PART I. LOCOMOTIVES. (continued 2)
Reading edition
Referring to the tables in succession we have,
By table 1, Traction for 100 tons, on a level, at 25 miles per hour, 1,550 lbs.
By table 2, Traction for 100 tons, on a 30 feet grade, 1,273 lbs.
Whole traction required, 2,823 lbs.
By the formula, table 3, the weight upon the drivers must be
2823 × 6 = 16938 lbs., or 8 tons.
By table 4, with a wheel five feet in diameter, and a stroke of twenty inches, we have the decimal .2122.
By table 5, the mean cylinder pressure being sixty pounds per inch, and piston twelve inches in diameter, we have as the total pressure
On both pistons, 13,572 lbs.
And finally, 13572 × .2122 = 2,880 lbs.
The requirement being 2,823 lbs.
By table 6, we see that five feet wheels at twenty-five miles per hour, use 33,600 cylinders of steam per hour.
By table 7, the capacity of a cylinder 12 × 20 is 1.31 367cubic feet; also 33600 × 1.31 = 44016 cubic feet of steam per hour.
Assuming the mean cylinder pressure at sixty pounds, and the entering pressure at eighty pounds, also the loss in passing from the boiler at twenty pounds, we must generate the steam at one hundred pounds per square inch.
By table 8, we see that when steam is produced under one hundred pounds pressure per inch, each cubic foot of water makes 293 cubic feet of steam; whence
44016 293 = 150,
is the number of cubic feet of water to be evaporated per hour. At sixteen cubic feet of water per hour per square foot of grate, we thus require
15.0 16 or 9.4 feet, nearly;
and by table 9, we find the heating surface necessary to evaporate 150 cubic feet of water per hour, with nine square feet of grate surface, to be 779 square feet; and by the formula, with 9.4 square feet, we have,
S = √9.4 × 150 × 21.2 = 797 square feet,
the fuel being coke; for wood, multiply the grate area (as mentioned before) by 1.4 and the grate area will be 1.4 × 9.4 = 13.16. The tube surface of course remains the same, as, when the necessary amount of heat is developed, the same surface only is enough to apply it to the water.
To obtain 779 square feet of heating surface, we see, by table 10, that it is given by
100 tubes 17 feet long and 1¾ inch diameter,
or 100 tubes 16 feet long and 1⅞ inch diameter,
368or 100 tubes 15 feet long and 2 inch diameter,
or 100 tubes 14 feet long and 2⅛ inch diameter,
or 100 tubes 12½ feet long and 2⅜ inch diameter,
or 100 tubes 12 feet long and 2½ inch diameter,
or by consulting the table, and having given the number and length, the number and diameter, or the length and diameter, we may easily find the third factor of the surface. Thus the length being eleven feet, and diameter two inches, 779 feet is obtained by
779 11 × 3.1416 × 167 = 135 tubes.
To obtain the diameter of barrel to contain 135 two inch tubes, we use the formula
D = √(A/B[n(d+c)2] .7854).
We have already found d = 2 inches, n = 135, whence c will be by formula,
c = N 240 = 0.54,
and
d + c = 2.54,
also,
(d + c)2 = 6.45,
and
135 × 6.45 = 871+;
and allowing three fourths of the boiler cross section to be filled with tubes, we have,
4 3 of 871 = 1161;
also,
1161 .7854 = 1478,
the square root of which is 38.5 nearly, to which add 38.5 8 369or 4.8 inches, (see page 359), and we have
38.5 + 4.8 = 43.3 inches,
as the inside diameter of boiler, whence the following locomotive to meet the requirement as stated.
Weight upon driving wheels, 16,938 lbs.,
Cylinders, 12 × 12 inches,
Wheels, 5 feet,
Tubes, 135—11 feet × 2 inches,
Grate, 13.16 square feet,
Barrel, (inside diameter,) 43.3 inches,
and under the most favorable circumstances, the chimney may be 40 inches high, 12.7 inches in diameter; the blast orifice 5.8 inches in diameter; and the capacity of smoke box 39½ cubic feet.
363. We may vary the tractive power of an engine by using the steam at a greater or less degree of expansion, but the adhesion remains the same. If an engine was built able to work a road partly level, and partly on steep grades, varying the power simply by varying the expansion, it would be unnecessarily heavy for the easy parts of the road. The expansive principle may be advantageously employed in adjusting the power to the difference of resistance on any one division of a road, and also to the varying load which each day’s traffic will present.
