190 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[JVLY, 



trust tliat not only they "ill in-opeily resent it, Imt tliat the Pro- 

 fessor of Arrliitec'ture liimselt' «ill now rouse liiniself J'rom his 

 letli.irf;y, and stand np for the lionour and tlie interests of liis own 

 art. If he do not do so, tlie sooner lie has a successor the Letter ; 

 for even should it be " Mr. Pecksniff" himself, he cannot jmssibly 

 do less, and niifrl't prohahly do a little more. Mr. (ockerell is, 

 we have no doubt, a very well-nieaninjj: gentleman, and sufficiently 

 uell (jualificd to discharge the duties of his office, so long as diffi- 

 culties do not j)resent themselves ; but he does not show himself 

 to lie the man wlio is both capable of and determined to meet diffi- 

 culties boldly, and to exert himself energetically in behalf of that 

 ait which his jirofessorship at the Academy points him out to the 

 public as the representative. If he has expostulated with the 

 Academy in regard to their treatment of arcliitecture. he does 

 himself very great injustice in concealing it from the world; 

 thereby leaving it to be inferred that he is altogether indifferent 

 to the matter. 



After this fiiwlc, if so it should be called, thcuigli what we have 

 said is ueitlier nncaUed for nor nnjirovoked, we were going to say 

 tliat we resume, and proceed with our remarks on the subjects 

 exhiliited, when, as ill luck, or at any rate luck of some sort or 

 other, will have it, we are perforce, compelled to jiostpone them 

 till our next inimber, when we shall lay them before our readers. 

 In the meanwhile, we have at any rate given them something to 

 cogitate upon, inviting those who may agree with us to support us 

 in our opinions by expressing their ow n, and assuring those who 

 may liappen to dissent from them that we are ipiite ready and wil- 

 ling to receive and listen to whatever they may have to advance 

 tliat shall countenance the treatment wliicli architecture receives 

 at the hands of that specimen of royalty — the Royal Academy ! 



COLLISION OF TRAINS. 



In the following paper we propose to determine the shock ex- 

 perienced at any part of a railway train during a collision, and to 

 propose methods for obviating the mischief that ensues. To sim- 

 plify our ideas, let us first suppose the weights of the separate 

 carriages all equal, and the buffers removed. Let the number of 

 carriages be N ; the impulse on the first carriage that sustains the 

 shock R; >■„ the impulse between the »th and j/ -{- Itli carriage : 

 then the velocity in all parts of the train being the same relatively, 

 both before and after impact, the carriages being supposed in- 

 elastic, and the masses of all the carriages equal, we shall have the 

 following equation : — 



»Vi + L' — )"n + l = '"/i + l —I'll, for all values of ii ; 

 or, r,i + •_• - 2 r„ + i -{- rn — 0; 



If the masses of tlie carriages had been unequal, »/„ tlie mass 

 of the »th carriage, we should have had N equations of the form 



r„ + 2 — rn + 1 rn+ I — Tn ,•.,,, 

 -— trom wiuch to determine r„, &c. 



mn + 2 »Ih + i ■ 



From this we conclude, that in a train of ei/>t(i/li/-loadcd carriages 

 III" .sinir'i iiirrmKC-s (lirectlji lis the itistinirc of mil/ i/iren cnrriai/e from 

 til" mil nf the triiin furthest from the point of inijiuet. 



The design of buffers is to diminish the violence of the shock ; that 

 is to say, to change impulse (which is intense jircssure continued 

 for a very short time) into a lesser pressure continued for a longer 

 time ; but. as we shall immediately show, it is not [jractically pos- 

 sible to construct buffers capable of thus translating the whole or 

 any considerable ])art of a violent shock — such, for instance, as is 

 exjierienced when an express-engine accidentally is turned into a 

 siding u])on a heavy luggage-engine. To take an example : — Let the 

 express-engine weigh 'iO tons ; its rate be -lO miles an hour ; the sta- 

 tionary luggage-engine weigh .30 tons: then, \(in,pi\ be the masses 



)' (»i m') 

 7)1 -{■ m" 

 V expressed in feet per second =: 60 nearly ; 



of the trains, uthe velocity of the express, and R: 



^ _ 20 (22i0) _ ,_ 30(2240) 



32 



32 



— nearly, in masses of a lb. weight. 



