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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/18747-8.txt b/18747-8.txt new file mode 100644 index 0000000..7bf7c7b --- /dev/null +++ b/18747-8.txt @@ -0,0 +1,1018 @@ +The Project Gutenberg EBook of Transactions of the American Society of +Civil Engineers, Vol. LXX, Dec. 1910, by Beverly S. Randolph + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 + Locomotive Performance On Grades Of Various Lengths, Paper No. 1172 + +Author: Beverly S. Randolph + +Release Date: July 3, 2006 [EBook #18747] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK AMERICAN SOCIETY OF CIVIL ENGINEERS *** + + + + +Produced by Juliet Sutherland, Sigal Alon and the Online +Distributed Proofreading Team at http://www.pgdp.net + + + + + + + + + +AMERICAN SOCIETY OF CIVIL ENGINEERS + +INSTITUTED 1852 + + +TRANSACTIONS + +Paper No. 1172 + + +LOCOMOTIVE PERFORMANCE ON GRADES OF +VARIOUS LENGTHS. + +BY BEVERLY S. RANDOLPH, M. AM. SOC. C. E. + +WITH DISCUSSION BY MESSRS. C. D. PURDON, JOHN C. TRAUTWINE, JR., +AND BEVERLY S. RANDOLPH. + + + + +In the location of new railways and the improvement of lines already in +operation, it is now well recognized that large economies can be +effected by the careful study of train resistance due to grades and +alignment, distributing this resistance so as to secure a minimum cost +of operation with the means available for construction. + +While engaged in such studies some years ago, the attention of the +writer was attracted by the fact that the usual method of calculating +the traction of a locomotive--by assuming from 20 to 25% of the weight +on the drivers--was subject to no small modification in practice. + +In order to obtain a working basis, for use in relation to this feature, +he undertook the collection of data from the practical operation of +various roads. Subsequent engagements in an entirely different direction +caused this to be laid aside until the present time. The results are +given in Table 1, from which it will be seen that the percentage of +driver weight utilized in draft is a function of the length as well as +the rate of grade encountered in the practical operation of railways. + +In this table, performance will be found expressed as the percentage of +the weight on the drivers which is utilized in draft. This is calculated +on a basis of 6 lb. per ton of train resistance, for dates prior to +1880, this being the amount given by the late A. M. Wellington, M. Am. +Soc. C.. E.,[A] and 4.7 lb. per ton for those of 1908-10, as obtained by +A. C. Dennis, M. Am. Soc. C. E.,[B] assuming this difference to +represent the advance in practice from 1880 to the present time. Most of +the data have been obtained from the "Catalogue of the Baldwin +Locomotive Works" for 1881, to which have been added some later figures +from "Record No. 65" of the same establishment, and also some obtained +by the writer directly from the roads concerned. Being taken thus at +random, the results may be accepted as fairly representative of American +practice. + +Attention should be directed to the fact that the performance of the +10-34 E, Consolidation locomotive on the Lehigh Valley Railroad in 1871 +is practically equal to that of the latest Mallet compounds on the Great +Northern Railway. In other words, in the ratio between the ability to +produce steam and the weight on the drivers there has been no change in +the last forty years. This would indicate that the figures are not +likely to be changed much as long as steam-driven locomotives are in +use. What will obtain with the introduction of electric traction is +"another story." + +These results have also been platted, and are presented in Fig. 1, with +the lengths of grade as abscissas and the percentages of weight utilized +as ordinates. The curve sketched to represent a general average will +show the conditions at a glance. The results may at first sight seem +irregular, but the agreement is really remarkable when the variety of +sources is considered; that in many cases the "reputed" rate of grade is +doubtless given without actual measurement; that the results also +include momentum, the ability to utilize which depends on the conditions +of grade, alignment, and operating practice which obtain about the foot +of each grade; and that the same amount of energy due to momentum will +carry a train farther on a light grade than on a heavy one. + +There are four items in Table 1 which vary materially from the general +consensus. For Item 9, the authorities of the road particularly state +that their loads are light, because, owing to the congested condition of +their business, their trains must make fast time. Item 10 represents +very old practice, certainly prior to 1882, and is "second-hand." The +load consisted of empty coal cars, and the line was very tortuous, so +that it is quite probable that the resistance assumed in the calculation +is far below the actual. Items 15 and 17 are both high. To account for +this, it is to be noted that this road has been recently completed, +regardless of cost in the matter of both track and rolling stock, and +doubtless represents the highest development of railroad practice. Its +rolling stock is all new, and is probably in better condition to offer +low resistance than it will ever be again, and there were no "foreign" +cars in the trains considered. The train resistance, therefore, may be +naturally assumed to be much less than that of roads hauling all classes +of cars, many of which are barely good enough to pass inspection. As the +grades are light in both cases, this feature of train resistance is +larger than in items including heavier grades. Attention should be +called to the fact that a line connecting the two points representing +these items on Fig. 1 would make only a small angle with the sketched +curve, and would be practically parallel to a similar line connecting +the points represented by Items 13 and 16. There is, therefore, an +agreement of ratios, which is all that needs consideration in this +discussion. + +[Illustration: FIG. 1.--DIAGRAM SHOWING PERCENTAGE OF WEIGHT ON DRIVERS +WHICH IS UTILIZED IN TRACTION ON GRADES OF VARIOUS LENGTHS] + +Wellington, in his monumental work on railway location, presents a table +of this character. The percentages of weight on the drivers which is +utilized in draft show the greatest irregularity. He does not give the +length of the grades considered, so that it is impossible to say how far +the introduction of this feature would have contributed to bring order +out of the chaos. In his discussion of the table he admits the +unsatisfactory character of the results, and finally decides on 25% as a +rough average, "very approximately the safe operating load in regular +service." He further states that a number of results, which he omits for +want of space, exceeds 33 per cent. The highest shown in Table 1 will be +found in Item 1 (0.06 mile, 0.066 grade), showing 33 per cent. There is +no momentum effect here, as the grade is a short incline extending down +to the river, and the start is necessarily a "dead" one. The reports of +Item 3, which shows 31%, and Item 5, which shows 27%, state specifically +that the locomotives will stop and start the loads given at any point on +the grade. + +The results of a series of experiments reported by Mr. A. C. Dennis in +his paper, "Virtual Grades for Freight Trains," previously referred to, +indicate a utilization of somewhat more than 23%, decreasing with the +speed. + +All this indicates that the general failure of locomotives to utilize +more than from 16 to 18% on long grades, as shown by Table 1, can only +be due to the failure of the boilers to supply the necessary steam. +While the higher percentage shown for the shorter grades may be ascribed +largely to momentum present when the foot of the grade is reached, the +energy due to stored heat is responsible for a large portion of it. + +When a locomotive has been standing still, or running with the steam +consumption materially below the production, the pressure accumulates +until it reaches the point at which the safety valve is "set." This +means that the entire machine is heated to a temperature sufficient to +maintain this pressure in the boiler. When the steam consumption begins +to exceed the production, this temperature is reduced to a point where +the consumption and production balance. + +The heat represented by this difference in temperature has passed into +the steam used, thus adding to the energy supplied by the combustion +going on in the furnace. The engines, therefore, are able to do +considerably more work during the time the pressure is falling than they +can do after the fall has ceased. + +The curve in Fig. 1 would indicate that the energy derived from the two +sources just discussed is practically dissipated at 15 miles, though the +position of the points representing Items 16, 18, 19, 20, and 21 would +indicate that this takes place more frequently between 10 and 12 miles. +From this point onward the performance depends on the efficiency of the +steam production, which does not appear to be able to utilize more than +16% of the weight on the drivers. The diagrams presented by Mr. Dennis +in his paper on virtual grades, and by John A. Fulton, M. Am. Soc. +C. E., in his discussion of that paper, indicate that similar results +would be shown were they extended to include the distance named. + +From this it would appear that a locomotive is capable of hauling a +larger train on grades less than 10 miles in length than on longer +grades, and that, even when unexpectedly stopped, it is capable of +starting again as soon as the steam pressure is sufficiently built up. +Conversely, it