64 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



comparison between the two systems of an increased and ordinary gaug^c of 

 railways. 



If the object had been only to ascertain and develope the power required 

 to work the Great Western Railway, this would li.ve been shown by these 

 experiments, and it would have been less an object of utility to determine 

 what part of that power was expended in overcoming the resistance of <lie 

 engines, wliat part was due to the friction and resistances of the carriages, 

 and what amount of obstruction was caused by the road. But wlien the 

 inquiry was extended to a comparison with other railways, it then became 

 necessary to separate the results, the engines employed on the Great Western 

 Railway being, in some respects, different from those employed on other rail- 

 ways ; the carriages are also different, and the construction of the rcid vary- 

 ing likewise. 



The carriages on the Great Western Railway are mounted on wheels four 

 feet diameter, whereas the wheels of the carriages on the other railways are 

 generally, and those on which the experiments were made were upon wheels 

 three feet diameter. The first inquiry, therefore, appeared to be to determine 

 the comparative friction of four feet and three feet wheels, or wheels of dif- 

 ferent diameters. 



Again, the experiiuents with the trains included the resistance opposed to 

 the carriages and engines by the road, and the construction of the rails being 

 different from those on which the other experiments were made, it became 

 necessary to determine what effect the peculiar construction of the road had 

 upon the aggregate resistance determined by these experiments, and to ascer- 

 tain the comparative friction of a road with continuous bearings and piles and 

 a road upon isolated supports, or such as those on which the several experi- 

 ments were made. 



These investigations, therefore, comprise the second proposition, viz. : — 

 The mechanical advantage or diminution of friction, by being enabled to in- 

 crease the diameter of the wheels without raising the bodies of the carriages, 

 and in what respect, and to what extent the friction of the carriages is affected 

 by the peculiar construction of the road. The first process will, therefore, be 

 to determine the actual friction or resistance of the carriages on the respective 

 railways. Many modes have been adopted by different experimentalists, of 

 determining this on railroads; that of variously constructed dynamometers, 

 the force of gravity, and several other modes. 



The action of the dynamometers is so very irregular, requires such perfect 

 instruments, and even with the utmost possible care it is extremely difficult 

 to ascertain the correct resistance; the vernier in a state of constant vibra- 

 tion or oscillation, that no correct mean result can be determined by observa- 

 tion. I had a dynamometer constructed in 1835, which was mounted on a 

 truck, and, by a set of rollers connected with the travelling wheels, unwound 

 a roll of paper, upon which the vibrations of the vernier was traced by a 

 gjencil. By this mode of application the real vibrations of the vernier was 

 recorded, in a precisely similar manner to that which will hereafter be shown 

 to have been used in these experiments to record the motion of the carriages, 

 and by which a mean result can at any time be obtained by admeasurement 

 of the diagram. This machine being, however, constructed for a 56 inch 

 gauge of railway, and being rather cumbrous and bulky, could not be 

 adapted to the Great Western Railway in time for the purpose of this inquiry, 

 and this instrument is likewise liable to the objection of all dynamometers; 

 that being placed behind the tender, they do not show the entire resistance of 

 the train, the tender intercepting the effect of the atmosphere, and diminish- 

 ing, tlierefore. the entire resistance. 



Ttie gradients of the Great Western Railway also, being nearly that of a 

 level, the action of gravity could not be made use of for determining ihe fric- 

 tion ; and therefore there appeared no other mode than the following, by 

 which the resistance could with any degree of accuracy be determined : — 



A piece of road, perfectly straight, and as nearly level as could be obtained, 

 ■was selected ; this road was staked out with pusts at every 110 yards. An 

 engine and train of carriages, the friction of which was to be ascertained, was 

 brought to one end of the stage so staked off ; the steam was set on, and the 

 engme and train put in motion, until they acquired a velocity of about 20 

 miles an hour; the steam was then shut off, the engine stopped,"and the train 

 of carriages being previously detached from the engine, they were allowed to 

 run along the line until the friction and resistance of the atmosphere brought 

 them to rest ; during the whule of the experiment, the time of passing each 

 post was carefully noted down, and also the time when the carriages came to 

 rest. 



Note P, Appendix, is an account of the experiments and formulse, for 

 ascertaining the comparative friction of three and four feet wheek on the 

 Great Western Railway. 



Note Q, the experiments made on that and other railways, for the purpose 

 of ascertaining the comparative resistance of railway trains. 



These experiments were made at a velocity, at the commencement of the 

 experiment, not exceeding 20 miles an hour, and varying from that until the 

 carriages came to re-t ; and appeared to be the only mode of obtaining the 

 friction by a precisely similar manner on the Great Western and other rail- 

 ways. The resistance of the most important section of the experiments with 

 the engines are not, however, comprised within the rate of speed at which 

 the preceding experiments with the engines were made. We have already 

 remarked the very great diminution of effect at a high rate of speed, especially 

 when a velocity of from 35 to 40 miles an hour was attained; it became, 

 therefore, of the utmost importance to ascertain whether the diminution of 

 effect »as referable to the engines, or to the resistance of the carriages at those 

 higher rates of speed. 



The chief part of the resistance to which practical attention has been di- ' 



reefed is that which is properly called friction. That the atmosphere offered 

 some resistance has been always, of course, admitted, but this resistance has 

 been generally considered to be so insignificant, compared with the resistance 

 depending on friction, (hat in all calculations which have come within my 

 knowledge it has been wholly disregarded. 



