Part 2

The writer hopes that the author will follow up this subject, and that other members will join, as a full discussion will no doubt bring some results on a question which seems to be highly important.

JOHN C. TRAUTWINE, JR., ASSOC. AM. SOC. C. E. (by letter).--In his collection of data, Mr. Randolph includes two ancient cases taken from the earliest editions (1872-1883) of Trautwine's "Civil Engineer's Pocket-Book," referring to performances on the Mahanoy and Broad Mountain Railroad (now the Frackville Branch of the Reading) and on the Pennsylvania Railroad, respectively.

In the private notes of John C. Trautwine, Sr., these two cases are recorded as follows:

"On the Mahanoy & Broad Mtn. R. R., _tank_ Engines of 35 tons, _all on 8 drivers_, draw 40 _empty_ coal cars weighing 100 tons, _up_ a continuous grade of 175 ft. per mile for 3-1/2 miles; & around curves of 450, 500, 600 ft. &c. rad., at 8 miles an hour. (1864) This is equal to 77-14/100 tons for a 27-ton engine." (Vol. III, p. 176.)

"On the Penn Central 95 ft. grades for 9-3/4 miles, a 29-ton engine all on 8 drivers takes 125 tons of freight and 112 tons of engine, tender, & cars, in all 237 tons,[C] and a passenger engine takes up 3 cars at 24 miles an hour (large 8 wheels). When more than 3, an auxiliary engine."

It will be seen that Mr. Randolph is well within bounds in ascribing to the Mahanoy and Broad Mountain case (his No. 10) a date "certainly prior to 1882," the date being given, in the notes, as 1864; while another entry just below it, for the Pennsylvania Railroad case, is dated 1860.

It also seems, as stated by Mr. Randolph, quite probable that the frictional resistance (6 lb. per 2,000 lb.) assumed by him in the calculation is far below the actual for this Case 10. The small, empty, four-wheel cars weighed only 4,400 lb. each. Furthermore, the "tons," in the Trautwine reports of these experiments, were tons of 2,240 lb. On the other hand, the maximum curvature was 12° 45' (not 14°, as given by the author), and the engine was a tank locomotive, whereas the author has credited it with a 25-ton tender.

After making all corrections, it will be found that, in order to bring the point, for this Case 10, up to the author's curve, instead of his 6 lb. per 2,000 lb., a frictional resistance of 66 lb. per 2,000 lb. would be required, a resistance just equal to the gravity resistance on the 3.3% grade, making a total resistance of 132 lb. per 2,000 lb.

While this 66 lb. per ton is very high, it is perhaps not too high for the known conditions, as above described. For modern rolling stock, Mr. A. K. Shurtleff gives the formula:[D]

Frictional resistance, on tangent, } in pounds per 2,000 pounds } = 1 + 90 ÷ C,

where _C_ = weight of car and load, in tons of 2,000 lb. This would give, for 4,400-lb. (2.2-ton) cars, a frictional resistance of 42 lb. per 2,000 lb.; and, on the usual assumption of 0.8 lb. per 2,000 lb. for each degree of curvature, the 12.75° curves of this line would give 10 lb. per ton additional, making a total of 52 lb. per 2,000 lb. over and above grade resistance, under modern conditions.

In the 9th to 17th editions of Trautwine (1885-1900), these early accounts were superseded by numerous later instances, including some of those quoted by the author.

In the 18th and 19th editions (1902-1909) are given data respecting performances on the Catawissa Branch of the Reading (Shamokin Division) in 1898-1901. These give the maximum and minimum loads hauled up a nearly continuous grade of 31.47 ft. per mile (0.59%) from Catawissa to Lofty (34.03 miles) by engines of different classes, with different helpers and without helpers.

Table 2 (in which the writer follows the author in assuming frictional resistance at 4.7 lb. per 2,000 lb.) shows the cases giving the maximum and minimum values of the quantity represented by the ordinates in the author's diagram, namely, "Traction, in percentage of weight on drivers."

