CHAPTER XVIII

Demonstration to the Judges of Action of Reciprocating Parts. Explanation of this Action. Mr. Williams’ Instrument for Exhibiting this Action.

The subject of the equalizing action of the reciprocating parts of the engine was not considered in the report of the judges. Indeed, the speed of that engine, 125 revolutions per minute, was not sufficient to develop this action to any important extent. But there was another reason behind that. I invited the judges directly after the close of the fair, but before making their report, to witness a demonstration of this action in my little shop engine, which invitation was accepted by them, and the following exhibition was made, but this was not alluded to in their report, the reason of which will be given on a later page.

The engine had a 5-inch cylinder by 12 inches stroke, and its regular speed was 300 revolutions per minute. I kept Saturday afternoon holiday, one of the good things I had brought from England, and so on Saturday afternoon I had a clear field for this exhibition.

I had previously prepared two governor pulleys to speed the engine up to the increased speeds required, which speeds had been ascertained by calculation. I was so certain of the correctness of this calculation that I did not make any preliminary trial, did not think of such a thing.

PresidentF. A. P. Barnard

After running the engine for a short time at its usual speed, I changed the governor pulley for the smaller one of the two I had prepared, by which the speed would be increased to about 400 revolutions per minute, and loosened the crank-pin brasses so that they were slack fully a thirty-second of an inch. On starting the engine in this condition, of course, it pounded violently on the crank-pin. As the speed was gradually permitted to increase the knock softened, and just before the governor rose it disappeared entirely, and at the calculated speed the engine ran in entire silence.

After running in this manner for a while I prepared for the second part of my show. I put the crank-pin brasses back to their usual running adjustment, loosened the brasses of the cross-head pin fully a thirty-second of an inch, and put on a larger governor pulley, which, if I remember rightly, ran the engine at about 550 revolutions per minute. Under these conditions we utilized only the inertia of piston, rod and cross-head, without that of the connecting-rod.

On starting, the engine of course pounded heavily on the cross-head pin. As the speed increased the same decrease in the noise was observed as on the first trial, only later in the course of the acceleration, and again just before the governor rose the pounding had completely died away, and at the calculated speed the engine ran again in entire silence.

Like everything else, this action seems mysterious until it comes to be understood, when it is seen to be quite simple, as the following explanation will show.

Let us take a horizontal engine of 2 feet stroke, making 200 revolutions per minute, so having a piston travel or average velocity of 800 feet per minute, which was my engine in the Paris Exposition of 1867.

We will suppose the piston to be driven through the crank, by which its motion is controlled, the power being got from some other motor, and that the cylinder heads have been removed so that the piston meets no resistance. We will also disregard the effect of the angular vibration of the connecting-rod, and assume the motion of the piston to be the same at each end of the cylinder.

On each stroke the crank does two things: First, it increases the motion of the piston from a state of rest to a velocity equal to the uniform velocity of the crank-pin in its circular path: and,second, it brings the piston to rest again, ready to have the same operation repeated in the reverse direction during the return stroke.

At the mid-stroke the crank is at right angles with the line of centers, and the velocity of the piston is 800 × ¹⁄₂π = 1256.64 feet per minute, or 20.944 feet per second, and no pressure is being exerted on the piston either to accelerate or retard its motion.

Graphical representation of piston stroke

The pressure of the crank during a stroke, first to impart motion to the piston and second to arrest this motion, is represented by two opposite and equal triangles. Let the lineAB, in the above figure, be the center line of a cylinder and its length represent the length of the stroke. Let the lineAC, normal to the lineAB, represent the force required to start the piston from a state of rest. Then the triangleAOCwill represent the accelerating force that must be exerted on the piston at every point in the half stroke to bring up its velocity, until atOthis equals that of the crank-pin in its circle of revolution, and the accelerating force, diminishing uniformly, has ceased. The opposite equal triangleBODshows the resistance of the crank required to bring the piston to rest again.

How do we know this?

I will answer this question by the graphical method, the only one I know, and which I think will be understood by readers generally.

