American Technical Society. # Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) online

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Online Library → American Technical Society → Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) → online text (page 15 of 30)

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height by the strength of the spring we get the desired result.

For instance, if we had used a 30 pound spring (that is one which

causes the pencil of the indicator to move one inch for every 30

pounds pressure in the cylinder) the height 1* inches would

equal 30 X 1| = 45 pounds pressure.

Example. An indicator card has an area of 1.925 square

inches and is 2.2 inches long. If a 60 pound spring is used

what is the mean pressure?

The mean height equals J _ = .875 inch and

.875 X 60 = 52.5 pounds.

INDICATORS. 25

'Suppose the engine from which the above card was taken had

a piston 14 inches in diameter and a stroke of 24 inches. If it

were running at 150 revolutions per minnte what is its horse-

power ? Assume the mean effective pressure to be the same for

both sides of the piston.

1L p = PLAN

33,000

_ 52.5 X 2 X 153.94 X 300

33^000

=147. (about)

In most engines more work is done at one end of the cylinder

that at the other ; it is not safe then to assume the mean effective

pressure of one side the same as that of the other. Cards should

be taken from each end and calculated for mean effective pressure

separately-, then averaged. Also the area of one side of the piston

is greater than the other on account of the piston-rod. The two

ends may be figured separately or the average area of the two sides

of the piston may be used as the vahfe of A.

Another method is to find the work done at each end of the

cylinder and then add the results. This enables the engineer to

know if his valves are set so that each end does about the same

amount of work.

An engine has the following dimensions. The piston is 12

inches in diameter, the piston-rod is 21 inches in diameter and tke

length of stroke is 34 inches. While running at 92 revolutions

cards were taken. The area of the card from the head end was

5.36 square inches, that of the crank end was 5.30 square inches,

and a 40 pound spring was used. The cards were 3.72 inches

long. We wish to know what horse-power the engine developed

and which end was doing the most work.

The area of the piston is 113.097 square inches for the head

end and 113.097 3.5466 = 109.55 square inches for the crank

end.

Then for the head end,

T p P LAN P X 34 X 113.097 X 92 RQqq p

-33,000 "llTxlipOO -

and for the crank end,

HP- PL AN _ P X 34 X 109.55 X 92 _ p

H - F- ~ 33,000 -12"X~-

809

26 INDICATORS.

The value of P is found from the cards. Since the cards

were 3.72 inches long and the area of the card from the head end

r of*

was 5.36 square inches the mean ordinate is ' . = 1.44 inches

which equals 1.44 X 40 = 57.6 pounds. The horse-power would

be,

.8933 X 57.6 = 51.45

For the crank end the mean effective pressure is found as

before,

J 5 ^ 3 = 1.425 and 1.425 X 40 = 57.

3.72

The horse-power would be,

.8653 X 57 = 49.32

The horse-power is evidently the sum of these two quantities

or 51.45 + 49.32 = 100.77.

The head end is doing more work than the crank end but the

difference is slight being only,

51.45 49.32 = 2.13 horse-power,

or about 2.1 per cent, of the total power.

Considerable arithmetical work is necessary when the I. JI. P.

is found from the formula,

pi A XT

I. II. P. = J -

33,000

and the chances for error are of course, great. To Safe time and

reduce the chance for error a table of engine constants has been

prepared. The number of strokes, or twice the number of revo-

lutions, multiplied by the length of stroke in feet is called the

PLAN

piston speed. Then in the formula 1. H. P. ==_ , L N =

33,000

piston speed in feet per minute. In the following table, the I. H. P.

of an engine is easily computed by multiplying the constant, cor-

responding to the diameter of the piston, by the piston speed and

by the M. E. P. Or, in other words, the constants in the table

equal the horse-power for an engine with a given diameter of

piston having a piston speed of one foot per minute and a M. E. P.

of one pound.

210

INDICATORS

TABLE OF ENGINE CONSTANTS.

Even

Inches.

0000952

.0002142

.0008568

.0011662

.0015232

.0019278

.0046648

.0053550

.0077112

.0095200

.0104S58

.0115192

.0125902

.0137088

.0148750

.0173502

.0186592

.0214200

.0228718

.0243712

.0259182

.0275128

.0291550

.0325822

.0343672

.010007;-:

.0440062

.0460768

.0481950

.0503608

.0525742

.0548352

.0571438

.0668542

.0694008

.0719950

.0773262

.0800632

.0828478

+ 1

.0000301

.0001074

.onoior.o

.0006251

.0015711

.0019817

.0047484

.0054446

.0069797

.0078187

.0106211

.0116505

.0127274

.0138519

.0150241

.0162439

.0175112

.0201887

.0245619

.0261149

.0277155,

.0310594

.0345937

.0364322

.0383184

.0402521

.0422335

.0442624

.0484631

.0528542

.0551212

.0574357

.0597979

.0622076

.0646649

.0671699

.0697225

.0749704

.0776657

.0804087

+ 1

.0000372

.0001205

.0002514

.0004299

.0006560

.0009297

.0012510

.0016198

.0025004

.0030121

.0035714

.0041783

.0055349

.0062847

.0070819

.0079268

.0107472

.0117825

.0151739

.0163997

.0176729

.0217785

.0232422

.0247535

.0279189

.040-1972

.0445194

.0466019

.0487320

.0509097

.0531349

.0554079

.0577284

.0600965

.0625122

.0674864

.0700449

.0726510

.0753047

.0780060

.0807549

+1

or

.375.

