^ ^.<*', V^ '''./i.% t^i ^ 0> "i^"^^ - <^ IMAGE EVALUATJON TEST TARGET (MT-3) /. «^/ V fe ,> <- vVp v^^* .v^^ •C.V «?. r/^* LO LL 1.25 ^ «£ li:0 U III 1.6 Photographic Sdences v^uipOrdUUii 23 WEST AAIN STREET WEBSTEM.N.Y. 14580 (716) 872-4503 V V N> itus.) tfanadian ^mtXxi o! tflvil tf nflincm. IKCOaPOUATKD 1887. TBANSAOTIONS. >K B.i«1%la9ooietj, M a body, does not hold itiiuU reapmislble {or the faati and oplnloiu at«tod in aur ot Ita publiciitlous. {To be read Thursday 1th May.) RAILWAY CURVES. By Hknby K. Wioksteed, M. Can. 8oc. C.E. As milwaya have become nuire iiumoroiiH, aaJ havu puslied their w«y into regions whore traffic is thin or couip('tii...n lias become very keen, the study of ttio " economics " of opoiatioii has come to be more general among railway uicii and the iiiHuoMce of the diifii'i'nt olementsi of location on tie cost of running and maintenance belter understood. The earlier railways built tlirougli districts where irade was already established, and having only waggon roads to enni|iete with, had merely to secure a good safe road at some reasonable cost, !ind thc>ir triiffic and dividends were assured ; but with conii^ tition. and in the case of roads running in advance of sottlcuient, it became often necessary to secure the very grcaU'.st oprrative oconomv in tlic one case and the very lowest constructive cost in tlieollu r. in onlir to admit of the road's becoming a financial success. There are those elements in the location of a railway between two given points, which can be utilized more or lo-s interchangeably to reduce its cost below that of the straight line on plan and profile, which represents the perfect line — increase in distance, curvature and gra- dients, and all have a more or less dctrimciKal .^H'lct on tlir operative value. In all roads they all three are made use of to some exti'nt, but even at the present day there is evidiMit a very marked difl'erence of opinion as to their relative hurtlulness. In our older trunk roads, as in the English lines on which they were modelled, the lirsl two s<'eni to have been avoided at almost any cost. .As nearly an air liue as po.ssi- ble was obtained, and such grii,di(!uts resorted to as would tit the ground without exces-ive work. In the case of the English lines, the long rigid wheel b.isc ot ear.> and engines limited greatly thi> radius of the curvature, which could be used with safety and with very tiat curves. Opportunities for reduc- ing the pitch of gradients by lengthening the distiinee did not so often occur; but even since the universal adoption of the swivelling truck on all rolling slock on this continent, there still remained a marked repugnance to going even a very littli.' way off the general heading to secure an easier line, and riilwayscvcn of ihciVery ehea| est cluBS were run up hill and down, almost as the crow tlics: and to bring the cost within the means of the promoters, such gradients were adopted as have in many cases completely ruined their earning powers for all time to come. bar be it trom me to urge the promiscuous use of sharp curves and the j)ractiee oi running assured every trifling obstacle, which ia the opposite extreme towards which some engineers belonging to a later schotjl have gravitated. The best location for a road depends on many things : the purp(jbe for which the road is built, the direction and volume of traffic, and the capital available, etc., etc., and no hard and tast rule cau be laid down lor general adoption. All I wish to point out is, that where, from financial weakuess or other cause, it becomes necessary to choose between a somewhat circuitous routi^ having easy grades and a com- paratively straight one with heavy grades, the former will in a large majority of cases be the proper oilc to adopt, even if the differeuou in diBtancc bo quite coDsidcrable, and ;hat where the choice is merely between sharp curves and heavy gradients, there can seldom )m any r«a«ou for hesitation whatever. \ The financial reasons for this are not, difficult to understiind. On a straiL'ht luvul track, train rcaistauces at moderate speeds amouut to about ti lbs. per ton. On a 10^" curve, thi.s is about doubled, in other word.s the incnascd resistance due to u lO*-' curve is only the s».me that we should liave on a Knidc of ■;, i)cr cent, or 16 feet per mile. Yet h.