should be practicable to use a higher rate of ascent on +shorter grades on any given line without decreasing the load which can +be hauled over it. In other words, what is known as the "ruling grade" +is a function, strictly speaking, of the length as well as the rate of +grade. + +In any discussions of the practicability of using a higher rate on the +short grades, which the writer has seen, the most valid objection has +appeared to be the danger of stalling and consequent delay. As far as +momentum is relied on, this objection is valid. Within the limits of the +load which can be handled by the steam, it has small value, as it is +only a question of waiting a few minutes until the pressure can be built +up to the point at which the load can be handled. As this need only be +an occasional occurrence, it is not to be balanced against any material +saving in cost of construction. + +The writer does not know of any experiments which will throw much light +on the value of heat storage as separated from momentum, though the +following discussion may prove suggestive: + +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. + | | | |Compensation. + | | | | |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. + | | | | | | | | | | + | | | | | | | | | | +--+-----+------+------+----+-----+--+-----+-----+-----+-------------------- + 1| 0.06|0.066 | | | 115| | 37.5| 29 |0.358| 8-28-1/3 C + 2| 0.33|0.0203|25°20'| | 242|25| 35 | 23 |0.285| 8-28 C + 3| 1.0 |0.06 |16° |0.05| 192|22| 57.5| 50 |0.310|10-36 E + 4| 1.3 |0.0127| | | 600|16| 40 | 32.5|0.300|Mogul. + 5| 1.4 |0.0128| 3°12'| | 750|15| 51 | 44 |0.270|10-34 E + 6| 2.0 |0.01 | | |1,000|15| 51 | 44 |0.291|10-34 E + 7| 2.2 |0.013 | 3° | | 725|15| 51 | 44 |0.245|10-34 E + 8| 2.5 |0.0144| 6° | | 400|27| 42 | 32 |0.237|10-32 E + 9| 2.5 |0.004 | | |2,700|70| 96.7| 85.8|0.207| H 6 - A +10| 3.5 |0.033 |14° | | 100|25| 35 | 35 |0.160| +11| 3.6 |0.035 |10° |0.05| 236|22| 57.5| 50 |0.245|10-36 E +12| 4.0 |0.0085| 4° | |1,020|30| 51 | 44 |0.256|10-34 E +13| 6.0 |0.0145| | | 308|25| 38 | 28 |0.207|10-28 D +14| 6.0 |0.020 |10° |0.05| 460|32| 57.5| 50 |0.242|10-34 E +15| 7.5 |0.002 | | C |6,152|86|134.5|109.5|0.243|Mallet. +16| 9.75|0.018 | | | 200|18| 29 | 29 |0.170| +17|10.0 |0.006 | | C |6,173|86|299 |265 |0.203|Mallet. +18|12.0 |0.018 |10° | | 280|30| 51 | 44 |0.160|10-34 E +19|12.0 |0.022 | | | 850|74|175 |156 |0.166|D-D 16 +20|13.0 |0.022 | | | 800|74|177 |158 |0.153|D-D 1 +21|13.0 |0.022 |14° | | 415|50| 91 | 83 |0.154|Consol. +22|16.0 |0.0044| | | 950|30| 51 | 44 |0.164|10-34 E +23|20.0 |0.022 | | | 500|62| 97.5| 90 |0.170|F 8, Consol. +24|20.0 |0.022 | | | 800|74|177 |158 |0.159|L-1, Mallet. +=========================================================================== + + +============================================================================ + |Maker. |Railroad. |Reporting Officer. |Year. +--+--------+----------------------------+-----------------------------+----- + 1|Baldwin.|Morgan's Louisiana & Texas |Newell Tilton, Asst. Supt. |1880 + 2| " |Long Island |S. Spencer, Gen. Supt. |1878 + 3| " |Atchison, Topeka & Santa Fe |J. D. Burr, Asst. Engr. |1879 + 4| " |Chillan & 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 the weight on the drivers, and using the +lesser of the two results as the tractive power. + +Locomotives of different classes, and hauling known loads, were run over +a freight division, the cars being weighed for the purpose; thus the +maximum load which could be handled over a division, or different parts +of a division, was ascertained, and this proportion of tonnage to +tractive power was used in rating all classes. + +Of course, this method was not mathematically accurate, as the condition +of track, the weather, and the personal equation of the locomotive +engineers all had an effect, but, later, when correcting the rating by +tests with dynamometers, it was found that the results were fairly +practical. + +There were three hills where the rate of grade was the same as the rest +of the division, but where the length was much in excess of other grades +of the same rate. + +Designating these hills as _A_, _B_, and _C_, the lengths are, +respectively, 2.44, 3.57, and 4.41 miles. There were no other grades of +the same rate exceeding 1 mile. + +In one class of freight engines, 10-wheel Brooks, the weight of the +engine was 197,900 lb.; tender, 132,800 lb.; weight on drivers, 142,600 +lb.; boiler pressure, 200 lb.; and tractive power of cylinders, 33,300 +lb. + +On Hill _A_ these engines are rated at 865 tons, as compared with 945 on +other parts of the division. As the engine weighs 165 tons and the +caboose 15 tons, 180 tons should be added, making the figures, 1,045 and +1,125 tons. Thus the length of the grade, 2.44 miles, makes the tractive +power on it 92% of that on shorter grades. + +On Hill _B_, the rating, adding 180 tons as above, is 1,160 and 1,230 +tons, respectively, giving 94% for 3.57 miles. + +On Hill _C_, the rating, with 180 tons added, is 1,130 and 1,230 tons, +making 92% for 4.41 miles. + +Taking the same basis as the author, namely, 4.7 lb. per ton, rate of +grade × 20, and weight on drivers, gives: + +Hill _A_, 18.078%, remainder of division, 19.462% +Hill _B_, 20.068%, " " " 21.279% +Hill _C_, 19.549%, " " " 21.279% + +It will be noted that the author uses the weight on the drivers as the +criterion, but the tractive power is not directly as the weight on the +drivers, some engines being over-cylindered, or under-cylindered; in the +class of engines above mentioned the tractive power is 23.35% of the +weight on the drivers. + +The writer made a study of several dynamometer tests on Hill _C_. There +is a grade of the same rate, about 1 mile long, near this hill, and a +station near its foot, but there is sufficient level grade between this +station and the foot of the hill to get a good start. + +All the engines of the above class, loaded for Hill _C_, gained speed on +the 1-mile grade, but began to fall below the theoretical speed at a +point about 2-1/4 miles from the foot of the hill. This condition +occurred when the trains stopped at the station and also when they +passed it at a rate of some 16 or 18 miles per hour, the speed becoming +less and less as the top of the hill was approached. + +The writer concludes that the author might stretch his opinion as to +using heavier rates of grade on shorter hills than 10 miles, and indeed +his diagram seems to intimate as much, and that, for economical +operation, the maximum rate of grade should be reduced after a length of +about 2 miles has been reached, and more and more in proportion to the +length of the hill, in order that the same rating could be applied all +over a division. + +This conclusion might be modified by local conditions, such as an +important town where cars might be added to or taken from the train. + +While it does not seem practicable to the writer to calculate what the +reduction of rate of grade should be, a consensus of results of +operation on different lengths of grade might give sufficient data to +reach some conclusion on the matter. + +The American Railway Engineering and Maintenance of Way Association has +a Committee on "Railway Economics," which is studying such matters, but +so far as the writer knows it has not given this question any +consideration. + +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.] + + + + + +End of the Project Gutenberg EBook of Transactions of the American Society +of Civil Engineers, Vol. LXX, Dec. 1910, by Beverly S. 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Randolph. + </title> + <style type="text/css"> +/*<![CDATA[ XML blockout */ +<!-- + p { margin-top: .75em; + text-align: justify; + margin-bottom: .75em; + } + h1,h2,h3,h4,h5,h6 { + text-align: center; /* all headings centered */ + clear: both; + } + hr { width: 33%; + margin-top: 2em; + margin-bottom: 2em; + margin-left: auto; + margin-right: auto; + clear: both; + } + + table {margin-left: auto; margin-right: auto;} + + td {border-width: 1px; border-color: gray; font-size: 85%;} + tr.topr td {border-top-width: 6px; border-color: gray; + border-style: double solid solid solid; font-size: 75%; text-align: center;} + tr.topr2 td {border-top-width: 6px; border-color: gray; + border-style: double solid dotted solid;} + tr.midr td {border-style: none solid dotted solid;} + tr.botr td {border-bottom-width: 6px; border-color: gray; + border-style: none solid double solid;} + tr.botr2 td {border-bottom-width: 6px; border-color: gray; + border-style: none solid none solid;} + .tdcenter {text-align: center;} /* aligning cell content to the center */ + .tdright {text-align: right; padding-right: .4em; margin-left: .5em} /* aligning cell content to the right */ + .tdrightld {text-align: right; padding-right: .9em;} /* aligning cell content to the right, less digit */ + .tdrightld2 {text-align: right; padding-right: 1.4em;} /* aligning cell content to the right, less 2 digits */ + .tdrightnd {text-align: right; padding-right: 1.2em;} /* aligning cell content to the right, no decimal */ + .tdrightnd3 {text-align: right; padding-right: 2.2em;} /* aligning cell content to the right, no decimal */ + .tdleft {text-align: left; padding-left: .4em;} + .tdleftld {text-align: left; padding-left: .9em;} + + body{margin-left: 10%; + margin-right: 10%; + } + + a {text-decoration: none;} + + img {border: none;} + + .pagenum { /* uncomment the next line for invisible page numbers */ + /* visibility: hidden; */ + position: absolute; + left: 92%; + font-size: smaller; + text-align: right; + color: gray; + font-style: normal; font-weight: normal; font-variant: normal; + background-color: inherit; + } /* page numbers */ + + .blockquot{margin-left: 5%; margin-right: 