.0000450

.0001342

.0002711

.0004554

.0006876

.0009672

.0012944

.0025618

.0030794

.0036447

.0042576

.0049181

.0056261

.0063817

.0071850

.0108739

.0119152

.0130040

.0141405

.0153216

.0165563

.0178355

.0191624

.0249457

.0265106

.0281231

.0297831

.0314908

.03.50489

.0387973

.0407430

.0427362

.0447771

.0490016

.0511853

.0534165

.0556953

.0729801

.0756398

.0783476

.0811019

.0000535

.0001487

.0002915

.0004819

.0007199

.0010055

.0013387

.0017195

.0021479

.0031475

.0037187

.0043375

.0057179

.0064795

.0072887

.0081452

.0090499

.0100019

.0110015

.0120487

.0131435

.0142859

.0154759

.0167135

.0207119

.0221399

.0236155

.0251387

.0267095

.0450355

.0471299

.0492719

.0514615

.0559835

.0655987

.0681215

.0759755

.0786887

.0814495

.0842579

.0871139

+ *

or

.625.

.0001640

.0003127

.0005091

.0007530

.0010445

.0013837

.0017705

.0022048

.0032163

.0037934

.0044182

.0050906

.0058105

.0065780

.0082560

.0091663

.0101243

.0111299

.0121830

.0132837

.0144321

.0156280

.0168716

.0181627

.0195015

.0223218

.0238033

.0253325

.03020.56

.0319251

.0336922

.0355070

.0432420

.0452947

.0473951

.0495430

.0517386

.0562725

.0634304

.0659115

.0684402

.0710166

.0736406

.0763120

.0790312

.0817980

.0874743

+ 1

or

.75.

+ 5

or

.875.

.0000729

.0003347

.0005370

.0007869

.0010844

.0014295

.0018222

.0027502

.0044997

.0051780

.0059039

.0066774

.0074985

.0083672

.0102474

.0112589

.0123179

.0134247

.0145789

.0157809

.0170304

.0183275

.0196722

.0210645

.0225044

.0271097

.0287399

.0304179

.0321434

.0357372

.0376055

.0414849

.0434959

.0455547

.0476609

.0498149

.0520164

.0542655

.0588066

.0637379

.0662250

.0687597

.0713419

.0739719

.0766494

.0793745

.0821472

.0849675

.0000837

.0001967

.0003.574

.0005656

.0008215

.0011249

.0014759

.0018746

.0023-209

.0028147

.0033561

.0039452

.004,5819

.0052661

.0059979

.0067774

.0076044

.0084791

.0094013

.0103712

.0113886

.0124537

.0135664

.0147266

.0159345

.0171899

.0184929

.0198436

.0212418

.0226877

.0241812

.0257222

.0273109

.0289471

.0306309

.0323624

.0341415

.0397642

.0417337

.0437507

.0458154

.0479276

.0508875

.0522949

.0545499

.0568526

.0592029

.06161107

.0640462

.0665392

.0690799

.0716681

.0743039

.0769874

.0797185

.0824971

.08,53234

.0881973

211

28

INDICATORS.

To Use the Table. If the diameter of the piston is an even

number, the constant is found in the second column ; if it contains

a fraction the constant is found by following the column horizon-

tally until the required fraction is reached. The constant multi-

plied by the piston speed in feet per minute ar.d by the M. E. P.

in pounds per square inch gives the I. H. P.

Example. An engine runs at 75 revolutions. The stroke is

4 feet; if the M. E. P,. is 48 pounds and the piston 27f inches in

diameter what is the I. H. P.

From the table the constant for a piston 27 1 inches in diam

eter is .0178355. The piston speed is 150 X 4 = 600 feet per

minute. Then the I. H. P. is,

.0178355 X 600 X 48 = 513.66

The horse-power as above calculated is called the indicated

horse-power and is usually written I. H. P. Although the above

calculation shows the amount of power the engine develops it does

Fig, 18.

not show the available power since part of the indicated horse-

power is used to run the engine itself, that is, to overcome the

friction of the parts. To determine how much power can be used

to run machinery some form of absorption dynamometer or friction

brake is attached to the engine. The power thus obtained is

called the Brake Horse Power or B. H. P. It is more satisfactory

for both the owner and builder to know the B. H. P. than to know

the I. H. P.

The Prony Brake, Fig. 18, is one of the simplest absorption

dynamometers. The two wooden blocks A and C are held together

against the rim of the pulley P by bolts . The thumb-nuts, e, , being

212

INDICATORS. 29

used to adjust the pressure. By means of the bolts the arm L is

held tp the upper block. From this arm is suspended the ball

weight, w, which by sliding along the arm counterbalances the

weight of the arm and pan at the other end. The pulley revolves

at the required speed in the direction indicated by the arrow.

The bolts are tightened until the lever remains stationary in a

horizontal position when a known weight, W, is hung at the end.

The amount of work absorbed by the brake depends upon the

weight W, the length, R, and the speed. It is independent of

the diameter of the pulley and the pressure of the block because

the moments of force about the center of the pulley are equal

when the lever L, is horizontal. Letting/ equal the co-efficient

of friction, p the pressure of the blocks and r the radius of the

pulley,

fpr = WR

The work done at the face of the pulley equals the force mul-

tiplied by the distance or the pressure multiplied by the number

of feet passed through.

Let N = the number of revolutions per minute. Then the

distance passed through per minute equals 2 TT r N and the work

done equals 2 TT r N f p. Then &&fp r =' W R, the work done

at the rim of the pulley equals the left hand side of the equation

multiplied by 2 TT N, and to keep both sides equal we multiply

W R by 2 TT N. Hence the work done is expressed by the formula

2 TT N W R and,

B p 27rN WR

33,000

= .0001904 N W R

A Prony brake with an arm 4 feet long was attached to the

pulley on the fly wheel of an engine. The weight in the scale

pan was 50 pounds and the speed of the engine 300 revolutions.

Find the brake horse power.

B. H. P. = .0001904 X 300 X 50 X 4

= 11.424

The rope brake shown in Fig. 19 is easily constructed of

material at hand and being self-adjusting needs no accurate fitting.