>tv oltcii we .see ;jradcs of 60 to 80 foet per mile u.scd in oon- ju-iftioii witli curves of 3'^ or 4*^, where the use .)f nharper curves would have made a longer rise at say one-half that rate practicable at the same cost and allowed of the train load being doubled. No rail- way niananer needs to be told what an economy is effected by adding even 3 or 4 cars to his trains. There are, however, other facU>ra besides the low cost of hauling, which iiihanee the popularity ami carninf,- powers of a road: speed, safety and comfort in the running of trains and the cost of inainteuance of track and rolling stock. A.S regards the effect of curvature upon the Hrst speed, 10*' curves can he traversed and are traversed every day at 30 miles per hour ; aiul with modern air brake c(|uipmont the loss of time caused by slack.Miinii the .•sure against the side of the rail on sharji curves tiiaii on Hal "lies, .'^harpeu the curve to the extreme limit possible, and the wheel will at last mount the rail, not because the directive foiee .■xerei^ed by the rail is greater, but because the obliquity of the plaue of the wh.'el U) the raii becomes greater than the an"le of friction between the two. Turnouts with curvatures of C"' and more are traversed daily and hourly by express trains, at speeds of 20 to 30 miles an hour on our best roads, although there are in the case of the turnout the additional elements of dauger caused by the break in continuity of the outside rail at the frog, and the absence of su])erelevation to c«uuteract the e('Utrifugal force, as aUo that the turnout is .learly always very nearly a reversed curve, the tangent from the iioiut of frog being seldom more than I'.tl or M) feel. .\ well laid 8'^ curve on the open road is vastly safer at HO miles than the turnout at 20. Yet we constantly see this anomaiy ol 0° turnout- traversed by th.' same trains on the same roads where on the open road a 'J'" or 3" standard has been enforced at a heavy eo.st, Witii ivard to the obstructicm of view by a (^urve, it ueeda no demonstrat'ion to shew that a rock bluff or building close to the track will limit the range of vision on a 2 ' .mrve to within a few feet ol what it is on a 10" ; and unless we can eliminate the onrvature altogether, we can caiu little in this respect by len.?thenmg the radiu^^. There are without dimbt mat.y accidents attributable more or le.ss directly to curvature, but in very few of those which I have had an opportunity ol itwiuiring into does it seem to me that the radius of curvature had inucli effect, and iu many It ss.iuid appear that ^omc defect i« the roU- i^ <; ing stock was the dirfct cau8i', although i)erhBii8 oven witli this ilefect axistent the accident would hardly liavo occunvd tliowlien- thau on a .curve. The recent accident on the Iiiu ruolouial at St. Joseph, l'i>r instanoo, is a cane in point, and appears to me diatinctly traceable lo the wanner in which the brake beanin and shoes are generally hun^' on pas- aeuf^er cars. One shoe presies the tVonl side ol' the leadinn wheel, and io a majority of cases at a point a little below (sometiuies lar beow ) the axle, the friction of the wheel tends to lii't it ; and once lifted, it the, brake is below the centre, it cannot drop aj;ain until the brake is released. The brake beams are a^'ain huni; fr.iu ihe body of the ear. 'not from ihe truck. Now, imagine the ear body inclined, owing to superelevation of the track, and bearing rather more heavily on the inside springs and eompressim; ilum, tiii; brakes are applied and the wheel is clamped in this position. Belore they are relea.sed the cant is reversed and the wheel is lifted, or at any rate tlie pressure ou the rail is so reduced that it mounts the rail with great ea.se. Tlie author has so often s."en this lifting action where lie has watched wheels to which the brakes were suddenly applied with full pr. ssiire, ilial he has no doubt what«;ver that this was the cause of the derailment in question,aa of many other similar ones. We generally read iu the evidence that the brakes have been applied, and that within a few .seconds the derailment occurs. In the case of engine derailments we .seldom or never hear of the leading truck getting off,— there are no brakes ou it, —seldom or never of the leading truck of the tender leaving the rails, the elo.se coupling to the engine prevents tliis , but tlie rear truck is constantly being derailed, and very often from th(i cause pointed out, and which, by the way, was very ably discussed, and the remedy poiute'd out in a recent issue of the Euguiferuty AVir*. So much for the elements of danger inlificiit in curvature. On the other hand, some of the- most terrible accidents which have ever appalled us have been directly caused by gradients. The Irish disaster at .Vrmagh is one of ill.