10%;} + .section {margin-top: 1.5em;} + + .center {text-align: center;} + .smcap {font-variant: small-caps;} + .lowercase {text-transform:lowercase; } + .u {text-decoration: underline;} + + .caption {font-weight: bold;} + + .figcenter {margin: auto; text-align: center;} + + .figleft {float: left; clear: left; margin-left: 0; margin-bottom: 1em; margin-top: + 1em; margin-right: 1em; padding: 0; text-align: center;} + + .figright {float: right; clear: right; margin-left: 1em; margin-bottom: 1em; + margin-top: 1em; margin-right: 0; padding: 0; text-align: center;} + + .footnotes {border: dashed 1px;} + .footnote {margin-left: 10%; margin-right: 10%; font-size: 0.9em;} + .footnote .label {position: absolute; right: 84%; text-align: right;} + .fnanchor {vertical-align: super; font-size: .8em; text-decoration: none;} + // --> + /* XML end ]]>*/ + </style> + </head> +<body> + + +<pre> + +The Project Gutenberg EBook of Transactions of the American Society of +Civil Engineers, Vol. LXX, Dec. 1910, by Beverly S. Randolph + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 + Locomotive Performance On Grades Of Various Lengths, Paper No. 1172 + +Author: Beverly S. Randolph + +Release Date: July 3, 2006 [EBook #18747] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK AMERICAN SOCIETY OF CIVIL ENGINEERS *** + + + + +Produced by Juliet Sutherland, Sigal Alon and the Online +Distributed Proofreading Team at http://www.pgdp.net + + + + + + +</pre> + + + +<p><span class='pagenum'><a name="Page_321" id="Page_321">[321]</a></span></p> + + + + +<h2>AMERICAN SOCIETY OF CIVIL ENGINEERS</h2> + +<h3>INSTITUTED 1852</h3> + +<hr style="width: 45%;" /> + +<h1>TRANSACTIONS</h1> + +<hr style="width: 45%;" /> + +<h3>Paper No. 1172</h3> + + +<h1>LOCOMOTIVE PERFORMANCE ON GRADES OF +VARIOUS LENGTHS.</h1> + +<h2><span class="smcap">By Beverly S. Randolph, M. Am. Soc. C. E.</span></h2> + +<hr style="width: 45%;" /> + +<h2><span class="smcap">With Discussion by Messrs. C. D. Purdon, John C. Trautwine, Jr., +and Beverly S. Randolph.</span> +</h2> + +<hr style="width: 45%;" /> + + + +<p>In the location of new railways and the improvement of lines +already in operation, it is now well recognized that large economies +can be effected by the careful study of train resistance due to grades +and alignment, distributing this resistance so as to secure a minimum +cost of operation with the means available for construction.</p> + +<p>While engaged in such studies some years ago, the attention of the +writer was attracted by the fact that the usual method of calculating +the traction of a locomotive—by assuming from 20 to 25% of the +weight on the drivers—was subject to no small modification in practice.</p> + +<p>In order to obtain a working basis, for use in relation to this +feature, he undertook the collection of data from the practical operation +of various roads. Subsequent engagements in an entirely different +direction caused this to be laid aside until the present time. The +results are given in <a href="#table1">Table 1</a>, from which it will be seen that the +percentage of driver weight utilized in draft is a function of the +length as well as the rate of grade encountered in the practical operation +of railways.</p> + +<p>In this table, performance will be found expressed as the percentage +of the weight on the drivers which is utilized in draft. This +is calculated on a basis of 6 lb. per ton of train resistance, for dates +<span class='pagenum'><a name="Page_322" id="Page_322">[322]</a></span>prior to 1880, this being the amount given by the late A. M. Wellington, +M. Am. Soc. C.. E.,<a name="FNanchor_A_3" id="FNanchor_A_3"></a><a href="#Footnote_A_3" class="fnanchor">[A]</a> and 4.7 lb. per ton for those of 1908-10, as +obtained by A. C. Dennis, M. Am. Soc. C. E.,<a name="FNanchor_B_4" id="FNanchor_B_4"></a><a href="#Footnote_B_4" class="fnanchor">[B]</a> assuming this difference +to represent the advance in practice from 1880 to the present +time. Most of the data have been obtained from the "Catalogue of +the Baldwin Locomotive Works" for 1881, to which have been added +some later figures from "Record No. 65" of the same establishment, +and also some obtained by the writer directly from the roads concerned. +Being taken thus at random, the results may be accepted as +fairly representative of American practice.</p> + +<p>Attention should be directed to the fact that the performance of +the 10-34 E, Consolidation locomotive on the Lehigh Valley Railroad +in 1871 is practically equal to that of the latest Mallet compounds on +the Great Northern Railway. In other words, in the ratio between +the ability to produce steam and the weight on the drivers there has +been no change in the last forty years. This would indicate that the +figures are not likely to be changed much as long as steam-driven +locomotives are in use. What will obtain with the introduction of +electric traction is "another story."</p> + +<p>These results have also been platted, and are presented in <a href="#fig1">Fig. 1</a>, +with the lengths of grade as abscissas and the percentages of weight +utilized as ordinates. The curve sketched to represent a general +average will show the conditions at a glance. The results may at first +sight seem irregular, but the agreement is really remarkable when the +variety of sources is considered; that in many cases the "reputed" rate +of grade is doubtless given without actual measurement; that the +results also include momentum, the ability to utilize which depends +on the conditions of grade, alignment, and operating practice which +obtain about the foot of each grade; and that the same amount of +energy due to momentum will carry a train farther on a light grade +than on a heavy one.</p> + +<p>There are four items in <a href="#table1">Table 1</a> which vary materially from the +general consensus. For Item 9, the authorities of the road particularly +state that their loads are light, because, owing to the congested +condition of their business, their trains must make fast time. Item 10 +represents very old practice, certainly prior to 1882, and is "second-hand." +<span class='pagenum'><a name="Page_323" id="Page_323">[323]</a></span>The load consisted of empty coal cars, and the line was very +tortuous, so that it is quite probable that the resistance assumed in +the calculation is far below the actual. Items 15 and 17 are both +high. To account for this, it is to be noted that this road has been +recently completed, regardless of cost in the matter of both track and +rolling stock, and doubtless represents the highest development of +railroad practice. Its rolling stock is all new, and is probably in +better condition to offer low resistance than it will ever be again, and +there were no "foreign" cars in the trains considered. The train +resistance, therefore, may be naturally assumed to be much less than +that of roads hauling all classes of cars, many of which are barely +good enough to pass inspection. As the grades are light in both cases, +this feature of train resistance is larger than in items including +heavier grades. Attention should be called to the fact that a line +connecting the two points representing these items on <a href="#fig1">Fig. 1</a> would +make only a small angle with the sketched curve, and would be +practically parallel to a similar line connecting the points represented<span class='pagenum'><a name="Page_324" id="Page_324">[324]</a></span> +by Items 13 and 16. There is, therefore, an agreement of ratios, which +is all that needs consideration in this discussion.</p> + +<div class="figcenter" style="width: 629px;"> +<img id="fig1" src="images/fig1.png" width="629" height="459" +alt="Fig. 1.—DIAGRAM SHOWING PERCENTAGE OF WEIGHT ON DRIVERS WHICH IS UTILIZED IN TRACTION ON GRADES OF VARIOUS LENGTHS" +title="Fig. 1.—DIAGRAM SHOWING PERCENTAGE OF WEIGHT ON DRIVERS WHICH IS UTILIZED IN TRACTION ON GRADES OF VARIOUS LENGTHS" /> +<span class="caption">Fig. 1.—DIAGRAM SHOWING PERCENTAGE OF WEIGHT ON DRIVERS WHICH IS +UTILIZED IN TRACTION ON GRADES OF VARIOUS LENGTHS</span> +</div> + +<p>Wellington, in his monumental work on railway location, presents +a table of this character. The percentages of weight on the drivers +which is utilized in draft show the greatest irregularity. He does +not give the length of the grades considered, so that it is impossible +to say how far the introduction of this feature would have contributed +to bring order out of the chaos. In his discussion of the table he +admits the unsatisfactory character of the results, and finally decides +on 25% as a rough average, "very approximately the safe operating +load in regular service." He further states that a number of results, +which he omits for want of space, exceeds 33 per cent. The highest +shown in <a href="#table1">Table 1</a> will be found in Item 1 (0.06 mile, 0.066 grade), +showing 33 per cent. There is no momentum effect here, as the grade +is a short incline extending down to the river, and the start is necessarily +a "dead" one. The reports of Item 3, which shows 31%, and +Item 5, which shows 27%, state specifically that the locomotives will +stop and start the loads given at any point on the grade.</p> + +<p>The results of a series of experiments reported by Mr. A. C. Dennis +in his paper, "Virtual Grades for Freight Trains," previously referred +to, indicate a utilization of somewhat more than 23%, decreasing +with the speed.</p> + +<p>All this indicates that the general failure of locomotives to utilize +more than from 16 to 18% on long grades, as shown by <a href="#table1">Table 1</a>, can +only be due to the failure of the boilers to supply the necessary steam. +While the higher percentage shown for the shorter grades may be +ascribed largely to momentum present when the foot of the grade is +reached, the energy due to stored heat is responsible for a large +portion of it.