the Week of Proper 26 / Ordinary 31
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Power Transmission
1911 Encyclopedia Britannica
The appliances connected with installations for the utilization of natural sources of energy may be classified into three groups: I. Prime movers, by means of which the natural form of energy is transformed into mechanical energy. To this group belong all such appliances as water turbines, steam turbines, steam engines and boilers, gas producers, gas engines, oil engines, &c.
2. Machinery of any kind which is driven by energy made available by the prime mover. To this group belong all machine tools, textile machinery, pumping machinery, cranes - in fact every kind of machine which requires any considerable quantity of energy to drive it.
3. The appliances by means of which the energy made available by the prime mover is transmitted to the machine designed to utilise it. The term power is used to denote the rate at which energy is transmitted. The unit of power in common use is the horse power, and one horse power means a rate of transmission of 550 foot-pounds per second.
In many cases the prime mover is combined with the machine in such a way that the transmitting mechanism is not distinctly differentiated from either the prime mover or the machine, as in the case of the locomotive engine. In other cases the energy made available by the prime mover is distributed to a number of separate machines at a distance from the prime mover, as in the case of an engineer's workshop. In this case the transmitting mechanism by means of which the energy is distributed to the several machines has a distinct individuality. In other cases prime movers are located in places where the natural source of energy is abundant, namely, near waterfalls, or in the neighbourhood of coal-fields, and the energy made available is transmitted in bulk to factories, &c., at relatively great distances. In this case the method and mechanism of distribution become of paramount importance, since the distance between the prime mover and the places where the energy is to be utilized by machines is only limited by the efficiency of the mechanism of distribution.
Prime movers are considered in the articles Steam Engine; GAS Engine; OIL Engine, and Hydraulics, and machines in various special articles. The methods and mechanisms of distribution or transmission alone form the subjects of the present article, and the different methods in general use readily fall into four divisions: I. Mechanical. 3. Pneumatic.
2. Hydraulic. 4. Electrical.
I
[[Mechanical § I]]. Methods. - The mechanical transmission of power is effected in general by means of belts or ropes, by shafts or by wheel gearing and chains. Each individual method may be used separately or in combination. The problems involved in the design and arrangement of the mechanisms for the mechanical distribution of power are conveniently approached by the consideration of the way in which the mechanical energy made available by an engine is distributed to the several machines in the factory. By a belt on the fly-wheel of the prime mover the power is transmitted to the line shaft, and pulleys suitably placed along the line shaft by means of other belts transmit power, first, to small countershafts carrying fast and loose pulleys and striking gear for starting or stopping each engine at will, and then to the driving pulleys of the several machines. (See also Pulleys.) § 2. Quantitative Estimation of the Power Transmitted. - In dealing with the matter quantitatively the engine crank-shaft may be taken as the starting point of the transmission, and the first motion-shaft of the machine as the end of the transmission so far as that particular machine is concerned.
Let T be the mean torque or turning effort which the engine exerts continuously on the crank shaft when it is making N revolutions per second. It is more convenient to express the revolutions per second in terms of the angular velocity w, that is, in radians per second. The relation between these quantities is w=21rN. Then the rate at which work is done by the engine crank shaft is Tw foot-pounds per second, equivalent to Tw/550 horse power. This is now distributed to the several machines in varying proportions. Assuming for the sake of simplicity that the whole of the power is absorbed by one machine, let T 1 be the torque on the first motionshaft of the machine, and let w l be its angular velocity, then the rate at which the machine is absorbing energy is T l w i foot-pounds per second. A certain quantity of energy is absorbed by the transmitting mechanism itself for the purpose of overcoming frictional and other resistances, otherwise the rate of absorption of energy by the machine would exactly equal the rate at which it was produced by the prime mover assuming steady conditions of working. Actually therefore T l w 1 would be less than Tw so that T i w i = riTw, (I) where, is called the efficiency of the transmission. Considering now the general problem of a multiple machine transmission, if w i , T are the several torques and angular velocities of the respective first motion shafts of the machines, (T1wi+T2w2±T3w3+ ....) = i Tw (2) expresses the relations which must exist at any instant of steady motion. This is not quite a complete statement of the actual conditions because some of the provided energy is always in course of being stored and unstored from instant to instant as kinetic energy in the moving parts of the mechanism. Here, n is the over-all efficiency of the distributing mechanism. We now consider the separate parts of the transmitting mechanism.
