B

C

is given us by an indicator diagram on a certain scale of lbs. per sq. inch to the inch, thus ABCDE, BCD being the top line of the diagram taken for the particular end we are considering, and AE the bottom line of a diagram from the other end of the cylinder. Then the ordinate between BCD and AE gives us the difference between the steam pressure on the side considered, and that on the other side of the piston, i.e. gives the effective pressure driving the piston.

F

Fig. 160.

D

30

Now, on the same scale as the diagram, set up AF to represent poV.2/ga lbs. per sq. inch, bisect AE in O, and join FO, producing it to cut DE in G.

Then between A and O the pressure which is available to produce crank effort is got by subtracting the ordinate of OF from that of BCD; while between O and B there is, in addition to the ordinate of BCD, an effort produced equivalent to pressure represented by the ordinate of OG. We can represent this total effect by using FG instead of AB as a base to measure from. Then doing this the vertical ordinates between BCD and the base FG represent the effective pressures producing crank effort. The process here given is known as correcting the diagram for inertia.

Fast Running Engines.-The figure as drawn would be for an engine running at medium speed, and it is seen that the effect is to reduce the inequality of pressure caused by an early cut-off. The effect, however, increases very rapidly as the speed increases, since þ∞ V„2, and in fast running engines it becomes of great importance. In such cases F may rise to, and even above B. This latter case is shown in Fig. 161, and what it shows is that, before K, either the crank drags the piston along, the steam pressure not being sufficient

to keep it up, or else—in engines such as Brotherhood's,

B K C

Fig. 161.

D

E

where the connecting-rod bearing does not encircle a gudgeon pin, but simply bears against it so that it cannot pull the end of the rod leaves the piston.

Now, directly we pass K, the piston commences to drive, thus the gudgeon pin, which was bearing against the front brass of the crosshead, Fig. 162 (a), dragging it, now suddenly comes into bearing with the back brass, Fig. 162 (b), being now driven by it. This, of course, causes a knock in the bearing, and exactly the same In the Brotherhood

happens in the crank bearing. engine the piston and connecting rod end would come together, causing a knock there also.

(a)

(b)

Fig. 162.

In the ordinary doubleacting engine this reversal and knock must take place, and the only difference above is that it takes place at K instead of the commencement of the stroke; but in the Brotherhood single-acting engine the avoidance of reversal is one of the chief points aimed at, hence in these the speed is limited by the necessity for keeping F below B.

EXAMPLES.

1. From the diagram drawn for question 2, chap. ix., find the values of the fluctuations of energy, and the corresponding coefficients.

Ans. 22.4, 25.5, 28, 24.9 tons-ft.; .036, .042, .046, .04, coefficients.

2. An engine of 150 H. P. runs at 100 revolutions. Find the weight of a fly-wheel 10 ft. diameter to keep the fluctuation of speed within 2% of the mean speed. Ratio of connecting rod to crank-Ist, 4 to 1; 2d, 6 to 1.

Ans. Ist, k=.1358, whence W=1.76 ton; 2d, k=.1245, whence W=1.61 ton.

3. If there be two of the preceding cylinders on cranks at right angles, what weight of reciprocating parts would render a fly-wheel unnecessary? Stroke 3 ft.

Ans. Each set.

Ist, 19 tons; 2d, 18 tons.

4. A vertical cylinder is supplied with steam of 50 lbs. pressure by gauge, the cut-off is at half stroke, back pressure 16 lbs., diameter of piston 40 ins., piston speed 800 ft. per minute, stroke 3' 6", weight of piston, etc., 2 tons. Find the effective

pressure at each quarter of the up and down strokes.

Ans. Up-Commencement, 2.4; 1st, 16.4; 2d, 30.4; 3d, 27.7; end, 33.4.

Down-Commencement, 9.6; 1st, 23.6; 2d, 37.6; 3d, 34.9; end, 40.6 lbs. per sq. inch.

5. The stroke of an engine running at 250 revolutions is 8 ins., diameter of piston 8 ins., initial steam pressure 55 lbs. Find the greatest weight of piston, etc., which can be allowed, so that the connecting rod may be always in compression. engine is single-acting.

The Ans. 388 lbs.

6. In the first case of question (2), supposing that at the commencement of the stroke the crank shaft is revolving accurately at its mean speed, find the greatest and least speeds, and thus show that the mean speed is practically their arithmetic mean.

CHAPTER XII

DYNAMOMETERS-BRAKES—AND GOVERNORS

WE have fully explained in chap. iv. how the power of an engine, so far as it is shown by its Indicated Horse Power, or I. H. P., is measured. But the I. H. P. of an engine is more truly a measure of the power of the boiler than of the engine, since it gives the energy exerted by the steam, and not the work which the engine can do against the resistance. In the absence of friction, the two quantities mentioned would be equal for a whole period. But in the actual case the work done is less than the energy exerted by an amount depending on the magnitude of the friction of the machinery.

Taking now two engines of equal I. H. P., their commercial value will depend, to a great extent, on the ratio which the work done bears to the energy exerted; or, in other words, on their efficiencies; and hence the determination of the work done by an engine is of quite as much if not more importance than the determination of its I. H. P.

There are two ways in which the work done can be found, viz.—

First, by calculation of the work wasted on friction. For this purpose we should require to know accurately the laws of friction which suit the pressures, velocities, and lubricants employed; these laws are outside our present limits, and, moreover, it is doubtful if they can be given with certainty at all. Then, again, given the

required knowledge, the process would be long and cumbrous. We are thus led to consider the

Second method, an instrument is used which actually measures the work done, as an indicator does the energy exerted.

Instruments for this purpose are called Dynamometers, and they are of two types, the type used depending on the conditions under which the trial is to take place. If the engine is required to carry on its ordinary work while the test is being applied, a Transmission Dynamometer is used; while when the engine can be used for the time entirely for the purposes of the test, an Absorption Dynamometer may be used.

We will now examine the working of one or two examples of both these types, when the reason for their names will appear.

Transmission Dynamometer.-Fig. 163 shows

one form of this type.

A is a pulley on the engine shaft, and B a pulley on the shaft to be driven, and to which the resisting moment is applied. C and D are equal pulleys, mounted on a crosspiece E, of length 27, which can turn round O. A drives B by means of a belt which passes under A, over C and D, and under B.

Now, when A rotates clockwise, the tension T1 on the right-hand side becomes greater than T2 on the left

(see page 120). In passing over C and D, the tensions remain unaltered, except for the very slight friction of the axles, which we neglect. Then the difference of tension T1 - T2 causes B to turn.

2

The arrows in the figure show the directions of the pulls of the belt on the pulleys, and hence we see that