- most d.^trnelive. and a similar one occurred some years ago on the Southern J'aeilie. These are directly chargeable to heavy grades, and a number of others are indirectly chargeable to the .same cause in this way. \ train is timvd to make, aay, 45 miles per hour between stations on a road having heavy undu- lating gradients on the up grade— this is, let us assume impossible and the speed falls to 25 miles at the head of it. Assuming the next summit to be of the sacie elevation, the speed at the bettom of the sag must be iu order to keep up the averaL'e ti'j miles per hour, tiiis is.-o easy to attain on the downgrade that it is very common ii.dee,l ; bul when, as is often the case, the line is complicated at tlio bottom by evuves. structures, or by frogs and switches, it is by no lnean^ a safe s|.eid, and the cousequences are often disastrous. Breaking away is also a fruitful cause of trouble on steep grades. 3rdly. Comfort.— Piobably the most serious argument of all against the use of sharp curves as commonly introduced is the discomfort which they cause to passengers (especially to those in sleeping cars) when traversed at high rates of sjaed. Travellini; over a long .streteh of one of our trunk roads nothing ago, the author was several times hurled across the car while endeavouring to div^s and tlie imiiaet wiis so violent at times that it was difficult to persuade himself that there was not something of danger as well as discomfort. Steep grades, on the contrary, whatever may be their effects on the pockets of the shareholders or the safety of the passengers, do not influence the comfort of the latter, iind the average one merely wonders why the train is moving so slowly at the top of a grade, or experiences a slight exliilaration when it noars the bottom, and tiiat is all about it. Lastly, maintenance of way and wear and tear. There is certainly quite a difference in this respect between the curve and the straight line, but there is also a great difference between the grode and the level and between the heavy grade and the ligh' creep- ing and buckling of rails, use of , sand to aid adhesive broken links, frequent application ot brakes, all tend to keep both the roadmasters and the mechanical depurtmeut.s busy, and run up the cost of repairs. And here again wo find that it is cmvalun: " per se " which makes the trouble, and the radiu» of curvature has a comparatively small etieot. Iu other vords, having 90^' of eurvr lure, it makes little differ- ence whether il is present as 3001* feet of a ;>' cui Ve or m, 1)00 it. of 3 :, i(>' :u.(l it is (!o..«a.itlv muintainod that as far as repairs U. ro^iA^ ,,r.> (.onronie.l, SOliO ft. of 3^' rurvr is a littl.' more oxpi-nsive tl.an !«>0 ft. ufii 1(V. ami 2l00lt.ofian-onl. Without asserting this, tho author is contcmt I.. I>eli.-v.' that uii^.t ordinary oiroumstaacs tliey are "' \vi- h'nv -.'.n th.n ahovi' tliat.mly in tlio itoiu ofc.uufort topassiMi- gers is tlHT. n.m-h to l,o said a^aiuM tt.o use .^f much shar|H,r ourvoi than tlioM' in ..nlinavv use, s;.y up to S'^ or 10'^. Wh.'tl.er tiv author is risiht or wron- in his e.-iRhisioim as above, i, is .vrtain that the ten^.^n^y is unvards their use and towards ihtltenin-thoj^radesasn.ucl. as possible. This is a mouey-malc.uK aue and whereas the .luestiou of -rades is one of dollars and cents fn.m li.Nl to last Th.> ..l)ieetion to cMirves is admitted oven by thoso „,ost opposed to then, to he lar;;ely a matter of sentiment The avera-'e business man will buy an aeeldent tieket, and risk his lile on the erookedest ot roads, but he will not, iuv.'st his u.oney in a road whieli Hwiu' to the cost of operation, will uoi pay dividends. When monev is s<.aree, and heavy work cannot he resorU^d to, to veduee .M-adients. we have no ehoice, ther..fore, very often b.)twecn a ..,.,.,ked road and no road .t all. .Vnd there is this strong argument „„ ,. „„«. ,„„| i„ favour of adnplin^' sharp -curves rather than heavy „,aaes, that havin, a rise of .say :!2.. 