§ 3. Belts. - Let a pulley A (fig. 1) drive a pulley B by means of a leather belt, and let the direction of motion be as indicated by the arrows on the pulleys. When the pulleys are revolving uniformly, A FIG. I.
transmitting power to B, one side of the belt will be tight and the other side will be slack, but both sides will be in a state of tension. Let t and u be the respective tensions on the tight and slack side; then the torque exerted by the belt on the pulley B is (t - u)r, where r is the radius of the pulley in feet, and the rate at which the belt does work on the pulley is ( t - u)rw foot-pounds per second. If the horse-power required to drive the machine be represented by h.p., then ( t - u)rw=550 h.p., (3) assuming the efficiency of the transmission to be unity. This equation contains two unknown tensions, and before either can be found another condition is necessary. This is supplied by the relation between the tensions, the arc of contact 0, in radians (fig. 2), the coefficient of friction ,u between the belt and the pulley, the mass of the belt and the speed of the belt.
Consider an element of the belt (fig. 2) sub tending an angle do at the centre of the pul ley, and let t be the tension on one side of a }dB the element and ( t+dt) the tension of the other side. The ten sion tending to cause the element to slide bodily round the sur face of the pulley is dt. The normal pressure between the element and the face of the pulley due to the tensions is t do, but this is diminished by the force necessary to constrain the element to move in the circular path determined by the curvature of the pulley. If W is the weight of the belt per foot, the constraining force required for this purpose is Wv 2 d0/g, where v is the linear velocity of the belt in feet per second. Hence the frictional resistance of the element to sliding is ( t - Wv 2 /g).do, and this must be equal to the difference of tensions dt when the element is on the point of slipping, so that ( 1 - Wv 2 /g)µdo = dt. The solution of this equation is t - Wv 2 /g e (4) u - Wv-lg _ - eµ, where t is now the maximum tension and u the minimum tension, and e is the base of the Napierian system of logarithms, 2.718. Equations (3) and (4) supply the condition from which the power transmitted by a given belt at a given speed can be found. For ordinary work the term involving v may be neglected, so that (4) becomes t/u = eµ8. (5) Equations (3) and (5) are ordinarily used for the preliminary design of a belt to calculate t, the maximum tension in the belt necessary to transmit a stated horse power at a stated speed, and then the cross section is proportioned so that the stress per square inch shall not exceed a certain safe limit determined from practice.
To facilitate the calculations in connexion with equation (5), tables are constructed giving the ratio t/u for various values of µ and 0. (See W. C. Unwin, Machine Design, 12th ed., p. 377.) The ratio should be calculated for the smaller pulley. If the belt is arranged as in fig. 1, that is, with the slack side uppermost, the drop of the belt tends to increase 0 and hence the ratio tlu for both pulleys.
§ 4. Example of Preliminary Design of a Belt
The following example illustrates the use of the equations for the design of a belt in the ordinary way. Find the width of a belt to transmit 20 h.p. from the flywheel of an engine to a shaft which runs at 180 revolutions per miunte (equal to 18.84 radians per second), the pulley on the shaft being 3 ft. diameter. Assume the engine flywheel to be of such diameter and at such a distance from the driven pulley that the arc of contact is 120°, equal to 2.094 radians, and further assume that the coefficient of friction µ= 0.3. Then from equation (5) 11u= e2.094 X 0.3 =2.7180.6282; that is log e t/u = o
6282, from which t/u=1.87, and u=t/1.87. Using this in (3) we have 41-1/I. 87) 1.5 X 18.84 = 55 o X 20, from which 838 lb. Allowing a working strength of 300 lb per square inch, the area required is 2.8 sq. in.,' so that if the belt is 4 in. thick its width would be 11.2 in., or if 3 6 in. thick, 15 in. approximately. The effect of the force constraining the circular motion in diminishing the horse power transmitted may now be ascertained by calculating the horse power which a belt of the size found will actually transmit when the maximum tension t is 838 lb. A belt of the area found above would weigh about 1.4 lb. per foot. The velocity of the belt, v = wr =18.84 X 1.5 =28.26 ft. per second. The term Wv 2 /g therefore has the numerical value 4.7. Hence equation (2) becomes ( t -34.7)/(u-34.7) =1.87, from which, inserting the value 838 for t, a =464.5 lb. Using this value of u in equation (I). = (838-464.5)X 18.84 X1.5 H.P 1 1 0 - 9 5
55 Thus with the comparatively low belt speed of 28 ft. per second the horse power is only diminished by about 5%. As the velocity increases the transmitted horse power increases, but the loss from this cause rapidly increases, and there will be one speed for every belt at which the horse power transmitted is a maximum. An increase of speed above this results in a diminution of transmitted horse power.