Suppose we would move a load of two hundred tons over the road below; and suppose, also, that we require the cylinder pressures set opposite the several divisions.
10 miles, level, 60 lbs.,
10 miles, 10 feet per mile, 80 lbs.,
10 miles, 20 feet per mile, 100 lbs.,
10 miles, 30 feet per mile, 120 lbs.
370The boiler pressure being 150 lbs., and the pressure at entering the cylinder 145 lbs.,
An admission of 71 per cent. gives a mean pressure of 120 lbs.,
An admission of 55 per cent. gives a mean pressure of 100 lbs.,
An admission of 40 per cent. gives a mean pressure of 80 lbs.,
An admission of 28 per cent. gives a mean pressure of 60 lbs.,
And if the 1st notch of the sector admits, 75 per cent,
And if the 2d notch of the sector admits, 70 per cent,
And if the 3d notch of the sector admits, 65 per cent,
And if the 4th notch of the sector admits, 60 per cent,
And if the 5th notch of the sector admits, 55 per cent,
And if the 6th notch of the sector admits, 50 per cent,
And if the 7th notch of the sector admits, 45 per cent,
And if the 8th notch of the sector admits, 40 per cent,
And if the 9th notch of the sector admits, 35 per cent,
And if the 10th notch of the sector admits, 30 per cent.
We should work the engine as follows:—
From 0 to 10 miles, use the 10th notch,
From 10 to 20 miles, use the 8th notch,
From 20 to 30 miles, use the 5th notch,
From 30 to 40 miles, use the 2d notch,
371APPLICATION OF LOCOMOTIVE ENGINES TO RAILROADS.
364. Department 1. Freight.
GENERAL CLASSIFICATION.
Number of division. Maximum grades. Designation of parts. Order 1 50 tons. Order 2 100 tons. Order 3 250 tons. Order 4 500 tons. Order 5 750 tons. Order 6 1,000 tons.
1 Level. Grate area. Tube surface. Cylinders. Wheels. Weight.
2 10 feet per mile.
3 20 feet per mile.
4 40 feet per mile.
5 60 feet per mile.
6 80 feet per mile.
7 100 feet per mile.
372The speed is assumed from twelve to fifteen miles per hour. The mean cylinder pressure is assumed at sixty lbs. per square inch; the initial pressure at ninety pounds, and the boiler pressure at 120 lbs. per square inch. The grate areas are designed for coke; for wood multiply the same by 1.4.
365. Department 2. Passenger.
Classification. Order 1 50 tons. Order 2 100 tons. Order 3 150 tons. Order 4 200 tons. Designation of parts.
Division 1 Level. 25 miles per hour. Grate area. Tube surface. Cylinders. Wheels. Weight.
Division 2 20′ grades. 25 miles per hour.
Division 3 40′ grades. 25 miles per hour.
Division 4 60′ grades. 25 miles per hour.
Division 5 80′ grades. 25 miles per hour.
Division 6 100′ grades. 25 miles per hour.
373The engines in the Northern States require more power in winter than in summer.
To the above classification might be added, an engine for “making up trains,” and similar station work; such an engine should be able to start easily the extreme weights of trains, from fifty to one thousand tons, and should be fitted with a power of varying its adhesion.
374FORMULA.
W × [V2 171 + 8] = R.
Example.
The speed being thirty miles per hour, and load 250 tons.
R will be [(30 × 30) 171 + 8] × 250 = 3315 lbs.
375366. Table 1. Showing the required traction on a level for loads from fifty to one thousand tons, and for velocities from ten to one hundred miles per hour.
Velocity. 50 Tons. 75 Tons. 100 Tons. 250 Tons. 500 Tons. 750 Tons. 1000 Tons.
10 429 643 858 2146 4292 6435 8585
12 442 663 884 2210 4421 6630 8842
15 465 698 931 2328 4657 6982 9315
20 517 773 1034 2585 5170 7735
25 582 874 1165 2912 5825
30 663 994 1326 3315 6630
40 868 1302 1736 4340
50 1131 1696 2262 5655
60 1452 2180 2905
100 3324 4986 6648
376FORMULA.