11, in 1 miles or 80 tt per mde, eonneetin. two level or nearly level .stretches, it is ■mp(.ssible to re- ,|u..e this hereafter to S miles of a 4t» ft. .rade-otherwHC than by the eon.plete al^andonmcut of at least S ndles of road,-no part ol theon- „iual road will serve for the nltered one. Whereas a few sharp curves nu. olien he taken out .u- reduced by S^adu^Hy <'U"'"S 'nto a hdla.de ■a one point, an 1 lillin^^out at another; and the cost of do.n^'. tins, dis- tributed over several years, durin. whieh the road is earn.n,' money, will -eareely be felt, alth.n.^h it would havr l.een m.-ious and perhap.s nrohibiiive if undertaken in the lirst place. This practice <,f openinii roads at the earliest possible moment, and improving them as ,rowiu, traffic warrants the e..peu.e, has become so very common and is so eminently reasonable and sensible, that th.s is in iielf in many case.- sufficient reason to decide the choice between the two hurtful elements. In a luajori.v of lines the traffie i< li.ht in the Urs, plaee^ and gra- cUudlv iuerease" . Hence, lor the lirst lew years We must endeavour to keep-th.. capital cost and fixed charges as low as poss.Me, they being, tl/heaviest charges a.ainst the revenue. As the traffic, .rows the .nalntenance account .rows almost in the same rat^^o, and become, ot ,,reater relative importiuice. heuee we are justiHod m increasing the capital aeeouiit to dimini.sh it. Without fnvtlui- diseu-sion as to wh> and wheretore. when and whe.e they should be used, which i,^ a little foreign to the purpo.se ot this paper, the author proposes to investigate supposing .sharp curves o be a,!opted, what th.,.ir form should be, and how we may best make them us little hurtful and as comfortable U, ride over as may be. To overcome the evil ertects of centrifuual force U is the common practice, as .very one knows, to oievate the outer lad to an amount which vlries with the speed intended. This amount is generally put down at .05 feet for every degree of curvature c.rrespond.ng to a speed of 3G miles per hour, and the results are good for the onlinary range curL The author's own experience is that this gives rat er too much for the very sharp curves, which are run over at low «pecds^aad not enough for the flat ones; but for curves Irom 1^ to 8 . this rule i. ^^^ Et;;' irih:; curve, thiselevation or cant ..uite efi^ctivo in Interacting the cntrif^gal ibrce, ^^^^ -^^^^:'^ :'^!f'^ ^:;;Zl .r too little matters little, as the body nutckly adjusts its 11 a h«k out r the perpendicular to correct the deficiency or surplu . W th 6 .. tL cL'ion we may ride around a 10" cur., at mil. an^^ and experi.nce neither d oiger nor discomtort; but il we Uiange ahruptlv rom a straight line to a 10^ curve, we must either have the S Lfficientlv elJ;aiedon the curve, or have .1 mchesol elevation u the tangent, and in either case we have a sharp jerk as the car .t^ikos th^ curve, after which it travels steadily ..ough until it leave. . h osMn «-h«. another minor lurch is experienced. The reason for the harder lurch at the beginning of the ourve, the \ author htt« ner^r wen flxpla'ni"l, i'X<'t<).t, in thai'ffiDtnf inciifflriint i lev. ation at tin- point of uuifiitur.! ; Imt im iiiMitioiinl i!nn«ii in ai t'ollnwK On tht tiuigi'ijl thi" tniiik IVium' i>' |miiill'l In tin' iitin nflli'; liif • and both wheW flaug.'fi ino tiav.lliiiK ulnir ot lli- mil, aii(J Kinorwlly owing to play, uliick gau'^i', iiml worn HiiMHf" mi infill or uioro from it. Avery Himpli' milciiliil ion will kIiow llnit with llii'< 1 iiiiili ol" piny the trnok will iiiii Hiniinlit mi iil HK cinvf I'or ^dnn' Hi I'r.'i licfoiv tli,. flange will couin in contui" Willi ilir lull, hikI tlin clFunnc in iliniuion i» then auKiilnr inHlfiul o('(!in'iiliir, Iimiioi' tin- luivli wliii'li im uniontil of supi'.releviition will foiinli'iiii'l, ll ii on lliit hikmihiiI that wiilf-iioil gauge and (U'railuu'nlH ulnioitl inviiriiihly occur iit the iihIji of curves^ There it* not only an all^Mllur olntnuc in the nintioii of ilic cur far iiiort- marked, than ut any oiln^r portion oflhc ciirvu. but therein thciujpa(;t of the flaiifre ajiuiiitit ihcrall, ami IhcHinlilin ulnnmt iuniani.iui;ou» chango in direction of the truck ii'clf wilh lefeicuce lo the car body. The want of frconcw in HwivnllinK motion of the truck, owing to a u •xoeasive headint^oii the friition hloiiku i;r other caunt', 1h unotlier very fruitful eauHf of derailiueiil. To obviate thiH shoflk at Hjc imilxof iiurven, varimnt ferine have boen proposed— parabolic, lo««rithniii'aiMl olhcii.; but time arc not only ao oumbersoniu to lay out an to be alijnmi. ii-cIck^ in practical looatiun, but do not always effcol tliu ilcMircil objttcl . It will be seen from lite foruifoinK tliat the |ierl'ect curve Ib one iu which the radius ^•radually and iv^nliirly diinininhcn I'rnni iiiBnity to the minimum iu such a diotiinee, that llie ■.npcielcvalion i« iml aecoin- l.lisheci by a steep rincor falliu tillnr mil. 