First, we observe that the distance the piston must move from the commencement to any point in the first half of its stroke, in order that it shall keep up with the crank, is the versed sine of the angle which the crank then forms with the line ofcenters. So the table of versed sines tells us where the piston is when the crank is at any point in its revolution, from 0 to 90°.

Graphical representation of crank path

For example, let the quadrantABin the following figure represent the path of the crank, and the lineAOthat of the piston. LetOFbe the position reached by the crank.AOFis the angle formed by the crank with line of centers, and supposed to be 60°.FEnormal toAOis the sine of this angle, andAEthe versed sine. The latter is the distance traveled by the piston from the pointA, and is .5, the length of the crank being 1.

Secondly, we ascertain how far the piston must advance for every degree or minute or second of the revolution of the crank in its quadrant by merely subtracting from its versed sine that of the preceding one. Thus the versed sine of 60° being .5, and that of 59° being .4849619251, the difference .0150380749 is the motion of the piston, or its mean velocity while the crank is traversing the 60th degree of its revolution.

Thirdly, we want to know the rate at which the motion of the piston is accelerated during any interval.

This acceleration is found by subtracting from the motion during each interval that during the preceding one. For example, the motion of the piston during the 60th degree being, as already seen, .0150380749, and that during the 59th degree being .0148811893, the difference between them, .0001568856, is the acceleration or amount of motion added during the 60th degree.

By this simple process we find the acceleration of the piston during the first degree of the revolution of the crank to be .0003046096, and that during the 90th degree to be .0000053161. But this latter is the amount by which the acceleration was reduced during the preceding degree. Therefore at the end of this degree the acceleration has ceased entirely.

Now, by erecting on the center lineAC, at the end of each degree, ordinates which are extensions of the sine of the angle, and the lengths of which represent the acceleration during that degree we find that these all terminate on the diagonal lineCO. Thus, when the crank has reached the 60th degree, and the pistonhas advanced half the distance to the mid-stroke or toE, Fig. 32, the acceleration during the 60th degree has been .0001523049, or one half of that during the first degree.

But how do we know the amount of the accelerating force exerted by the crank at the beginning of the stroke? This question is answered as follows:

We find that for the first three degrees the accelerating force is, for the purpose of our computations, constant, the diminution not appearing until we have passed the sixth place of decimals.

Let us now suppose the crank 1 foot in length to make 1 revolution per minute, so moving through 6° of arc in 1 second. At this uniform rate of acceleration the piston would be moved in 1 second the versed sine of 1° .0001523048 × 6² = .0054829728 of a foot.

A falling body uniformly accelerated by a force equal to its own weight moves in 1 second 16.083 feet. Therefore this uniform stress on the crank is.005482972816.083= .000341, which is the well-established coefficient of centrifugal force—the centrifugal force of one pound making one revolution per minute in a circle of one foot radius.

So we find that the heightACof this triangle represents the centrifugal force of the reciprocating parts which, in any case, we can ascertain by the formula

WRr²C,

Wbeing the weight of the body;Rbeing the length of the crank;rbeing the number of revolutions per minute, andCbeing the coefficient .000341.

This accounts for the fact that the reciprocating parts are perfectly balanced by an equal weight revolving opposite the crank.

In my treatise on the Richards Indicator and the Development and Application of Force in the Steam-engine, I have given a full exposition of this action here briefly outlined, and to that the reader is referred.

I have only to add that this computation is for horizontal engines. In vertical engines the effect of gravity must be considered, adding on the upward stroke and deducting on the downwardstroke. Also the counterbalance in the crank-disk of vertical engines must be limited to the horizontal fling of the crank end of the connecting-rod, and all balancing must be as nearly as possible in the same plane.

In this respect double-crank engines have this advantage, that one half of the counterweight can be put on each side of the center line.