WR L.
Example.
The tractive power to overcome the resistance of 750 tons upon a sixty feet grade is
750 × 60 5280 = 19050.
377367. Table 2. Showing the tractive power necessary to overcome grades from ten to one hundred feet per mile with loads from one to one thousand tons.
Grade. 1 Ton. 50 Tons. 75 Tons. 100 Tons. 250 Tons. 500 Tons. 750 Tons. 1000 Tons. Grade.
10 4 212 318 424 1061 2121 3181 4240 10
20 8 424 636 848 2122 4242 6362 8480 20
30 13 636 955 1273 3170 6363 9545 12730 30
40 16 848 1272 1696 4244 8484 12724 16960 40
50 20 1060 1590 2120 5305 10605 15905 21200 50
60 26 1272 1910 2546 6340 12726 19050 25460 60
70 30 1500 2240 3000 7500 15000 22400 30000 70
80 33 1697 2545 3393 8489 16969 25459 33950 80
100 40 2120 3180 4240 10610 21210 31810 42400 100
Grade. 1 Ton. 50 Tons. 75 Tons. 100 Tons. 250 Tons. 500 Tons. 750 Tons. 1000 Tons. Grade.
378FORMULA.
6T.
Example.
Required traction 5,000 lbs.; upon driving axles the weight is 5000 × 6 = 30,000 lbs.
379368. Table 3. Giving the weight which should be placed upon the driving axles to secure any amount of adhesion; the latter being one sixth of the weight.
Required traction. Weight in pounds. Weight in tons.
500 3000 1.34
1000 6000 2.69
2000 12000 5.36
3000 18000 8.04
4000 24000 10.80
5000 30000 13.40
6000 36000 16.07
7000 42000 18.75
8000 48000 21.43
9000 54000 24.11
10000 60000 26.80
12000 72000 32.14
14000 84000 37.50
16000 96000 42.86
18000 108000 48.22
20000 120000 53.60
380FORMULA.
2S c.
Where S = stroke.
c = circumference of wheel, (both in inches.)
Example.
Let stroke be twenty inches, and diameter of wheel five feet, the ratio will be
40 188.4 = 0.2122.
381369. Table of decimals, which, multiplied by the total piston pressures (table 5) will give the traction in pounds, or ratio between double stroke and wheel circumference. Table 4.
Wheel. STROKE IN INCHES. Wheel.
18 20 22 24 26 28 30 32 34 36
3½ 2728 3031 3334 3638 3½
3¾ 2553 2837 3120 3404 3688 3¾
4 2386 2652 2918 3182 3444 3708 4
4¼ 2250 2500 2750 3000 3250 3500 3750 4¼
4½ 2151 2390 2593 2830 3071 3294 3529 3764 4½
4¾ 2012 2235 2459 2682 2905 3129 3352 3575 3800 4¾
5 1910 2122 2334 2546 2766 2979 3192 3405 3617 3830 5
5½ 1736 1929 2122 2315 2500 2692 2885 3077 3273 3473 5½
6 1591 1768 1945 2122 2321 2500 2678 2857 3036 3215 6
6½ 1468 1632 1796 1958 2131 2295 2459 2623 2790 2951 6½
7 1364 1516 1667 1819 1970 2121 2273 2424 2576 2727 7
7½ 1272 1414 1556 1691 1831 1972 2114 2254 2394 2535 7½
8 1194 1326 1417 1592 1688 1818 1948 2078 2208 2337 8
Wheel. 18 20 22 24 26 28 30 32 34 36 Wheel.
STROKE IN INCHES.
382FORMULA.
2(d2 .7854 × p) = P.
Where d = diameter.
p = pressure per inch.
Example.
The whole pressure at one hundred pounds per inch on two sixteen inch pistons will be
2[16 × 16 × 0.7854 × 100] = 40212.
383370. Table 5. Total pressures upon pistons from ten to twenty-four inches in diameter, and for steam pressures from fifty to one hundred and fifty pounds per square inch.
Diam. of cyl’r. Area of one Piston. WHOLE PISTON PRESSURE ON BOTH PISTONS, AT A PER INCH PRESSURE OF Diam. of cyl’r.
