J848. 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



109 



Tlie view Mr. Bidder took of the mode in which the subject should be 

 considered, was not with reference to tlie reflection of the particles due to 

 the angle of incidence, but with reference to the absolute velocity imparted 

 to the particles of water the vessel would have to displace. For instance, if 

 the angle of the vessel was such, that the sine was one-half the radius, then 

 the velocity of the particles in contact would he reduced one-half, and the 

 resistance would be reduced to one-fourth ; subject to the previous explana- 

 tion of the heaping of the water against the bows. 



With reference to a plane disc dragged through a fluid ; it formed for 

 itself a sort of natural prow of dead water, whiih was drawn forward with 

 it; but the form of this prow varied with the velocity of the passing current, 

 and hence the anomalies which had been observed in all experiments on the 

 subject. 



He could not agree with the infallibility of the Pitot tube ; for he thought, 

 that in proportion as the vertical tube was moved from the stem, an error 

 must arise from the lifting of the stem and the dropping of the stern as the 

 velocity increased. 



Palmer's experiments gave anomalous results. The resistances came out 

 as the tubes rather than the squares of the velocities. This Mr. Bidder 

 thought must be attributed, in a great degree, to the friction arising from 

 the small area of the channel, as compared to the surface of the body of the 

 boat, and that of the slieet of pent. up water between the flat bottom of the 

 boat and the bottom of the shallow canal. 



In trying experiments upon large vessels, he conceived, that a tug boat 

 could scarcely get up sufiicient speed (o obtain satisfactory results, and that 

 it was necessary for the vessel to be floating in perfectly still water, in calm 

 weather ; or else the circumstances being changed the results must be modi- 

 fied accordingly. 



As regarded the resistance offered by the paddle floats, when they were 

 dragged through the water, as alluded to by Mr. Heppel, when it was re- 

 membered that the absolute velocity of the paddles impinging upon the 

 water did not usually exceed 4 miles per hour, to propel a vessel at the rate 

 of 12 to 15 miles per hour, it would follow, that as soon as the engines were 

 stopped, unless the paddles were disengaged simultaneously, they would be 

 dragged through the water at the same velocity at which the vessel was 

 proceeding. In that case, the resistance offered by the p.Tddles, would be so 

 enormously disproportionate to that offered by the body of the vessel, as to 

 render the results entirely nugatory. 



Mr. Walker confirmed Mr. Bidder's statement of the results of the ex- 

 periments tried in the East India dock, which were communicated to the 

 Royal Society in 1827.' The machinery employed for those experiments 

 was very simple. It consisted of a crab-winch with a barrel 3 feet in diame- 

 ter, and handles of a sufficient length for the necessary number of men to 

 work at it. The line, of | inch diameter, was attached at one end to the 

 barrel, and at the other to a dynamometer in the bow of a boat, 18 ft. 6 in. 

 long, liy 6 feet broad, with a depth of immersion of 2 feet ; the greatest im- 

 mersed cross section was 9 feet. The experiments were tried in the Import 

 Pock, where there was a space of 1,410 feet in length, 560 feet in width, and 

 24 feet in depth ; so that there was no resistance from the sides or bottom 

 of the dock. The velocities were calculated from the time of passing through 

 176 yards, or one-tenth of a mile; that length being marked off in the mid- 

 dle of the distance traversed by the boat. The speed was attained by a given 

 number of men working at the winch, and was regulated by the vibration of 

 a pendulum. 



The results obtained were, that in almost every instance the resistance 

 showed an increase, amounting to the square of the velocity for the distance 

 traversed ; but where the velocity was considerable the resistance followed a 

 still higher ratio. In a narrow channel the increase would have been con- 

 siderably greater. The excess beyond the square, must, he conceived, be 

 attributed, in a great degree, to the raising, or heaping, of the water against 

 the bows at high velocities, and to the simultaneous depression of the stern. 



In these experiments the weight, or power, required, was of course, at 

 least, in the ratio of the cube. For instance, if one man at the winch pro- 

 duced a velocity = 1, eight men were required to produce a velocity = 2 j hut 

 as in the same time double the space was passed over, the exertion of power 

 over the same space was the half of 8, or 4 ; but the velocity being twice 

 the former velocity, it required twice the power, or eight men while they 

 were at work ; the distance was, however, traversed in half the time, so that 

 the expense of power by doubling the velocity was only as 4 to 1. 



The results shown by dragging the bluff prow or the sharp prow foremost, 

 at various velocities, showed clearly, that very different figures should be 

 taken for vessels intended for carrying cargo, from those intended for great 



Mr. Bidder said, that Mr. Barlow, in his deductions from Mr. Palmer's 

 experiments,^ stated, " that in the case of loaded canal boats the resistance 

 varied in a higher ratio, viz. ; as the cube of the velocity very nearly, if not 

 exactly," and from the experiments he had computed the power of traction 

 on a canal, thus : — 



At 4 miles per hour 1 lb. would draw 200 lb. 

 At 2 miles „ lib. „ 16001b. 



The rule adopted by some of the principal marine engine makers (as 



Vide Minutes of Proceedings, 1842, vol. li. p. 102. 

 ' Vide Phil. Trans., 1828, vol. cxviii, p. 15. 

 e Vide " Trans. Instit. C.E,," vol. 1, p. 165. 



Messrs. Boulton, Watt, and Co.)," for ascertaining the sailing qualities of the 

 vessel, viz. : multiplying the sectional area by the cube of the power, and 

 dividing the product by the velocity, bad, he believed, been found a true 

 test; and if when the power in the same vessel had been increased, the 

 quotient had been found uniform, which he had also reason to believe was 

 the case, another proof was afforded of the correctness of the theory, of the 

 resistance being as the square of the velocity. 



