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1901.) - I have replaced m by m', as only the parts moving with the crosshead and part of the connecting rod give rise to higher period forces. Beyond this difference and the introduction of the factor .2540, this expression only differs from (11) by all angles being doubled. If, then, starting from any particular engine A we keep the forward crank at top center and double all the angles by which the other cranks and eccentrics stand to the forward crank, we get a new engine B. Neglecting differences of m and ' m' in expressions (11) and (15), engine B will have the same degree of balance or unbalance for first period forces and couples as engine A has for second period. Similarly, by quadrupling the crank angles we get an arrangement by which the balance or unbalance of fourth period may be easily judged. 'And so on for all periods. First, let us apply this to the crank angles of the Deutschland, which is balanced on the Y. S. T. plan. Deutschland's crank angles. Deutschland's crank angles doubled. A La a Fig. 1 gives the crank angles taken from Herr Schlick's paper "On Some Experiments Made on Board the Atlantic Liner Deutschland during her Trial Trip in June, 1900," read at the spring meeting, Institute Naval Architects, 1901. Fig. 2 gives the crank angles doubled. This brings cranks I and II both near top center when cranks III and IV are both near bottom center. The second period couple is, therefore, very large. If cranks I and II had lain in the direction OA, and cranks III and IV in the direction OB (these directions bisecting the angles between the pairs of cranks.) the second period couple would have been within half a per cent. of the greatest possible.** In Fig. 2 the angles of the cranks give a couple, less than this in about the proportion cos 4 (48°--40')=.928. (The exact value of this couple could only be found after knowing the masses attached to cranks I, II, III, and IV, but it would differ little from the above.) Thus the Y. S. T. system gives a second period couple not far from the worst possible; and this will be found always to be the case in this system. Herr Schlick's, 1900, Institute Naval Architects' paper was written to prove that, besides the first period balance, the force of second period could be bal- anced also. But as this force is always of small amount, surely its exact balance is of little importance when so large a couple is left unbalanced. Noticing these couples at the end of his paper, Herr Schlick says: "It is evident from the foregoing that there always remains a small couple of forces, and it might be feared that these would cause vibrations. This is, however, in most.cases, practically impossible. As in one revolu- tion of the crank shaft two maxima and two minima of equal magnitude arise, therefore the vibrations of the longitudinal axis of the steamer could only be produced when the number of revolutions of the engine is only half that of the vibrations in the longitudinal axis, viz., when the engine is working dead slow. But with half the number of revolutions, the couples which arise are only one-fourth of the values given above." Surely this is a remarkable statement. If true, would it not apply equally to the second period force? In which case the reason for the whole paper disappears; especially as, in all cases on the Y. S. T. system, the second peried force is never more than a very small fraction of the greatest combined force of this period that the four cranks could exert, since the second period forces from the various cranks partly oppose one another; while, on the otlier hand, as just shown, the second period couple is near the greatest possible value. It may further be asked if any com- petent observer has ever seen a vibration diagram that did not give clear evidence of the simultaneous presence of more than one period of vibra- tion, thus showing that the ship was vibrating in more than one mode at the same time; responding, on account of approximate synchronism, to unbalanced forces or couples of various periods? If so, would he say that the engine must run at half speed before there will be any response to the unbalanced second. period couples?) The above statement, indeed the reason for the whole of his paper, is more difficult to understand in view of a statement in his 1901 paper, that "most of the vessels supplied with my system of balanced. engines have been run for trial with the propellers uncoupled to examine the effect of balancing; and on all these trials vibra- tions have never been noticed, even when the engine reached the critical number of revolutions, whereas engines not balanced always show excessive vibrations when running with disconnected propellers as soon as the critical number of revolutions is reached."' If this quotation was strictly accurate, it would be difficult to under- stand the object of writing a long paper to discuss the exact arrangement of cranks by which a small second period force may be annulled. The. fact:is, if our. discussion thus far is correct, that engines on the Y. S. T. plan are not perfectly balanced, and.we find it difficult to believe that they " should not noticeably vibrate the ship when the propellers are discon- nected, as it is alleged other unbalanced engines do, for this could only be explained by assuming that:a lack of balance in the Y. S. T. engine produces a different effect from lack of balance in others. dence than he adduces to establish the fact that the comparatively large effects shown by. the vertical vibrations were due to the greater resistance ssh oe ee iy) 2 t **Cos 5 AOB = -- cos 4 (9°--40') = -- .996. If AOB had been in a straight line, the couple would, obviously, have been the largest possible. _ bad workmanship on the propeller. I : _ Very careful consideration of Herr Schlick's paper of 1901 fails to convince us of the® correctness of his