50 60 70 80 90 100 110 120 130 140 150
10 78.5 7950 9420 10990 12560 14130 15700 17270 18840 20410 21980 23550 10
11 95.0 9500 11400 13300 15200 17100 19000 20900 22800 24700 26600 28500 11
12 113.1 11310 13572 15834 18096 20358 22620 24882 27144 29406 31768 33930 12
13 132.7 13270 15924 18564 21232 23906 26540 29194 31848 34502 37156 39810 13
14 153.9 15390 18468 21546 24624 27702 30780 33858 36756 40014 43092 46170 14
15 176.7 17670 21204 24738 28272 31806 35340 38874 42408 55942 49476 53010 15
16 201.1 20110 24132 28154 32176 36198 40220 44242 48264 52062 56308 60330 16
17 227.0 22700 27240 31780 36320 40860 45400 49940 54480 59020 63560 68100 17
18 254.5 25450 30540 35630 40720 45810 50900 55990 61080 66170 71260 76350 18
19 283.5 28350 34020 39690 45360 51030 56700 62370 68040 73710 79380 85050 19
20 314.2 31420 37704 43988 50272 56556 62840 69124 75408 81692 87976 95260 20
21 346.4 34640 41568 48496 55424 62352 69380 76208 83136 90064 96992 103920 21
22 380.1 38010 45612 53214 60816 68418 77020 83622 91224 98826 106428 114030 22
23 415.5 41550 49860 58170 66480 74790 83100 91410 99720 108030 116340 124650 23
24 452.4 45240 54288 63336 72384 81432 90480 99528 108576 117626 126672 135720 24
384FORMULA.
N = 5280 c × 4.
Where N = the number.
c = wheel circumference.
Example.
Speed twenty-five miles per hour, wheels four and a half feet, the number of cylinders per hour is
25 × 5280 4 × 3.1416 × 4 = 37348
385371. Table 6. Showing the hourly consumption of steam in terms of the capacity of one cylinder, with wheels from three and a half to eight feet, and speeds from ten to sixty miles per hour.
Wheel. Wheel in inches. Revolutions per mile. NUMBER OF CYLINDERS PER HOUR AT A VELOCITY OF
10 12 15 20 25 30 40 50 60
3½ 42 480 19200 23040
3¾ 45 449 17960 21552 26940
4 48 421 16840 20208 25260 33681
4¼ 51 397 15880 19056 23820 31760 39700
4½ 54 373 14920 17904 22380 29840 37300
4¾ 57 361 14440 17328 21660 28880 36100
5 60 336 20160 26880 33600
5½ 66 306 18360 24480 30600 36720
6 72 281 22480 28100 33720 44960
6½ 78 259 20720 25900 31080 41440 51800 62160
7 84 240 19200 24000 28800 38400 48000 57600
7⅛ 90 224 22400 26880 35840 44800 53760
8 96 211 21109 25320 33760 42200 50640
386FORMULA.
D2 × .7854 × Stroke 1728 = C.
Example.
Cubic content of a cylinder 15 × 24 is
15 × 15 × 0.7854 × 24 1728 = 2.44 cubic feet.
387372. Table 7. Capacity of cylinders in cubic feet of from ten to twenty-four inches in diameter, and from eighteen to thirty-six inches stroke.
Diam. of cyl’r. CAPACITY OF CYLINDERS IN CUBIC FEET, STROKE BEING Diam. of cyl’r.
18 20 22 24 26 28 30 32 34 36
10 082 091 100 109 118 127 136 145 10
11 093 104 115 126 137 148 159 170 181 11
12 118 131 144 157 170 183 196 209 222 235 12
13 133 149 165 181 197 213 229 245 261 277 13
14 160 178 196 214 232 250 268 286 304 322 14
15 184 204 224 244 264 284 304 324 344 364 15
16 208 232 255 278 301 324 347 370 393 416 16
17 235 263 289 315 341 367 393 419 445 471 17
18 263 294 323 352 381 410 439 468 497 526 18
19 361 394 427 460 493 526 559 592 19
20 400 437 474 511 548 585 622 659 20
21 481 521 561 601 641 681 721 21
22 528 572 616 660 704 748 792 22
23 625 674 723 772 821 876 23
24 681 733 785 837 889 941 24
389373. Table 8. Giving the volume, pressure, temperature, and density of steam.
Steam pressure. Relative volume or cubic feet of steam, water being 1. Temperature. Total heat. Weight of a cubic foot. Steam pressure.