Mr. Spiller thought the results of Mr. Palmer's experiments were to 

 have been anticipated, from their being tried in a narrow and shallow chan- 

 nel ; the progress of the boat was necessarily retarded by the friction of the 

 water against the sides and the bottom, a mass of water was carried along 

 with the boat, and not having space to expand, reacted against the boat, 

 unduly increasing the resistance, particularly at high velocities, Under ordi- 

 nary circumstances the resistance would be as the square of the velocity, and 

 a vessel going at a given velocity required eight times the power. 



Mr. Scott Russell, thought the incongruities in the results of the ex- 

 periments arose from want of due attention in noting all the circumstances 

 attending them. The forms of the vessels were not particularly registered, 

 nor were the various forms experimented upon, under similar circumstances. 

 Now, as the law of resistance must vary with every difference of form, al- 

 though a general rule might be given, it could not be relied upon in practice, 

 and it became essential to analyse every experiment carefully before any de- 

 duction was made. One point to be particularly noticed, was the resistance 

 of different forms of the bows of vessels, and of the quarters, as the law 

 would vary as they were changed. Any experiment made in a channel of 

 contracted dimensions, perhaps only three or four times that of the area of 

 the midship section, could nut be trusted ; the law of resistance would vary 

 with the form and dimensions of the channel, and great allowance must be 

 made for lateral friction. In short, as a practical man, and speaking upon 

 the authority of nearly ten thousand experiments, made upon large vessels in 

 open spaces, under every variety of circumstances, he must still think the 

 mode of experimenting by the steam-tug that which was best calculated to 

 furnish accurate results. 



Nor was he less wedded to the observations by Pilot's tube, using it as an 

 instrument for measuring velocity. He would of course have the zero point 

 adjustable; and its delicacy might be further tested by having another tube 

 beside it ; one of them indicating the immersion, and the other the velo- 

 city. 



Mr. K. Stephenson said, the object appeared to be, to ascertain the law 

 of resistance with respect to large vessels, as deductions from the expeii- 

 ments on small bodies did not seem to apply. He could scarcely agree in 

 the propriety of relying upon the results obtained l^y dragging a vessel 

 through the water by a steam-tug, which was only capable of obiaining low 

 speeds. He thought that a steam vessel contained within itself the best 

 mode of trying experiments, by means of the indicator attached to the en- 

 gines. He was of opinion, that method would be found preferable to any 

 other, if the vessel was tried at various rates of inimersinn, different speeds, 

 and under circumstances that enabled deductions to be drawn. 



Mr. Bidder replied, that in practising such a mode of experimenting, it 

 would be first necessary to ascertain with accuracy the slip of the paddles, 

 and the allowance to be made for the angles of impact and the depth of im- 

 mersion, all which diflicult problems were as yet little treated of and but 

 imperfectly understood. 



He was not satisfied with the accuracy of the Pitot tube, even as a mea- 

 sure of velocity, as the statical pressure must be affected by the varying ve- 

 locity, and false results would be indicated. 



Mr. Scott Russell said, it was true that if the tube and the funnel mouth 



3 Extract from a letter from J. Brown, Esq., dated January 28th, 1833 :— 

 In the years 1818 and 1819, Mr. Waft made a series of oxperiinents with his vessel, 

 the ' Caledonia,' to ascertain her vclucity under different circumsljmces, and amongst the 

 rest, the effect with one engine disengaged from the other. Each was nominally 14 h.p , 

 and the operation of uncoupling one occupied about five mii^utee, so that the trials in 

 both instances were precisely under the same circumstances as to tide and wind. 



A measured mile in Long Reach Wiis tun with and against the tide six or eight times, 

 and the average taken. 



In 1818, with paddle-wheels of 10 feet 6 inches diameter, the results of these experi- 

 ments were as follow : — 



Miles. 

 With both engines at work, eight experiments gave average .. 8 (ll 



With one engine ditto, eight exi)crinients gave average .. -. 6*17 



In 1819 these were repeated with paddle-wheels 13 feet diameter : — 

 Both engines working during eight experiments, gave an average of . . 8'63 

 One engine „ eight ditto .. .. .. 6'64 



Again, both ditto „ eigh'een ditto ,. .. .. 8-29 



One ditto „ eighteen ditto .. .. .. 6-24 



Similar trials were made with the 'Magnet' in 1827. Two engines of 



CO h.p.— with MJ?s. 



Both engines at work during four experiments, the average speed was 9*72 



One engine ditto ,, four ditto .. .. .. 7-42 



You will remark, that the velocity with one engine in all these experiments, is some- 

 thing under what should arise, but is accounted for from the circumstance, that the 

 number of strokes per minute, was reduced below the maximum, fiom the excess of 

 lead. 



The results are however sufficiently near to establish the fact, that the power required 

 is as the cube to the velocity, and according to this the ' Caledonia' experiments in 1818, 

 with one enrine, should have given 6*o5 miles, instead of t)-l7 miles ; and in 1819, o-72 

 miles, instead of t5'64 miles; and 6-58 miles, instead of 6-24 miles. 



In none of these experiments was the indicator applied to the engines; the actual 

 power exerted by each was, therefore, not ascertained, but the nominal power was '^^'^n. 

 In those of the ' Magnet' this instrument was used in the experiment quoted, and the 

 actual power, when both engines were at work, was ascertained to be equal 227 h.p.. 

 giving 9-72 miles velocity; with one engine 103 h.p., 7-42 miles velocity; which is withm 

 the second place of decimals what it should be, say 7*47 miles. 