§ 5. Belt Velocity for Maximum Horse Power
If the weight of a belt per foot is given, the speed at which the maximum horse power is transmitted for an assigned value of the maximum tension t can be calculated from equations (3) and (4) as follows: Let t be the given maximum tension with which a belt weighing W lb per foot may be worked. Then solving equation (4) for u, subtracting t from each side, and changing the signs all through: t - u= (t - Wv 2 /g ) (1 - e µ e). And the rate of working U, in foot-pounds per second, is U = (t - u)v = (Iv - WO /g ) (1 - e µe). Differentiating U with regard to v, equating to zero, and solving for v, we have v= (tg/3W). Utilizing the data of the previous example to illustrate this matter, t=838 lb per square inch, W =1.4 lb per foot, and consequently, from the above expression, v=80 ft. per second approximately. A lower speed than this should be adopted, however, because the above investigation does not include the loss incurred by the continual bending of the belt round the circumference of the pulley. The loss from this cause increases with the velocity of the belt, and operates to make the velocity for maximum horse power considerably lower than that given above.
§ 6. Flexibility
When a belt or rope is working power is absorbed in its continual bending round the pulleys, the amount depending upon the flexibility of the belt and the speed. If C is the couple required to bend the belt to the radius of the pulley, the rate at which work is done is Cw foot-pounds per second. The value of C for a given belt varies approximately inversely as the radius of the pulley, so that the loss of power from this cause will vary inversely as the radius of the pulley and directly as the speed of revolution. Hence thin flexible belts are to be preferred to thick stiff ones. Besides the loss of power in transmission due to this cause, the bending causes a stress in the belt which is to be added to the direct stress due to the tensions in the belt in order to find the maximum stress. In ordinary leather belts the bending stress is usually negligible; in ropes, however, especially wire rope, it assumes paramount importance, since it tends to overstrain the outermost strands and if these give way the life of the rope is soon determined.
§ 7. Rope Driving
About 1856 James Combe, of Belfast, introduced the practice of transmitting power by means of ropes running in grooves turned circumferentially in the rim of (From Abram Combe, Proc. Inst. Mech. Eng.) FIG. 3. - Rope driving; half-crossed rope drive, separate rope to each groove.
Powertransmission-1.jpg
the pulley (fig. 3). The ropes may be led off in groups to the different floors of the factory to pulleys keyed to the distributing shafting. A groove was adopted having an angle of about 450, XXII. 8 t+dt FIG. 2.
and this is the angle now used in the practice of Messrs Combe, Barbour and Combe, of Belfast. A section of the rim of a rope driving wheel showing the shape of the groove for a rope 14 in. diameter is shown in fig. 4, and a rope driving pulley designed for six 11-in.
4----. - 2 g Pith - --, ropes is shown in fig. 5. A rope is less flexible than a belt, and therefore care must be taken not to arrange rope drives with pulleys having too small a diameter relatively to the diameter of the rope. The principles of §§ 3, 4, 5 and 6, apply equally to ropes, but with the practical modification that the working stress in the rope is a much smaller fraction of the ultimate strength than in the FIG. 5. - Rope Pulley, 10 ft. diam., 6 grooves, 22 in. pitch, weight about 35 cwt. Constructed by Combe, Barbour & Combe, Ltd., Belfast.