</p> + +<p>When a locomotive has been standing still, or running with the +steam consumption materially below the production, the pressure +accumulates until it reaches the point at which the safety valve is +"set." This means that the entire machine is heated to a temperature +sufficient to maintain this pressure in the boiler. When the steam consumption +begins to exceed the production, this temperature is reduced +to a point where the consumption and production balance.</p> + +<p>The heat represented by this difference in temperature has passed +into the steam used, thus adding to the energy supplied by the combustion<span class='pagenum'><a name="Page_325" id="Page_325">[325]</a></span> +going on in the furnace. The engines, therefore, are able to +do considerably more work during the time the pressure is falling +than they can do after the fall has ceased.</p> + +<p>The curve in <a href="#fig1">Fig. 1</a> would indicate that the energy derived from +the two sources just discussed is practically dissipated at 15 miles, +though the position of the points representing Items 16, 18, 19, 20, +and 21 would indicate that this takes place more frequently between +10 and 12 miles. From this point onward the performance depends on +the efficiency of the steam production, which does not appear to be +able to utilize more than 16% of the weight on the drivers. The +diagrams presented by Mr. Dennis in his paper on virtual grades, +and by John A. Fulton, M. Am. Soc. C. E., in his discussion of that +paper, indicate that similar results would be shown were they extended +to include the distance named.</p> + +<p>From this it would appear that a locomotive is capable of hauling +a larger train on grades less than 10 miles in length than on longer +grades, and that, even when unexpectedly stopped, it is capable of +starting again as soon as the steam pressure is sufficiently built up. +Conversely, it should be practicable to use a higher rate of ascent on +shorter grades on any given line without decreasing the load which +can be hauled over it. In other words, what is known as the "ruling +grade" is a function, strictly speaking, of the length as well as the +rate of grade.</p> + +<p>In any discussions of the practicability of using a higher rate +on the short grades, which the writer has seen, the most valid +objection has appeared to be the danger of stalling and consequent +delay. As far as momentum is relied on, this objection is valid. +Within the limits of the load which can be handled by the steam, it +has small value, as it is only a question of waiting a few minutes +until the pressure can be built up to the point at which the load can be +handled. As this need only be an occasional occurrence, it is not to +be balanced against any material saving in cost of construction.</p> + +<p>The writer does not know of any experiments which will throw +much light on the value of heat storage as separated from momentum, +though the following discussion may prove suggestive:</p> + +<p>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<span class='pagenum'><a name="Page_328" id="Page_328">[328]</a></span> +grade (as in Item 15 of <a href="#table1">Table 1</a>) 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.</p> + +<h4 id="table1">TABLE 1.</h4> + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary="Table 1"> +<tr class='topr'> + <td>Item No.</td> + <td>Length of grade, in miles.</td> + <td>Rate of grade.</td> + <td>Maximum curvature.</td> + <td>Compen<br />sation.</td> + <td>Gross weight of load, in tons.</td> + <td>Weight of tender, in tons.</td> + <td>Weight of locomotive, in tons.</td> + <td>Weight on drivers, in tons.</td> + <td>Percentage of weight on drivers utilized in draft.</td> + <td>Class.</td> + <td>Maker.</td> + <td>Railroad.</td> + <td>Reporting Officer.</td> + <td>Year.</td> + <td>Source of Data.</td> + <td>Remarks.</td> +</tr> +<tr class='midr'> + <td class='tdright'> 1</td> + <td class='tdright'> 0.06</td> + <td class='tdleft'>0.066</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 115</td> + <td class='tdright'> </td> + <td class='tdright'> 37.5</td> + <td class='tdrightnd'> 29</td> + <td class='tdright'>0.358</td> + <td class='tdcenter'> 8-28-1/3 C</td> + <td class='tdcenter'>Baldwin.</td> + <td class='tdleft'>Morgan's Louisiana & Texas</td> + <td class='tdcenter'>Newell Tilton, Asst. Supt.</td> + <td class='tdleft'>1880</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 134</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'> 2</td> + <td class='tdright'> 0.33</td> + <td class='tdleft'>0.0203</td> + <td class='tdleft'>25°20'</td> + <td class='tdleft'> </td> + <td class='tdright'> 242</td> + <td class='tdright'>25</td> + <td class='tdrightnd'> 35</td> + <td class='tdrightnd'> 23</td> + <td class='tdright'>0.285</td> + <td class='tdcenter'> 8-28 C</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Long Island</td> + <td class='tdcenter'>S. Spencer, Gen. Supt.</td> + <td class='tdleft'>1878</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 72</td> + <td class='tdleft'>10 miles per hour.</td> +</tr> +<tr class='midr'> + <td class='tdright'> 3</td> + <td class='tdrightld'>1.0</td> + <td class='tdleft'>0.06</td> + <td class='tdleft'>16°</td> + <td class='tdleft'>0.05</td> + <td class='tdright'> 192</td> + <td class='tdright'>22</td> + <td class='tdright'> 57.5</td> + <td class='tdrightnd'> 50</td> + <td class='tdright'>0.310</td> + <td class='tdcenter'>10-36 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Atchison, Topeka & Santa Fe</td> + <td class='tdcenter'>J. D. Burr, Asst. Engr.</td> + <td class='tdleft'>1879</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 115</td> + <td class='tdleft'>8 miles per hour. Stops and starts on grade.</td> +</tr> +<tr class='midr'> + <td class='tdright'> 4</td> + <td class='tdrightld'>1.3</td> + <td class='tdleft'>0.0127</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 600</td> + <td class='tdright'>16</td> + <td class='tdrightnd'> 40</td> + <td class='tdright'> 32.5</td> + <td class='tdright'>0.300</td> + <td class='tdcenter'>Mogul.</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Chillan & Talcahuana</td> + <td class='tdcenter'>J. E. Martin, Local Supt.</td> + <td class='tdleft'>1879</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 100</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'> 5</td> + <td class='tdrightld'>1.4</td> + <td class='tdleft'>0.0128</td> + <td class='tdleftld'> 3°12'</td> + <td class='tdleft'> </td> + <td class='tdright'> 750</td> + <td class='tdright'>15</td> + <td class='tdrightnd'> 51</td> + <td class='tdrightnd'> 44</td> + <td class='tdright'>0.270</td> + <td class='tdcenter'>10-34 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Chicago, Burlington & Quincy</td> + <td class='tdcenter'>H. B. Stone</td> + <td class='tdleft'>1880</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 116</td> + <td class='tdleft'>Stops and starts at any point on grade.</td> +</tr> +<tr class='midr'> + <td class='tdright'> 6</td> + <td class='tdrightld'>2.0</td> + <td class='tdleft'>0.01</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'>1,000</td> + <td class='tdright'>15</td> + <td class='tdrightnd'> 51</td> + <td class='tdrightnd'> 44</td> + <td class='tdright'>0.291</td> + <td class='tdcenter'>10-34 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Chicago, Burlington & Quincy</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>1880</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 116</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'> 7</td> + <td class='tdrightld'>2.2</td> + <td class='tdleft'>0.013</td> + <td class='tdleftld'> 3°</td> + <td class='tdleft'> </td> + <td class='tdright'> 725</td> + <td class='tdright'>15</td> + <td class='tdrightnd'> 51</td> + <td class='tdrightnd'> 44</td> + <td class='tdright'>0.245</td> + <td class='tdcenter'>10-34 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Chicago, Burlington & Quincy</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>1880</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 116</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'> 8</td> + <td class='tdrightld'>2.5</td> + <td class='tdleft'>0.0144</td> + <td class='tdleftld'> 6°</td> + <td class='tdleft'> </td> + <td class='tdright'> 400</td> + <td class='tdright'>27</td> + <td class='tdrightnd'> 42</td> + <td class='tdrightnd'> 32</td> + <td class='tdright'>0.237</td> + <td class='tdcenter'>10-32 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>St. Louis & San Francisco</td> + <td class='tdcenter'>C. W. Rogers, Gen. Mgr.</td> + <td class='tdleft'>1879</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 87</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'> 9</td> + <td class='tdrightld'>2.5</td> + <td class='tdleft'>0.004</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'>2,700</td> + <td class='tdright'>70</td> + <td class='tdright'> 96.7</td> + <td class='tdright'> 85.8</td> + <td class='tdright'>0.207</td> + <td class='tdcenter'> H 6 - A</td> + <td class='tdcenter'>Pa. R.R</td> + <td class='tdleft'>Cumberland Valley.</td> + <td class='tdcenter'> </td> + <td class='tdleft'>1910</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>10</td> + <td class='tdrightld'>3.5</td> + <td class='tdleft'>0.033</td> + <td class='tdleft'>14°</td> + <td class='tdleft'> </td> + <td class='tdright'> 100</td> + <td class='tdright'>25</td> + <td class='tdrightnd'> 35</td> + <td class='tdrightnd'> 35</td> + <td class='tdright'>0.160</td> + <td class='tdcenter'> </td> + <td class='tdcenter'> </td> + <td class='tdleft'> </td> + <td class='tdcenter'> </td> + <td class='tdleft'>1910</td> + <td class='tdleft'>Trautwine's Pocket Book, Ed. 1882, p. 412</td> + <td class='tdleft'>Empty cars; many curves and reversions.