It is evident that the heavier the reciprocating parts and the more rapid the speed the greater the security for smooth and silent running. However loose the brasses and however sudden the impact of the steam on the piston, and however early or late the admission, there can be no sound or jar, if the inertia of the reciprocating parts is sufficient to equal the force of the entering steam, and if this is in excess it can do no harm. It is also evident that under these conditions at any point in the stroke the change of pressure to the opposite side of the crank-pin is made insensibly.

Some two or three weeks after this exhibition I received a note from President Barnard asking me to call upon him. On my responding to this invitation, he said to me that he had listened to my exposition of this action before the Polytechnic Club of the Institute, but he did not understand it; he had witnessed the experiments with my shop engine, but while he could not question the action in silencing all knock on the centers, still he did not understand it, and not until he investigated the problem in his own way by the method of the calculus did it become plain to him, and he could not see how I had ever been able to arrive at the exposition of the action without employing that method. This explains why the subject had not been considered in the report of the judges. President Barnard afterward kindly gave me a copy of his demonstration, to insert in my book on the Richards Indicator.

It seems appropriate to insert here the following letter received long after from a very prominent engineer of that day.

“Long Branch, N. J., Aug. 7th, 1872.“Mr.Chas. T. Porter:“My dear Sir:Since I had the pleasure of reading the paper which you read before the Polytechnic Club last winter, I haveregarded your demonstration as not less original than subversive. It is, for the first time I believe, apprehended and asserted, not merely that thevis inertiaof the reciprocating masses is not primarily an adverse element in the economy of the crank-engine, but that a certain amount of weight in the piston and its connections, and in high-speed engines a very considerable amount, is an absolute theoretical necessity.“As this will be deemed rank heresy by folks who have been making skeleton pistons of wrought iron, it is well perhaps that you are entrenched at the outset behind theexperimentum crucisof loose brasses.“Very truly yours,“Joseph Nason.”

“Long Branch, N. J., Aug. 7th, 1872.

“Mr.Chas. T. Porter:

“My dear Sir:Since I had the pleasure of reading the paper which you read before the Polytechnic Club last winter, I haveregarded your demonstration as not less original than subversive. It is, for the first time I believe, apprehended and asserted, not merely that thevis inertiaof the reciprocating masses is not primarily an adverse element in the economy of the crank-engine, but that a certain amount of weight in the piston and its connections, and in high-speed engines a very considerable amount, is an absolute theoretical necessity.

“As this will be deemed rank heresy by folks who have been making skeleton pistons of wrought iron, it is well perhaps that you are entrenched at the outset behind theexperimentum crucisof loose brasses.“Very truly yours,“Joseph Nason.”

The followingfiguresrepresent an elegant invention of Mr. Edwin F. Williams, which exhibits graphically the acceleration and retardation of the reciprocating parts of an engine.

In these views,Ais the cross-head in its mid-position;Bis the lath by which the paper drum of an indicator is actuated through the cordn. The lower end of this lath is fixed in its position on the cross-head by the studj, on which it turns freely.yis the end of a vibrating arm, which permits the point of suspension of the lathBto fall below the position shown, as required in the motion of the cross-head on account of the lower end of the lath being so fixed.dis a cylindrical box, partly open, which is secured on the side of the cross-head, in a position parallel with motion, by the armP. The end of this arm is on the studj, inside the lathB. It is prevented from turning on this stud by the set-screwK, and its fixed position is further assured by the studr.

In the boxdis the cylindrical weighth, running freely on rollers, not shown, and bored to receive a springe, of known strength. This spring is secured in two heads, one of which is screwed into the box and the other into the weight. The force required to move the weighthis thus applied to it through the spring.

The operation of this instrument is as follows: The cross-head being at its mid-stroke, as represented, has acquired its full velocity. At this point no force is being exerted, either to impart or to arrest its motion. The same is the case with the free weighth. No pressure is here being exerted, either to compress or to elongate the springe.

Joseph Nason

Fig. 1Fig. 5SCALE 40265 REVS. PER MIN.11¹⁄₄″ × 16″ PORTER-ALLEN.Fig. 4SCALE 40265 REVS. PER MIN.4.416„„SEC.Fig. 2Fig. 3Apparatus for Graphically Showing the Acceleration and Retardation of the Reciprocating Parts of an Engine.

