THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



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this plane, there was a pretty strong wind directly in favour of the motion of 

 tlie train down the plane. 



Scientific experiments shew, that the increase of resistance from the at- 

 mospere is in a higher ratio than that of the square of the velocity ; the expe- 

 riments just mentioned confirm this, for while the squares of the velocities in- 

 crease in the ratio of 100 to 107, or 7 per cent., the resistance is increased in 

 the ratio of 100 to 115, or 15 per cent. 



These experiments, though conclusive as regarded the effect of the atmo- 

 sphere in this case, and though they give a total amount of resistance, were 

 insufficient to determine the proportion in which this resistance was due to the 

 atmosphere, and to friction. Various methods of determining this presented 

 themselves. If a train were moved down an inclined plane commencing from 

 a state of rest, or with any given speed, and allowed to be gradually ac- 

 celerated, suhject to the combined resistances of friction and the atmosphere ; 

 the circumstances of its motion could be investigated by the principles of 

 mathematics, assuming that the friction was, as it is generally considered to 

 be, independent of the velocity, and that the atmosphere varies either as the 

 square, or as any other assumed power of the speed. This, however, com- 

 prehended complicated problems, and it t' erefore became desirable that some 

 more direct method of deriving the required quantities should be adopted, and 

 if possible by direct experiment. By subjecting to experiment the same or 

 similar trains down different inclinations, different velocities would be attained, 

 and these velocities would balance the different resistances due to such inclina- 

 tions, and distinct data would be thus obtained, which being properly com- 

 bined and compared, would show the friction and the atmospheric resistance 

 separately. It was difficult, however, to find inclined planes precisely suited 

 to this purpose, and the following experiments, combined with those on the 

 Whiston Plane, were made for {he purpose. 



An inclined plane occurs on the Grand Junction Railway, descending from 

 Madeley towards Crewe, the inclination of which is I in 177; four carriages 

 were selected, and loaded so as to render the gross load equal to that of the four 

 carriages with which the last three experiments were made on the Whiston 

 Plane, — that is, their gross load amounted to 18 tons 1 cwt. These carriages 

 were propelled by an engine to the summit of the Rladeley Plane, and 

 descended down it in the same manner, as was done with the carriages in the 

 former experiments on the Whiston Plane. A uniform speed was in like 

 manner obtained, which continued to the foot of the plane. In the first ex- 

 periment this speed was 30, 4- lOths feet per second, and in the second 31, 

 4-lOihs feet per second; the mean of th^ two being 3U, 0-Ulths feet per 

 second, or '21 miles an hour. The force of 18 tons I cwt. down this plane 

 being '228-4 lbs. it follows that this represents the resistance of such a train 

 moving at "21 miles an hour- Prom this and the experiments down the 

 Whiston Plane, two distinct data were obtained for the total resistance, in- 

 cluding atmosphere and friction, viz. at S'2^ miles an hour, the sum of the 

 resistances was 421 lbs., and at 21 miles an hour it was 228i lbs. By com- 

 bining these results, a simple mathematical process gives us the resistance due 

 to friction equal to one 4.33rd part of the weight, or 5'17 lbs. per ton ; hence 

 the total resistance due to friction for the coach train used in these experi- 

 ments was 933 lbs. and therefore the resistance due to the atmosphere moving 

 at 32j miles an hour was 329 lbs., and at 21 miles an hour I.Sj lbs. 



From these experiments, therefore, it follows, that of the whole resistance 

 which the moving power had to encounter in these experiments, when a speed 

 of about 32 miles an hour is maintained, 22 per cent, only is due to friction, 

 while 78 per cent, is due to atmospheric resistance. 



Having thus ascertained that a comparatively small proportion of the whole 

 resistance is due to friction, it ceased to be a matter of surprise that the 

 methods of calculating the resistance of trains, based exclusively on the laws 

 of friction, should give discordant and unsatisfactory results. Yet such 

 methods ai'e the only ones which appear to have been hitherto applied to this 

 enquiry. By such uietliods the common estimates of from 7 to 9 pounds a 

 ton from friction have been obtained, and as such estimates have been derived 

 from carriages in motion, and without any allowance for atmospheric resist- 

 ance, it is obvious that to whatever extent that resistance may have affected the 

 calculations, to the same extent has the estimate of friction derived from them 

 been augmented beyond the truth ; and this will satisfactorily account for the 

 amount of friction derived from the above calculations, which are independent 

 of atmospheric resistance, being so considerably under the common estimate. 



These comparative results were, however, obtained from one set of experi- 

 ments only on each plane ; and although they determine most conclusively, 

 that a very considerable resistance arises from the effect of the atmosphere; 

 yet I would not have it understood that the amount of friction, properly so 

 called, as determined by these experiments, should be adopted as a standard ; 

 there can be no doubt that its precise amount is much less than the received 

 opinion, but it would require fui'ther experiments, more in number, and 

 more varied, to detei'mine the amounts which should be adopted as a standard 

 at different velocities and with different weight of ti'ains. 



The expeinments ou the comparative friction of the four and three feet 

 wlieels, and also those made to ascertain the resistance of the road, having 

 been made by puttmg the cariHages into considerable velocity, and allowing 

 them to come to rest, the velocity was therefore variable, from the extreme 

 motion to rest. -\s the atmospheric re>islance vaiies as the si[uare of the 

 velocity, while the friction of attrition on the axles, and the resistance of the 

 wheels on the rails are constant at all i s'cc'.ties it requires a complicated 

 formula for calculating the amount of each separately, and it requires also a 

 series of experiments to come to a correct conclusion. 