For large powers the number of ropes may be increased. It is con-

sidered a most convenient and reliable brake. In Fig. 19 the spring

213

30

INDICATORS.

balance, B, is shown in a horizontal position. This is not at all

necessary ; if convenient the vertical position may be used. The

ropes are held to the pulley or fly-wheel face by blocks of wood, O.

The weights at W may be replaced by a spring balance if

desirable.

To calculate the Brake Horse Power, subtract the pull regis-

tered -by the spring balance, B, from the load at W. The lever

arm is the radius of the pulley plus i the diameter of the rope.

The formula is,

BMP- 2?rRN (W B)

33,000

= .0001904 RN(W-B)*

Example. A rope brake is attached to a gas engine. The

average reading of the spring balance is 8 pounds. W = 80

pounds. If the radius of the brake wheel is 28 inches and the

rope 1 inch in diameter, what is the B. H. P. when the engine

makes 350 revolutions per minute ?

11 = 28 + l = 28 inches = ^ feet

B. II. P = .0001004 EN (W B)'

= .0001004 x 2 - X 72 X 350

= 11.4 Ans

If both the indicated horse-power and the brake horse-power

* NOTE: If B is greater than W, the engine is running in the opposite

direction. Use the formula B. H. P. = .0001904 R N (B W) .

214

INDICATORS. 31

are known the power used in friction is found by subtracting the

B. H. P. from the I. II. P.

The mechanical efficiency of the engine is the ratio of the

B. H. P. to the I. H. P. or,

E= JB.H.P.

I. H. P.

If an engine of 18.2 indicated horse-power develops at a trial

16.02 brake horse-power, what is its mechanical efficiency?

E= B - " P -

I. H. P.

= -l 6 ^ = .88

18.2

= 88 % Efficiency.

Brakes should be well lubricated. For small powers the

heat generated by friction between the ropes or blocks and the

rim of the wheel, will be conducted away by radiation but for

large powers some additional means is necessary. In case there

are flanges on the wheel, water can be introduced into the wheel,

the flanges keeping it from flowing out and centrifugal force keep-

ing it in contact with the rim. The. amount of water can be regu-

lated so that all may be evaporated, or a scoop can be arranged to

carry off the water. In all cases the water should flow

continuously.

To Find the Area of Cards. M. E. P. or the mean effective

pressure is equal to the area of the indicator diagram divided by

the length. The length is easily found by measurement but to

find the area is more difficult since the shape is irregular. If the

figure were regular its area could be found by geometry or by

simple formulas.

The area of the indicator card can be found in two ways.

By dividing the diagram into sections and by the use of a plani-

meter. The former is only an approximate method ; the area thus

found is nearly correct if the number of divisions is great.

Tangents at each end, perpendicular to the atmospheric line

are first drawn. The horizontal distance between these tangents

is then divided into 10 or more equal parts. The horizontal length

of each section is then divided into two equal parts and lines per-

pendicular to the atmospheric line drawn through these points of

215

INDICATORS.

division. The sum of the lengths of all these lines is divided l>y

the number of lines to get the average. This average length or

average ordinate multiplied "by the scale of spring gives the mean

effective pressure.

Fig. 20 is the card from the crank end of an engine. The

DL

Fig. 20.

line C L is the atmospheric line and the lines A D and E F are

drawn perpendicular to it and tangent to the extreme ends of the

diagram. The line A E is divided into 1 equal parts and lines

Fig. 21.

are drawn through points marking the centers of the divisions.

On each of these lines the length is marked. The sum of the

lengths is 15.18 and 15.18 divided by 10 is 1.518. If the scale

of spring is 40 pounds, 1.518 multiplied by 40 is the M. E. P. or

0.7 = M. E. P.

216

INDICATORS.

33

The liorizontal lengtli may be divided into any number of

?qual parts but 10 or 20 makes the computation easy. The oper-

ation of finding the M. E. P. for the head end is exactly the same.

The average M. E. P. for one revolution of the engine is the

average of the two mean effective pressures."

In case the diagram is very irregular it should be divided

into 20 equal parts instead of 10. If there is a loop in the dia-

gram as shown in Fig. 21 the area of the loop must be subtracted

from the area of the other part as it represents work done by the

piston on the steam and therefore loss.

The lengths may be marked off on a piece of paper if a good

scale is not at hand.

A more accurate result is obtained by using an instrument

called the planimeter. There are several planimeters and aver-

aging instruments in common use for determining the mean effec-

tive pressure of indicator cards. The planimeter shown in Fig.

217

34 INDICATORS.

22 is one of the most simple and is called the Amsler Polar Plani-

meter from its inventor Prof. Amsler. The cut is about one-half

the size of the instrument. It consists of two arniB free to move

about a pivot and a roller graduated in inches and tenths of

inches. A vernier is placed with the roller so the areas may be

read in hundredths of a square inch. The point A is kept sta-

tionary and the tracer B is moved once around the outline of the

diagram. The area in square inches of the diagram is read from

the roller C and the vernier E.

To Use the Planimeter. The diagram should be fastened to

some flat unglazed surface, such as a drawing board, by means of

thumb tacks, springs or pins. The point A is pressed into the

paper so that it will hold in place. The point B is set at any

point in the outline of the diagram and the roller set at zero.

Follow the outline of the diagram carefully in the direction of

the hands of a watch as indicated by the arrows in Fig. 22 until

the tracer has moved completely around the diagram. The result

is then read to hundredths of an inch from the roller. Suppose

after tracing over the outline we find that the largest figure that

has passed the zero of the vernier is 3 ; the number of graduations

(tenths) that have passed the zero to be 5 and the number

(hundredths) of the graduations in the roller that exactly coincides

with a graduation on the vernier to be 9. Then the area is 8.59

square inches.