It became, however, of the greatest importance to investigate, to the 

 fullest extent, every resistance offered to the motion of railway trains, espe- 

 cially at high rates of speed, and it was therefore determined to institute a 

 course of experiments, with a view to determine, by some direct and con- 

 clusive means, the actual amount of atmospheric resistance, independently of 

 any principles of calculation founded upon the laws of friction. 



The method adopted was founded upon the following considerations ; — By 

 numerous experiiuents which have been made by different philosophers on 

 the resistance of the air, it has been satisfactorily ascertained that that resist- 

 ance variesjn a proportion somewhat higher than that of the square of the 

 velocity of the moving body. W hatever, therefore, might be the actual amount 

 of this resistance, at any particular speed, it was to be expected that its increase 

 would be very rapid, even by a small increase of speed. If, therefore, a rail- 

 way train was moved down an inclined plane, of an inclination so steep that 

 gravity would produce considerable acceleration of motion, the resistance of 

 the motion, so far as that lesistance depends on the air, would be subject to a 

 rapid increase. Now, if tlie resistance of tlie atmosphere be considerable, it 

 is quite clear that tlie speed which the train would acquire in descending the 

 inclination might be such as to tender that resistance so great that, combined 

 with the friction, it would be in equilibrium with the gravitation of the train 

 down the inclination ; and in such case the necessary consequence would be, 

 that the train would cease to be accelerated, that it would require an uniform 

 speed in the descent, which it would retain without any augmentation until 

 its arrival at the foot of the plane. 



The Whiston inclined plane on the Liverpool and Manchester Railway 

 being straight and about a mile and a half in length, falling at the rate of 1 in 

 96, afforded a favourable opportunity for the experimental test. A train of 

 four first class carriages was accordingly prepared and brought to tlie level at 

 the summit of this inclination. In the first instance the carriages were not 

 loaded, save by the persons employed in making the observations, and the 

 gross weight of the train was lo, 6-lOth tons. Aa engine was placed behind 

 them, so as to push thera towards the summit of the plane, and then to dis- 

 miss them down it with a considerable speed. They commenced the descent 

 accordingly, moving 100 yards in seven seconds, or nearly 30 miles an hour. 

 As was expected, a uniform speed was soon acquired, which suffered no 

 change until the arrival of the train at the foot of the plane; this uniform 

 speed in the first experiment was 45 feet per second. The experiment was 

 repeated in the same manner, when a uniform speed was again attained of 46, 

 3-tenths feet per second, the mean spefid in these two experiments being 45, 

 6-lOths feet per second, or about 31 miles an hour. The carriages were now 

 loaded with a weight equivalent to their usual load of passengers, by which 

 the gross weight of the train was increased to 16 tons 1 cwt. ; the gravitation 

 of the train being thus increased it was expected that the speed would also in- 

 crease, the momentum of the descending body being adequate to encounter a 

 proportionally greater resistance of the air. Three experiments were then 

 made with the trains thus loaded, which showed results of considerable 

 uniformity ; in the first experiment the uniform speed attained was 46, 

 8-lOths feet per second ; in the second, 48 feet; and in the third, 47 I-lOth 

 feet per second, the mean of which is 47, 3-1 Oths feet per second, or 32|- 

 miles an hour. 



The force exerted by 15, 6-lOths tons down an inclination of 1 in 06 is 

 equivalent to 364 pounds, and as this was the weight of the train in the 

 first experiments, it follows that such a coach train moving at 31 miles an 

 hour suffers a resistance of that amount, which includes both friction and 

 atmospheric resistance. 



Again, the force exerted by 18 ton 1 cwt. down the same inclination is 

 421.12 pounds, and as the train having this weight moved with a uniform 

 velocity of 32^ miles an hour down the plane, this was its resistance at that 

 speed. 



These experiments are quite conclusive as to the agency of the atmo- 

 sphere, in resisting the motion of trains on railways. It has never been 

 pretended that the actual resistance from friction amounts to more than 

 nine pounds a ton of the load, and many have stated that it does not exceed 

 seven pounds, and some that it is so low as six pounds. But even if the 

 highest of these estimates be taken, it would follow that the whole of the 

 resistance of 421 pounds, encountered by the train moving at 32^ miles an 

 an hour, only 162 pounds are due to friction, while about 260 pounds are 

 due to the atmosphere. But we shall presently show that this estimate of 

 the resistance from friction is overrated, and that, therefore the amount of 

 the atmospheric resistance here referred to is considerably underrated. 



In comparing the results of these two sets of experiments, it will be ap- 

 parent in how great a degree the resistance is increased even by a small 

 increase of speed. The mean speed in the first two experiments was 13 miles 

 an hour, and in the last three 32 j ; the ratio of these velocities is about 100 

 to 10;3, the speed being in the latter case increased three per cent. Now the 

 resistances in the two cases were in the direct ratio of the gross weight of the 

 trains, which ratio was 100 to 115. Thus to gain an increase of speed amount- 

 ing to 3 per cent., an expenditure of power amounting to 15 per cent, is ne- 

 cessary. Nor can it be said, that the great amount of resistance here mani- 

 fested was produced by a head wind, though even were such admitted to he 

 the case, such an admission would equally involve the principle of a powerful 



atmospheric resistance ; bnt in fiict, in all tbe experiments performed upon 