As, however, that part of the resistance of can'iages T\hich depends upon 

 the increase of the diameter of the wheels, has been, by the preceding experi- 

 saent proved to be so estremely small iii projtortiou to the entire icsislaucc ; 



and as the experiments with the thi-ee and four feet wheels were made upon 

 waggons, (there not being both descriptions of wheel upon the passengers' 

 cari-iages), I did not think it advisable to give results deduced from compli- 

 cated formula, in this report; they are, liowever, given in the Appendix, Note 

 S, together with the formula by Dr. I^ardner, for calculating the resistance. 



There can be no doubt, that the fi'iction on the axles, and also the resist- 

 ance of the wheels on the rails, will be diminished in the ratio of the diameter 

 of the wheels; but on the other hand, if large wheels have the effect of pre- 

 senting an increased frontage to the carriages, it is doubtful to what extent 

 they are productive of a diminution of resistance, at high rates of speed : — 

 witii heavy loads at a slow rate of speed, there is no doubt that a i-eductiou 

 of friction will be effected by them, but our enquiries are with high rates of 

 speed, and, therefore, until further expciimenls are made, it cannot be deter- 

 mined what the effect will be by ait increase of diameter of the wheels. 



The above reasons, likewise, preclude us from determining with perfect 

 accuracy, the relative resistance of the Great \A'estern rails, and those of other 

 railways ; the mode of conducting the experiments being the same as above 

 stated, viz. of putting the can-iages in motion and running them to rest. The 

 atmospheric resistance being affected by a difference of the area of frontage 

 of the carriages, and the carriages on railways of a narrow width having a less 

 frontage than those of the Great Western, unless wo could determine what 

 effect the increaseil frontage had at all the varying velocities, we could not 

 determine that part of the resistance which arises from the wheels upon the 

 rails. 



This is, indeed, more difficnlt than that ofdetermiuing the relative resistance 

 of wheels of different diameters, the experiments in the latter case, being made 

 with carriages of the same construction, whereas in the former case, they 

 made with carriages of a different construction. 



It will be afterwards seen, that the rails of the Great Western Railway pre- 

 sent a less rigid surface to the wheels than stone blocks, but about the same 

 or rather less than wooden cross sleepers; and as it may bn presumed, every 

 other circumstance remaining the same, that the resistance opposed to the 

 rolling of the wheels upon railroad, will be in some degree proportionate to 

 the rigidity of the surface on which they roll, especially when the material 

 composing tlie surface is the same ; we may, therefore, conclude that the 

 resistance opposed to the carriage wheels upon the Great Western Railway, 

 will be about the same as that of a railway laid with cross sleepers, hut greater 

 than one constructed with stone blocks: — to what extent the present question 

 is affected by this, will be afterwards considered. 



We come now to the first part of the third proposition, viz. The compara- 

 tive advantage, or firmness of base or road track, of the (ireat Western Rail- 

 way, constructed with continuous timber bearings, with or without piles. 



The only mode by which this could be determined in a satisfactory man? 

 ner, appeared to me to he by direct experiment, by ascertaining the extent of 

 deflection produced on the rails of the Great Western Railway by the passage 

 of trains of known weights along them ; and by making similar experiments 

 on other railways differently constructed, thus to determine which of them 

 were least affected by the passage of the load. 



In an enquiry in I 835, as to the best description of rails and fastenings for 

 the Liverpool and Manchester Railway, by Professor Barlow, he employed 

 an instrument which he called a Dcflectonieter, to test the amount of deflec- 

 tion produced by the passage of the trains along rails of different dcsciiptions. 

 This instrument, however, only recorded the extreme or maximum deflection, 

 and as in many cases jerks were produced by the lurching of the engine and 

 carriages, which threw the vernier of the instrument upwards in a very dis- 

 torted manner, the result was by no means so satisfactory as could be wished. 

 He likewise only employed one instrument, consequently the observed deflec- 

 tions in the middle of the rail, being affected by the depression of the blocks 

 supporting eaeh end, the entire effect was not shewni. 



It occurted to me iImU by improving the fonn of this instrument, and by 

 applying the same apparatus which has been previously described as being 

 used for the dynamometer, the motion of the arm of the deflectometer, or 

 instrument showing the deflection of the rails, might he recorded, and 

 we should then obtain a diagram of the deflections of the rails as the 

 (rains passed over them ; and by employing three instruments at the same 

 time, one at each point of bearing at the blocks, {or transoms of the con 

 tinuous rails,) and one midway between the transoms, or in the middle of 

 the rail, and having all these connected together, so as to record their 

 action at the same time, we thus obtain correct diagrams of the deflections 

 produced at each of these points as the train passes over. 



By this plan we not only had produced diagrams, showing the actua 

 amount of deflection of the rails and bearings ; but we had exhibited upon 

 paper, the nature of the action of the deflection produced, and consequently a 

 correct outline of the effect of the passage of the trains on rails of difl'erent 

 kinds. 



On consideriHg the subject of the deflection produced hy the passage of the 

 trains on a railroad, it will be readily conceived that the deflection vertically 

 is not the only effect ; if the rails are not perfectly perpendicular, and the rim 

 of the wheel perfectly cylindrical, which in practice is seldom or ever the case; 

 or, if the base of the block or timber bearing be not perfectly horizontal, sup- 

 porting the load with equal firmness throughout the whole area of its base ; 

 when the incumbent weight comes upon the rail, there will be a certain extent 

 of deflection horizontally, as well as vertically. On almost all railroads tho 

 periphery of the wheel is conical, and the rails are laid at such an angle as to 

 correspond with the cone of the wheels ; the line of pressure of the incumbent 

 weight is not therefore vertical, but in a line at right angles to the cone of the 

 wheel, and has of course a tendency to produce horizcmtal deflection, and this 

 will also be further increased when' the llaiich of the wheel presses against thy 