It will be seen that the maximum percentage (16.1) is practically identical with that found by the author (16) for grade lengths exceeding 17 miles.

Near the middle of the 34-mile distance there is a stretch of 1.51 miles, on which the average grade is only 5.93 ft. per mile (0.112%), and this stretch divides the remaining distance into two practically continuous grades, 19.39 and 13.13 miles long, respectively; but, as the same loads are hauled over these two portions by the same engines, the results are virtually identical, the maxima furnishing two more points closely coinciding with the author's diagram.

TABLE 2.--TRACTIVE FORCE, CATAWISSA TO LOFTY.

======================================================================== Length of grade, in miles | | 34.03 | | Grade {in feet per mile | | 31.47 {percentage |_A_ | 0.597 | | Resistances, in pounds per 2,000 lb., | | Gravity (=20 _A_) = 11.94. Friction = 4.70 |_B_ | 16.64 | | Load: | Cars. | Locomotive.| Tender. | | Maximum[E] | 1,561 | 44.60 | 25.25 |_C_ | 1,631 Minimum[F] | 1,031 | 60.50 | 34.50 |_C_ | 1,126 | | Traction (= _B_ _C_ ÷ 2,000 ) Maximum[E] |_D_ | 13.60 Minimum[F] |_D_ | 9.38 Weight on Drivers: | Locomotive.| Helper. | | Maximum[E] | 21.60 | 63.00 |_E_ | 84.60 Minimum[F] | 47.00 | 72.00 |_E_ | 119.00 | | Percentage ( = _D_ ÷ _E_ ). | | Maximum |_F_ | 16.1 Minimum |_F_ | 7.9 ========================================================================

FOOTNOTES:

[Footnote E: Giving maximum values of percentage, _F_.]

[Footnote F: Giving minimum values of percentage, _F_.]

BEVERLY S. RANDOLPH, M. AM. SOC. C. E. (by letter).--The percentages given by Mr. Purdon would seem to indicate that the length of the grades did not affect the loads in the cases cited, but these percentages are so much below those shown in the table, for similar distances, as to indicate some special conditions which the writer has been unable to find in the text.

The use of the percentage of weight on drivers which is utilized in traction as a measure of the efficiency of the locomotive, while, probably, not applicable to individual machines, is sound for the purposes of comparison of results to be obtained on various portions of a line as far as affected by conditions of grade and alignment. It has the advantage of disregarding questions of temperature, condition of track, character of fuel, etc., which, being the same on all portions of the line, naturally balance and do not affect the comparison. It is, of course, simply a method of expressing the final efficiency of the various parts of the locomotive, and, since it depends entirely on actual results already accomplished, leaves no room for difference of opinion or theoretical error.

The writer has always considered an "under-cylindered" locomotive as a defective machine. All weight is a distinct debit, in the shape of wear and tear of track and running gear, resistance due to gravity on grades, interest on cost, etc. When this weight fails to earn a credit in the way of tractive efficiency, it should not be present.

The statement relative to the performance of locomotives on "Hill _C_" is interesting, especially in that it appears to have been immaterial whether they made a dead start after stopping at the station or approached the foot of the hill at 16 to 18 miles per hour. The momentum would appear to be an insignificant factor.

It is gratifying to note that Mr. Trautwine has been able to brace up the weak member of Table 1 so completely with his detailed data; also that his other results strengthen the conclusions reached in the paper.

FOOTNOTES:

[Footnote A: "The Economic Theory of Railway Location," 1887 edition, p. 502.]

[Footnote B: _Transactions_, Am. Soc. C. E., Vol. L, p. 1.]

[Footnote C: "Nearly 200 tons _exclusive_ of eng. & ten." (Vol. III, p. 176-1/10.)]

[Footnote D: American Railway Engineering and Maintenance of Way Association, Bulletin 84, February, 1907, p. 99.]