</td> +</tr> +<tr class='midr'> + <td class='tdright'>11</td> + <td class='tdrightld'>3.6</td> + <td class='tdleft'>0.035</td> + <td class='tdleft'>10°</td> + <td class='tdleft'>0.05</td> + <td class='tdright'> 236</td> + <td class='tdright'>22</td> + <td class='tdrightnd'> 57.5</td> + <td class='tdrightnd'> 50</td> + <td class='tdright'>0.245</td> + <td class='tdcenter'>10-36 E</td> + <td class='tdcenter'>Baldwin.</td> + <td class='tdleft'>Atchison, Topeka & Santa Fe</td> + <td class='tdcenter'>J. D. Burr, Asst. Engr.</td> + <td class='tdleft'>1879</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 114</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>12</td> + <td class='tdrightld'>4.0</td> + <td class='tdleft'>0.0085</td> + <td class='tdleftld'> 4°</td> + <td class='tdleft'> </td> + <td class='tdright'>1,020</td> + <td class='tdright'>30</td> + <td class='tdrightnd'> 51</td> + <td class='tdrightnd'> 44</td> + <td class='tdright'>0.256</td> + <td class='tdcenter'>10-34 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Missouri Pacific</td> + <td class='tdcenter'>John Hewitt, Supt. M. P.</td> + <td class='tdleft'>1880</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 112</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>13</td> + <td class='tdrightld'>6.0</td> + <td class='tdleft'>0.0145</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 308</td> + <td class='tdright'>25</td> + <td class='tdrightnd'> 38</td> + <td class='tdrightnd'> 28</td> + <td class='tdright'>0.207</td> + <td class='tdcenter'>10-28 D</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Western Maryland</td> + <td class='tdcenter'>D. Holtz, M. of Mach'y.</td> + <td class='tdleft'>1878</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 86</td> + <td class='tdleft'>12 miles per hour.</td> +</tr> +<tr class='midr'> + <td class='tdright'>14</td> + <td class='tdrightld'>6.0</td> + <td class='tdleft'>0.020</td> + <td class='tdleft'>10°</td> + <td class='tdleft'>0.05</td> + <td class='tdright'> 460</td> + <td class='tdright'>32</td> + <td class='tdrightnd'> 57.5</td> + <td class='tdrightnd'> 50</td> + <td class='tdright'>0.242</td> + <td class='tdcenter'>10-34 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Atchison, Topeka & Santa Fe</td> + <td class='tdcenter'>J. D. Burr, Asst. Engr.</td> + <td class='tdleft'>1879</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 114</td> + <td class='tdleft'>8 miles per hour.</td> +</tr> +<tr class='midr'> + <td class='tdright'>15</td> + <td class='tdrightld'>7.5</td> + <td class='tdleft'>0.002</td> + <td class='tdleft'> </td> + <td class='tdleft'> C</td> + <td class='tdright'>6,152</td> + <td class='tdright'>86</td> + <td class='tdright'>134.5</td> + <td class='tdright'>109.5</td> + <td class='tdright'>0.243</td> + <td class='tdcenter'>Mallet.</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Virginian Ry.</td> + <td class='tdcenter'> </td> + <td class='tdleft'>1910</td> + <td class='tdleft'><i>Engineering News</i>, Jan. 13, 1910.</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>16</td> + <td class='tdright'> 9.75</td> + <td class='tdleft'>0.018</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 200</td> + <td class='tdright'>18</td> + <td class='tdrightnd'> 29</td> + <td class='tdrightnd'> 29</td> + <td class='tdright'>0.170</td> + <td class='tdcenter'> </td> + <td class='tdcenter'> </td> + <td class='tdleft'>Pennsylvania</td> + <td class='tdcenter'> </td> + <td class='tdleft'>1910</td> + <td class='tdleft'>Trautwine's Pocket Book, Ed. 1882, p. 412</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>17</td> + <td class='tdrightld'>10.0</td> + <td class='tdleft'>0.006</td> + <td class='tdleft'> </td> + <td class='tdleft'> C</td> + <td class='tdright'>6,173</td> + <td class='tdright'>86</td> + <td class='tdrightnd'>299</td> + <td class='tdrightnd'>265</td> + <td class='tdright'>0.203</td> + <td class='tdcenter'>Mallet.</td> + <td class='tdcenter'>Baldwin.</td> + <td class='tdleft'>Virginian Ry.</td> + <td class='tdcenter'> </td> + <td class='tdleft'>1910</td> + <td class='tdleft'><i>Engineering News</i>, Jan. 13, 1910.</td> + <td class='tdleft'>Road locomotive and helper.</td> +</tr> +<tr class='midr'> + <td class='tdright'>18</td> + <td class='tdrightld'>12.0</td> + <td class='tdleft'>0.018</td> + <td class='tdleft'>10°</td> + <td class='tdleft'> </td> + <td class='tdright'> 280</td> + <td class='tdright'>30</td> + <td class='tdrightnd'> 51</td> + <td class='tdrightnd'> 44</td> + <td class='tdright'>0.160</td> + <td class='tdcenter'>10-34 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Lehigh Valley, Wyoming Div.</td> + <td class='tdcenter'>A. Mitchell, Div. Supt.</td> + <td class='tdleft'>1871</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 112</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>19</td> + <td class='tdrightld'>12.0</td> + <td class='tdleft'>0.022</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 850</td> + <td class='tdright'>74</td> + <td class='tdrightnd'>175</td> + <td class='tdrightnd'>156</td> + <td class='tdright'>0.166</td> + <td class='tdcenter'>D-D 16</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Great Northern</td> + <td class='tdcenter'>Grafton Greenough.</td> + <td class='tdleft'>1908</td> + <td class='tdleft'>Baldwin Loco. Wks. Record, No. 65, p. 29</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>20</td> + <td class='tdrightld'>13.0</td> + <td class='tdleft'>0.022</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 800</td> + <td class='tdright'>74</td> + <td class='tdrightnd'>177</td> + <td class='tdrightnd'>158</td> + <td class='tdright'>0.153</td> + <td class='tdcenter'>D-D 1</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Great Northern</td> + <td class='tdcenter'>Grafton Greenough.</td> + <td class='tdleft'>1908</td> + <td class='tdleft'>Baldwin Loco. Wks. Record, No. 65, p. 29</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>21</td> + <td class='tdrightld'>13.0</td> + <td class='tdleft'>0.022</td> + <td class='tdleft'>14°</td> + <td class='tdleft'> </td> + <td class='tdright'> 415</td> + <td class='tdright'>50</td> + <td class='tdrightnd'> 91</td> + <td class='tdrightnd'> 83</td> + <td class='tdright'>0.154</td> + <td class='tdcenter'>Consol.</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Baltimore & Ohio</td> + <td class='tdcenter'>F. E. Blaser, Div. Supt.</td> + <td class='tdleft'>1910</td> + <td class='tdleft'> </td> + <td class='tdleft'>Very crooked line. Uncompensated.</td> +</tr> +<tr class='midr'> + <td class='tdright'>22</td> + <td class='tdrightld'>16.0</td> + <td class='tdleft'>0.0044</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 950</td> + <td class='tdright'>30</td> + <td class='tdrightnd'> 51</td> + <td class='tdrightnd'> 44</td> + <td class='tdright'>0.164</td> + <td class='tdcenter'>10-34 E</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Central of N. J.</td> + <td class='tdcenter'>W. W. Stearns, Asst.Gen.Supt.</td> + <td class='tdleft'>1880</td> + <td class='tdleft'>Baldwin Catalogue, 1881, p. 113</td> + <td class='tdleft'> </td> +</tr> +<tr class='midr'> + <td class='tdright'>23</td> + <td class='tdrightld'>20.0</td> + <td class='tdleft'>0.022</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 500</td> + <td class='tdright'>62</td> + <td class='tdrightnd'> 97.5</td> + <td class='tdrightnd'> 90</td> + <td class='tdright'>0.170</td> + <td class='tdcenter'>F 8, Consol.</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Great Northern</td> + <td class='tdcenter'>Grafton Greenough.</td> + <td class='tdleft'>1908</td> + <td class='tdleft'>Baldwin Loco. Wks. Record, No. 65, p. 29</td> + <td class='tdleft'> </td> +</tr> +<tr class='botr'> + <td class='tdright'>24</td> + <td class='tdrightld'>20.0</td> + <td class='tdleft'>0.022</td> + <td class='tdleft'> </td> + <td class='tdleft'> </td> + <td class='tdright'> 800</td> + <td class='tdright'>74</td> + <td class='tdrightnd'>177</td> + <td class='tdrightnd'>158</td> + <td class='tdright'>0.159</td> + <td class='tdcenter'>L-1, Mallet.</td> + <td class='tdcenter'> "</td> + <td class='tdleft'>Great Northern</td> + <td class='tdcenter'>Grafton Greenough.</td> + <td class='tdleft'>1906</td> + <td class='tdleft'>Baldwin Loco. Wks. Record, No. 65, p. 29</td> + <td class='tdleft'> </td> +</tr> +</table></div> + + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + + + +<hr style="width: 65%;" /> +<p><span class='pagenum'><a name="Page_329" id="Page_329">[329]</a></span></p> + +<h2><a name="DISCUSSION" id="DISCUSSION"></a>DISCUSSION</h2> + + +<p class="section"><span class="smcap">C. D. Purdon, M. Am. Soc. C. E.</span> (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 the weight on the drivers, +and using the lesser of the two results as the tractive power.</p> + +<p>Locomotives of different classes, and hauling known loads, were run +over a freight division, the cars being weighed for the purpose; thus +the maximum load which could be handled over a division, or different +parts of a division, was ascertained, and this proportion of tonnage +to tractive power was used in rating all classes.</p> + +<p>Of course, this method was not mathematically accurate, as the +condition of track, the weather, and the personal equation of the +locomotive engineers all had an effect, but, later, when correcting the +rating by tests with dynamometers, it was found that the results were +fairly practical.