Often at the start the roller is not adjusted so that the zeros

coincide but the reading is taken and subtracted from the final

reading. Thus if the first reading is 4.63 and the second 7.31 the

area is 7.31 4.63 = 2.68 square inches. In case the second

reading is less than the first, add 10 to the second reading then

subtract.

This instrument is very valuable to an engineer who takes

indicator cards. The results obtained are very accurate, the error

being small. Ten or twelve diagrams can be measured by this

instrument in the same time that is necessary to measm-e a single

card by the method of ordinates.

It is well to run over the area three or four times and take

an average as the tracing of the diagram cannot be absolutely COP

rect at any time.

218

INDICATORS.

THERHAL EFFICIENCY.

The thermal efficiency of the steam engine is found in the

same manner as that of any other heat engine. The efficiency

depends upon the limits of temperature and not upon the nature

of the working medium.

Let T l absolute temperature of the heat received by the engine.

T 2 = absolute temperature of the heat rejected by the engine.

E = efficiency of engine.

Then,

or, the efficiency equals the temperature of the heat rejected, sub-

tracted from the temperature of the heat received and the result

divided by the temperature of the heat received.

Suppose an engine is supplied with steam at 120 pounds

absolute pressure and the exhaust is atmospheric pressure. What

is the efficiency?

The absolute temperature corresponding to 120 pounds abso-

lute pressure is 341.05 -j- 461 and the temperature of atmos-

pheric pressure is212 + 461.

Then,

802.05 673

E = - _ = .16 or 16 per cent.

802.05

If the engine had been of the condensing type and the

exhaust pressure one pound above the vacuum, the efficiency

would be as follows :

The temperature of one pound absolute pressure is 101.99

+ 461.

E = W*M=_6***_ = Qr per cent>

802.05

In actual engines this efficiency cannot be obtained localise

the difference between the amount of heat received and that

rejected is not all converted into work. Part of it is lost by

radiation, conduction, leakage, etc. Also cylinder condensation

reduces the efficiency.

The Theoretical Indicator Diagram. An indicator diagram

is the result of two movements ; a horizontal movement of the

219

36 INDICATORS.

paper and a vertical movement of the pencil. The horizontal

movement exactly corresponds to the movement of the piston of

the engine and the vertical movement exactly corresponds to the

pressure of steam in the cylinder.

The shape of the indicator card depends upon the manner in

which steam is admitted to and released from the cylinder. Dif-

ferent engines give different shaped indicator cards and the cards

taken from an engine vary with the conditions. Figs. 1 and 2

show theoretical indicator cards from a non-condensing engine

without clearance ; the former being for the case that has admis-

sion during the whole stroke. The diagram of Fig. 2 shows the

cut off at ^ stroke. All practical engines have clearance and

slight compression ; so the theoretical diagram assumes the shape

shown in Fig. 23. In this card

the admission line H A is verti-

cal, the steam line A C is hori-

zontal, the expansion line C D

an hyperbolic curve, the exhaust

line D B vertical, the back pres-

sure line B F horizontal and the

compression curve an hyperbola.

The actual shape is somewhat

rig ' 23 * different from the theoretical

mainly because the valves do not open and close quickly, the ports

offer some resistance to the passage of the steam and the back

pressure is neither atmospheric in the non-condensing engine nor

absolute vacuum in the condensing engine.

The diagram shown in Fig. 24 is a practical diagram and

like those taken from engines.

The atmospheric line L M is the line drawn by the pencil of

the indicator when the connection to the engine is closed and both

sides of the piston of the indicator are open to the atmosphere.

It is the zero of the steam gage.

The admission line H A shows the rise of pressure due to the

admission of steam to the cylinder. If the steam is admitted

quickly when the engine is nearly on dead center this line will l>e

very nearly vertical.

The steam line A C is drawn while the valve admits steam

220

INDICATORS.

to the ' cylinder. This line is horizontal if there is no wire-

drawing.

The point of cut off C, indicates the point at which the

admission of steam is stopped by the closing of the valve. This

point is rounding since the valve closes slowly. Sometimes it is

difficult to determine the exact point where cut off takes place ; it

is usually where the curve changes from concave to convex.

The expansion curve C D shows the fall in pressure as the

ssteam expands while the piston moves toward the end of the stroke.

The point of release D shows the point at which the exhaust

N

Fig. 24.

valve opens. The rounding is due to the slow action of the valve

when opening. Because of this slow action of the valve, release

begins a little before the end of the forward stroke.

The exhaust line D E F represents the loss in pressure which

occurs while the valve opens to exhaust at and near the end of the

stroke.

The back pressure line F G shows the back pressure against

which the piston acts during the return stroke. For a condens-

ing engine this line is below the atmospheric line L M, the dis-

tance below being dependent upon the state of the vacuum in the

condenser. For cards taken from a non-condensing engine the

back pressure line is a little above the atmospheric line.

The point of exhaust closure G is the point where the valve

221

INDICATORS.

closes to exhaust. The exact point is not clearly denned as the

curve shows a change of pressure due to the gradual closing of the

valve. -

The compression curve G II shows the rise of pressure due

to the compression of the steam remaining in the cylinder after

the valve has closed to exhaust.

The zero line of pressure or line of absolute vacuum O X is

drawn below and parallel to the atmospheric line. The distance

between the lines O X and L M represents 14.7 pounds pressure.

The clearance line O Y is drawn perpendicular to the line of

absolute vacuum and at a distance from the end of the diagram

_l _2 ^3 4 5

Fig. 25.

equal to the same per cent, of the length of the diagram as the

clearance volume is of the piston displacement, or

L N clearance volume

L M volume of cylinder

It is readily seen that the area of an actual indicator diagram

is less than that of a theoretical card." This is because of the

round corners at cut off and exhaust, the back pressure and the

compression. Sometimes it is useful, especially in designing

engines, to draw the theoretical indicator card.

