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22 MARINE REVIEW. [December '5; ssw 5 1x Period Fig A 2 a6 126 Ls 2 Period. Fig. B. %, : > : : E th 4 - i n Yarrow-Schlick-Tweedy 'System.--Showing very approximately the unbalanced forces and moments of second and four a Bee ees periods for steamship Deutschland at 90 revolutions. case. Thus for second period we must multiply the forces and moments for the four cranks in Fig. A by 5% for the reduction of mass, and by .2540, the coefficient in equation (14). For fourth period the multipliers are 4 and .0041. Second Period. Crank oon ays 186 X .2540 x 54 = 29.5 tons. Zero. Crank ID 253.6558 268 X .2540 X %--= 43 tons. 8082 X .2540 X 4 = 489 ft. tons. Gani Ts osc 268 X .2540 X 544 = 48 'tons. 8263 X .2540 X 54 = 1312 ft. tons, Cranky IW ove sci os 186.6 X .2540 X 5 = 29.6 tons. 7900 X .2540 X 5 = 1254 ft. tons. _ Fourth Period. Crank I ..........,05. Force. Force. 0041 X 54 = .48 tons. Moment. Moment, Zero. Crank Wt ooo... - 268 X .0041 x 54 = .69 tons. 3082 X .0041 x 5% = 7.9 ft. tons. Crank it 2.60525 268 X .0041 x % = .69 tons. 8263 X .0041 X 54 = 21.2 ft. tons. CLEAMRAY 6c casas 186.6 X .0041 X 54 = .48 tons. 7900 X .0041 X 54 = 22.2 ft. tons. Figs. B and C gives the crank angles doubled and quadrupled, respec- tively. The above forces and moments are laid off parallel to the corre- sponding cranks, as in Fig. A, but in Figs. B and C the polygons do not close, showing.that the engine is unbalanced for second and fourth period. The defect of balance is: Force. Moment. Second period ........ Deo R Mas hop biet Suisey sitio < ane rcges eG 1.7 tons. 1910 ft. tons. MOUTEN, DOUIOG ask ieee gs dices scieswice se csieae heehee Scie ASE tone: 37.2 ft. tons, These values are for one engine only. _ Second Period--The force is quite unimportant, but the moment is very great. It is strange that Mr. Schlick should havé devoted his elabo- rate paper of 1900 to showing how this force could béireduced to zero, and have passed over the moment as quite negligible. The importance of forces and moments of a given value is-greater the shorter their period, since the shorter the period the more aay will energy of vibration be supplied, other things being equal. Just as an engine running fast will give more horse-power from the same steam loads than the same engine running slow. Thus 1,910 ft..tons of second period is as important as a much larger moment of first period. Fourth Period--The remark just made applies with greater force to this period. Besides, these forces and moments are here estimated for a perfectly rigid foundation. They are due to large masses with an extremely small amplitude of vibration, Whenever the ship responds their values will increase, and we can readily 'see that in the case of fourth or higher period, where the original amplitude is minute, the response from the ship may be such as to increase the exciting forces and moments many times. Also, as a vibration becomes more rapid, the amplitude, which can be tolerated, diminishes very quickly. This great increase of amplitude can- not, of course, occur where the original amplitude is comparatively large, as in the first and second periods. The full discussion of the question is very difficult, but we can readily see that forces of a high period must not be treated as negligible, because they are relatively small. Experience shows that they give rise to very sensible effects. Let us now notice an engine proposed by Messrs. Robinson and Sankey in a paper. read before the Institute of Naval Architects in 1895. If we make a three-crank engine with cranks at 120°, and all the masses, m, attached to each crank equal, the first period force will be zero. For it is ' mw?R. -{cos $ +.cos (9 + 120°) + cos (9 -- 120°)} mw?R ' = - X cos J (1 + 2 cos 120°). = 0, since cos 120° -- -- g WY Ok ey IE "EB. LP IP. HE HP. LP. Eee oye i eee), oe woo Zo... 1 eng. fig.3. 2 eng. Continuous bed plate. 'unnatural that he should notice the point, as the balanc 4th Period. Pig: Cc But the first-period couple is obviously not zero. Now mount two exactly similar engines of this kind, but right and left hand, on one bed- plate, Fig. 3. Corresponding cylinders, say the H.P., are to be contigu- ous, so that the cylinder centers, if not equal, may be symmetrically placed. Couple the shafts so that the contiguous cranks of the two engines pass top center at the same time. Then will the center cranks of each engine pass top center together, and also the outer cranks. : : : First period forces are zero. First period couples from each engine exactly oppose, and are therefore zero for the combination; that is, the first period balance is exact. Crank angles Double the crank angles and we get ex- Book rankan g! double J actly the same arrangement. of.cranks, but G aed ed left-handed. Hence the second period bal- iS ance is exact. I. HT : : Quadruple the original crank angles and Crankangles quadrupled we get the original arrangement. Hence the : . rp . fourth period balance is exact. Soe a Crank angles _ Increase the original crank angles six oe 6 ° times and all the cranks come into one plane. increased : times, Hence there is the maximum unbalanced force of sixth period. And.so on. 12 él. These changes are shown in Fig. 4. If we could bring these engines together till the two contiguous cranks were one, actuating a mass 2m, the six-cylinder engine would become a five-cylinder, with balance up to and including the fourth period. These engines have found almost no favor, and are not likely to, as they must be very costly and long.. Space is too valuable on board ship. Their balance is, however, much more exact than can be obtained with four cranks. Mr. MacAlpine lays much stress upon the fact that calculations for balance of the four, five, or six-crank engines, and also for the revolving counterbalances at the ends of the engine, proceed on the assumption that the ship is rigid over the length of the engines, and that the assumption is specially inadmissible when considering the shorter period vibrations; in fact, that the whole question is one of the elasticity of the ship, It is not ( 1 e of the engine he proposes does not involve this assumption to anything like the same ex- tent, but I cannot think that this point is of moré than the most secondary 'importance. '| Before proceeding to consider in detail the MacAlpine system... of balancing, and' in order that we may not omit any system which has a legitimate claim to be considered in relation to the balancing problem, we may give some thought to the steam turbine. The splendid work done by the:Hon.:C: A. Parsons in the development of this form of motot and the remarkable success which has attained its application. to torpedo vessels in the way of securing extraordinary speeds, has led many enthusiastic mem- bers of the profession to believe that this motor is destined ultimately to