position, and it would require much more definite evi=~ MARINE REVIEW. -- st experience by one blade of each propeller over that acting on the other blades. The propellers are, no doubt, of high class workmanship, and it is difficult to believe that any such marked difference in pitch or surface in one particular blade of each propeller would exist as is required in Herr Schlick's deductions. To be convincing, his paper should have given care- ful measurements of pitch and surface, which would have enabled his claims to be investigated numerically. These measurements could very readily have been made at any time the Deutschland was in dry dock. A slight diminution of pitch in the blades A, referred to in his paper, should have been accompanied by a disappearance of the first period vertical vibration, giving another easy confirmation of his theorv, which ascribes the vibration of the Deutschland entirely to what must be considered very The comfort of the ship would also thereby have been increased. As further supporting the opposite view, that with a well-made propeller the vibrations almost entirely originate in the action of the engine, I may give the following quotation from Mr. Yarrow's 1892 paper: : "From our experiments we have overwhelming proof that the vibra- tion of a torpedo boat is precisely the same in extent and character when the screw is on, and the vessel driven through the water, as when it is stationary and the engines simply revolving without doing work, the pro- peller being removed." We have every reason to be certain that these large second-period couples, shown by Fig. 2, may vibrate the ship. That a ship responds readily to first-period couples can easily be proved. Thus, Mr. Yarrow, in a three-crank engine, made the moving weights of all three cylinders equal, thereby annulling, almost perfectly, the free force, but leaving the couple. He says, in his 1892 paper: "Thus we prevented any vertical movements of the center of gravity of the engines; yet we found no improvement. This clearly indicates that the rocking vibrations are of more importance than the vertical vibrations in triple-expansion engines." As proving the same, Mr. MacAlpire points to the experiments on H. M. S. Powerful and Terrible. If first-period couples are so important, why should it be reasonable absolutely to ignore second-period couples? From the large proportion of the reports one hears, ships having engines on the Y. S. T. plan seem to behave in the manner that the complete theory would lead us to expect. I will now examine very approximately the unbalanced forces and moments of second and fourth period for the Deutschland. All the data used here will be found in Engineering for Nov. 23, 1900, and: March 22, 1901. Fig. A, Plate III, gives the crank angles, and Fig. D the crank centers in millimeters, and feet and inches, and the cylinders worked from each crank. The size of the engine is: Diameter of two H.P. cylinders, Diameter first Int. cylinders, Diameter second Int cylinders, Diameter two L.P. cylinders Stroke of pistons, 'Connecting rod=4' cranks. The weights of the moying parts. for cranks II and IIL were calcu- lated from the general arrangement. of engine, and cylinder and crank shaft details, published in Engineering. They can only be looked on as approximate, but the details are given to so large size and so fully dimen- sioned that an error.of more than from 5 to 10 per cent. is improbable. The mass taken--32.4ons--is probably a little under the truth. The com- paratively small effects from. the valve gears are omitted here. The engine is supposed to be running,at ninety revolutioris per minute, giving a piston speed of 1092 ft. per minute, which is about that usually main- tained in the Atlantic greyhounds. ( 90 X 27 w = ----_---- = 9,4248 w? = 88.8, 60 m, for cranks II and I1I=82 tons. r=72.8--12, feet. mw?r 32 < 88.8 x 72.8 --_----_-- = ---- = 268 tons; g 12 x 32.2 the highest inertia force of first period for cranks II and III. If we take zll moments about crank I we have: Maximum value of moment for crank .II=26811.5 --3082 ft. tons. Maximum value of moment for crank III=2683049--8263 ft. tons. We can now determine the other moments and forces, necessary for first period balance, from Fig. A. Lay off oa to represent to scale 8263 ft..tons. Draw ab parallel to crank IV and produce crank II in ob. ob then represents the necessary moment for crank II and ab that for crank IV. ob=3082' ft. tons. ab=7900 ft. tons. It may be noted that the data we are using is redundant. That it does not give us any trouble is proof that the crank angles have been correctly determined. I need not stop to remark on the data necessary and sufhcient to make the required determination in any case. That will be found discussed in some of the papers referred to above. 930 mm.= 36.61 in: 1870 mm.= 73.6 in. 2640 mm.=103.9 in. 2700 mm.=106.3 in. 1850 tam.== 72.8 in, 7900 The force for crank IV is ee ape tons, 42% being the arm of the yy, moment.; (See Fig. D.) Now draw the force polygon ocdeo, Fig. A,.by making the sides proportional to the forces for the several cranks, to which they are paralled. We find eo=186 tons. Higher period forces and moments. Only the parts having the same motion as the crosshead, and a part of the connécting rod*** give rise to these shorter period forces. The mass of:thése parts for the Deutschland is about 20 tons for each of-the cranks II and III;'or 5 of the mass producing first period. forces. ., Light counterbalances'on cranks I and IV make the proportionate, reduction for these cranks about the same. Again, the connecting-rod length being four cranks, the coefficients in the infinite series of equation (14) apply to this **The proportion of the whole rod to be taken is the ratio which the distan between the center of gravity of the rod and the center of crank-pin bears to i ' whole length of the rod. ----rr------