222

INDICATORS. 9

For instance, if we had used a 30 pound spring (that is one which

causes the pencil of the indicator to move one inch for every 30

pounds pressure in the cylinder) the height 1* inches would

equal 30 X 1| = 45 pounds pressure.

Example. An indicator card has an area of 1.925 square

inches and is 2.2 inches long. If a 60 pound spring is used

what is the mean pressure?

The mean height equals J _ = .875 inch and

.875 X 60 = 52.5 pounds.

INDICATORS. 25

'Suppose the engine from which the above card was taken had

a piston 14 inches in diameter and a stroke of 24 inches. If it

were running at 150 revolutions per minnte what is its horse-

power ? Assume the mean effective pressure to be the same for

both sides of the piston.

1L p = PLAN

33,000

_ 52.5 X 2 X 153.94 X 300

33^000

=147. (about)

In most engines more work is done at one end of the cylinder

that at the other ; it is not safe then to assume the mean effective

pressure of one side the same as that of the other. Cards should

be taken from each end and calculated for mean effective pressure

separately-, then averaged. Also the area of one side of the piston

is greater than the other on account of the piston-rod. The two

ends may be figured separately or the average area of the two sides

of the piston may be used as the vahfe of A.

Another method is to find the work done at each end of the

cylinder and then add the results. This enables the engineer to

know if his valves are set so that each end does about the same

amount of work.

An engine has the following dimensions. The piston is 12

inches in diameter, the piston-rod is 21 inches in diameter and tke

length of stroke is 34 inches. While running at 92 revolutions

cards were taken. The area of the card from the head end was

5.36 square inches, that of the crank end was 5.30 square inches,

and a 40 pound spring was used. The cards were 3.72 inches

long. We wish to know what horse-power the engine developed

and which end was doing the most work.

The area of the piston is 113.097 square inches for the head

end and 113.097 3.5466 = 109.55 square inches for the crank

end.

Then for the head end,

T p P LAN P X 34 X 113.097 X 92 RQqq p

-33,000 "llTxlipOO -

and for the crank end,

HP- PL AN _ P X 34 X 109.55 X 92 _ p

H - F- ~ 33,000 -12"X~-

809

26 INDICATORS.

The value of P is found from the cards. Since the cards

were 3.72 inches long and the area of the card from the head end

r of*

was 5.36 square inches the mean ordinate is ' . = 1.44 inches

which equals 1.44 X 40 = 57.6 pounds. The horse-power would

be,

.8933 X 57.6 = 51.45

For the crank end the mean effective pressure is found as

before,

J 5 ^ 3 = 1.425 and 1.425 X 40 = 57.

3.72

The horse-power would be,

.8653 X 57 = 49.32

The horse-power is evidently the sum of these two quantities

or 51.45 + 49.32 = 100.77.

The head end is doing more work than the crank end but the

difference is slight being only,

51.45 49.32 = 2.13 horse-power,

or about 2.1 per cent, of the total power.

Considerable arithmetical work is necessary when the I. JI. P.

is found from the formula,

pi A XT

I. II. P. = J -

33,000

and the chances for error are of course, great. To Safe time and

reduce the chance for error a table of engine constants has been

prepared. The number of strokes, or twice the number of revo-

lutions, multiplied by the length of stroke in feet is called the

PLAN

piston speed. Then in the formula 1. H. P. ==_ , L N =

33,000

piston speed in feet per minute. In the following table, the I. H. P.

of an engine is easily computed by multiplying the constant, cor-

responding to the diameter of the piston, by the piston speed and

by the M. E. P. Or, in other words, the constants in the table

equal the horse-power for an engine with a given diameter of

piston having a piston speed of one foot per minute and a M. E. P.

of one pound.

210

INDICATORS

TABLE OF ENGINE CONSTANTS.

Even

Inches.

0000952

.0002142

.0008568

.0011662

.0015232

.0019278

.0046648

.0053550

.0077112

.0095200

.0104S58

.0115192

.0125902

.0137088

.0148750

.0173502

.0186592

.0214200

.0228718

.0243712

.0259182

.0275128

.0291550

.0325822

.0343672

.010007;-:

.0440062

.0460768

.0481950

.0503608

.0525742

.0548352

.0571438

.0668542

.0694008

.0719950

.0773262

.0800632

.0828478

+ 1

.0000301

.0001074

.onoior.o

.0006251

.0015711

.0019817

.0047484

.0054446

.0069797

.0078187

.0106211

.0116505

.0127274

.0138519

.0150241

.0162439

.0175112

.0201887

.0245619

.0261149

.0277155,

.0310594

.0345937

.0364322

.0383184

.0402521

.0422335

.0442624

.0484631

.0528542

.0551212

.0574357

.0597979

.0622076

.0646649

.0671699

.0697225

.0749704

.0776657

.0804087

+ 1

.0000372

.0001205

.0002514

.0004299

.0006560

.0009297

.0012510

.0016198

.0025004

.0030121

.0035714

.0041783

.0055349

.0062847

.0070819

.0079268

.0107472

.0117825

.0151739

.0163997

.0176729

.0217785

.0232422

.0247535

.0279189

.040-1972

.0445194

.0466019

.0487320

.0509097

.0531349

.0554079

.0577284

.0600965

.0625122

.0674864

.0700449

.0726510

.0753047

.0780060

.0807549

+1

or

.375.