Smallest diameter of | Diameter | Pulley, which should | H.P. per Rope for | of Rope. | be used with the | smallest Pulley at too | Rope. | revs. per minute. | in. | in. | 4 | 14 | s | I | 21 | I | 18 | 42 | 8 | 28 | 66 | 16 case of belting and the ratio of the tensions is much greater. The following table, based upon the experience of Messrs Combe, presents the practical possibilities in a convenient form: - The speed originally adopted for the rope was 55 ft. per second This speed has been exceeded, but, as indicated above, for any particular case there is one speed at which the maximum horse power is transmitted, and this speed is chosen with due regard to the effect of centrifugal tension and the loss due to the continual bending of the rope round the pulley. Instead of using one rope for each groove, a single continuous rope may be used, driving from one common pulley several shafts at different speeds. For further information see Abram Combe, Proc. Inst. Mech. Eng. (July 1896). Experiments to compare the efficiencies of rope and belt driving were carried out at Lille in 1894 by the Societe Industrielle du Nord de la France, for an account of which see D. S. Capper, Proc. Inst. Mech. Eng. (October 1896). Cotton ropes are used extensively for transmitting power in factories, and though more expensive than Manila ropes, are more durable when worked under suitable conditions. § 8. Shafts. - When a shaft transmits power from a prime mover to a machine, every section of it sustains a turning couple or torque T, and if w is the angular velocity of rotation in radians per second, the rate of transmission is T. foot-pounds per second, and the relation between the horse power, torque and angular velocity is Tw=550 H.P. (6) The problem involved in the design of a shaft is so to proportion the size that the stress produced by the torque shall not exceed a certain limit, or that the relative angular displacement of two sections at right angles to the axis of the shaft at a given distance apart shall not exceed a certain angle, the particular features of the problem determining which condition shall operate in fixing the size. At a section of a solid round shaft where the diameter is D inches, the torque T inch-pounds, and the maximum shearing stress f pounds per square inch, the relation between the quantities is given by T = i D3 f/ 1 6, (7) and the relation between the torque T, the diameter D, the relative angular displacement 0 of two sections L inches apart by T =Ce rD 4 /32L, (8) where C is the modulus of rigidity for the material of the shaft. Observe that 0 is here measured in radians. The ordinary problems of shaft transmission by solid round shafts subject to a uniform torque only can be solved by means of these equations. Calculate the horse power which a shaft 4 in. diameter can transmit, revolving 120 times per minute (12.56 radians per second), when the maximum shearing stress f is limited to 11,000 lb per square inch. From equation (7) the maximum torque which may be applied to the shaft is T =138,400 inch-pounds. From (6) H.P. = 138,400 X 12.56 _ 264. The example may be continued to 12X550 find how much the shaft will twist in a length of to ft. Substituting the value of the torque in inch-pounds in equation (8), and taking 11,500,000 for the value of C, 6 138,400 X120 X32 _ 0,057 radians, 11,500,00o X3.14X256 - and this is equivalent to 3.3°. In the case of hollow round shafts where D is the external diameter and d the internal diameter equation (7) becomes T=irf(D 4 - d 4)/ 16D, (9) and equation (8) becomes T = Ceir(D 4 - d 4)/32L. (to) The assumption tacitly made hitherto that the torque T remains constant is rarely true in practice; it usually varies from instant to instant, often in a periodic manner, and an appropriate value of f must be taken to suit any particular case. Again it rarely happens that a shaft sustains a torque only. There is usually a bending moment associated with it. For a discussion of the proper values of f, to suit cases where the stress is variable, and the way a bending moment of known amount may be combined with a known torque, see Strength Of Materials. It is sufficient to state here that if M is the bending moment in inch-pounds, and T the torque in inch-pounds, the magnitude of the greatest direct stress in the shaft due to the effect of the torque and twisting moment acting together is the same as would be produced by the application of a torque of M+1,1 (T2 -{-M2) inch-pounds. (I I) It will be readily understood that in designing a shaft for the distribution of power to a factory where power is taken off at different places along the shaft, the