A train moving at a rate of 60 ft. per sec., and reaching the foot of a grade, will have acquired a "velocity head" of 56.7 ft., equivalent to stored energy of 56.7 × 2,000 = 113,400 ft-lb. per ton. On a 0.002 grade (as in Item 15 of [Table 1]) the resistance would be, gravity 4 lb. + train 4.7 lb. = 8.7 lb., against which the energy above given would carry the train through 113,400 ÷ 8.7 = 13,034 ft., say, 2.5 miles, leaving 5 miles to be provided for by the steam production. Examining the items in the table having grades in excess of 10 miles, it will be noted that 16% is about all the weight on drivers which can be utilized by the current supply of steam. In Item 15 the energy derived from all sources is equivalent to 24.3%; hence the stored heat may be considered as responsible for an equivalent of 24.3% - 16% = 8.3% for a distance of 5 miles.
TABLE 1.
| Item No. | Length of grade, in miles. | Rate of grade. | Maximum curvature. | Compen sation. | Gross weight of load, in tons. | Weight of tender, in tons. | Weight of locomotive, in tons. | Weight on drivers, in tons. | Percentage of weight on drivers utilized in draft. | Class. | Maker. | Railroad. | Reporting Officer. | Year. | Source of Data. | Remarks. |
| 1 | 0.06 | 0.066 | 115 | 37.5 | 29 | 0.358 | 8-28-1/3 C | Baldwin. | Morgan's Louisiana & Texas | Newell Tilton, Asst. Supt. | 1880 | Baldwin Catalogue, 1881, p. 134 | ||||
| 2 | 0.33 | 0.0203 | 25°20' | 242 | 25 | 35 | 23 | 0.285 | 8-28 C | " | Long Island | S. Spencer, Gen. Supt. | 1878 | Baldwin Catalogue, 1881, p. 72 | 10 miles per hour. | |
| 3 | 1.0 | 0.06 | 16° | 0.05 | 192 | 22 | 57.5 | 50 | 0.310 | 10-36 E | " | Atchison, Topeka & Santa Fe | J. D. Burr, Asst. Engr. | 1879 | Baldwin Catalogue, 1881, p. 115 | 8 miles per hour. Stops and starts on grade. |
| 4 | 1.3 | 0.0127 | 600 | 16 | 40 | 32.5 | 0.300 | Mogul. | " | Chillan & Talcahuana | J. E. Martin, Local Supt. | 1879 | Baldwin Catalogue, 1881, p. 100 | |||
| 5 | 1.4 | 0.0128 | 3°12' | 750 | 15 | 51 | 44 | 0.270 | 10-34 E | " | Chicago, Burlington & Quincy | H. B. Stone | 1880 | Baldwin Catalogue, 1881, p. 116 | Stops and starts at any point on grade. | |
| 6 | 2.0 | 0.01 | 1,000 | 15 | 51 | 44 | 0.291 | 10-34 E | " | Chicago, Burlington & Quincy | " | 1880 | Baldwin Catalogue, 1881, p. 116 | |||
| 7 | 2.2 | 0.013 | 3° | 725 | 15 | 51 | 44 | 0.245 | 10-34 E | " | Chicago, Burlington & Quincy | " | 1880 | Baldwin Catalogue, 1881, p. 116 | ||
| 8 | 2.5 | 0.0144 | 6° | 400 | 27 | 42 | 32 | 0.237 | 10-32 E | " | St. Louis & San Francisco | C. W. Rogers, Gen. Mgr. | 1879 | Baldwin Catalogue, 1881, p. 87 | ||
| 9 | 2.5 | 0.004 | 2,700 | 70 | 96.7 | 85.8 | 0.207 | H 6 - A | Pa. R.R | Cumberland Valley. | 1910 | |||||
| 10 | 3.5 | 0.033 | 14° | 100 | 25 | 35 | 35 | 0.160 | 1910 | Trautwine's Pocket Book, Ed. 1882, p. 412 | Empty cars; many curves and reversions. | |||||
| 11 | 3.6 | 0.035 | 10° | 0.05 | 236 | 22 | 57.5 | 50 | 0.245 | 10-36 E | Baldwin. | Atchison, Topeka & Santa Fe | J. D. Burr, Asst. Engr. | 1879 | Baldwin Catalogue, 1881, p. 114 | |
| 12 | 4.0 | 0.0085 | 4° | 1,020 | 30 | 51 | 44 | 0.256 | 10-34 E | " | Missouri Pacific | John Hewitt, Supt. M. P. | 1880 | Baldwin Catalogue, 1881, p. 112 | ||
| 13 | 6.0 | 0.0145 | 308 | 25 | 38 | 28 | 0.207 | 10-28 D | " | Western Maryland | D. Holtz, M. of Mach'y. | 1878 | Baldwin Catalogue, 1881, p. 86 | 12 miles per hour. | ||