'I'liii inininiuin radius and maximum elevation is then retained to within the same distance of the end, when the levcrMc proccxH lakes pliicu. \l a Kittdiei'' of I in 600 the maximum for a HI'' mirye uf Ti f'.-i will be uttaincd at aoo feet, and at every SO fcpt .06 fttiit cnrt'cspiindinK to I" oiirvaturo should be gained. The decree of curvature nl any point on this 300 feet should be directly pfoporlimial to its dintanee from i he point of curvature {'all the latter I», Fi;i I. uml the end.* of th.' scvernl 30ft. Chords. P., 1'.; I'., )'. „„ lh"u llie curvature is roprcsenled. at any of them by its coirespondlns^ index nuiubur, l.°:i.' li." etc This curve is luckily not only theoretically the best for the purpose, but easy to ruu in on the uround, cilhor with the transit or by otl'sets from the tauj;ent and from the tliial curve produced, and the elfcct on the caf.y ridin^of the I'ar is marvellous, Any leiit;lh of i.-hord may be used, the longer for Hatter oiirvus, on which high sjiced is contempla- ted, the shorter for sharp'-H' curves thmi 10''. when it i-< ditheult pi rhaps to get Rufficient room lor the loiiKi'r, I'or ordinary practice the ;tO fcv t or 1 rail length will be found very convcnienl for n ,.. Let P Piu iu t^'H- I ''" ""<-''' ■* '""'*''' Uli'l'i'fml.V leielcratinj; from 0" at P to 10" at P|„ whence it reiniiin» cnnslanl. The nieuii curvature will be 6^', anil the length beiiiK !<00 feet the total dctlection is 15" represented by the angle T, I H, In like manner it may b(^ demonstra- ted that the total defieetion at I', is 1'' ,ti ~ M\' at F, \\\^ or 2=" 24' in fact proportional Ui llni Mj^mres of the index numbers. It can also be deuioiistrBt4!d that the lanircntial an^rles T, P, l'i,T.- P P^etc, T, F r,o I"'" 1 "' l'"' '"'"' "I'lHcctions, and are also propor- tional to the sC|Uares of the indux nunibnrn, thuwiries being a', 12', 27', 48', etc., up to 5*. "Here then we have the irtnans of running in the curve with equal easu to a oircular are, suiting lint transit at I", and turning of the angles corresponding not to ill'' distances ihcinsclvcs but to the squares of those disiancus arrived at Pi" we put in a hub, incvo the transit up, and sighting bauk lU P turn oM' 10'' to the tangent ?w .s, whence we can run the 1(1^' curve in the ordinary way. Arrived at the other end of tlm curve, the procnis is quito simple, although a little more figuring is involved, Suppo8<.' we have run the eurvc round to I'l. from V., and wo wish to run the transition curve friilii I'm t^» P, producing the 10° curve towards P, it will be seen at once I hut the iransitinn curve leaves it at precisely the same rate as it leaves the tangent in starting from P, and the series of angloH will bti the dlfl'oreiioe between those for a 10° curve and those given. p ^ will be ~ 5" y ,8- I'.HO Iush 3 « r.Z?' (1 being*) p^ ■■■■ - &-• .«-.!•, " 12-2.4H p, " •< 6° « .9-4".a0 " 27:b4.03 etfl., oto, oto., oto. J», '< '• WxH-lO" •• 5"- 10* 00' If It Ijf thv taiitiftit Ui the K)"" rurv.' produced, until parallol to tt, It will be ividnit tlmt the point of taii'^ent i.x opposite I'r„ or midway of tlir trimsitioii ciirvi', aud from tin: forpgoing that P, ifi ciiuidi^iinii frnii! the circvilur curvf mid from (lit- tangoiit on liiii. r «idf of it. Matlifiiiiiticaliv, lliis is uoi exactly iruo, hut for tilt' ])urpow; we iuv niii«idi'iiiiL; it is |irartit'ally so. A littlf couoider- atlou will show that as in ihr liiifular ourvc tin- ottk'ts from tlui tau- iirnt arc pri'imitiniial tn tin; si|Uuri's of tlii' dislaiiros from tht orij»iu, s» ill this L'lirvi' we aii> coiisidi'riiij; the corrrsiiipiidiii); oflk-ts from TT ■ the jKjiiit J'l I'., tte., are propoitiouul to Ihi- tuhus of the distances to till' euhi's of iii<- iiidt'X loi'iiibiTs, and corruspuud to the series I, 'i, 'JT, «14. i' givtii similar to th.nn in the field books for eiroular curv.'s ; the fiKurins in every cn.te irt riilb.r more complex tbiin for nimpl" curves, but tlio inxtrumetital work i^ no more difficult, and once tlu' niuU-r li»s umsirrcd iIm- .Acucral cburac teri»tic»of thi* form of curve lie will readily hoIvo tlicm ior bimsclf, uud probably be able to demouHtrutf the cnrrectmsn of the