.-. R := nearly 50,100 units of momentum, or the momentum 

 is the same as would be occasioned by a mass of ;i,200 lb. weight 

 im])iiiging on a fixed olistacle at the rate of 504 feet a second. 



Let us now determine the pressure on the head of a buffer which 

 is capable of translating this shock into a continuous pressure. 

 Let the filay of the buffer be supposed 2 feet, and the thrust vary 

 as the distjmce by wliich the rod is depressed. Let ;) be the 

 pressure when the rod is thrust in a distance j- ; P the pressure 

 when the rod is tlirust in a distance 1 : then/) = P.r. 



At the time /, from the commencement of the impact, let the 

 end of the buffer liave moved forward a .space =: z ; the head of 

 the buffer has nupved forward a space =: ;; - .r : therefore, the 

 luggage-engine has been pushed forward a space =: a — x. 

 Therefore, neglecting the mass of the buffer as small compared 

 with the masses of either of the engines, we shall have these 

 equations (the luggage-engine being supposed without buffers) : — 



d'z . d'a: 



dt 

 Eliminating 



/f/.r\2 



dt^^'^'^^'^dT' 

 p . P 



er = -(^^) 



\ni m J 



/P P \ 

 When X = 2 the blow is expended, and r" = 4 I — + — ; / • 



v" (ifi 7n") 



. • . P = -p-^ i^ ■=. 756,000 lb. ; and the gi-eatest pres- 



4 (»i -\- )»') 



sure = P X 2 = twice this quantity, or 675 tons. 



It is needless to say that such a buffer is purely imaginary. A 

 far better plan would be, to have one or two carriages of very 

 slight construction, and filled with any kind of soft and yielding 

 material, at Iiotb ends of a train. There is little doubt but a con- 

 trivance of this kind would destroy entirely the effect of many shocks 

 which, unless so counteracted, would be sufficiently violent to en- 

 danger life. In the above example, to avoid the difficulty of calcu- 

 lating the effect of several buffers acting at once, the case of a 

 single engine impinging on another has been considered. But 

 when trains are attached, it is dear th.at the shock will be still 

 greater than that just calculated. 



If the play of the buffers — that is, the distance through which 

 they are capable of moving, be extrenietij small as compared with 

 the length of the carriages, the velocity at every part of the 



train will be the same. Therefore, -r—: is the same at every part ; 



and if P«, Pn — 1, be the pressures on the »*th carriage, arising 

 from the buffers, Ph — Pn — i = P„ — i— P« — :; (the weight of 

 the carriages being supposed uniform), — and, as before, if F be 

 the pressure on the buffer of the carriage nearest the shock, — 



P„will= ^. 



Returning to the equation ( , ) 



when -— = 0, and tlie buffer 

 at 



\m m I 



From this we see the gieat advantage of having a long play oA 

 the buffers : the pressure P will be diminished in a ratio varying 

 as the square of the length to wliich the buffer plays — that is. if 

 the length of one buffer-rod be twice tlie length of another, and the 

 strength of the spring of the first be only one-fourth the strength 

 of the sjiriiig of the last, the amount of shock destroyed by either 

 will be the same. 



The practical effect of buffers, as they are ordinarily disposed 

 throughout a train, is to resolve so much of the impact as they 

 cannot altogether absorb, into a series of impacts of lesse 

 momentum ; for let us consider what would happen supposing s 

 train, the several parts of which are separated by buffers, to im- 

 pinge on a fixed, immoveable obstacle. So long as the buffers are 



all acting, P,( =: -cj- ; consequently, the pressure on the first 



pair of buffers is greater than the pressure on those behind. Let V 

 be the velocity destroyed by the total shock, cV the velocitj- 

 destroyed by the time the first pair of buffers has ceased to .-ict : 

 then a velocity (1 — e). V has to be destroyed in the fir«t carriage by 



= "= h — I X 



\m ml 



driven as far as it will 



