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It is to be observed that the inertia of parts has been ignored; also the cushion. Proceeding under the same supposition, an inspection of Figs. 4 and 5 shows that, up to the point E, it would be better that no steam be admitted to the cylinder, because the resultant work is negative by the amount A G E. The point E corresponds to the angle of repose of the crank, under the supposition that running friction equals standing friction. At the point K, the negative work is just neutralized, and no loss or gain would result by staying the admission of steam so far.

To find the point K, we put the negative work, expressed in terms of O, equal the useful work similarly expressed. That is:

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in which omit the first term of the second member for a first approximation. In a second approximation it may be included.

To find the point E, put the positive and negative moments equal each other.

Hence

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2

(22)

This will give a value of e, equal about half that of Eq. 21 as it evidently should.

In case of a back-pressure P,, lay off a sinusoid, dotted at A P B, Fig. 5, with greatest depth equal to P,; the greatest height of AN B being always equal the effective pressure of admission. Then for W K, Fig. 3, equal two-thirds absolute pressure, lay off P R, Fig. 5, equal two-thirds the height of P N and C. Also then take P1, See

Eq. 17, equal the effective pressure of admission.

EFFICIENCY DETERMINED BY TEMPERATURE.

A journal and box in good running condition, and in continuity of action, must in some way receive and dispense the energy lost in its friction. This can be accounted for in the heat due to the excess of temperature of journal, and radiated, conducted and convected through or to the surrounding medium, usually air. If the amount of heat thus transferred could be accurately measured, that quantity

would furnish an excellent means for calculating the efficiency. Though the means for calculating this heat cannot be applied to ordinary journals with much accuracy, yet a result may be obtained which will serve to check the preceding calculations.

The heat emitted by a body with excess of temperature has been determined by Sir. W. Thomson for a lampblacked surface in air. His result is expressed by the relation

q=AS t° per sec.,

=

where q=the quantity of heat, A=a coefficient of emission, to the excess of temperature, and S-the surface exposed. For q in gramme degrees, S in square centimeters and t° in centigrade,

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one part being due to radiation and the other to conduction and convection of air. The part due to radiation should be modified by the difference in radiating power between a black and an iron surface, the former being to the latter as about six to one. Hence the o As to the part due to conduction and convection,

should be

1 6x800

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I have assumed that, in the experiments for A, the air received heat by contact, and then ascended in currents, it being warmed in the ascent from no excess to the full excess of the iron. The average excess of the current would then be about half that of the iron. To approximate to the current, its buoyancy was found and compared with a wind pressure. An excess of 100° F. was assumed for the bearing, and 50° for the air. A column of 2 feet height was taken as the height of crank of ordinary propeller engines. Then the upward pressure per square foot is about

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This

This will cause a wind current of 176 feet per minute. velocity, compared with average velocity of the parts about a crank as above, is about as 176 to 780 feet, or the crank-motion causes an artificial convection which is about four and a half times as rapid as natural convection at the crank when still. Hence the component in A due to convection should be multiplied by this value, and as the conduction is not largely affected by the condition of surface, we have our value of

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Introducing this, and changing q to thermal units per square foot of surface per 1° Fah. per second, we have:

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EXAMPLES OF EFFICIENCY OF CRANK-BEARINGS.

A few examples are given, mainly to indicate the importance of the results of the investigation, quantitatively.

First-Method by Friction.

For quantitative results of efficiency, a stated value of the coefficient of friction is necessary. To select a value of it from among the great variety of values given by experiment is a matter of judg

ment.

If variability of this coefficient is to be deplored, it is even more fortunate that it is possible to carry its value to the marvelously low figure, relatively, which has been obtained by President Thurston. His values are an incentive to use of good designs, materials and workmanship.

In the hundred-fold range given by President Thurston's extended experiments under various conditions of from .25 to .0025, it will probably be safe to assume that the value of the coefficient will, for ordinary crank-bearings, lie within the ten-fold range of from .05 to .005.