</p> + +<p>There were three hills where the rate of grade was the same as the +rest of the division, but where the length was much in excess of other +grades of the same rate.</p> + +<p>Designating these hills as <i>A</i>, <i>B</i>, and <i>C</i>, the lengths are, respectively, +2.44, 3.57, and 4.41 miles. There were no other grades of the same +rate exceeding 1 mile.</p> + +<p>In one class of freight engines, 10-wheel Brooks, the weight of the +engine was 197,900 lb.; tender, 132,800 lb.; weight on drivers, 142,600 +lb.; boiler pressure, 200 lb.; and tractive power of cylinders, 33,300 lb.</p> + +<p>On Hill <i>A</i> these engines are rated at 865 tons, as compared with +945 on other parts of the division. As the engine weighs 165 tons and +the caboose 15 tons, 180 tons should be added, making the figures, 1,045 +and 1,125 tons. Thus the length of the grade, 2.44 miles, makes the +tractive power on it 92% of that on shorter grades.</p> + +<p>On Hill <i>B</i>, the rating, adding 180 tons as above, is 1,160 and +1,230 tons, respectively, giving 94% for 3.57 miles.</p> + +<p>On Hill <i>C</i>, the rating, with 180 tons added, is 1,130 and 1,230 tons, +making 92% for 4.41 miles.</p> + +<p><span class='pagenum'><a name="Page_330" id="Page_330">[330]</a></span> +Taking the same basis as the author, namely, 4.7 lb. per ton, rate +of grade × 20, and weight on drivers, gives:</p> + +<div class="blockquot"> +<p> +Hill <i>A</i>, 18.078%, remainder of division, 19.462%<br /> +Hill <i>B</i>, 20.068%, remainder of division, 21.279%<br /> +Hill <i>C</i>, 19.549%, remainder of division, 21.279%<br /> +</p> +</div> + +<p>It will be noted that the author uses the weight on the drivers as +the criterion, but the tractive power is not directly as the weight on +the drivers, some engines being over-cylindered, or under-cylindered; +in the class of engines above mentioned the tractive power is 23.35% +of the weight on the drivers.</p> + +<p>The writer made a study of several dynamometer tests on Hill <i>C</i>. +There is a grade of the same rate, about 1 mile long, near this hill, +and a station near its foot, but there is sufficient level grade between +this station and the foot of the hill to get a good start.</p> + +<p>All the engines of the above class, loaded for Hill <i>C</i>, gained speed +on the 1-mile grade, but began to fall below the theoretical speed at a +point about 2-1/4 miles from the foot of the hill. This condition occurred +when the trains stopped at the station and also when they passed it +at a rate of some 16 or 18 miles per hour, the speed becoming less +and less as the top of the hill was approached.</p> + +<p>The writer concludes that the author might stretch his opinion as +to using heavier rates of grade on shorter hills than 10 miles, and +indeed his diagram seems to intimate as much, and that, for economical +operation, the maximum rate of grade should be reduced after a +length of about 2 miles has been reached, and more and more in +proportion to the length of the hill, in order that the same rating +could be applied all over a division.</p> + +<p>This conclusion might be modified by local conditions, such as an +important town where cars might be added to or taken from the +train.</p> + +<p>While it does not seem practicable to the writer to calculate what +the reduction of rate of grade should be, a consensus of results of +operation on different lengths of grade might give sufficient data to +reach some conclusion on the matter.</p> + +<p>The American Railway Engineering and Maintenance of Way +Association has a Committee on "Railway Economics," which is studying +such matters, but so far as the writer knows it has not given this +question any consideration.</p> + +<p>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.</p> + + +<p class="section"><span class="smcap">John C. Trautwine, Jr., Assoc. Am. Soc</span>. 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<span class='pagenum'><a name="Page_331" id="Page_331">[331]</a></span> +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.</p> + +<p>In the private notes of John C. Trautwine, Sr., these two cases +are recorded as follows:</p> + +<div class="blockquot"><p>"On the Mahanoy & Broad Mtn. R. R., <i>tank</i> Engines of 35 tons, <i>all +on 8 drivers</i>, draw 40 <i>empty</i> coal cars weighing 100 tons, <i>up</i> 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.)</p> + +<p>"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,<a name="FNanchor_C_5" id="FNanchor_C_5"></a><a href="#Footnote_C_5" class="fnanchor">[C]</a> and a passenger engine takes up 3 cars at +24 miles an hour (large 8 wheels). When more than 3, an auxiliary +engine."</p></div> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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:<a name="FNanchor_D_6" id="FNanchor_D_6"></a><a href="#Footnote_D_6" class="fnanchor">[D]</a></p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary="formatting formula"> +<tr> + <td class='tdleft'>Frictional resistance, on tangent,<br /> in pounds per 2,000 pounds</td> + <td valign='middle' class='tdleft' style="white-space: nowrap; font-size: 200%">}</td> + <td class='tdleft'>= 1 + 90 ÷ C,</td> +</tr> +</table> +</div> + +<p>where <i>C</i> = 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<span class='pagenum'><a name="Page_332" id="Page_332">[332]</a></span> +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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><a href="#table2">Table 2</a> (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."</p> + +<p>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.</p> + +<p>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.</p> + + +<h4 id="table2">TABLE 2.—<span class="smcap">Tractive Force, Catawissa to Lofty</span>.</h4> + + +<div class='center'> +<table border="0" width="100%" cellpadding="0" cellspacing="0" summary="Tractive Force, Catawissa to Lofty"> +<tr class="topr2"> + <td class='tdleft' colspan='2'>Length of grade, in miles</td> + <td class='tdleft' style='width: 2.5em;'> </td> + <td class='tdrightld' style='width: 5em;'> 34.03</td> +</tr> +<tr class="midr"> + <td class='tdleft' rowspan='2'>Grade</td> + <td class='tdleft'>in feet per mile</td> + <td class='tdleft'> </td> + <td class='tdrightld'> 31.47</td> +</tr> +<tr class="midr"> + <td class='tdleft'>percentage</td> + <td class='tdcenter'><i>A</i></td> + <td class='tdright'> 0.597</td> +</tr> +<tr class="midr"> + <td class='tdleft' colspan='2'>Resistances, in pounds per 2,000 lb.,<br /> + <span style="margin-left: 5.5em;">Gravity (=20 <i>A</i>) = 11.94. Friction = 4.70</span></td> + <td class='tdcenter'><i>B</i></td> + <td class='tdrightld'> 16.64</td> +</tr> +<tr class="midr"> + <td colspan='2' rowspan='3'> + <table border="0" width="100%" cellpadding="4" cellspacing="0" summary="internal table 1 for Tractive Force, Catawissa to Lofty"> + <tr class="midr"> + <td class='tdcenter'><span style="margin-left: 2.5em;">Load:</span></td> + <td class='tdcenter'> Cars.</td> + <td class='tdcenter'> Locomotive.</td> + <td class='tdcenter'> Tender.</td> + </tr> + <tr class="midr"> + <td class='tdcenter'><span style="margin-left: 2.5em;">Maximum<a name="FNanchor_E_1" id="FNanchor_E_1"></a><a href="#Footnote_E_1" class="fnanchor">[E]</a></span></td> + <td class='tdcenter'> 1,561</td> + <td class='tdcenter'> 44.60</td> + <td class='tdcenter'> 25.25</td> + </tr> + <tr class="botr2"> + <td class='tdcenter'><span style="margin-left: 2.5em;">Minimum<a name="FNanchor_F_2" id="FNanchor_F_2"></a><a href="#Footnote_F_2" class="fnanchor">[F]</a></span></td> + <td class='tdcenter'> 1,031</td> + <td class='tdcenter'> 60.50</td> + <td class='tdcenter'> 34.50</td> + </tr> + </table> + </td> + <td class='tdcenter'> </td> + <td class='tdleft'> </td> +</tr> +<tr class="midr"> + <td class='tdcenter'><i>C</i></td> + <td class='tdrightnd3'> 1,631</td> +</tr> +<tr class="midr"> + <td class='tdcenter'><i>C</i></td> + <td class='tdrightnd3'> 1,126</td> +</tr> +<tr class="midr"> + <td class='tdleft' rowspan='2'>Traction (= <i>B</i> <i>C</i> ÷ 2,000)</td> + <td class='tdleft'>Maximum<a href="#Footnote_E_1" class="fnanchor">[E]</a></td> + <td class='tdcenter'><i>D</i></td> + <td class='tdrightld'> 13.60</td> +</tr> +<tr class="midr"> + <td class='tdleft'> Minimum<a href="#Footnote_F_2" class="fnanchor">[F]</a></td> + <td class='tdcenter'><i>D</i></td> + <td class='tdrightld'> 9.38</td> +</tr> +<tr class="midr"> + <td colspan='2' rowspan='3'> + <table border="0" width="100%" cellpadding="4" cellspacing="0" summary="internal table 2 for Tractive Force, Catawissa to Lofty"> + <tr class="midr"> + <td class='tdcenter'><span style="margin-left: 2.5em;">Weight on Drivers:</span></td> + <td class='tdcenter'> Locomotive.</td> + <td class='tdcenter'> Helper.</td> + </tr> + <tr> + <td class='tdcenter'><span style="margin-left: 2.5em;">Maximum<a href="#Footnote_E_1" class="fnanchor">[E]</a></span></td> + <td class='tdcenter'> 21.60</td> + <td class='tdcenter'> 63.00</td> + </tr> + <tr> + <td class='tdcenter'><span style="margin-left: 2.5em;">Minimum<a href="#Footnote_F_2" class="fnanchor">[F]</a></span></td> + <td class='tdcenter'> 47.00</td> + <td class='tdcenter'> 72.00</td> + </tr> + </table> + </td> + <td class='tdcenter'> </td> + <td class='tdleft'> </td> +</tr> +<tr class="midr"> + <td class='tdcenter'><i>E</i></td> + <td class='tdrightld'> 84.60</td> +</tr> +<tr class="midr"> + <td class='tdcenter'><i>E</i></td> + <td class='tdrightld'> 119.00</td> +</tr> +<tr class="midr"> + <td class='tdleft' colspan='2'>Percentage ( = <i>D</i> ÷ <i>E</i> ).