The following text may have been generated by Optical Character Recognition, with varying degrees of accuracy. Reader beware!

1901.] MARINE REVIEW. 19 We have our limits of weight and space, the dynamical problem is definite, and the inexorable laws of nature will be our judge whether we have clearly comprehended the conditions or sufficiently submitted to them in carrying our theory into practice. It is a theoretical and practical prob- lem, and both sides must be fully attended to. Or, in the quotation very familiar in this country, "It is a condition and not a theory which con- fronts us." Much that deserves notice has proceeded on the assumption that the connecting rod might be treated as of infinite length, but, unfortunately, this leads to the omission of forces of considerable magnitude. If of infi- nite length, the inertia of the piston and other reciprocating weights would be of the same intensity at each end of the stroke, say at top and bottom stroke, in a vertical marine engine. Designate this force by F. Now let us see the effect of a connecting rod of finite length. It has long been known that if r is the crank radius and | the length of the connecting rod, the actual forces are: r 5 At top stroke, F [+] =) x ecialas = 4r. 1 So that, for the length of connecting rod very commonly employed, the forces. at top and bottom stroke, instead of being equal, as supposed, actually bear the ratio of 5 to 3; the force at top is nearly double the other. Any system which does not take account of this difference cannot be considered perfect. It may be looked on as a first approximation, but an approximation far from satisfactory. We have this defect in the Wells' engine, a type of engine which has been patented by many inventors under the impression it was balanced. In it, two cylinders are arranged, one above the other, in line. The upper and lower pistons are actuated by exactly opposite cranks, and the intention is: that the inertia of the lower t 3 At bottom stroke, F [1 | = F x - where 1 = 4r. 4 Fria. 19 piston and attached moving parts at, say, bottom stroke, will balance the inertia from the upper piston and its attached parts at top stroke. The intention is far from being fulfilled, as we have just. seen, and it was, doubtless, for this reason that Admiral Melville, a number of years ago, declined to approve it. The engine has some good points, but I think that defects are what has hindered its progress. When the Y. S. T. system was proposed, it was not suggested that it in any degree took account of the effect of the finite length of the connecting rod. 'That it does not do so will be shown fully in the sequel. This is the reason for the non-adop- tion of this system by our navy, and I believe that actual experience has justified this course. I will now develop the theory of the subject so far as to explain: suffi- ciently all of value that has been done, and will give the reasons for my belief that the MacAipine system of balancing is the best. The funda- mental problem may be said to be the counterbalancing of a simple revolving piece, and with this I will commence. Suppose a revolving shaft to have a projecting arm or crank. The centrifugal force of this part will tend to deflect the shaft in the direction of the arm. 'This centrifugal force is readily calculated. If M, is the mass of the arm in pounds, and R, the radius of its center of gravity from the shaft. center, in feet; also, if w is the angular velocity of the shaft in radians per second, and g the intensity of gravity, the whole centrifugal force, as is well known, is ' M,w?R, PySoy (1) ; : & ; F, being also in pounds. Now, to counteract this centrifugal force, all we: need do is to place a counterbalancing arm on the opposite side of the shaft, the line through the centers of gravity of the original and counterbalancing arms being at right angles to the axis of the shaft.. If, then, M, and R, are the mass and radius of the center of gravity for the counterbalance, we have the centrifugal force for it F, = --_--_,, (2) g Fra. 205 Plate 2. Cylinders 27, 39, 56 and 80 in. by 48 in. stroke; boiler pressure, 200 Ibs. and to get an exact balance we make M,R, = M,R;, : (3) We can thus exactly balance the cranks of any engine and the parts revolving with them, such as the lower part of the connecting rod. This would leave the vertical inertia forces from the upper part of the con- necting rod and the parts above it entirely unbalanced, and these would cause vertical vibrations of the ship. Now, it is the vertical vibrations that are principally troublesome. Even when the cranks are uncounter- balanced, the horizontal forces rarely have produced troublesome hori- zontal vibrations, the principal reason being that the ship is much stiffer when bent in a horiozntal than in a vertical plane. Probably, also, the waves produced carry away more readily the energy of horizontal than of panera vibrations, The vertical downward force from the counter- alance is M,w?R, F, cos § = cos 9, (4) g where 9 is the angle by which the crank has passed top center. This is obtained at once by resolving vertically the whole radial force from the counterbalance, It is a force due to a simple harmonic motion of the same period as the engine revolution. If the connecting rod were of infinite length, the piston and other reciprocating parts would also have a simple harmonic motion of this period, and the intensity of the upward force from them would be Mw?R F= cos %, (5) g where M is their total reciprocating mass and R the crank radius. _ As the forces in equations (4) and (5) follow the same law of varia- tion, the whole vertical inertia force could be counterbalanced if the con- necting rod could be made of infinite length. Now, if we examine the differences ofthe actual motion of the piston, and that it would have were the connecting rod infinite, we would find that these differences followed quite a different. law of variation from that of the above equations. Hence the simple harmonic motion, got by supposing an infinite connecting rod, is only an element of the actual motion with the connecting rod finite, and it is the only part of it which can be balanced by a counterbalance. Thus we may make the counterbalance such that M,R, = M,R, + MR. 5 (6) We will then have that part of the whole vertical force, which has a simple harmonic motion of the same period as the engine, counterbal- anced; but the horizontal forces will be overbalanced. As MR is not usually greatly different from M,R,, the correct horizontal balance wilh have been almost doubled, or, otherwise stated, the unbalanced horizontal forces will now be about as great as when no counterbalances were fitted, but in the opposite direction. Since, as noted above, the horizontal un- balanced forces do not usually cause trouble, there is no very great objec- tion from this point of view to a counterbalance as large as given by equation (6). Practice varies between the limits given by equations (3) and (6). One practical objection to the larger value, besides the very considerable addition to the weight of the engine, is that, if steaming at reduced initial pressure, the crank shaft may never be lifted off the lower brass of the main journals, thus causing imperfect lubrication, heating, and rapid wear, Instead of counterbalances on the cranks, revolving arms, placed usually forward and aft of the engine, have been fitted. In most cases, the total weight of counterbalance will be considerably smaller than if each crank is separately dealt with. Their exact position being determined to suit the _ design, their mass, radius, and the angles at which the stand to the cranks can readily be determined. This can be done dither entirely by calculation or by a semi-graphical process, It will be sufficient to indicate the former method here. Let the cranks be designated by the numbers 1, 2, 3, 4, etc., in order from the forward end, m,,m,, m,, mg, etc., are the corresponding moving masses. That is; the mass of the crank is to be reduced to crank radius, so that instead of M, of equation (1) we take