21 3 ON A SIMPLE CONSTRUOTION OF STEAM ENGINE GOVERNOR HAVING A CLOSE APPROXIMATION TO PERFECT ACTION. BY ME. JEREMIAH HEAD, OF MIDDLESBBOUGH. The irregularity of speed tolwhich all steam engines are liable arises from two principal causes : variation in the pressure of steam supplied, and variation in the amount of resistance to be overcome. Variation of steam pressure may arise from irregular firing, overtaxed boilers, or in the case of waste-heat boilers, from several dampers happening to be closed at once, and from other similar and obvious cauaes. Variation in resistance occurs when the work to be performed is from its nature intermittent ; this variation is at its minimum in such engines as those used for pumping or blowing, and at its maximum in engines such as are attached to saw-mills, rolling mills, grindstones and shears. If an engine readily lags in speed when the resistance increases, its efficiency is lessened just when most required ; and if it “runs away” when relieved of work, or when the steam pressure is higher than ordinary, the wear and tear of the machinery connected with it is increased, and at the same time steam is wasted in doing the mischief. These considerations were all fully recognised by Watt, who sought to remedy them by his well- known steam engine governor. Although imperfect and partial in its action, this governor is sufficient for many purposes; and its extreme simplicity has caused it to remain to the present time in more extensive use than any other. It acts on a throttle-valve inserted in the steam-pipe close to the valve-chest, and partly closes the throttle-valve when the normal speed is exceeded, and opens it wider when the speed falls below the ordinary rate. Governors thus exercise their control by varying the area of the aperture through which the steam passes to the cylinder; and a perfect governor would be that which ’would always accommodate this Downloaded from pme.sagepub.com at UNIV OF CINCINNATI on June 5, 2016 214 STEAM ENGINE GOVERNOR. variable aperture to suit exactly every variation in resistance to the engine or in pressure of steam. The governing apparatus however is necessarily limited in its power of control. If the engine be running at a speed below its proper number of revolutions, all that the governor can do is to open the throttle-valve wide; if the engine still lags, want of steam or insufficient diameter of cylinder is then the cause. On the contrary if the engine exceeds its proper number of revolutions, notwithstanding that the throttle-valve be fully closed, then steam must be leaking past in sufficient quantity to overcome whatever resistance may exist, and the remedy is to be found in better fitting of the throttle- valve. So long as the number of revolutions of the engine is absolutely constant, the governor, whatever its construction, will remain unaltered in position; but as it can never be made to anticipate a disturbance, but rather its operation must be the effect of B, disturbance, the existence of departures from the normal speed is a, necessary condition of its action. Hence no governor can keep an engine to an absolutely uniform rate of revolution under variations of pressure or resistance. But though absolute perfection is unattainable, it may be approached to almost any degree of nearness ; and the merit of any governor depends on the smallness of the amount of variation which it will permit, above and below the normal speed, before exercising its full control in opening or closing the throttle-valve. Thus supposing that an engine liable to extreme variations in resistance be arranged for a speed of 40 revolutions per minute; then if at 41 the governor were thrown into a state of uneasiness and rose further and further until the throttle-valve were almost closed, rather than permit a further increase or even a continuation of that speed; and if at 39 revolutions it manifested a similar restlessness, and fell lower and lower until the valve were fully open, rather than permit a further decrease or a continuation of the same speed ; then such a governor might be considered as practically perfect. But supposing another governor attached to a similar engine were to rise only a little at 41 revolutions, and stop contented there, and at 42 to rise yet a little higher, and there to remain, and so on for each increment of Downloaded from pme.sagepub.com at UNIV OF CINCINNATI on June 5, 2016 STEAM ENGINE QOVERNOR. 215 speed until 50 revolutions were necessary to enable it to keep the valve fully closed, or on the other hand 30 to keep it fully open; then it is evident that the second governor, permitting a variation of 10 revolutions per minute each way, above and below the normal speed, before exercising its maximum control, would be inferior to the first one, which permitted a variation of only one revolution each way. The second governor might however be good enough for many ordinary operations, and much better than none. The object of the present paper is to show that, while the ordinary Watt governor as at present in general use is of the nature of that last named, allowing a serious change of speed before it effects the required regulation in the supply of steam to the engine, yet it may, without any material increase of complexity or expense, be so modified in construction as to approach very nearly to the standard of theoretical perfection. The ordinary governor consists of an upright spindle, driven by the engine and therefore partaking of any irregularity in its speed, and carrying two arms, one on either side, attached to the top by a joint, and terminating in heavy balls. The balls hang close to the spindle when at rest, but when in motion are projected outwards by the centrifugal force of rotation. The suspending arms are free to rise with the balls, and are connected by rods and levers to the throttle-valve, so that when in their lowest position the valve is fully open, and when at the highest it is nearly or entirely closed. The arms and balls are in duplicate simply for the purpose of balancing each other ; and the whole forms a pair of what have been termed conicaI pendulums. The time of rotation of a conical pendulum depends solely on the height of the cone described by the suspending arm and ball ; and is the same as the time of oscillation of an ordinary pendulum having the same length as the vertical height of this cone measured from its apex to the centre of the ball. The centrifugal force which maintains the expanded position of the ball is directly proportionate to the radius of the circle described by the ball, and to the square of the angular velocity of rotation or the number of revolutions per I2 Downloaded from pme.sagepub.com at UNIV OF CINCINNATI on June 5, 2016 216 STEAM ENGINE GOVERNOR. minute; and in the particular case therefore when the number of revolutions is uniform, the centrifugal force is directly proportionate ' to the radius in all positions of the ball. The proportion between the weight of the ball and the horizontal force required for supporting it at any angle is also the proportion between the height of the cone described by the suspending arm and the radius of the circle described by the ball. When the governor balls are made to rise in the curve .of a parabola, the height of this cone is always the same, whatever may be the increase of length of the radius. This is owing to the property of the parabola, that the points of intersection with the axis, by a line drawn at right angles to the curve and by another drawn at right angles to the axis from the same point in the curve, are always at the same distance apart, whatever may be the position of the point in the curve from which the two lines are drawn ; in other words, the length of the subnormal is constant for every point of the curve. As therefore the horizontal force required to support the suspending arm and ball at any angle is directly proportionate to the length of radius of the described circle, and as the centrifugal force which supplies this required power is also in this case directly proportionate to the same radius, they will consequently be in equilibrium in every position. Hence whatever may be the position of the balls, whether low down or high up, when moving in the curve of a parabola, they will retain that position and will have no tendency to change it, provided only the number of revolutions per minute is kept unchanged. Opening or closing of the throttle-valve to any extent can accordingly be effected and maintained, without necessitating any alteration in the speed of the engine. This perfect action however can only be obtained when the balls rise in the curve of a parabola. But when they are hung from a point in the axis, and move in an arc of a circle, as in the ordinary governor, the height of the cone described by the suspending arms diminishes as the balls rise ; and at the same time that the height of cone diminishes, the horizontal or centrifugal force requisite for supporting the balls increases j consequently the centrifugal force is Downloaded from pme.sagepub.com at UNIV OF CINCINNATI on June 5, 2016 STEAM ENGINE GOVERNOR. 217 now required to increase more rapidly than in the simple ratio of the radius.