50 552 281 1200 1129 50
60 467 293 1203 1335 60
65 434 298 1205 1436 65
70 406 303 1206 1535 70
75 381 307 1208 1636 75
80 359 312 1209 1736 80
90 323 320 1212 1929 90
100 293 328 1214 2127 100
110 269 335 1216 2317 110
120 249 341 1218 2505 120
130 231 347 1220 2698 130
140 216 353 1221 2885 140
150 203 358 1223 3070 150
390FORMULA.
S =√ac × 21.2.
Where S = surface.
a = grate area.
c = cubic feet of water per hour.
Example.
Grate area sixteen square feet, cubic feet of water per hour two hundred, surface is
√16 × 200 × 21.2 = 1199.92.
391374. Table 9. Showing the necessary amount of grate area and heating surface for an hourly consumption of water.
Cubic ft. of water evap’d per hour. GRATE AREAS IN SQUARE FEET.
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
HEATING SURFACE CORRESPONDING TO ABOVE GRATE AREAS AND TO SIDE COLUMN.
100 561 599 636 670 703 734 764 793 821 848 874 900 924 948 972 995 1017 1039 1060 1081 1102 1122 1142 1161
110 588 628 667 702 737 770 802 831 861 888 916 943 969 994 1018 1042 1066 1089 1111 1133 1155 1176 1197 1217
120 614 657 697 734 770 805 837 869 900 927 957 985 1013 1039 1064 1089 1114 1138 1162 1184 1207 1229 1251 1272
130 639 683 725 764 801 837 871 904 936 965 996 1025 1053 1081 1107 1133 1159 1184 1208 1232 1255 1278 1300 1323
140 663 709 752 793 831 869 904 938 972 1003 1034 1064 1093 1122 1150 1177 1203 1229 1254 1279 1303 1327 1351 1374
150 686 734 779 821 860 900 935 971 1006 1038 1070 1101 1131 1161 1190 1218 1245 1272 1298 1323 1350 1373 1398 1422
160 758 805 848 889 927 966 1004 1039 1073 1106 1138 1169 1199 1229 1258 1286 1314 1341 1367 1393 1419 1444 1469
170 782 829 874 916 957 996 1034 1071 1106 1140 1173 1205 1236 1266 1296 1325 1354 1382 1409 1436 1462 1488 1514
180 805 853 900 943 985 1025 1064 1102 1138 1173 1207 1240 1272 1303 1334 1364 1393 1422 1450 1478 1505 1532 1558
190 877 924 969 1013 1053 1093 1132 1169 1205 1240 1274 1307 1339 1370 1401 1431 1461 1490 1518 1546 1573 1600
200 900 948 995 1039 1081 1122 1161 1199 1236 1272 1307 1341 1374 1406 1437 1468 1499 1529 1558 1586 1614 1642
210 928 974 1019 1064 1107 1149 1189 1229 1264 1298 1336 1374 1408 1441 1473 1505 1536 1566 1596 1625 1654 1683
220 1000 1042 1089 1133 1176 1217 1258 1291 1324 1365 1406 1441 1475 1508 1541 1572 1603 1634 1664 1693 1722
230 1019 1067 1114 1159 1203 1245 1286 1323 1359 1398 1437 1473 1508 1542 1575 1607 1639 1663 1701 1724 1761
240 1091 1138 1184 1229 1272 1314 1354 1393 1431 1468 1505 1541 1575 1609 1642 1675 1692 1738 1754 1799
250 1111 1162 1208 1254 1298 1341 1380 1422 1458 1499 1533 1572 1606 1642 1675 1709 1733 1774 1797 1836
260 1184 1232 1278 1323 1367 1406 1450 1484 1529 1560 1603 1636 1675 1708 1743 1774 1809 1840 1872
270 1207 1256 1303 1349 1401 1433 1478 1515 1557 1592 1634 1668 1692 1741 1776 1808 1843 1875 1908
280 1279 1327 1374 1435 1460 1505 1546 1586 1624 1664 1700 1738 1774 1809 1842 1877 1910 1943
290 1302 1351 1400 1452 1486 1532 1573 1614 1653 1693 1729 1754 1804 1841 1873 1910 1939 1977
300 1374 1425 1469 1512 1558 1600 1642 1682 1722 1758 1799 1834 1872 1904 1943 1968 2011
320 1469 1516 1564 1610 1654 1696 1738 1778 1816 1859 1894 1932 1970 2008 2024 2078
340 1564 1612 1658 1704 1748 1792 1833 1872 1915 1954 1993 2032 2069 2096 2141
360 1658 1706 1754 1800 1844 1886 1928 1971 2012 2050 2090 2128 2166 2204
380 1753 1802 1848 1894 1938 1982 2025 2066 2107 2148 2187 2226 2264
400 1800 1848 1900 1944 1990 2034 2077 2120 2162 2204 2244 2284 2322
425 1950 2014 2056 2077 2142 2187 2226 2268 2317 2353 2396
450 2014 2056 2120 2150 2190 2200 2300 2332 2374 2417 2459
475 2175 2210 2268 2310 2353 2416 2445 2480 2523
500 2332 2370 2412 2459 2523 2565 2608
392FORMULA.
