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| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-15 04:54:03 -0700 |
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diff --git a/18747-h/18747-h.htm b/18747-h/18747-h.htm new file mode 100644 index 0000000..5849f79 --- /dev/null +++ b/18747-h/18747-h.htm @@ -0,0 +1,1641 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> + +<html xmlns="http://www.w3.org/1999/xhtml"> + <head> + <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1" /> + <title> + The Project Gutenberg eBook of Locomotive Performance On Grades Of Various Lengths, by Beverly S. 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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