,,am]ican ,,society ,,( ,,civil ,,eng9e]s ,,in/itut$ #aheb ,,transactions ,pap] ,no4 #aagb ,,locomotive ,,p]=mance ,,on ,,grades ,,( ,,v>i\s ,,l5g?s4 ,,by ,,bev]ly ,s4 ,,r&olph1 ,m4 ,,am4 ,,soc4 ,c4 ,e4 ,,) ,,discussion ,,by ,,messrs4 ,c4 ,d4 ,,purdon1 ,,john ,c4 ,,trautw9e1 ,,jr41 ,,& ,,bev]ly ,s4 ,,r&olph4 ,9 ! location ( new railways & ! improvem5t ( l9es already 9 op]ation1 x is n[ well recogniz$ t l>ge economies c be effect$ by ! c>eful /udy ( tra9 resi/ance due to grades & alignm5t1 di/ribut+ ?is resi/ance s z to secure a m9imum co/ ( op]ation ) ! means available = con/ruction4 ,:ile engag$ 9 su* /udies "s ye>s ago1 ! att5tion ( ! writ] 0 attract$ by ! fact t ! usual me?od ( calculat+ ! traction ( a locomotive--by assum+ f #bj to #be ( ! weight on ! driv]s--0 subject to no small modification 9 practice4 ,9 ord] to obta9 a work+ basis1 = use 9 relation to ?is feature1 he und]took ! collection ( data f ! practical op]ation ( v>i\s roads4 ,subsequ5t engagem5ts 9 an entirely diff]5t direction caus$ ?is to be laid aside until ! pres5t "t4 ,! results are giv5 9 ,table #a1 f :i* x w be se5 t ! p]c5tage ( driv] weight utiliz$ 9 draft is a function ( ! l5g? z well z ! rate ( grade enc\nt]$ 9 ! practical op]ation ( railways4 ,9 ?is table1 p]=mance w be f\nd express$ z ! p]c5tage ( ! weight on ! driv]s :i* is utiliz$ 9 draft4 ,?is is calculat$ on a basis ( #f lb4 p] ton ( tra9 resi/ance1 = dates prior to #ahhj1 ?is be+ ! am\nt giv5 by ! late ,a4 ,m4 ,well+ton1 ,m4 ,am4 ,soc4 ,c44 ,e41,a & #d4g lb4 p] ton = ^? ( #aijh-aj1 z obta9$ by ,a4 ,c4 ,d5nis1 ,m4 ,am4 ,soc4 ,c4 ,e41,b assum+ ?is diff]5ce to repres5t ! advance 9 practice f #ahhj to ! pres5t "t4 ,mo/ ( ! data h be5 obta9$ f ! ,catalogue ( ! ,baldw9 ,locomotive ,works = #ahha1 to :i* h be5 add$ "s lat] figures f ,record ,no4 #fe ( ! same e/abli%m5t1 & also "s obta9$ by ! writ] directly f ! roads conc]n$4 ,be+ tak5 ?us at r&om1 ! results may be accept$ z fairly repres5tative ( ,am]ican practice4 ,att5tion %\ld be direct$ to ! fact t ! p]=mance ( ! #aj-cd ,e1 ,consolidation locomotive on ! ,lehigh ,valley ,railroad 9 #ahga is practically equal to t ( ! late/ ,mallet comp\nds on ! ,great ,nor!rn ,railway4 ,9 o!r words1 9 ! ratio betwe5 ! ability to produce /eam & ! weight on ! driv]s !re has be5 no *ange 9 ! la/ =ty ye>s4 ,?is w\ld indicate t ! figures are n likely to be *ang$ mu* z long z /eam-driv5 locomotives are 9 use4 ,:at w obta9 ) ! introduction ( electric traction is ano!r /ory4 ,^! results h also be5 platt$1 & are pres5t$ 9 ,fig4 #a1 ) ! l5g?s ( grade z abscissas & ! p]c5tages ( weight utiliz$ z ord9ates4 ,! curve sket*$ to repres5t a g5]al av]age w %[ ! conditions at a glance4 ,! results may at fir/ sight seem irregul>1 b ! agreem5t is really rem>kable :5 ! v>iety ( s\rces is consid]$2 t 9 _m cases ! reput$ rate ( grade is d\btless giv5 )\t actual measurem5t2 t ! results also include mom5tum1 ! ability to utilize :i* dep5ds on ! conditions ( grade1 alignm5t1 & op]at+ practice :i* obta9 ab\t ! foot ( ea* grade2 & t ! same am\nt ( en]gy due to mom5tum w c>ry a tra9 f>!r on a light grade ?an on a heavy "o4 ,!re are f\r items 9 ,table #a :i* v>y mat]ially f ! g5]al