results much more clearly thnn the writer. The author wiahek to suy further that with compound curves the modimoptrandi i.s mtirely siuiiiiir, the taugentiu! iiugles for each chord point being turned otl from the correspondinK points on the simple curve produced instead of from the tungent. Suppose we are running a transition eurve between a 0" and a 10" curve, the difference is 4" and the angles arc precisely the same as those between a taoKcnt and a 4" curve. Let P Pi P, Pa P, he the chord points, HO foet apart as before. Then the angles from the tan,?ent at P' the cud of the 0" curve, will be those for the curve produced r those for the transition curve. P, - 3" P, - 3° Pa -3° P.-S" .30 + 0".03 = .54 + 3' = .57 .60 + OM2 =1°.48 +12' = 2°.00' .90 + 0°.27 = 2".42 + 27' .^- 3°.09 1.20 + 0°.48 = 3°. 36' + 4?' - 4''.24 Moving the transit up to P. the angle between PP, produtsed and the tangent at P, will be 3" . 1.2 + 0''.48' ■ 2 - 3''.3« - \°M ■■ 5°.12' In ruuuiuK a hnij; eu.v.. over rough jjround, it will often happen (perhaps owing to unavoidable errors in taking thi' notes off the platted plan) that the final tangent does not li.' quiio in the ,,nsition we wish, but parallel to it. With a simple curve we should eithir start back to the bigii.ninu and try it again, or sharpen or flatten the end a little to bring itinto position. The first cou.se consumes much tm.e, and the last state of that curve is horaetines nearly as bad as the hist. The second method savours of patch work, :xnd is never quite satisfac- tory. The transition eu.ve, on the contrary, affords a means of adjust- ing such little differences with great accuracy, leaving the curve the- oretically as perfect as if it had come out right in the first place. Suppose again we have mn the curvi' in Fig. 1 out t.^ the .nd at V, and we wish to shift the tangent 2* feet further out or away from tt. The offset tt wns G 54, we wish to make it 9 feet. We have merely to increase the chord length in tlic proportion of the square roots ot these otfset«, C and being the original, and L\ and Oi the new chord and offset ; then C * u andC,= CV_Ol.=30^__^=35 nearly, the initial tangential angle will be 3.5' the total length of tran- sition curve 350 feet, and the total deflection 3.5 x 3 >: lO'' = 1050' or 17^30' instead of 15" we have merely then to set Pio in 25 feet further back on the curve, and proeecd with the new curve in the same way as before. h will be seen that tapered curves are considerab'y longer than simple ones with the same central angle, and consequently in readjust- ing a location having sharp curves oi contrary flexure separated by short tangents, we shall have to still further reduce these tangents. This, however, matters not, for the objection to absolute reversed curves disappears altogether when they take this form, calling angles to right + and to left — in the reversed curve the curvatures at the sue cessive chord points are 4." 3." 2.» l.*-^ 0.-l.°-2.°-3.^ etc., differ- ing alway.' by unity as before. In Fig. 4 we have a reversed tranaition cu'rvc between two 5" curves of contrary flexure with the same pitch as in Fig. 1. Merely remembering that we are starting from a 5.* curve instead of a tangent, we can set up on P. and run through to Pio just as easily as we could the constant curve in Fig. 1. The change in curvature is the difference between 5.« and-5.° or 10.^ consequently 7 the tiitul ItDuth ttiirt tolHl ortcit art! ilii' "unw in birth caiiei, the Uii. ;jcnti:il imgloH at P will be P '..'"'.•to X .3' - .»' = 45— 3'= 4'J' 1 I*','":!"" .rt— li' ^l.^HO- 12'= I.^'IS' (All positive I' :i";i(i 1 5— 1^'15'=3.''45 -1"15'=: 2.''30' ( or t/t Bi«bt. I"" •^■•••Mi V .! — .V'OO '=7,^3(1— 5"00 '= 2.'^30 ' ) Ami moviiin nil to l"ii> wn turn oft' l'i>r ibo taiixoiit nf the 5.^ o'lrvo ai tlu.t point, 2-\li» >i 3=7'-.30 -10" = -J^3t»' or 2"30' to left. Till iiutlior ti di-itaiioi; over which sut!. curves cxtnid by an amount .sufficient to ni-utralize the oxtra rertintauoc'. On a 111 ' curvi' tlKMiiloi-f till' gradt; should br flattiuod ,„ or thiMutitoats per KlO It. hi all discussions ol' this iiiUHtiou tht? train nioving up- ward* only has beou uonsidiTcd. Mr. A. M. WcUiui^ton, tor in.stanoe, who has wvitti'ii mori' ably and i-xhau.stivoly on locution qut-stioua tlian any 'jni; who lus pri ot-ilud liiiu. ijuitv nc'u;lt-'i'ts to take into account t'llfct of this curve couipen.