For the example of cranks, I have taken that of the "Iris," as above in Table I., the quantities chiefly concerned in the efficiency being given in the following:

IV. TABLE OF EFFICIENCIES OF CRANK-BEARINGS OF STEAM-ENGINES

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If the .05 is a fair sample of the value of the coefficient of friction for practice, it appears that compound engines have a decided advantage over duplex, as applied to propellers, in the matter of the crank alone; the percentage gained being about four and a half in the case of the actual crank length adopted in the "Iris," and with a twelve to twenty-fold expansion. The thirteen per cent. loss in the extreme case of the duplex is nearly that due to all causes in the turbine water-wheel, and is surely too much to be absorbed by one member of the steam engine, under any circumstances.

It appears that the large crank-bearings necessary in the modern style of marine engine, where several cylinders are put to work on one quick-running crank-shaft, should be compensated for by every means possible.

Probably too little attention has been given to the arrangement of the cylinders in these marine engines. The arrangement of the cranks has been made a subject of much study by marine engineers, with a view to steadiness of motion and of strains. This should not be overlooked as regards efficiency, for reduction of strains reduces bearings, and consequently increases the efficiency; but arrangement of cranks and arrangement of cylinders should be considered together, both leading to important advantages in the efficiency; the part belonging to crank-arrangement being reduction of bearing, while that due to cylinder-arrangement being increased equivalent crank length.

For instance, if the two cylinders of a duplex be situated at right angles, say one with axis vertical, and the other horizontal, and working on the same crank-pin, instead of both being vertical, each with a crank, and at the necessary distance asunder along the shaft; the loss at the crank would be less in the ratio of 1/2 to 2 for the case of non-expansion, but not quite as much in expansion. This result is for a given diameter of crank-bearings, and is seen to be true from the fact that the indicated power is the same each way, but the pressure or thrust against bearings is the diagonal of the square of which the sides, added together, make the thrust when the cylinders are side by side.

Again, if the one high-pressure cylinder could be situated diametrically opposite the two low-pressure ones of a compound engine, with cranks at 180°, and the former have its crank between the two other cranks; also if the work be divided equally between the high and low-pressure, the thrusts against the main crank bearings would be nearly all avoided, and the equivalent single crank would be one of twice the length of the actual cranks. This arrangement, as compared with that where the cylinders are side by side, with main bearings between, will reduce the work lost at crank to one-half, and the

r sin 0-BO-DQ=r sin 0-ƒ (A+α)

where

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is the coefficient of friction (nearly), and A and a the radii of the bearings. Then the moment without friction is Pr sin &; and with friction is P (r sin 6-f(A+a)).

The efficiency of the crank, for one position, is then evidently,

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Next, find the efficiency for the work transmitted from the connecting rod to the main shaft during a half revolution, or during a stroke of the engine, the pressure of steam in the cylinder being regarded as constant throughout the stroke, and transmitted to the connecting rod without loss; also assume, for convenience, that the connecting rod always acts in a line parallel to the axis of the cylinder; that is, the lines FO, BC, DE, GQ, &c., are parallel to that axis.

Then the work of a stroke will be

P. 2 r.

(3)

where 2r=twice the crank radius, stroke, and P=the total pressure on the piston. The work lost by friction for the stroke, taking the coefficient of friction the same for both bearings, will be

Рf. π A+Рf. л а=ƒn (A+α) P.

(4) where ƒ A and fa,=the radii DQ and BO respectively, and 7 times the same being the semicircumferences to those radii, which multiplied by P, give the prejudicial work due to friction, as shown by Fig. 1.

Hence, for the whole stroke, or a half revolution of crank, with constant steam pressure, we have the

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in which coeff. of friction, r-radius of crank, A-radius of main bearing, and a radius of crank pin.

This is, of course, the value also of the efficiency for the return stroke, and for the engine in continuous action.

This is nearly the expression for efficiency of crank of engines worked with the common D slide valve. But a more exact expression for this form of engine will be given later, in examples of cut-off at two-thirds or three-fourths.

It is noticeable that this expression is independent of the pressure of steam; that it diminishes as the coefficient of friction, and the sum of the radii of the crank bearings increase, and that it increases as the length of the crank increases. Regarding the coefficient of friction as constant, this efficiency is constant so long as the sum of the radii of bearings divided by the radius of crank is constant.

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