cons5sus4 ,= ,item #i1 ! au?orities ( ! road p>ticul>ly /ate t _! loads are light1 because1 ow+ to ! conge/$ condition ( _! bus9ess1 _! tra9s mu/ make fa/ "t4 ,item #aj repres5ts v old practice1 c]ta9ly prior to #ahhb1 & is second-h&4 ,! load consi/$ ( empty coal c>s1 & ! l9e 0 v tortu\s1 s t x is q probable t ! resi/ance assum$ 9 ! calculation is f> bel[ ! actual4 ,items #ae & #ag are bo? high4 ,to acc\nt = ?is1 x is to be not$ t ?is road has be5 rec5tly complet$1 reg>dless ( co/ 9 ! matt] ( bo? track & roll+ /ock1 & d\btless repres5ts ! highe/ developm5t ( railroad practice4 ,its roll+ /ock is all new1 & is probably 9 bett] condition to (f] l[ resi/ance ?an x w ev] be aga91 & !re 7 no =eign c>s 9 ! tra9s consid]$4 ,! tra9 resi/ance1 !re=e1 may be naturally assum$ to be mu* less ?an t ( roads haul+ all classes ( c>s1 _m ( :i* are b>ely good en\gh to pass inspection4 ,z ! grades are light 9 bo? cases1 ?is feature ( tra9 resi/ance is l>g] ?an 9 items includ+ heavi] grades4 ,att5tion %\ld be call$ to ! fact t a l9e connect+ ! two po9ts repres5t+ ^! items on ,fig4 #a w\ld make only a small angle ) ! sket*$ curve1 & w\ld be practically p>allel to a simil> l9e connect+ ! po9ts repres5t$ by ,items #ac & #af4 ,!re is1 !re=e1 an agreem5t ( ratios1 :i* is all t ne$s consid]ation 9 ?is discussion4 ,illu/ration3 ,,fig4 #a4--;,,diagram ,,%[+ ,,p]c5tage ,,( ,,weight ,,on ,,driv]s ,,:i* ,,is ,,utiliz$ ,,9 ,,traction ,,on ,,grades ,,( ,,v>i\s ,,l5g?s ,well+ton1 9 8 monum5tal "w on railway location1 pres5ts a table ( ?is "*4 ,! p]c5tages ( weight on ! driv]s :i* is utiliz$ 9 draft %[ ! greate/ irregul>ity4 ,he does n give ! l5g? ( ! grades consid]$1 s t x is impossible to say h[ f> ! introduction ( ?is feature w\ld h contribut$ to br+ ord] out ( ! *aos4 ,9 8 discussion ( ! table he admits ! unsatisfactory "* ( ! results1 & f9ally decides on #be z a r\gh av]age1 v approximately ! safe op]at+ load 9 regul> s]vice4 ,he fur!r /ates t a numb] ( results1 :i* he omits = want ( space1 exce$s #cc p] c5t4 ,! highe/ %[n 9 ,table #a w be f\nd 9 ,item #a 7#j4jf mile1 #j4jff grade71 %[+ #cc p] c5t4 ,!re is no mom5tum effect "h1 z ! grade is a %ort incl9e ext5d+ d[n to ! riv]1 & ! />t is necess>ily a dead "o4 ,! reports ( ,item #c1 :i* %[s #ca1 & ,item #e1 :i* %[s #bg1 /ate specifically t ! locomotives w /op & />t ! loads giv5 at any po9t on ! grade4 ,! results ( a s]ies ( exp]im5ts report$ by ,mr4 ,a4 ,c4 ,d5nis 9 8 pap]1 ,virtual ,grades = ,freight ,tra9s1 previ\sly ref]r$ to1 indicate a utilization ( some:at m ?an #bc1 decreas+ ) ! spe$4 ,all ?is indicates t ! g5]al failure ( locomotives to utilize m ?an f #af to #ah on long grades1 z %[n by ,table #a1 c only be due to ! failure ( ! boil]s to supply ! necess>y /eam4 ,:ile ! high] p]c5tage %[n = ! %ort] grades may be ascrib$ l>gely to mom5tum pres5t :5 ! foot ( ! grade is rea*$1 ! en]gy due to /or$ heat is responsible = a l>ge portion ( x4 ,:5 a locomotive has be5 /&+ /ill1 or runn+ ) ! /eam consumption mat]ially bel[ ! production1 ! pressure accumulates until x rea*es ! po9t at :i* ! safety valve is set4 ,?is means t ! entire ma*9e is heat$ to a temp]ature suffici5t to ma9ta9 ?is pressure 9 ! boil]4 ,:5 ! /eam consumption beg9s to exce$ ! production1 ?is temp]ature is r$uc$ to a po9t :]e ! consumption & production balance4 ,! heat repres5t$ by ?is diff]5ce 9 temp]ature has pass$ into ! /eam us$1 ?us add+ to ! en]gy suppli$ by ! combu/ion go+ on 9 ! furnace4 ,! eng9es1 !re=e1 are able to d consid]ably m "w dur+ ! "t ! pressure is fall+ ?an !y c d aft] ! fall has ceas$4 ,! curve 9 ,fig4 #a w\ld indicate t ! en]gy d]iv$ f ! two s\rces j discuss$ is practically dissipat$ at #ae miles1 ?\gh ! position ( ! po9ts repres5t+ ,items #af1 #ah1 #ai1 #bj1 & #ba w\ld indicate t ?is takes place m frequ5tly betwe5 #aj & #ab miles4 ,f ?is po9t onw>d ! p]=mance dep5ds on ! effici5cy ( ! /eam production1 :i* does n appe> to be able to utilize m ?an #af ( ! weight on ! driv]s4 ,! diagrams pres5t$ by ,mr4 ,d5nis 9 8 pap] on virtual grades1 & by ,john ,a4 ,fulton1 ,m4 ,am4 ,soc4 ,c4 ,e41 9 8 discussion ( t pap]1 indicate t simil> results w\ld be %[n 7 !y ext5d$ to include ! di/ance nam$4 ,f ?is x w\ld appe> t a locomotive is capable ( haul+ a l>g] tra9 on grades less ?an #aj miles 9 l5g? ?an on long] grades1 & t1 ev5 :5 unexpect$ly /opp$1 x is capable ( />t+ aga9 z soon z ! /eam pressure is suffici5tly built up4 ,conv]sely1 x %\ld be practicable to use a high] rate ( asc5t on %ort] grades on any giv5 l9e )\t decreas+ ! load :i* c be haul$ ov] x4 ,9 o!r words1 :at is kn[n z ! rul+ grade is a function1 /rictly speak+1 ( ! l5g? z well z ! rate ( grade4 ,9 any discussions ( ! practicability ( us+ a high] rate on ! %ort grades1 :i* ! writ] has se51 ! mo/ valid objection has appe>$ to be ! dang] ( /all+ & consequ5t delay4 ,z f> z mom5tum is reli$ on1 ?is objection is valid4 ,)9 ! limits ( ! load :i* c be h&l$ by ! /eam1 x has small value1 z x is only a "q ( wait+ a few m9utes until ! pressure c be built up to ! po9t at :i* ! load c be h&l$4 ,z ?is ne$ only be an occasional occurr5ce1 x is n to be balanc$ aga9/ any mat]ial sav+ 9 co/ ( con/ruction4 ,! writ] does n "k ( any exp]im5ts :i* w ?r[ mu* light on ! value ( heat /orage z sep>at$ f mom5tum1 ?\gh ! foll[+ discussion may prove sugge/ive3 ,a tra9 mov+ at a rate ( #fj ft4 p] sec41 & rea*+ ! foot ( a grade1 w h acquir$ a velocity head ( #ef4g ft41 equival5t to /or$ en]gy ( #ef4g #b1jjj #aac1djj ft-lb4 p] ton4 ,on a #j4jjb grade 7z 9 ,item #ae ( ,table #a7 ! resi/ance w\ld be1 gravity #d lb4 tra9 #d4g lb4 #h4g lb41 aga9/ :i* ! en]gy above giv5 w\ld c>ry ! tra9 ?r\gh #aac1djj #h4g #ac1jcd ft41 say1 #b4e miles1 leav+ #e miles to be provid$ = by ! /eam production4 ,exam9+ ! items 9 ! table hav+ grades 9 excess ( #aj miles1 x w be not$ t #af is ab\t all ! weight on driv]s :i* c be utiliz$ by ! curr5t supply ( /eam4 ,9 ,item #ae ! en]gy d]iv$ f all s\rces is equival5t to #bd4c2 h5ce ! /or$ heat may be consid]$ z responsible = an equival5t ( #bd4c - #af #h4c = a di/ance ( #e miles4 ,,table #a4 ,item ,no4 ,l5g? ( grade1 9 miles4 ,rate ( grade4 ,maximum curvature4 ,comp5sation4 ,gross weight ( load1 9 tons4 ,weight ( t5d]1 9 tons4 ,weight ( locomotive1 9 tons4 ,weight on driv]s1 9 tons4 ,p]c5tage ( weight on driv]s utiliz$ 9 draft4 ,class4 ---------------------------------------- ------------------------- #a #j4jfj4jff #aae #cg4e #bi #j4ceh #h-bh-a_/c ,c #b #j4ccj4jbjcbebj' #bdbbe #ce #bc #j4bhe #h-bh ,c #c #a4j #j4jf #af #j4je #aibbb #eg4e #ej #j4cajaj-cf ,e #d #a4c #j4jabg #fjjaf #dj #cb4ej4cjj,mogul4 #e #a4d #j4jabh #cab' #gejae #ea #dd #j4bgjaj-cd ,e #f #b4j #j4ja #a1jjjae #ea #dd #j4biaaj-cd ,e #g #b4b #j4jac #c #gbeae #ea #dd #j4bdeaj-cd ,e #h #b4e #j4jadd #f #djjbg #db #cb #j4bcgaj-cb ,e #i #b4e #j4jjd #b1gjjgj #if4g #he4hj4bjg ,h #f - ,a #aj #c4e #j4jcc #ad #ajjbe #ce #ce #j4afj #aa #c4f #j4jce #aj #j4je #bcfbb #eg4e #ej #j4bdeaj-cf ,e #ab #d4j #j4jjhe #d #a1jbjcj #ea #dd #j4befaj-cd ,e #ac #f4j #j4jade #cjhbe #ch #bh #j4bjgaj-bh ,d #ad #f4j #j4jbj #aj #j4je #dfjcb #eg4e #ej #j4bdbaj-cd ,e #ae #g4e #j4jjb ,c #f1aebhfacd4eaji4ej4bdc,mallet4 #af #i4gej4jah #bjjah #bi #bi #j4agj #agaj4j #j4jjf ,c #f1agchfbii #bfe #j4bjc,mallet4 #ahab4j #j4jah #aj #bhjcj #ea #dd #j4afjaj-cd ,e #aiab4j #j4jbb #hejgdage #aef #j4aff;,d-,d #af #bjac4j #j4jbb #hjjgdagg #aeh #j4aec;,d-,d #a #baac4j #j4jbb #ad #daeej #ia #hc #j4aed;,consol4 #bbaf4j #j4jjdd #iejcj #ea #dd #j4afdaj-cd ,e #bcbj4j #j4jbb #ejjfb #ig4e #ij #j4agj;,f #h1 ,consol4 #bdbj4j #j4jbb #hjjgdagg #aeh #j4aei,l-#a1 ,mallet4 ,mak]4 ,railroad4 ,report+ ,(fic]4 ,ye>4 ---------------------------------------- -------------------------------- #a;,baldw94,morgan's ,l\isiana ,texas ,newell ,tilton1 ,as/4 ,supt4 #ahhj #b ,long ,isl& ,s4 ,sp5c]1 ,g54 ,supt4 #ahgh #c ,at*ison1 ,topeka ,santa ,fe ,j4 ,d4 ,burr1 ,as/4 ,engr4 #ahgi #d ,*illan ,talcahuana ,j4 ,e4 ,m>t91 ,local ,supt4 #ahgi #e ,*icago1 ,burl+ton ,qu9cy,h4 ,b4 ,/one #ahhj #f ,*icago1 ,burl+ton ,qu9cy #ahhj #g ,*icago1 ,burl+ton ,qu9cy #ahhj #h ,/4 ,l\is ,san ,francisco ,c4 ,w4 ,rog]s1 ,g54 ,mgr4 #ahgi #i,pa4 ,r4,r ,cumb]l& ,valley4 #aiaj #aj #aiaj #aa;,baldw94,at*ison1 ,topeka ,santa ,fe ,j4 ,d4 ,burr1 ,as/4 ,engr4 #ahgi #ab ,miss\ri ,pacific ,john ,hewitt1 ,supt4 ,m4 ,p4 #ahhj #ac ,we/]n ,m>yl& ,d4 ,holtz1 ,m4 ( ,ma*'y4 #ahgh #ad ,at*ison1 ,topeka ,santa ,fe ,j4 ,d4 ,burr1 ,as/4 ,engr4 #ahgi #ae ,virg9ian ,ry4 #aiaj #af ,p5nsylvania #aiaj #ag;,baldw94,virg9ian ,ry4 #aiaj #ah ,lehigh ,valley1 ,wyom+ ,div4 ,a4 ,mit*ell1 ,div4 ,supt4 #ahga #ai ,great ,nor!rn ,grafton ,gre5\gh4 #aijh #bj ,great ,nor!rn ,grafton ,gre5\gh4 #aijh #ba ,baltimore ,ohio ,f4 ,e4 ,blas]1 ,div4 ,supt4 #aiaj #bb ,c5tral ( ,n4 ,j4 ,w4 ,w4 ,/e>ns1 ,as/4,g54,supt4#ahhj #bc ,great ,nor!rn ,grafton ,gre5\gh4 #aijh #bd ,great ,nor!rn ,grafton ,gre5\gh4 #aijf ,s\rce ( ,data4 ,rem>ks4 ---------------------------------------- ------------------------------------ #a;,baldw9 ,catalogue1 #ahha1 p4 #acd #b #ahha1 #gb #aj miles p] h\r4 #c #ahha1 #aae #h ,/ops & />ts on grade4 #d #ahha1 #ajj #e #ahha1 #aaf ,/ops & />ts at any po9t on grade4 #f #ahha1 #aaf #g #ahha1 #aaf #h #ahha1 #hg #i #aj,trautw9e's ,pocket ,book1 ,ed4 #ahhb1 p4 #dab;,empty c>s2 _m curves & rev]sions4 #aa;,baldw9 ,catalogue1 #ahha1 p4 #aad #ab #ahha1 #aab #ac #ahha1 #hf #ab miles p] h\r4 #ad #ahha1 #aad #h #ae;,eng9e]+ ,news1 ,jan4 #ac1 #aiaj4 #af,trautw9e's ,pocket ,book1 ,ed4 #ahhb1 p4 #dab #ag;,eng9e]+ ,news1 ,jan4 #ac1 #aiaj4 ,road locomotive & help]4 #ah;,baldw9 ,catalogue1 #ahha1 p4 #aab #ai;,baldw9 ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi #bj;,baldw9 ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi #ba ,v crook$ l9e4 ,uncomp5sat$4 #bb;,baldw9 ,catalogue1 #ahha1 p4 #aac #bc;,baldw9 ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi #bd;,baldw9 ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi ,9 proportion+ grade resi/ance = any l9e1 !re=e1 a locomotive may be c\nt$ on to utilize #bd4c ( ! weight on ! driv]s = a di/ance ( #e miles on a #j4jjb grade )\t any assi/ance f mom5tum1 &1 9 ! ev5t ( an unexpect$ /op1 %\ld be able1 z soon z a full head ( /eam is built up1 to />t ! tra9 & c>ry x ov] ! grade4 ,?is is probably a maximum1 consid]+ ! condition ( ! equipm5t ( ?is ,virg9ian ,railway1 z previ\sly m5tion$4 ,treat+ ,item #ad 9 ! same way1 a di/ance ( #b1caj ft4 is acc\nt$ = by mom5tum1 leav+1 say1 #e4e miles = ! /eam1 or ! l5g? ( a #j4jb grade on :i* a locomotive may be load$ on a basis ( tractive p[] equal to #bd4b ( ! weight on ! driv]s4 ,f ^! figures x may be conclud$ t on l9es hav+ grades f #ab to #ae or m miles 9 l5g?1 grades ( #c to #e miles 9 l5g? may be ins]t$ hav+ rates #ej 9 excess ( t ( ! long grades1 )\t decreas+ ! capacity ( ! l9e4 ,?is /atem5t1 ( c\rse1 is g5]al 9 its be>+s1 ea* case be+ subject to its especial limitations1 & subject to detail$ calculations4 ,x may be not$ t ! velocity ( #fj ft4 p] sec41 assum$ at ! foot ( ! grade1 is probably high] ?an %\ld be expect$ 9 practice2 x insures1 on ! o!r h&1 t q en\gh has be5 all[$ = mom5tum1 & t ! results are cons]vative4 ,argum5ts l ! =ego+ are always m or less trea*]\s2 be+ bas$ on /ati/ics1 !y are naturally subject to mat]ial modifications 9 ! pres5ce ( a l>g] array ( data1 !re=e1 mat]ial assi/ance 9 rea*+ practical conclusions c be giv5 by ! pres5tation ( additional data4 ,,discussion ,c4 ,d4 ,,purdon1 ,m4 ,,am4 ,,soc4 ,c4 ,e4 7by lett]74--,"s ye>s ago ! writ]1 9 mak+ /udies = grade revision1 f\nd t ! tractive p[] ( a locomotive up grade becomes less z ! l5g? ( ! grade increases1 & 9 "s unkn[n proportion4 ,?is 0 a practical confirmation ( ! say+ ( locomotive eng9e]s1 t ! eng9e got tir$ on long grades4 ,on a well-kn[n ,we/]n railroad1 ) :i* ! writ] is famili>1 exp]im5ts 7 made = ! purpose ( rat+ its locomotives4 ,! locomotives 7 fir/ divid$ into classes accord+ to _! tractive p[]1 ?is be+ calculat$ by ! usual rule1 ) factors ( size ( cyl9d]s1 boil] pressure1 & diamet] ( driv]s1 also by tak+ "o-f\r? ( ! weight on ! driv]s1 & us+ ! less] ( ! two results z ! tractive p[]4 ,locomotives ( diff]5t classes1 & haul+ kn[n loads1 7 run ov] a freight division1 ! c>s be+ weigh$ = ! purpose2 ?us ! maximum load :i* c\ld be h&l$ ov] a division1 or diff]5t p>ts ( a division1 0 asc]ta9$1 & ?is proportion ( tonnage to tractive p[] 0 us$ 9 rat+ all classes4 ,( c\rse1 ?is me?od 0 n ma!matically accurate1 z ! condition ( track1 ! wea!r1 & ! p]sonal equation ( ! locomotive eng9e]s all _h an effect1 b1 lat]1 :5 correct+ ! rat+ by te/s ) dynamomet]s1 x 0 f\nd t ! results 7 fairly practical4 ,!re 7 ?ree hills :]e ! rate ( grade 0 ! same z ! re/ ( ! division1 b :]e ! l5g? 0 mu* 9 excess ( o!r grades ( ! same rate4 ,designat+ ^! hills z ,a1 ,b1 & ,c1 ! l5g?s are1 respectively1 #b4dd1 #c4eg1 & #d4da miles4 ,!re 7 no o!r grades ( ! same rate exce$+ #a mile4 ,9 "o class ( freight eng9es1 #aj-:eel ,brooks1 ! weight ( ! eng9e 0 #aig1ijj lb42 t5d]1 #acb1hjj lb42 weight on driv]s1 #adb1fjj lb42 boil] pressure1 #bjj lb42 & tractive p[] ( cyl9d]s1 #cc1cjj lb4 ,on ,hill ,a ^! eng9es are rat$ at #hfe tons1 z comp>$ ) #ide on o!r p>ts ( ! division4 ,z ! eng9e weighs #afe tons & ! caboose #ae tons1 #ahj tons %\ld be add$1 mak+ ! figures1 #a1jde & #a1abe tons4 ,?us ! l5g? ( ! grade1 #b4dd miles1 makes ! tractive p[] on x #ib ( t on %ort] grades4 ,on ,hill ,b1 ! rat+1 add+ #ahj tons z above1 is #a1afj & #a1bcj tons1 respectively1 giv+ #id = #c4eg miles4 ,on ,hill ,c1 ! rat+1 ) #ahj tons add$1 is #a1acj & #a1bcj tons1 mak+ #ib = #d4da miles4 ,tak+ ! same basis z ! au?or1 namely1 #d4g lb4 p] ton1 rate ( grade #bj1 & weight on driv]s1 gives3 ,hill ,a1 #ah4jgh1 rema9d] ( division1 #ai4dfb ,hill ,b1 #bj4jfh1 #ba4bgi ,hill ,c1 #ai4edi1 #ba4bgi ,x w be not$ t ! au?or uses ! weight on ! driv]s z ! crit]ion1 b ! tractive p[] is n directly z ! weight on ! driv]s1 "s eng9es be+ ov]-cyl9d]$1 or "u-cyl9d]$2 9 ! class ( eng9es above m5tion$ ! tractive p[] is #bc4ce ( ! weight on ! driv]s4 ,! writ] made a /udy ( sev]al dynamomet] te/s on ,hill ,c4 ,!re is a grade ( ! same rate1 ab\t #a mile long1 ne> ?is hill1 & a /ation ne> its foot1 b !re is suffici5t level grade betwe5 ?is /ation & ! foot ( ! hill to get a good />t4 ,all ! eng9es ( ! above class1 load$ = ,hill ,c1 ga9$ spe$ on ! #a-mile grade1 b began to fall bel[ ! !oretical spe$ at a po9t ab\t #b-a_/d miles f ! foot ( ! hill4 ,?is condition occurr$ :5 ! tra9s /opp$ at ! /ation & also :5 !y pass$ x at a rate ( "s #af or #ah miles p] h\r1 ! spe$ becom+ less & less z ! top ( ! hill 0 approa*$4 ,! writ] concludes t ! au?or might /ret* 8 op9ion z to us+ heavi] rates ( grade on %ort] hills ?an #aj miles1 & inde$ 8 diagram seems to intimate z mu*1 & t1 = economical op]ation1 ! maximum rate ( grade %\ld be r$uc$ aft] a l5g? ( ab\t #b miles has be5 rea*$1 & m & m 9 proportion to ! l5g? ( ! hill1 9 ord] t ! same rat+ c\ld be appli$ all ov] a division4 ,?is conclusion might be modifi$ by local conditions1 su* z an important t[n :]e c>s might be add$ to or tak5 f ! tra94 ,:ile x does n seem practicable to ! writ] to calculate :at ! r$uction ( rate ( grade %\ld be1 a cons5sus ( results ( op]ation on diff]5t l5g?s ( grade might give suffici5t data to rea* "s conclusion on ! matt]4 ,! ,am]ican ,railway ,eng9e]+ & ,ma9t5ance ( ,way ,association has a ,committee on ,railway ,economics1 :i* is /udy+ su* matt]s1 b s f> z ! writ] kn[s x has n giv5 ?is "q any consid]ation4 ,! writ] hopes t ! au?or w foll[ up ?is subject1 & t o!r memb]s w jo91 z a full discussion w no d\bt br+ "s results on a "q :i* seems to be highly important4 ,,john ,c4 ,,trautw9e1 ,,jr41 ,,assoc4 ,,am4 ,,soc4 ,c4 ,e4 7by lett]74--,9 8 collection ( data1 ,mr4 ,r&olph includes two anci5t cases tak5 f ! e>lie/ editions 7#ahgb-ahhc7 ( ,trautw9e's ,civil ,eng9e]'s ,pocket-,book1 ref]r+ to p]=mances on ! ,mahanoy & ,broad ,m\nta9 ,railroad 7n[ ! ,frackville ,bran* ( ! ,read+7 & on ! ,p5nsylvania ,railroad1 respectively4 ,9 ! private notes ( ,john ,c4 ,trautw9e1 ,sr41 ^! two cases are record$ z foll[s3 ,on ! ,mahanoy ,broad ,mtn4 ,r4 ,r41 tank ,eng9es ( #ce tons1 all on #h driv]s1 draw #dj empty coal c>s weigh+ #ajj tons1 up a cont9u\s grade ( #age ft4 p] mile = #c-a_/b miles2 ar\nd curves ( #dej1 #ejj1 #fjj ft4 c4 rad41 at #h miles an h\r4 7#ahfd7 ,?is is equal to #gg-ad_/ajj tons = a #bg-ton eng9e4 7,vol4 ,,iii1 p4 #agf47 ,on ! ,p5n ,c5tral #ie ft4 grades = #i-c_/d miles1 a #bi-ton eng9e all on #h driv]s takes #abe tons ( freight & #aab tons ( eng9e1 t5d]1 c>s1 9 all #bcg tons1,c & a pass5g] eng9e takes up #c c>s at #bd miles an h\r 7l>ge #h :eels74 ,:5 m ?an #c1 an auxili>y eng9e4 ,x w be se5 t ,mr4 ,r&olph is well )9 b\nds 9 ascrib+ to ! ,mahanoy & ,broad ,m\nta9 case 78 ,no4 #aj7 a date c]ta9ly prior to #ahhb1 ! date be+ giv51 9 ! notes1 z #ahfd2 :ile ano!r entry j bel[ x1 = ! ,p5nsylvania ,railroad case1 is dat$ #ahfj4 ,x also seems1 z /at$ by ,mr4 ,r&olph1 q probable t ! frictional resi/ance 7#f lb4 p] #b1jjj lb47 assum$ by him 9 ! calculation is f> bel[ ! actual = ?is ,case #aj4 ,! small1 empty1 f\r-:eel c>s weigh$ only #d1djj lb4 ea*4 ,fur!rmore1 ! tons1 9 ! ,trautw9e reports ( ^! exp]im5ts1 7 tons ( #b1bdj lb4 ,on ! o!r h&1 ! maximum curvature 0 #ab #de' 7n #ad1 z giv5 by ! au?or71 & ! eng9e 0 a tank locomotive1 :]eas ! au?or has cr$it$ x ) a #be-ton t5d]4 ,aft] mak+ all corrections1 x w be f\nd t1 9 ord] to br+ ! po9t1 = ?is ,case #aj1 up to ! au?or's curve1 in/ead ( 8 #f lb4 p] #b1jjj lb41 a frictional resi/ance ( #ff lb4 p] #b1jjj lb4 w\ld be requir$1 a resi/ance j equal to ! gravity resi/ance on ! #c4c grade1 mak+ a total resi/ance ( #acb lb4 p] #b1jjj lb4 ,:ile ?is #ff lb4 p] ton is v high1 x is p]haps n too high = ! kn[n conditions1 z above describ$4 ,= mod]n roll+ /ock1 ,mr4 ,a4 ,k4 ,%urtleff gives ! =mula3,d ,frictional resi/ance1 on tang5t1 9 p\nds p] #b1jjj p\nds #a #ij ,c1 :]e ,c weight ( c> & load1 9 tons ( #b1jjj lb4 ,?is w\ld give1 = #d1djj-lb4 7#b4b-ton7 c>s1 a frictional resi/ance ( #db lb4 p] #b1jjj lb42 &1 on ! usual assumption ( #j4h lb4 p] #b1jjj lb4 = ea* degree ( curvature1 ! #ab4ge curves ( ?is l9e w\ld give #aj lb4 p] ton additional1 mak+ a total ( #eb lb4 p] #b1jjj lb4 ov] & above grade resi/ance1 "u mod]n conditions4 ,9 ! #i? to #ag? editions ( ,trautw9e 7#ahhe-aijj71 ^! e>ly acc\nts 7 sup]s$$ by num]\s lat] in/ances1 includ+ "s ( ^? quot$ by ! au?or4 ,9 ! #ah? & #ai? editions 7#aijb-aiji7 are giv5 data respect+ p]=mances on ! ,catawissa ,bran* ( ! ,read+ 7,%amok9 ,division7 9 #ahih-aija4 ,^! give ! maximum & m9imum loads haul$ up a ne>ly cont9u\s grade ( #ca4dg ft4 p] mile 7#j4ei7 f ,catawissa to ,l(ty 7#cd4jc miles7 by eng9es ( diff]5t classes1 ) diff]5t help]s & )\t help]s4 ,table #b 79 :i* ! writ] foll[s ! au?or 9 assum+ frictional resi/ance at #d4g lb4 p] #b1jjj lb47 %[s ! cases giv+ ! maximum & m9imum values ( ! quantity repres5t$ by ! ord9ates 9 ! au?or's diagram1 namely1 ,traction1 9 p]c5tage ( weight on driv]s4 ,x w be se5 t ! maximum p]c5tage 7#af4a7 is practically id5tical ) t f\nd by ! au?or 7#af7 = grade l5g?s exce$+ #ag miles4 ,ne> ! middle ( ! #cd-mile di/ance !re is a /ret* ( #a4ea miles1 on :i* ! av]age grade is only #e4ic ft4 p] mile 7#j4aab71 & ?is /ret* divides ! rema9+ di/ance into two practically cont9u\s grades1 #ai4ci & #ac4ac miles long1 respectively2 b1 z ! same loads are haul$ ov] ^! two portions by ! same eng9es1 ! results are virtually id5tical1 ! maxima furni%+ two m po9ts closely co9cid+ ) ! au?or's diagram4 ,,table #b4--,,tractive ,,=ce1 ,,catawissa ,,to ,,l(ty4 ,l5g? ( grade1 9 miles #cd4jc ,grade 9 feet p] mile #ca4dg p]c5tage ,a #j4eig ,resi/ances1 9 p\nds p] #b1jjj lb41 ,gravity 7#bj ,a7 #aa4id4 ,friction #d4gj ,b #af4fd ,load3 ,c>s4 ,locomotive4 ,t5d]4 ,maximum,e #a1efa #dd4fj #be4be ,c #a1fca ,m9imum,f #a1jca #fj4ej #cd4ej ,c #a1abf ,traction 7 ,b ,c #b1jjj 7 ,maximum,e ,d #ac4fj ,m9imum,f ,d #i4ch ,weight on ,driv]s3 ,locomotive4 ,help]4 ,maximum,e #ba4fj #fc4jj ,e #hd4fj ,m9imum,f #dg4jj #gb4jj ,e #aai4jj ,p]c5tage 7 ,d ,e 74 ,maximum ,f #af4a ,m9imum ,f #g4i ,,footnotes3 ,footnote ,e3 ,giv+ maximum values ( p]c5tage1 ,f4 ,footnote ,f3 ,giv+ m9imum values ( p]c5tage1 ,f4 ,,bev]ly ,s4 ,,r&olph1 ,m4 ,,am4 ,,soc4 ,c4 ,e4 7by lett]74--,! p]c5tages giv5 by ,mr4 ,purdon w\ld seem to indicate t ! l5g? ( ! grades did n affect ! loads 9 ! cases cit$1 b ^! p]c5tages are s mu* bel[ ^? %[n 9 ! table1 = simil> di/ances1 z to indicate "s special conditions :i* ! writ] has be5 unable to f9d 9 ! text4 ,! use ( ! p]c5tage ( weight on driv]s :i* is utiliz$ 9 traction z a measure ( ! effici5cy ( ! locomotive1 :ile1 probably1 n applicable to individual ma*9es1 is s\nd = ! purposes ( comp>ison ( results to be obta9$ on v>i\s portions ( a l9e z f> z affect$ by conditions ( grade & alignm5t4 ,x has ! advantage ( disreg>d+ que/ions ( temp]ature1 condition ( track1 "* ( fuel1 etc41 :i*1 be+ ! same on all portions ( ! l9e1 naturally balance & d n affect ! comp>ison4 ,x is1 ( c\rse1 simply a me?od ( express+ ! f9al effici5cy ( ! v>i\s p>ts ( ! locomotive1 &1 s9ce x dep5ds entirely on actual results already accompli%$1 leaves no room = diff]5ce ( op9ion or !oretical error4 ,! writ] has always consid]$ an "u-cyl9d]$ locomotive z a defective ma*9e4 ,all weight is a di/9ct debit1 9 ! %ape ( we> & te> ( track & runn+ ge>1 resi/ance due to gravity on grades1 int]e/ on co/1 etc4 ,:5 ?is weight fails to e>n a cr$it 9 ! way ( tractive effici5cy1 x %\ld n be pres5t4 ,! /atem5t relative to ! p]=mance ( locomotives on ,hill ,c is int]e/+1 especially 9 t x appe>s to h be5 immat]ial :e!r !y made a dead />t aft] /opp+ at ! /ation or approa*$ ! foot ( ! hill at #af to #ah miles p] h\r4 ,! mom5tum w\ld appe> to be an insignificant factor4 ,x is gratify+ to note t ,mr4 ,trautw9e has be5 able to brace up ! weak memb] ( ,table #a s completely ) 8 detail$ data2 also t 8 o!r results /r5g!n ! conclusions rea*$ 9 ! pap]4 ,,footnotes3 ,footnote ,a3 ,! ,economic ,!ory ( ,railway ,location1 #ahhg edition1 p4 #ejb4 ,footnote ,b3 ,transactions1 ,am4 ,soc4 ,c4 ,e41 ,vol4 ,l1 p4 #a4 ,footnote ,c3 ,ne>ly #bjj tons exclusive ( eng4 t54 7,vol4 ,,iii1 p4 #agf-a_/aj47 ,footnote ,d3 ,am]ican ,railway ,eng9e]+ & ,ma9t5ance ( ,way ,association1 ,bullet9 #hd1 ,febru>y1 #aijg1 p4 #ii4