^atioD on the swiftly uiovinf^ downward train. He shows as others havi before, and as any practical railway man knows for himself, the bad ell'eets of a sudden chanf^e ot gradient from steep to flat, in eausini; a '' piliuj: up " of the rear cars of a lon;^ trai»i a^ain.it the forward oms, wbieli are uieefina with ':> rcsi'tauce, often causing derailment iveii on strai^h: track; and lio strnnuly insists on lo'iff vertical curves eonnectiua- these ssrades of varying pitch. Now, with compensated cur 'os, this ictardation is doubled, tor the engine enteriiiu; the curve on its downward path experiences not only the loss of the accelerating force due to the ^^^ per cent, grade, but the resis- tance of ihe curve aa well, equivalent to another j'^ or ^^ in all, and the tendency to derailment in much more than doubled on account of the curved position of the train tending to force the center cars towards the out^iide of the curve, or in the same distance in which there is already a strong disposition owing to centrifugal force and the want of radiality in the axles. Here, the authoi' thinks, is another fruitful cause of wreck, to freight trains especially, which has not beeii fully inve.stiiiated l.iefoie, and which has ii'd to an unnueessary prejudice against curvature pir iie — uniHHCssary, becituse the cure is ca.sy. And lu're aiiain is another argument in favour of transition curves Able iiuthoritic> contend that (he rate ol' clian^v in the gradient should not exceed ^\, p.'r llHI. The total ehaii'ie being, as We have shewn, equi- valent to ,'•„ per cent., the vertical curve would have a length of 30U ft., or precisely the same as the transition curve we have been con- siilcnnu: ; and not only is the accelerating force urging the dow.iward train iiradually diminished, so that its loss is unhurtful, but the resistance to the upbound train is at all points precisely the same, and we have neither in plan nor protih; any sliirp angles or transitions from tangent to enrvi or IVoui steep urade to H;;t. As to supereievat.on of outside rail, it is generally conceded tligl it is better to i irry tliis to the full amount which theory demands for the hiuhest s|ieeil practicable on the curve, and that it is butter 111 have loo much elevation than too little, 'I"he authors own opinion in that the ordinary rule of '„ ft, for each degn^e corresponding to a III) mile sjieod is rather too little for the tlat curves from to 4°, about right at tj-^, and altogether too much for sharp curves from 10° to 20 ', and that an cxces.sivc elevation is more dangerous than the reverse, causing as it does at low speeds a ilimiuution of weight on till' outside wheel, which is the only one whiefi has anything to do with directing the train, and eon.'^equently rendering it tasier for the flange to rise over the rail. It should be remembered, too, that while the tangential tendency of the outside wheel merely causes grinding action of the flange agaitiKt the side of the rail, and stratus iutenai to iL .t rail itself, the iuside wheel is dependent on the thrust of the axle for guidance, and thru«]gh 8 I)it
  • ;t;i(t of the 5." o'lrve i"30' to left. liuits which liuoh i^ uavM' with aome «ei|- ijLTuUy without auy tVels that a htrgii r iiualified tf iiiaico it is ^oi)d practice in r which sue!, curves xtra rcriixtaucu. On c(l , „ or thi'! uiiboatii ht! truiu iiiovinii up- liui^tou, tor instance, u locutiou qufstioua s ti) take into uccouut ly uioviiif^ downward id as auj practical f ii sudden change ol' |j" 1)1' the rear cai-s of ; uici-tin<2 with ''■'< ttl^l'; track . and liu liusi- these tirades of on is doubled, for the perie.nces not only the . ^rade, but the resis- f', or fj in all, and the od on account of the center cars towards ice in which there is! 1 force and tho want is, is another fruitful ;li has not bee;i fully nneeessury prejudice he cure i.s ca.sy. And isition curves Able ! gradient should not We have shewn, equi- have a length of /iOU e we have betn coti- uruing the dovv.iward i uiihurtful, but the ;s precisf>ly the same, J auiiles or transitions lerally conceded that hich ihei>ry demands and that it is butter uthor'.'^ own opinion is 'ii corresponding to a curves from to 4*^, 'harp curves from 10° I.' dangerous than the liiuution (/f weight on 1 has anything to do iering it easier for the Langentiai tendency of of the flange against . rail itaclf, the iusidc guidance, and ttiro«igh from this iHiinI of vi.w als.p, it ,s b.lter to h.iv. at h'ist an r,,n;>l weight on both. The author has f, uud also on sharp curves, only intended and u«'d for low speeds with a hkh .leva! ion, that there is a t-ndency in th.