</td> + <td class='tdcenter'> </td> + <td class='tdleft'> </td> +</tr> +<tr class="midr"> + <td class='tdleft' colspan='2'><span style="margin-left: 5.5em;">Maximum</span></td> + <td class='tdcenter'><i>F</i></td> + <td class='tdrightld2'> 16.1</td> +</tr> +<tr class="botr"> + <td class='tdleft' colspan='2'><span style="margin-left: 5.5em;">Minimum</span></td> + <td class='tdcenter'><i>F</i></td> + <td class='tdrightld2'> 7.9</td> +</tr> +</table> +</div> + +<div class="footnote"><p><a name="Footnote_E_1" id="Footnote_E_1"></a><a href="#FNanchor_E_1"> +<span class="label">[E]</span></a> Giving maximum values of percentage, <i>F</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_F_2" id="Footnote_F_2"></a><a href="#FNanchor_F_2"> +<span class="label">[F]</span></a> Giving minimum values of percentage, <i>F</i>.</p></div> + + +<p class="section"><span class='pagenum'><a name="Page_333" id="Page_333">[333]</a></span> +<span class="smcap">Beverly S. Randolph, M. Am. Soc</span>. 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>The statement relative to the performance of locomotives on +"Hill <i>C</i>" 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.</p> + +<p>It is gratifying to note that Mr. Trautwine has been able to brace +up the weak member of <a href="#table1">Table 1</a> so completely with his detailed data; +also that his other results strengthen the conclusions reached in the +paper.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"><p><a name="Footnote_A_3" id="Footnote_A_3"></a><a href="#FNanchor_A_3"> +<span class="label">[A]</span></a> "The Economic Theory of Railway Location," 1887 edition, p. 502.</p></div> + +<div class="footnote"><p><a name="Footnote_B_4" id="Footnote_B_4"></a><a href="#FNanchor_B_4"> +<span class="label">[B]</span></a> <i>Transactions</i>, Am. Soc. C. E., Vol. L, p. 1.</p></div> + +<div class="footnote"><p><a name="Footnote_C_5" id="Footnote_C_5"></a><a href="#FNanchor_C_5"> +<span class="label">[C]</span></a> "Nearly 200 tons <i>exclusive</i> of eng. & ten." (Vol. III, p. 176-1/10.)</p></div> + +<div class="footnote"><p><a name="Footnote_D_6" id="Footnote_D_6"></a><a href="#FNanchor_D_6"> +<span class="label">[D]</span></a> American Railway Engineering and Maintenance of Way Association, Bulletin 84, +February, 1907, p. 99.</p></div> +</div> + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of Transactions of the American Society +of Civil Engineers, Vol. LXX, Dec. 1910, by Beverly S. 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Randolph + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 + Locomotive Performance On Grades Of Various Lengths, Paper No. 1172 + +Author: Beverly S. Randolph + +Release Date: July 3, 2006 [EBook #18747] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK AMERICAN SOCIETY OF CIVIL ENGINEERS *** + + + + +Produced by Juliet Sutherland, Sigal Alon and the Online +Distributed Proofreading Team at http://www.pgdp.net + + + + + + + + + +AMERICAN SOCIETY OF CIVIL ENGINEERS + +INSTITUTED 1852 + + +TRANSACTIONS + +Paper No. 1172 + + +LOCOMOTIVE PERFORMANCE ON GRADES OF +VARIOUS LENGTHS. + +BY BEVERLY S. RANDOLPH, M. AM. SOC. C. E. + +WITH DISCUSSION BY MESSRS. C. D. PURDON, JOHN C. TRAUTWINE, JR., +AND BEVERLY S. RANDOLPH. + + + + +In the location of new railways and the improvement of lines already in +operation, it is now well recognized that large economies can be +effected by the careful study of train resistance due to grades and +alignment, distributing this resistance so as to secure a minimum cost +of operation with the means available for construction. + +While engaged in such studies some years ago, the attention of the +writer was attracted by the fact that the usual method of calculating +the traction of a locomotive--by assuming from 20 to 25% of the weight +on the drivers--was subject to no small modification in practice. + +In order to obtain a working basis, for use in relation to this feature, +he undertook the collection of data from the practical operation of +various roads. Subsequent engagements in an entirely different direction +caused this to be laid aside until the present time. The results are +given in Table 1, from which it will be seen that the percentage of +driver weight utilized in draft is a function of the length as well as +the rate of grade encountered in the practical operation of railways. + +In this table, performance will be found expressed as the percentage of +the weight on the drivers which is utilized in draft. This is calculated +on a basis of 6 lb. per ton of train resistance, for dates prior to +1880, this being the amount given by the late A. M. Wellington, M. Am. +Soc. C.. E.,[A] and 4.7 lb. per ton for those of 1908-10, as obtained by +A. C. Dennis, M. Am. Soc. C. E.,[B] assuming this difference to +represent the advance in practice from 1880 to the present time. Most of +the data have been obtained from the "Catalogue of the Baldwin +Locomotive Works" for 1881, to which have been added some later figures +from "Record No. 65" of the same establishment, and also some obtained +by the writer directly from the roads concerned. Being taken thus at +random, the results may be accepted as fairly representative of American +practice. + +Attention should be directed to the fact that the performance of the +10-34 E, Consolidation locomotive on the Lehigh Valley Railroad in 1871 +is practically equal to that of the latest Mallet compounds on the Great +Northern Railway. In other words, in the ratio between the ability to +produce steam and the weight on the drivers there has been no change in +the last forty years. This would indicate that the figures are not +likely to be changed much as long as steam-driven locomotives are in +use. What will obtain with the introduction of electric traction is +"another story." + +These results have also been platted, and are presented in Fig. 1, with +the lengths of grade as abscissas and the percentages of weight utilized +as ordinates. The curve sketched to represent a general average will +show the conditions at a glance. The results may at first sight seem +irregular, but the agreement is really remarkable when the variety of +sources is considered; that in many cases the "reputed" rate of grade is +doubtless given without actual measurement; that the results also +include momentum, the ability to utilize which depends on the conditions +of grade, alignment, and operating practice which obtain about the foot +of each grade; and that the same amount of energy due to momentum will +carry a train farther on a light grade than on a heavy one. + +There are four items in Table 1 which vary materially from the general +consensus. For Item 9, the authorities of the road particularly state +that their loads are light, because, owing to the congested condition of +their business, their trains must make fast time. Item 10 represents +very old practice, certainly prior to 1882, and is "second-hand." The +load consisted of empty coal cars, and the line was very tortuous, so +that it is quite probable that the resistance assumed in the calculation +is far below the actual. Items 15 and 17 are both high. To account for +this, it is to be noted that this road has been recently completed, +regardless of cost in the matter of both track and rolling stock, and +doubtless represents the highest development of railroad practice. Its +rolling stock is all new, and is probably in better condition to offer +low resistance than it will ever be again, and there were no "foreign" +cars in the trains considered. The train resistance, therefore, may be +naturally assumed to be much less than that of roads hauling all classes +of cars, many of which are barely good enough to pass inspection. As the +grades are light in both cases, this feature of train resistance is +larger than in items including heavier grades. Attention should be +called to the fact that a line connecting the two points representing +these items on Fig. 1 would make only a small angle with the sketched +curve, and would be practically parallel to a similar line connecting +the points represented by Items 13 and 16. There is, therefore, an +agreement of ratios, which is all that needs consideration in this +discussion. + +[Illustration: FIG. 1.--DIAGRAM SHOWING PERCENTAGE OF WEIGHT ON DRIVERS +WHICH IS UTILIZED IN TRACTION ON GRADES OF VARIOUS LENGTHS] + +Wellington, in his monumental work on railway location, presents a table +of this character. The percentages of weight on the drivers which is +utilized in draft show the greatest irregularity. He does not give the +length of the grades considered, so that it is impossible to say how far +the introduction of this feature would have contributed to bring order +out of the chaos. In his discussion of the table he admits the +unsatisfactory character of the results, and finally decides on 25% as a +rough average, "very approximately the safe operating load in regular +service." He further states that a number of results, which he omits for +want of space, exceeds 33 per cent. The highest shown in Table 1 will be +found in Item 1 (0.06 mile, 0.066 grade), showing 33 per cent. There is +no momentum effect here, as the grade is a short incline extending down +to the river, and the start is necessarily a "dead" one. The reports of +Item 3, which shows 31%, and Item 5, which shows 27%, state specifically +that the locomotives will stop and start the loads given at any point on +the grade. + +The results of a series of experiments reported by Mr. A. C. Dennis in +his paper, "Virtual Grades for Freight Trains," previously referred to, +indicate a utilization of somewhat more than 23%, decreasing with the +speed. + +All this indicates that the general failure of locomotives to utilize +more than from 16 to 18% on long grades, as shown by Table 1, can only +be due to the failure of the boilers to supply the necessary steam. +While the higher percentage shown for the shorter grades may be ascribed +largely to momentum present when the foot of the grade is reached, the +energy due to stored heat is responsible for a large portion of it. + +When a locomotive has been standing still, or running with the steam +consumption materially below the production, the pressure accumulates +until it reaches the point at which the safety valve is "set." This +means that the entire machine is heated to a temperature sufficient to +maintain this pressure in the boiler. When the steam consumption begins +to exceed the production, this temperature is reduced to a point where +the consumption and production balance. + +The heat represented by this difference in temperature has passed into +the steam used, thus adding to the energy supplied by the combustion +going on in the furnace. The engines, therefore, are able to do +considerably more work during the time the pressure is falling than they +can do after the fall has ceased. + +The curve in Fig. 1 would indicate that the energy derived from the two +sources just discussed is practically dissipated at 15 miles, though the +position of the points representing Items 16, 18, 19, 20, and 21 would +indicate that this takes place more frequently between 10 and 12 miles. +From this point onward the performance depends on the efficiency of the +steam production, which does not appear to be able to utilize more than +16% of the weight on the drivers. The diagrams presented by Mr. Dennis +in his paper on virtual grades, and by John A. Fulton, M. Am. Soc. +C. E., in his discussion of that paper, indicate that similar results +would be shown were they extended to include the distance named. + +From this it would appear that a locomotive is capable of hauling a +larger train on grades less than 10 miles in length than on longer +grades, and that, even when unexpectedly stopped, it is capable of +starting again as soon as the steam pressure is sufficiently built up. +Conversely, it should be practicable to use a higher rate of ascent on +shorter grades on any given line without decreasing the load which can +be hauled over it. In other words, what is known as the "ruling grade" +is a function, strictly speaking, of the length as well as the rate of +grade. + +In any discussions of the practicability of using a higher rate on the +short grades, which the writer has seen, the most valid objection has +appeared to be the danger of stalling and consequent delay. As far as +momentum is relied on, this objection is valid. Within the limits of the +load which can be handled by the steam, it has small value, as it is +only a question of waiting a few minutes until the pressure can be built +up to the point at which the load can be handled. As this need only be +an occasional occurrence, it is not to be balanced against any material +saving in cost of construction. + +The writer does not know of any experiments which will throw much light +on the value of heat storage as separated from momentum, though the +following discussion may prove suggestive: + +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 x 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. + | | | |Compensation. + | | | | |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. + | | | | | | | | | | + | | | | | | | | | | +--+-----+------+------+----+-----+--+-----+-----+-----+-------------------- + 1| 0.06|0.066 | | | 115| | 37.5| 29 |0.358| 8-28-1/3 C + 2| 0.33|0.0203|25 deg.20'| | 242|25| 35 | 23 |0.285| 8-28 C + 3| 1.0 |0.06 |16 deg. |0.05| 192|22| 57.5| 50 |0.310|10-36 E + 4| 1.3 |0.0127| | | 600|16| 40 | 32.5|0.300|Mogul. + 5| 1.4 |0.0128| 3 deg.12'| | 750|15| 51 | 44 |0.270|10-34 E + 6| 2.0 |0.01 | | |1,000|15| 51 | 44 |0.291|10-34 E + 7| 2.2 |0.013 | 3 deg. | | 725|15| 51 | 44 |0.245|10-34 E + 8| 2.5 |0.0144| 6 deg. | | 400|27| 42 | 32 |0.237|10-32 E + 9| 2.5 |0.004 | | |2,700|70| 96.7| 85.8|0.207| H 6 - A +10| 3.5 |0.033 |14 deg. | | 100|25| 35 | 35 |0.160| +11| 3.6 |0.035 |10 deg. |0.05| 236|22| 57.5| 50 |0.245|10-36 E +12| 4.0 |0.0085| 4 deg. | |1,020|30| 51 | 44 |0.256|10-34 E +13| 6.0 |0.0145| | | 308|25| 38 | 28 |0.207|10-28 D +14| 6.0 |0.020 |10 deg. |0.05| 460|32| 57.5| 50 |0.242|10-34 E +15| 7.5 |0.002 | | C |6,152|86|134.5|109.5|0.243|Mallet. +16| 9.75|0.018 | | | 200|18| 29 | 29 |0.170| +17|10.0 |0.006 | | C |6,173|86|299 |265 |0.203|Mallet. +18|12.0 |0.018 |10 deg. | | 280|30| 51 | 44 |0.160|10-34 E +19|12.0 |0.022 | | | 850|74|175 |156 |0.166|D-D 16 +20|13.0 |0.022 | | | 800|74|177 |158 |0.153|D-D 1 +21|13.0 |0.022 |14 deg. | | 415|50| 91 | 83 |0.154|Consol. +22|16.0 |0.0044| | | 950|30| 51 | 44 |0.164|10-34 E +23|20.0 |0.022 | | | 500|62| 97.5| 90 |0.170|F 8, Consol. +24|20.0 |0.022 | | | 800|74|177 |158 |0.159|L-1, Mallet. +=========================================================================== + + +============================================================================ + |Maker. |Railroad. |Reporting Officer. |Year. +--+--------+----------------------------+-----------------------------+----- + 1|Baldwin.|Morgan's Louisiana & Texas |Newell Tilton, Asst. Supt. |1880 + 2| " |Long Island |S. Spencer, Gen. Supt. |1878 + 3| " |Atchison, Topeka & Santa Fe |J. D. Burr, Asst. Engr. |1879 + 4| " |Chillan & 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 the weight on the drivers, and using the +lesser of the two results as the tractive power. + +Locomotives of different classes, and hauling known loads, were run over +a freight division, the cars being weighed for the purpose; thus the +maximum load which could be handled over a division, or different parts +of a division, was ascertained, and this proportion of tonnage to +tractive power was used in rating all classes. + +Of course, this method was not mathematically accurate, as the condition +of track, the weather, and the personal equation of the locomotive +engineers all had an effect, but, later, when correcting the rating by +tests with dynamometers, it was found that the results were fairly +practical. + +There were three hills where the rate of grade was the same as the rest +of the division, but where the length was much in excess of other grades +of the same rate. + +Designating these hills as _A_, _B_, and _C_, the lengths are, +respectively, 2.44, 3.57, and 4.41 miles. There were no other grades of +the same rate exceeding 1 mile. + +In one class of freight engines, 10-wheel Brooks, the weight of the +engine was 197,900 lb.; tender, 132,800 lb.; weight on drivers, 142,600 +lb.; boiler pressure, 200 lb.; and tractive power of cylinders, 33,300 +lb. + +On Hill _A_ these engines are rated at 865 tons, as compared with 945 on +other parts of the division. As the engine weighs 165 tons and the +caboose 15 tons, 180 tons should be added, making the figures, 1,045 and +1,125 tons. Thus the length of the grade, 2.44 miles, makes the tractive +power on it 92% of that on shorter grades. + +On Hill _B_, the rating, adding 180 tons as above, is 1,160 and 1,230 +tons, respectively, giving 94% for 3.57 miles. + +On Hill _C_, the rating, with 180 tons added, is 1,130 and 1,230 tons, +making 92% for 4.41 miles. + +Taking the same basis as the author, namely, 4.7 lb. per ton, rate of +grade x 20, and weight on drivers, gives: + +Hill _A_, 18.078%, remainder of division, 19.462% +Hill _B_, 20.068%, " " " 21.279% +Hill _C_, 19.549%, " " " 21.279% + +It will be noted that the author uses the weight on the drivers as the +criterion, but the tractive power is not directly as the weight on the +drivers, some engines being over-cylindered, or under-cylindered; in the +class of engines above mentioned the tractive power is 23.35% of the +weight on the drivers. + +The writer made a study of several dynamometer tests on Hill _C_. There +is a grade of the same rate, about 1 mile long, near this hill, and a +station near its foot, but there is sufficient level grade between this +station and the foot of the hill to get a good start. + +All the engines of the above class, loaded for Hill _C_, gained speed on +the 1-mile grade, but began to fall below the theoretical speed at a +point about 2-1/4 miles from the foot of the hill. This condition +occurred when the trains stopped at the station and also when they +passed it at a rate of some 16 or 18 miles per hour, the speed becoming +less and less as the top of the hill was approached. + +The writer concludes that the author might stretch his opinion as to +using heavier rates of grade on shorter hills than 10 miles, and indeed +his diagram seems to intimate as much, and that, for economical +operation, the maximum rate of grade should be reduced after a length of +about 2 miles has been reached, and more and more in proportion to the +length of the hill, in order that the same rating could be applied all +over a division. + +This conclusion might be modified by local conditions, such as an +important town where cars might be added to or taken from the train. + +While it does not seem practicable to the writer to calculate what the +reduction of rate of grade should be, a consensus of results of +operation on different lengths of grade might give sufficient data to +reach some conclusion on the matter. + +The American Railway Engineering and Maintenance of Way Association has +a Committee on "Railway Economics," which is studying such matters, but +so far as the writer knows it has not given this question any +consideration. + +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 deg. 45' (not 14 deg., 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 deg. 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.] + + + + + +End of the Project Gutenberg EBook of Transactions of the American Society +of Civil Engineers, Vol. LXX, Dec. 1910, by Beverly S. 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