.0000450

.0001342

.0002711

.0004554

.0006876

.0009672

.0012944

.0025618

.0030794

.0036447

.0042576

.0049181

.0056261

.0063817

.0071850

.0108739

.0119152

.0130040

.0141405

.0153216

.0165563

.0178355

.0191624

.0249457

.0265106

.0281231

.0297831

.0314908

.03.50489

.0387973

.0407430

.0427362

.0447771

.0490016

.0511853

.0534165

.0556953

.0729801

.0756398

.0783476

.0811019

.0000535

.0001487

.0002915

.0004819

.0007199

.0010055

.0013387

.0017195

.0021479

.0031475

.0037187

.0043375

.0057179

.0064795

.0072887

.0081452

.0090499

.0100019

.0110015

.0120487

.0131435

.0142859

.0154759

.0167135

.0207119

.0221399

.0236155

.0251387

.0267095

.0450355

.0471299

.0492719

.0514615

.0559835

.0655987

.0681215

.0759755

.0786887

.0814495

.0842579

.0871139

+ *

or

.625.

.0001640

.0003127

.0005091

.0007530

.0010445

.0013837

.0017705

.0022048

.0032163

.0037934

.0044182

.0050906

.0058105

.0065780

.0082560

.0091663

.0101243

.0111299

.0121830

.0132837

.0144321

.0156280

.0168716

.0181627

.0195015

.0223218

.0238033

.0253325

.03020.56

.0319251

.0336922

.0355070

.0432420

.0452947

.0473951

.0495430

.0517386

.0562725

.0634304

.0659115

.0684402

.0710166

.0736406

.0763120

.0790312

.0817980

.0874743

+ 1

or

.75.

+ 5

or

.875.

.0000729

.0003347

.0005370

.0007869

.0010844

.0014295

.0018222

.0027502

.0044997

.0051780

.0059039

.0066774

.0074985

.0083672

.0102474

.0112589

.0123179

.0134247

.0145789

.0157809

.0170304

.0183275

.0196722

.0210645

.0225044

.0271097

.0287399

.0304179

.0321434

.0357372

.0376055

.0414849

.0434959

.0455547

.0476609

.0498149

.0520164

.0542655

.0588066

.0637379

.0662250

.0687597

.0713419

.0739719

.0766494

.0793745

.0821472

.0849675

.0000837

.0001967

.0003.574

.0005656

.0008215

.0011249

.0014759

.0018746

.0023-209

.0028147

.0033561

.0039452

.004,5819

.0052661

.0059979

.0067774

.0076044

.0084791

.0094013

.0103712

.0113886

.0124537

.0135664

.0147266

.0159345

.0171899

.0184929

.0198436

.0212418

.0226877

.0241812

.0257222

.0273109

.0289471

.0306309

.0323624

.0341415

.0397642

.0417337

.0437507

.0458154

.0479276

.0508875

.0522949

.0545499

.0568526

.0592029

.06161107

.0640462

.0665392

.0690799

.0716681

.0743039

.0769874

.0797185

.0824971

.08,53234

.0881973

211

28

INDICATORS.

To Use the Table. If the diameter of the piston is an even

number, the constant is found in the second column ; if it contains

a fraction the constant is found by following the column horizon-

tally until the required fraction is reached. The constant multi-

plied by the piston speed in feet per minute ar.d by the M. E. P.

in pounds per square inch gives the I. H. P.

Example. An engine runs at 75 revolutions. The stroke is

4 feet; if the M. E. P,. is 48 pounds and the piston 27f inches in

diameter what is the I. H. P.

From the table the constant for a piston 27 1 inches in diam

eter is .0178355. The piston speed is 150 X 4 = 600 feet per

minute. Then the I. H. P. is,

.0178355 X 600 X 48 = 513.66

The horse-power as above calculated is called the indicated

horse-power and is usually written I. H. P. Although the above

calculation shows the amount of power the engine develops it does

Fig, 18.

not show the available power since part of the indicated horse-

power is used to run the engine itself, that is, to overcome the

friction of the parts. To determine how much power can be used

to run machinery some form of absorption dynamometer or friction

brake is attached to the engine. The power thus obtained is

called the Brake Horse Power or B. H. P. It is more satisfactory

for both the owner and builder to know the B. H. P. than to know

the I. H. P.

The Prony Brake, Fig. 18, is one of the simplest absorption

dynamometers. The two wooden blocks A and C are held together

against the rim of the pulley P by bolts . The thumb-nuts, e, , being

212

INDICATORS. 29

used to adjust the pressure. By means of the bolts the arm L is

held tp the upper block. From this arm is suspended the ball

weight, w, which by sliding along the arm counterbalances the

weight of the arm and pan at the other end. The pulley revolves

at the required speed in the direction indicated by the arrow.

The bolts are tightened until the lever remains stationary in a

horizontal position when a known weight, W, is hung at the end.

The amount of work absorbed by the brake depends upon the

weight W, the length, R, and the speed. It is independent of

the diameter of the pulley and the pressure of the block because

the moments of force about the center of the pulley are equal

when the lever L, is horizontal. Letting/ equal the co-efficient

of friction, p the pressure of the blocks and r the radius of the

pulley,

fpr = WR

The work done at the face of the pulley equals the force mul-

tiplied by the distance or the pressure multiplied by the number

of feet passed through.

Let N = the number of revolutions per minute. Then the

distance passed through per minute equals 2 TT r N and the work

done equals 2 TT r N f p. Then &&fp r =' W R, the work done

at the rim of the pulley equals the left hand side of the equation

multiplied by 2 TT N, and to keep both sides equal we multiply

W R by 2 TT N. Hence the work done is expressed by the formula

2 TT N W R and,

B p 27rN WR

33,000

= .0001904 N W R

A Prony brake with an arm 4 feet long was attached to the

pulley on the fly wheel of an engine. The weight in the scale

pan was 50 pounds and the speed of the engine 300 revolutions.

Find the brake horse power.

B. H. P. = .0001904 X 300 X 50 X 4

= 11.424

The rope brake shown in Fig. 19 is easily constructed of

material at hand and being self-adjusting needs no accurate fitting.