| 14 | 6.0 | 0.020 | 10° | 0.05 | 460 | 32 | 57.5 | 50 | 0.242 | 10-34 E | " | Atchison, Topeka & Santa Fe | J. D. Burr, Asst. Engr. | 1879 | Baldwin Catalogue, 1881, p. 114 | 8 miles per hour. |
| 15 | 7.5 | 0.002 | C | 6,152 | 86 | 134.5 | 109.5 | 0.243 | Mallet. | " | Virginian Ry. | 1910 | Engineering News, Jan. 13, 1910. | |||
| 16 | 9.75 | 0.018 | 200 | 18 | 29 | 29 | 0.170 | Pennsylvania | 1910 | Trautwine's Pocket Book, Ed. 1882, p. 412 | ||||||
| 17 | 10.0 | 0.006 | C | 6,173 | 86 | 299 | 265 | 0.203 | Mallet. | Baldwin. | Virginian Ry. | 1910 | Engineering News, Jan. 13, 1910. | Road locomotive and helper. | ||
| 18 | 12.0 | 0.018 | 10° | 280 | 30 | 51 | 44 | 0.160 | 10-34 E | " | Lehigh Valley, Wyoming Div. | A. Mitchell, Div. Supt. | 1871 | Baldwin Catalogue, 1881, p. 112 | ||
| 19 | 12.0 | 0.022 | 850 | 74 | 175 | 156 | 0.166 | D-D 16 | " | Great Northern | Grafton Greenough. | 1908 | Baldwin Loco. Wks. Record, No. 65, p. 29 | |||
| 20 | 13.0 | 0.022 | 800 | 74 | 177 | 158 | 0.153 | D-D 1 | " | Great Northern | Grafton Greenough. | 1908 | Baldwin Loco. Wks. Record, No. 65, p. 29 | |||
| 21 | 13.0 | 0.022 | 14° | 415 | 50 | 91 | 83 | 0.154 | Consol. | " | Baltimore & Ohio | F. E. Blaser, Div. Supt. | 1910 | Very crooked line. Uncompensated. | ||
| 22 | 16.0 | 0.0044 | 950 | 30 | 51 | 44 | 0.164 | 10-34 E | " | Central of N. J. | W. W. Stearns, Asst.Gen.Supt. | 1880 | Baldwin Catalogue, 1881, p. 113 | |||
| 23 | 20.0 | 0.022 | 500 | 62 | 97.5 | 90 | 0.170 | F 8, Consol. | " | Great Northern | Grafton Greenough. | 1908 | Baldwin Loco. Wks. Record, No. 65, p. 29 | |||
| 24 | 20.0 | 0.022 | 800 | 74 | 177 | 158 | 0.159 | L-1, Mallet. | " | Great Northern | Grafton Greenough. | 1906 | Baldwin Loco. Wks. Record, No. 65, p. 29 |
In proportioning grade resistance for any line, therefore, a locomotive may be counted on to utilize 24.3% of the weight on the drivers for a distance of 5 miles on a 0.002 grade without any assistance from momentum, and, in the event of an unexpected stop, should be able, as soon as a full head of steam is built up, to start the train and carry it over the grade. This is probably a maximum, considering the condition of the equipment of this Virginian Railway, as previously mentioned.
Treating Item 14 in the same way, a distance of 2,310 ft. is accounted for by momentum, leaving, say, 5.5 miles for the steam, or the length of a 0.02 grade on which a locomotive may be loaded on a basis of tractive power equal to 24.2% of the weight on the drivers.
From these figures it may be concluded that on lines having grades from 12 to 15 or more miles in length, grades of 3 to 5 miles in length may be inserted having rates 50% in excess of that of the long grades, without decreasing the capacity of the line. This statement, of course, is general in its bearings, each case being subject to its especial limitations, and subject to detailed calculations.
It may be noted that the velocity of 60 ft. per sec., assumed at the foot of the grade, is probably higher than should be expected in practice; it insures, on the other hand, that quite enough has been allowed for momentum, and that the results are conservative.
Arguments like the foregoing are always more or less treacherous; being based on statistics, they are naturally subject to material modifications in the presence of a larger array of data, therefore, material assistance in reaching practical conclusions can be given by the presentation of additional data.