N = S Ldπ or S Ld3.1416.
Where S = whole surface,
Where L = length,
Where d = diameter, in feet,
Where π = 3.1416,
Where N = the number.
Example.
Diameter two inches, surface 1466, length fourteen feet, we have,
N = 1466 14 × 0.167 × 3.1416 = 200.
393375. Table 10. Giving the number and dimensions of tubes to obtain any given amount of surface.
L’gth. Diam. 1½ Diam. 1¾ Diam. 1⅞ Diam. 2 Diam. 2⅛ Diam. 2¼ Diam. 2⅜ Diam. 2½ L’gth.
8 314 336 397 419 445 471 504 523 8
8½ 334 389 422 445 473 500 535 556 8½
9 352 411 447 471 507 530 566 588 9
9½ 372 435 471 497 523 559 597 621 9½
10 392 457 496 524 556 589 628 655 10
10½ 411 480 521 549 584 618 659 687 10½
11 431 503 545 576 612 647 690 720 11
11½ 451 526 570 602 640 677 721 753 11½
12 471 549 595 628 667 705 752 786 12
12½ 490 572 620 654 695 735 783 818 12½
13 510 595 645 681 723 764 814 851 13
13½ 530 617 669 707 750 793 845 884 13½
14 549 640 695 733 778 823 876 916 14
14½ 569 663 719 759 806 852 907 949 14½
15 589 686 744 785 834 882 938 982 15
15½ 608 708 769 811 861 911 969 1015 15½
16 628 731 794 837 889 941 1000 1048 16
16½ 648 754 819 863 917 971 1031 1081 16½
17 668 777 843 889 945 1000 1062 1114 17
394FORMULA.
13.5√a – 28,
where a is the percentage of admission.
Example.
What is the mean pressure, with an initial pressure of one hundred pounds, and sixty per cent. admission.
13.5√60 – 28 = (13.5 × 7.7) – 28 = 76 100 of 100, or 76 lbs.
395376. Table 11. Showing the mean cylinder steam pressure for any percentage of admission, the initial pressure being from 50 to 150 lbs. per inch.
Initial pressure in pounds. MEAN CYLINDER PRESSURE, ADMISSION BEING IN HUNDREDTHS OF THE STROKE.
10 15 20 25 30 35 40 45 50 55 60 65 70 75
50 7 12 16 20 23 26 28 31 33 36 38 40 42 44
60 9 14 19 24 28 31 34 37 40 43 46 49 51 53
70 10 17 22 28 33 36 40 43 47 50 54 57 59 62
80 12 19 26 32 38 42 41 49 54 58 62 65 68 71
90 13 22 29 36 42 47 51 54 60 65 69 73 76 80
100 15 24 32 40 47 52 57 62 67 72 77 81 85 89
110 16 26 35 44 52 57 63 68 74 79 85 89 93 98
120 18 29 38 48 56 62 68 74 80 86 91 97 102 107
130 19 31 42 52 61 68 74 81 87 94 99 105 110 116
145 21 34 45 56 65 73 80 87 94 101 107 113 119 125
160 22 36 48 60 70 78 85 93 100 108 114 121 127 134
396