For large powers the number of ropes may be increased. It is con-

sidered a most convenient and reliable brake. In Fig. 19 the spring

213

30

INDICATORS.

balance, B, is shown in a horizontal position. This is not at all

necessary ; if convenient the vertical position may be used. The

ropes are held to the pulley or fly-wheel face by blocks of wood, O.

The weights at W may be replaced by a spring balance if

desirable.

To calculate the Brake Horse Power, subtract the pull regis-

tered -by the spring balance, B, from the load at W. The lever

arm is the radius of the pulley plus i the diameter of the rope.

The formula is,

BMP- 2?rRN (W B)

33,000

= .0001904 RN(W-B)*

Example. A rope brake is attached to a gas engine. The

average reading of the spring balance is 8 pounds. W = 80

pounds. If the radius of the brake wheel is 28 inches and the

rope 1 inch in diameter, what is the B. H. P. when the engine

makes 350 revolutions per minute ?

11 = 28 + l = 28 inches = ^ feet

B. II. P = .0001004 EN (W B)'

= .0001004 x 2 - X 72 X 350

= 11.4 Ans

If both the indicated horse-power and the brake horse-power

* NOTE: If B is greater than W, the engine is running in the opposite

direction. Use the formula B. H. P. = .0001904 R N (B W) .

214

INDICATORS. 31

are known the power used in friction is found by subtracting the

B. H. P. from the I. II. P.

The mechanical efficiency of the engine is the ratio of the

B. H. P. to the I. H. P. or,

E= JB.H.P.

I. H. P.

If an engine of 18.2 indicated horse-power develops at a trial

16.02 brake horse-power, what is its mechanical efficiency?

E= B - " P -

I. H. P.

= -l 6 ^ = .88

18.2

= 88 % Efficiency.

Brakes should be well lubricated. For small powers the

heat generated by friction between the ropes or blocks and the

rim of the wheel, will be conducted away by radiation but for

large powers some additional means is necessary. In case there

are flanges on the wheel, water can be introduced into the wheel,

the flanges keeping it from flowing out and centrifugal force keep-

ing it in contact with the rim. The. amount of water can be regu-

lated so that all may be evaporated, or a scoop can be arranged to

carry off the water. In all cases the water should flow

continuously.

To Find the Area of Cards. M. E. P. or the mean effective

pressure is equal to the area of the indicator diagram divided by

the length. The length is easily found by measurement but to

find the area is more difficult since the shape is irregular. If the

figure were regular its area could be found by geometry or by

simple formulas.

The area of the indicator card can be found in two ways.

By dividing the diagram into sections and by the use of a plani-

meter. The former is only an approximate method ; the area thus

found is nearly correct if the number of divisions is great.

Tangents at each end, perpendicular to the atmospheric line

are first drawn. The horizontal distance between these tangents

is then divided into 10 or more equal parts. The horizontal length

of each section is then divided into two equal parts and lines per-

pendicular to the atmospheric line drawn through these points of

215

INDICATORS.

division. The sum of the lengths of all these lines is divided l>y

the number of lines to get the average. This average length or

average ordinate multiplied "by the scale of spring gives the mean

effective pressure.

Fig. 20 is the card from the crank end of an engine. The

DL

Fig. 20.

line C L is the atmospheric line and the lines A D and E F are

drawn perpendicular to it and tangent to the extreme ends of the

diagram. The line A E is divided into 1 equal parts and lines

Fig. 21.

are drawn through points marking the centers of the divisions.

On each of these lines the length is marked. The sum of the

lengths is 15.18 and 15.18 divided by 10 is 1.518. If the scale

of spring is 40 pounds, 1.518 multiplied by 40 is the M. E. P. or

0.7 = M. E. P.

216

INDICATORS.

33

The liorizontal lengtli may be divided into any number of

?qual parts but 10 or 20 makes the computation easy. The oper-

ation of finding the M. E. P. for the head end is exactly the same.

The average M. E. P. for one revolution of the engine is the

average of the two mean effective pressures."

In case the diagram is very irregular it should be divided

into 20 equal parts instead of 10. If there is a loop in the dia-

gram as shown in Fig. 21 the area of the loop must be subtracted

from the area of the other part as it represents work done by the

piston on the steam and therefore loss.

The lengths may be marked off on a piece of paper if a good

scale is not at hand.

A more accurate result is obtained by using an instrument

called the planimeter. There are several planimeters and aver-

aging instruments in common use for determining the mean effec-

tive pressure of indicator cards. The planimeter shown in Fig.

217

34 INDICATORS.

22 is one of the most simple and is called the Amsler Polar Plani-

meter from its inventor Prof. Amsler. The cut is about one-half

the size of the instrument. It consists of two arniB free to move

about a pivot and a roller graduated in inches and tenths of

inches. A vernier is placed with the roller so the areas may be

read in hundredths of a square inch. The point A is kept sta-

tionary and the tracer B is moved once around the outline of the

diagram. The area in square inches of the diagram is read from

the roller C and the vernier E.

To Use the Planimeter. The diagram should be fastened to

some flat unglazed surface, such as a drawing board, by means of

thumb tacks, springs or pins. The point A is pressed into the

paper so that it will hold in place. The point B is set at any

point in the outline of the diagram and the roller set at zero.

Follow the outline of the diagram carefully in the direction of

the hands of a watch as indicated by the arrows in Fig. 22 until

the tracer has moved completely around the diagram. The result

is then read to hundredths of an inch from the roller. Suppose

after tracing over the outline we find that the largest figure that

has passed the zero of the vernier is 3 ; the number of graduations

(tenths) that have passed the zero to be 5 and the number

(hundredths) of the graduations in the roller that exactly coincides

with a graduation on the vernier to be 9. Then the area is 8.59

square inches.