^ track to move inward-, the tits sliding on the oallast. Widening the gauge contribuU-H to cttHU in travcrsinn curvcH, and in the sharper ones is absolutely n. e.ssary ; on a 10" curv.i ^ of an i.icli is sufficient, but in order to obviate tne shock wh.o'. tlie author has dwelt on above, in cntorini? tho curve, the «augo should b.s ligh. and close at either end i with tr.insition curves, it is easy to widen the .rauge r.iiforinly from the begiii'ung of the eurvc to the j-oint ot constant curvature. Lastly, it cannot Ic too strongly insisted on that curves should be run -leeurately witl. the instrum.nt, and enters placed permanently at sh; ' intervals, wilii Kiiebl..s tacks m their hcuii, markin- the exact position of th,; lin.'. Tlu' truck gauge should have a notch" marking its center, so that the foreman can at a glance moo whether th.' track is centered or not, without the use of thi! tape, and the track h'Vel should have a seiisilivc bubble and an attai'hmcnt for • ■vttiiig the suiierilcvalio'i e.tactly. " The outside rail should be kept equidistant from the ccntir, and any variation in widtli of gauge thrown altogether cm the inside rai'. The folly, nay, wickedness, of h.-aviii.' the lining of .-urves to tl-.e foreman's eye and the elevation to his inner couscio'isness, is just as gross and unpurdonab.e as wouh' Lo reu'ulatlou of the depth of cuttings and h..i..l,t of bridges by li'C same standard, and is very much more likely t„ lead to accident. Centners shouhl never be mor. than lOO feet apart, .,,,,1 on cunes never more than Till feet; on Ht ' eu-ves they slmnld be placed at haH every 25or:{;) fe, t, and more frequently on tho sharper curves. , . , , ,. ,i On a 2(>° curve, which the author rae in within the last l.^w ii.onllis, in.l which has been in constant us. ever sine, by passenger trains, the cfnU'i-s wero placed every 10 feet, and ri,'idly adhered to ; the gauge was widened 1 inch, and the elev.tion is .. inches, which is rather too much than too little. No sprea ling of the ^au.'o has taken place, anjl on the greater i-ortiuii not one dollar has b.ea spent in rep.urs ; such ivpairs'lis have b vn done Were on account of subsidiMicj of new bank, and ih.'y would have been equally necessary on tangent. Not the .li..l,test .liiliculty or cspcns- has been e.^pe-icnecd in operating this curve for a year, cither summer or winter. .V stop is necessary for all trains within a few feet of o.e end, a ul all tre.ins therefore traverse it very slowly ; but the author wouhl n<.t hesitate to run oViU- it at li) miles OT hour While nut advocating the us. of such eslreme curves cm the open road, exc pt t ■mpor irily an I in cxtrcie cas's, the author leels sat!sHe,l tliat prop'rly laid, :,djuste.l, compensated, and tapered eurves of 10 ' or .'ven more might liave b .en used to save money with much better results as to safety and economy, in many cases where heavy ..i-ades have been adopted to the same end, and that a great deal ot the preiudi.r which is sliewn, especially anion., the older men of ..ur pro- f v:i„n a-ainst tlio free use .d'it, to save the capital ae,.,.ni.l and increase ,he openaive value, is to a large extent sentimental and groundless ; and the autiior will be glad if this paper sug.-ests ai.ytlung worthy of di,scussi..n or comment, whether favourable to his views or the reverse. .Station*. 1" l"'. 1'. p. P' P P P P pio T.\soe.st'i.. Axr.i.K. Tot :. I)K,|-i,i:eri"N. ()."4J'— o."o;t' l.^'.-UV— (l..-'P2' = •2,-'i:.'— ii."-i7'^ :!."Oti'— o..-'|X" :!."t.v— l."l-v ,'-,.-l,V— •J.''2T' (;.won'_:!.-'|.2' tir-t.v— 't.^o:-.' 7u;(0.— .'i.^JOO = I.-'IS' = 2.-12' = 2.-:tii' ^2>'42' = 2.-»'< = 2.''4H' = 2.-42' = 2.-:u) l.:)0— ().' H.(ll)— {)■• 4.:ii)— 1. ti.oo— 2.' 7.:in- :!. !».o;)— '.. l().:io— 7. l2.:io— !•. i:!.:;o-r.'. l.'ilIU— 1,"). •Mt'J'- -•21 ■■ ..>{■ ••4.V- -'2t'' -21 '■ -O'.i -110' = 2."2I' = :(.-:i(;' ':i.-t:-.' -:i.-:!i!' «:i.-(m = 2.'-'2l' -^i.-Jl' ^d.-oo' - "H ' ^ n »> H 73 • )— i **, H^ -i > •n W r •X P. I pi :i() I I'' p- ' tio 2- P3 1 !io :i- pi 120 .1" pr. '150 i 5" p* ISO i (i- it-t-'' PT l2I0 i ?- J2.-27' P'>1210 I «- \'-l"Vi' 0' 0' 12' :»!' 27' 1.-21' 4S' ■) J.) ( ' l.-l,V :;,-4.-.' 2r 0' 0. 0.!' 0. 21' 0. 71' 1. fi7' :t. 27' I'!) e270 PluliOO '10- :4-o:!' "00 7 -21 'I H. !I7' ",).■'.■!()'■ i:!. ;t9' !2.-l)',l lit. flii' l,-,.-01)' 2'J.-15'