The centrifugal moment at any instant is— 4 X 0'00034WRN2H where W is the weight of one ball. And the centripetal moment is- Load on spring × R, See Fig. 214a for the meaning of R,, viz. the distance of the virtual centre from the point of suspension of the arm. Taking position 4, we have for the centrifugal moment at 450 revolutions per minute = 4 X 0'00034 X 2'5 x 2.88 x 4502 x 1'58 260 pound-inches and for the centripetal moment The load on the spring = 111 lbs. ; and R, = 2.78 = centripetal moment = 111 X 2.78 310 pound-inches McLaren's Crank-shaft Governor.-In this governor SR,; but C varies as R, hence if there be no we have CR = tension on the spring when R is zero, it will be evident that S will vary directly as R; but C also varies in the same manner, hence the centrifugal and centripetal moment lines are nearly straight and coincident. The centrifugal lines are not absolutely straight, because the weight does not move exactly on a radial line from the centre of the crank-shaft. Governor Dashpots.-A dashpot consists essentially of a cylinder with a leaky piston, around which oil, air, or other fluid has to leak. An extremely small force will move the piston slowly, but very great resistance is offered by the fluid if a rapid movement be attempted. Very sensitive governors are therefore generally fitted with dashpots, to prevent them from suddenly flying in or out, and thus causing the engine to hunt. If a governor be required to work over a very wide range of power, such as all the load suddenly thrown off, a sensitive, almost isochronous governor with dashpot gives the best result; but if very fine governing be required over small variations of load, a slightly less sensitive governor without a dashpot will be the best. However good a governor may be, it cannot possibly govern well unless the engine be provided with sufficient flywheel power. If an engine have, say, a 2-per-cent. cyclical variation and a very sensitive governor, the balls will be constantly fluctuating in and out during every stroke. Power of Governors. The "power" of a governor is its capacity for overcoming external resistances. The greater the power, the greater the external resistance it will overcome with a given alteration in speed. Nearly all governor failures are due to their lack of power. The useful energy stored in a governor is readily found thus, approximately : Simple Watt governor, crossed-arm and others of a similar type Energy = weight of both balls × vertical rise of balls Porter and other loaded governors weight of both balls x vertical rise of balls + weight of central weight x its vertical rise Spring governors Energy weight of both balls x vertical rise (if any) of balls = "( max. load on spring + min. load on spring 2 × the stretch or compression of spring spring) Q where n the number of springs employed; express weights in pounds, and distances in feet. The following may be taken as a rough guide as to the energy that should be stored in a governor to get good results: it is always better to store too much rather than too little energy in a governor : In the earlier editions of this book values were given for automatic expansion gears, which were based on the only data available to the author at the time; but since collecting a considerable amount of information, he fears that no definite values can be given in this form. For example, in the case of governors acting through reversible mechanisms on wellbalanced slide-valves, about 100 foot-pounds of energy per inch diameter of the high-pressure cylinder is found to give good results; but in other cases, with unbalanced slide-valves, five times that amount of energy stored is found to be insufficient. If the driving mechanism of the governor be non-reversible, only about one-half of this amount of energy will be required. A better method of dealing with this question is to calculate, by such diagrams as those given in the "Mechanisms" chapter, the actual effort that the governor is capable of exerting on the valve rod, and ensuring that this effort shall be greatly in excess . of that required to drive the slide-valve. Experiments show that the latter amounts to about one-fifth to one-sixth of the total pressure on the back of a slide-valve (i.e. the whole area of the back the steam pressure) in the case of unbalanced valves. The effort a governor is capable of exerting can also be arrived at approximately by finding the energy stored in the springs, and dividing it by the distance the slide-valve moves while the springs move through their extreme range. Generally speaking, it is better to so design the governor that the valve-gear cannot react upon it, then no amount of pressure on the valve-gear will alter the height of the governor; that is to say, the reversed efficiency of the mechanism which alters the cut-off must be negative, or the efficiency of the mechanism must be less than 50 per cent. On referring to the McLaren governor, it will be seen that no amount of pressure on the eccentric will cause the main weight W to move in or out. CHAPTER VII. FRICTION. WHEN one body, whether solid, liquid, or gaseous, is caused to slide over the surface of another, a resistance to sliding is experienced, which is termed the "friction" between the two bodies. Many theories have been advanced to account for the friction between sliding bodies, but none are quite satisfactory. To attribute it merely to the roughness between the surfaces is but a very crude and incomplete statement; the theory that the surfaces somewhat resemble a short-bristled brush or velvet pile much more nearly accounts for known phenomena, but still is far from being satisfactory. However, our province is not to account for what happens, but simply to observe and classify, and, if possible, to sum up our whole experience in a brief statement or formula. Frictional Resistance (F). If a block of weight W be placed on a horizontal plane, as shown, and the force F applied parallel to the surface be required to make it slide, the force F W = N F FIG. 216. is termed the frictional resistance of the block. The normal pressure between the surfaces is N. Coefficient of Friction (p).-Referring to the figure above, the ratio: or = μ, and is termed the coefficient of W N friction. It is, in more popular terms, the ratio the friction bears to the normal pressure between the surfaces. It may be found by dragging a block along a plane surface and measuring F and N, or it may be found by tilting the surface as in Fig. 217. The plane is tilted till the block just begins to slide. The vertical |