Often at the start the roller is not adjusted so that the zeros

coincide but the reading is taken and subtracted from the final

reading. Thus if the first reading is 4.63 and the second 7.31 the

area is 7.31 4.63 = 2.68 square inches. In case the second

reading is less than the first, add 10 to the second reading then

subtract.

This instrument is very valuable to an engineer who takes

indicator cards. The results obtained are very accurate, the error

being small. Ten or twelve diagrams can be measured by this

instrument in the same time that is necessary to measm-e a single

card by the method of ordinates.

It is well to run over the area three or four times and take

an average as the tracing of the diagram cannot be absolutely COP

rect at any time.

218

INDICATORS.

THERHAL EFFICIENCY.

The thermal efficiency of the steam engine is found in the

same manner as that of any other heat engine. The efficiency

depends upon the limits of temperature and not upon the nature

of the working medium.

Let T l absolute temperature of the heat received by the engine.

T 2 = absolute temperature of the heat rejected by the engine.

E = efficiency of engine.

Then,

or, the efficiency equals the temperature of the heat rejected, sub-

tracted from the temperature of the heat received and the result

divided by the temperature of the heat received.

Suppose an engine is supplied with steam at 120 pounds

absolute pressure and the exhaust is atmospheric pressure. What

is the efficiency?

The absolute temperature corresponding to 120 pounds abso-

lute pressure is 341.05 -j- 461 and the temperature of atmos-

pheric pressure is212 + 461.

Then,

802.05 673

E = - _ = .16 or 16 per cent.

802.05

If the engine had been of the condensing type and the

exhaust pressure one pound above the vacuum, the efficiency

would be as follows :

The temperature of one pound absolute pressure is 101.99

+ 461.

E = W*M=_6***_ = Qr per cent>

802.05

In actual engines this efficiency cannot be obtained localise

the difference between the amount of heat received and that

rejected is not all converted into work. Part of it is lost by

radiation, conduction, leakage, etc. Also cylinder condensation

reduces the efficiency.

The Theoretical Indicator Diagram. An indicator diagram

is the result of two movements ; a horizontal movement of the

219

36 INDICATORS.

paper and a vertical movement of the pencil. The horizontal

movement exactly corresponds to the movement of the piston of

the engine and the vertical movement exactly corresponds to the

pressure of steam in the cylinder.

The shape of the indicator card depends upon the manner in

which steam is admitted to and released from the cylinder. Dif-

ferent engines give different shaped indicator cards and the cards

taken from an engine vary with the conditions. Figs. 1 and 2

show theoretical indicator cards from a non-condensing engine

without clearance ; the former being for the case that has admis-

sion during the whole stroke. The diagram of Fig. 2 shows the

cut off at ^ stroke. All practical engines have clearance and

slight compression ; so the theoretical diagram assumes the shape

shown in Fig. 23. In this card

the admission line H A is verti-

cal, the steam line A C is hori-

zontal, the expansion line C D

an hyperbolic curve, the exhaust

line D B vertical, the back pres-

sure line B F horizontal and the

compression curve an hyperbola.

The actual shape is somewhat

rig ' 23 * different from the theoretical

mainly because the valves do not open and close quickly, the ports

offer some resistance to the passage of the steam and the back

pressure is neither atmospheric in the non-condensing engine nor

absolute vacuum in the condensing engine.

The diagram shown in Fig. 24 is a practical diagram and

like those taken from engines.

The atmospheric line L M is the line drawn by the pencil of

the indicator when the connection to the engine is closed and both

sides of the piston of the indicator are open to the atmosphere.

It is the zero of the steam gage.

The admission line H A shows the rise of pressure due to the

admission of steam to the cylinder. If the steam is admitted

quickly when the engine is nearly on dead center this line will l>e

very nearly vertical.

The steam line A C is drawn while the valve admits steam

220

INDICATORS.

to the ' cylinder. This line is horizontal if there is no wire-

drawing.

The point of cut off C, indicates the point at which the

admission of steam is stopped by the closing of the valve. This

point is rounding since the valve closes slowly. Sometimes it is

difficult to determine the exact point where cut off takes place ; it

is usually where the curve changes from concave to convex.

The expansion curve C D shows the fall in pressure as the

ssteam expands while the piston moves toward the end of the stroke.

The point of release D shows the point at which the exhaust

N

Fig. 24.

valve opens. The rounding is due to the slow action of the valve

when opening. Because of this slow action of the valve, release

begins a little before the end of the forward stroke.

The exhaust line D E F represents the loss in pressure which

occurs while the valve opens to exhaust at and near the end of the

stroke.

The back pressure line F G shows the back pressure against

which the piston acts during the return stroke. For a condens-

ing engine this line is below the atmospheric line L M, the dis-

tance below being dependent upon the state of the vacuum in the

condenser. For cards taken from a non-condensing engine the

back pressure line is a little above the atmospheric line.

The point of exhaust closure G is the point where the valve

221

INDICATORS.

closes to exhaust. The exact point is not clearly denned as the

curve shows a change of pressure due to the gradual closing of the

valve. -

The compression curve G II shows the rise of pressure due

to the compression of the steam remaining in the cylinder after

the valve has closed to exhaust.

The zero line of pressure or line of absolute vacuum O X is

drawn below and parallel to the atmospheric line. The distance

between the lines O X and L M represents 14.7 pounds pressure.

The clearance line O Y is drawn perpendicular to the line of

absolute vacuum and at a distance from the end of the diagram

_l _2 ^3 4 5

Fig. 25.

equal to the same per cent, of the length of the diagram as the

clearance volume is of the piston displacement, or

L N clearance volume

L M volume of cylinder

It is readily seen that the area of an actual indicator diagram

is less than that of a theoretical card." This is because of the

round corners at cut off and exhaust, the back pressure and the

compression. Sometimes it is useful, especially in designing

engines, to draw the theoretical indicator card.

222

INDICATORS. 9

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