaft and crank, must move over an angle measured by the arc _q t p_. If the small eccentric is used, it and the crank must move through an angle measured by the arc _u t n_. In other words, the crank must turn a considerably greater distance before steam is cut off with an eccentric having a large than with one having a small throw.

[63] It will be seen that this causes the position of the centre of
the eccentric to be reversed.

_Fig. 142._

_Fig. 143._

Scale ³⁄₁₆ in. = 1 inch.]

It is also quite obvious from fig. 142 why the port is opened a shorter distance with a small than with a large eccentric. The distances _o s_ and _o b_ are equal to half the throws of the eccentrics, or 1³⁄₄ and 2¹⁄₂ in. The linear advance _o r_ is in both cases ⁷⁄₈ in., and therefore after the port begins to open the valve will be moved by the small eccentric a distance which is equal to 1³⁄₄ - ⁷⁄₈ = ⁷⁄₈ in., and by the large one 2¹⁄₂ - ⁷⁄₈ = 1⁵⁄₈ in.

_Fig. 144._

Scale ³⁄₁₆ in. = 1 inch.]

QUESTION 234. _What is the effect on the admission of giving an eccentric with a small throw the same angular advance as one with a large throw, and then reducing the lap of the valve so that the lead will be the same in both cases?_

_Answer._ The admission and the cut-off will then occur at the same points of the stroke, but the ports will not be opened so wide. This is illustrated in fig. 143, in which the paths of two eccentrics having the same throw as those in fig. 142 are represented. The centre, _a_, of the larger eccentric is represented in the same position in fig. 143 as in fig. 142. If a line is drawn from the centre of the larger eccentric to that of the axle, and if the centre, _h_, of the smaller eccentric is located on the intersection of this line with the circle representing its path, then the smaller eccentric will have the same angular advance, but the linear advance measured by the distance _o t_ will be only ⁵⁄₈ in. If the valve have the same lap as in fig. 142, its steam edges at the beginning of the stroke, if the small eccentric is employed, will occupy the position represented by the dotted lines _A_ and _B_. If these edges are cut off, as shown by the full lines and shading, then the valve will have the same lead as in fig. 142. It is obvious, too, that if the smaller eccentric has the same angular advance it will reach the point _v_, at which, with the reduced lap, the steam will be cut off, at the same time that the centre, _a_, of the large eccentric will reach _p_, at which point it cuts off the steam with the valve having the large lap. There is, however, this difference in the distribution, that in the one case the valve opens the port a distance equal to _t s_, and in the other a distance equal to _r b_. As _o t_ is equal to the linear advance of the small eccentric, or ⁵⁄₈ in., and _o s_ to half the throw of the eccentric, or 1³⁄₄, _t s_ is equal to 1³⁄₄ - ⁵⁄₈ = 1¹⁄₈ in. The distance _r b_, as shown above, is equal to 2¹⁄₂ - ⁷⁄₈ = 1⁵⁄₈ in., so that the effect produced upon the admission of using an eccentric with a small throw and corresponding amount of lap is, that the ports are not opened so wide as with an eccentric having a larger throw.

_Fig. 145._

Scale ³⁄₁₆ in. = 1 foot.]

QUESTION 235. _How do eccentrics with a short throw, and valves with a corresponding amount of lap, affect the admission with a link motion as compared with eccentrics having a larger amount of throw and greater lap of valve?_

_Answer._ The chief difference is that the ports are not opened so wide for the same period of admission. Thus in fig. 144 is a series of motion-curves drawn with a model of a link motion like that illustrated in fig. 103. The eccentrics had 5 in. throw, and the valve ⁷⁄₈ in. lap outside and ¹⁄₁₆ in. inside. Fig. 145 represents a series of curves, drawn with the same arrangement of valve-gear, excepting that the eccentrics had 3¹⁄₂ in. throw and the valve ¹⁄₂ in. lap. In both cases the curves represent the motion of the valve when cutting off at the same point of the stroke. The following table will show the relative amount of opening of the port.

========+============================
| Width of Opening
| of Steam-port.
+------------+---------------
Point of| Eccentric | Eccentric
Cut-Off.|5 in. throw.|3¹⁄₂ in. throw.
--------+------------+---------------
6 in. | ⁷⁄₃₂ in. | ⁵⁄₃₂ in.
8 „ | ⁹⁄₃₂ „ | ³⁄₁₆ „
10 „ | ¹¹⁄₃₂ „ | ⁷⁄₃₂ „
12 „ | ⁷⁄₁₆ „ | ⁹⁄₃₂ „
15 „ | ⁵⁄₈ „ | ³⁄₈ „
18 „ | ³¹⁄₃₂ „ | ¹¹⁄₁₆ „
21 „ | 1¹⁄₄[64] „ | 1¹⁄₃₂ „
--------+------------+---------------

[64] The valve throws over 1³⁄₄ in. at this point.

It will be seen from this that the eccentric with 5 in. throw gives a greater width of opening for every point of cut-off than the one with 3¹⁄₂ in. throw. For the higher admissions this is not important, but when steam is cut off short it will be observed that the width of the opening is very small. At high speeds the small opening is a great disadvantage.

QUESTION 236. _Has it been determined what amount of opening is required for given speeds of the piston?_

_Answer._ Not with any degree of accuracy. It is customary to make the area of the ports about one-tenth that of the piston. It is certain, however, that with steam-ports of this proportion an opening considerably less than their whole area is sufficient to maintain steam at boiler pressure in the cylinders. One of the defects of the link motion is that the opening of the port is very small when the steam is cut off short. It is best, therefore, to secure the largest practicable opening of the ports for the lower points of cut-off.