Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 | Page 4

Talcahuana |J. E. Martin, Local Supt. |1879 5| " |Chicago, Burlington & Quincy|H. B. Stone |1880 6| " |Chicago, Burlington & Quincy| " |1880 7| " |Chicago, Burlington & Quincy| " |1880 8| " |St. Louis & San Francisco |C. W. Rogers, Gen. Mgr. |1879 9|Pa. R.R |Cumberland Valley. | |1910 10| | | |1910 11|Baldwin.|Atchison, Topeka & Santa Fe |J. D. Burr, Asst. Engr. |1879 12| " |Missouri Pacific |John Hewitt, Supt. M. P. |1880 13| " |Western Maryland |D. Holtz, M. of Mach'y. |1878 14| " |Atchison, Topeka & Santa Fe |J. D. Burr, Asst. Engr. |1879 15| " |Virginian Ry. | |1910 16| |Pennsylvania | |1910 17|Baldwin.|Virginian Ry. | |1910 18| " |Lehigh Valley, Wyoming Div. |A. Mitchell, Div. Supt. |1871 19| " |Great Northern |Grafton Greenough. |1908 20| " |Great Northern |Grafton Greenough. |1908 21| " |Baltimore & Ohio |F. E. Blaser, Div. Supt. |1910 22| " |Central of N. J. |W. W. Stearns, Asst.Gen.Supt.|1880 23| " |Great Northern |Grafton Greenough. |1908 24| " |Great Northern |Grafton Greenough. |1906 ============================================================================
============================================================================== |Source of Data. |Remarks. --+-----------------------------------------+--------------------------------- 1|Baldwin Catalogue, 1881, p. 134 | 2| " " 1881, " 72 |10 miles per hour. 3| " " 1881, " 115 | 8 " " " | | Stops and starts on grade. 4| " " 1881, " 100 | 5| " " 1881, " 116 |Stops and starts at any point | | on grade. 6| " " 1881, " 116 | 7| " " 1881, " 116 | 8| " " 1881, " 87 | 9| | 10|Trautwine's Pocket Book, Ed. 1882, p. 412|Empty cars; many curves and | | reversions. 11|Baldwin Catalogue, 1881, p. 114 | 12| " " 1881, " 112 | 13| " " 1881, " 86 |12 miles per hour. 14| " " 1881, " 114 | 8 " " " 15|Engineering News, Jan. 13, 1910. | 16|Trautwine's Pocket Book, Ed. 1882, p. 412| 17|Engineering News, Jan. 13, 1910. |Road locomotive and helper. 18|Baldwin Catalogue, 1881, p. 112 | 19|Baldwin Loco. Wks. Record, No. 65, p. 29| 20|Baldwin Loco. Wks. Record, No. 65, p. 29| 21| |Very crooked line. Uncompensated. 22|Baldwin Catalogue, 1881, p. 113 | 23|Baldwin Loco. Wks. Record, No. 65, p. 29| 24|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.

DISCUSSION
C. D. PURDON, M. AM. SOC. C. E. (by letter).--Some years ago the writer, in making studies for grade revision, found that the tractive power of a locomotive up grade becomes less as the length of the grade increases, and in some unknown proportion. This was a practical confirmation of the saying of locomotive engineers, that the engine "got tired" on long grades. On a well-known Western railroad, with which the writer is familiar, experiments were made for the purpose of rating its locomotives. The locomotives were first divided into classes according to their tractive power, this being calculated by the usual rule, with factors of size of cylinders, boiler pressure, and diameter of drivers, also by taking one-fourth of