Fig. 1Fig. 5SCALE 40265 REVS. PER MIN.11¹⁄₄″ × 16″ PORTER-ALLEN.Fig. 4SCALE 40265 REVS. PER MIN.4.416„„SEC.Fig. 2Fig. 3

Apparatus for Graphically Showing the Acceleration and Retardation of the Reciprocating Parts of an Engine.

Let the motion be in the direction from the crank. The crank now begins insensibly, by pulling through the springe, to arrest the motion of the weighth. This pull will increase in intensity to the end of the stroke, when the weight is brought to rest, and the spring will become correspondingly elongated. Then, by a continuance of the same pull, the crank puts the cross-head and this free weight in motion in the reverse direction. This pull gradually relaxes, until at the mid-stroke it has ceased. The weighthhas acquired its full velocity again; all stress is off the spring, and the spring and weight are back in the positions in the boxdfrom which they started. This action is repeated during the opposite half of the revolution, but in the reverse direction, the pull being changed to a push, and the spring being compressed instead of elongated. Thus at every point the position of this free weight shows the amount of the accelerating or retarding force that is being exerted upon it at that point, elongating or compressing the spring.

This varying accelerating or retarding force is recorded as follows: A paperb,Fig. 2, is stretched on the surfaceff. This surface is the arc of a circle described about the centerj, and is secured on the lathB, so that as this lath vibrates by the motion of the cross-head the different points in the length of the paper pass successively under the pencil. This is set in the end of the long armaof the right-angled lever-arms 4 to 1 seen inFig. 2, which is actuated by the rodepassing centrally through the spring and secured in the headc. This pencil has thus imparted to it a transverse motion four times as great as the longitudinal motion of the weighthin the boxd. The pencil is kept lifted from the paper (as permitted by the elasticity of the arma) by the cordm. By letting the pencil down and turning the engine by hand, the neutral linex,Fig. 2, is drawn. Then when the engine is running, on letting the pencil come in contact with the paper, the diagonal lines are drawn as shown onFig. 2.

Edwin F. Williams

If the rotation of the shaft were uniform and there were no lost motion in the shaft or connecting-rod, this diagonal line would repeat itself precisely, and would be a straight line modified by the angular vibration of the connecting-rod. On the other hand, these lost motions and the variations in the rotative speed must be exactly recorded, the latter being exhibited with a degree of accuracy not attainable by computation and plotting, and their correctness would be self-demonstrated. For this purpose this instrument must be found highly valuable, if it is really desired to have these variations revealed rather than concealed.Fig. 5represents the inertia diagram drawn by this instrument applied to a Porter-Allen engine running in the Boston Post Office at the speed of 265 revolutions per minute.Fig. 4shows the same diagram with the transverse motion of the pencil enlarged to correspond with the scale of the indicator, so exhibiting the force actually exerted on the crank-pin at every point, which is represented by the shaded area, and from which the rotative effect on the crank can be computed. The steam pressure absorbed at the commencement of the stroke by the inertia of these parts is represented by the blank area above the atmospheric linexx. This is not all imparted to the crank at the end on account of the compression.

I have myself had no experience in the use of this instrument, but I do not see why it might not be so made that the diagonal line or lines inFig. 4would be drawn at once. The variations of motion would thus be shown much more accurately than they can be by the enlargement of these small indications. This would require the springeto bear the same relation to the inertia of the weighththat the spring of the indicator bears to the steam pressure on its piston area. The steam diagram and the inertia diagram would then be drawn to the same scale. A separate instrument would be required for each scale. It would seem desirable that this instrument, which is not expensive, should be brought before the public in this practical shape.

The 16″×30″ engine exhibited at this fair of the American Institute was sold from the exhibition to the Arlington Mills, at Lawrence, Mass. For a reason that will appear later, I have always regarded this sale as the most important one that I ever made.

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