diameter of the shaft near the engine must be proportioned to transmit the total power transmitted whilst the parts of the shaft more remote from the engine are made smaller, since the power transmitted there is smaller. Missing image Powertransmission-2.jpg § 9. Gearing Pitch Chains. - Gearing is used to transmit power from one shaft to another. The shafts may be parallel; or inclined to one another, so that if produced they would meet in a point; or inclined to one another so that if produced they would not meet in a point. In the first case the gear wheels are called spur wheels, sometimes cog wheels; in the second case bevel wheels, or, if the angle between the shafts is 9e, mitre wheels; and in the third case they are called skew bevels. In all cases the teeth should be so shaped that the velocity ratio between the shafts remains constant, although in very rare cases gearing is designed to work with a variable velocity ratio as part of some special machines. For the principles governing the shape of the teeth to fulfil the condition that the velocity ratio between the wheels shall be constant, see Mechanics, § Applied. The size of the teeth is determined by the torque the gearing is required to transmit. Pitch chains are closely allied to gearing; a familiar example is in the driving chain of a bicycle. Pitch chains are used to a limited extent as a substitute for belts, and the teeth of the chains and the teeth of the wheels with which they work are shaped on the same principles as those governing the design of the teeth of wheels. If a pair of wheels is required to transmit a certain maximum horse power, the angular velocity of the shaft being w, the pressure P which the teeth must be designed to sustain at the pitch circle is 55 o H.P. /wR, where R is the radius of the pitch circle of the wheel, whose angular velocity is w. § to. Velocity RatioIn the case of transmission either by belts, ropes, shafts or gearing, the operating principle is that the rate of working is constant, assuming that the efficiency of the transmission is unity, and that the product Tw is therefore constant, whether the shafts are connected by ropes or gearing. Considering therefore two shafts, T I w i =T 2 w 2; that is w;/w 2 =T 2 /T i; i.e. the angular velocity ratio is inversely as the torque ratio. Hence the higher the speed at which a shaft runs, the smaller the torque for the transmission of a given horse power, and the smaller the tension on the belts or ropes for the transmission of a given horse power. § I i. Long Distance Transmission of Power. - C. F. Hirn originated the transmission of power by means of wire ropes at Colmar in Alsace in 1850. Such a telodynamic transmission consists of a series of wire ropes running on wheels or pulleys supported on piers at spans varying from 300 to 500 ft. between the prime mover and the place where the power is utilized. The slack of the ropes is supported in some cases on guide pulleys distributed between the main piers. In this way 300 h.p. was transmitted over a distance of 6500 ft. at Freiberg by means of a series of wire ropes running at 62 ft. per second on pulleys 177 in. diameter. The individual ropes of the series, each transmitting 300 h.p., were each I 08 in. diameter and contained to strands of 9 wires per strand, the wires being each 0'072 in. diameter. Similar installations existed at Schaffhausen, Oberursal, Bellegarde, Tortona and Zurich. For particulars of these transmissions with full details see W. C. Unwin's Howard Lectures on the " Development and Transmission of Power from Central Stations " (Journ. Soc. Arts, 1893, published in book form 1894). The system of telodynamic transmission would no doubt have developed to a much greater extent than it has done but for the advent of electrical transmission, which made practicable the transmission of power to distances utterly beyond the possibilities of any mechanical system. See W. J. M. Rankine, Treatise on Machinery and Millwork; and W. C. Unwin, Elements of Machine Design; and for telodynamic transmission see F. Reuleaux, Die Konstrukteur. (W. E. D.) H. - Hydraulic The first proposal for a general transmission of hydraulic power was made by Bramah in 1802. In 1846 Lord Armstrong's hydraulic crane was erected at Newcastle, and was worked from the town water mains, but the pressure in such mains was too low and uncertain to secure satisfactory results. The invention of the accumulator in 1850 enabled much higher pressures to be used; since then 700 lb per square inch has been adopted in most private hydraulic power transmission plants. An attempt to give a public supply of hydraulic power was made in 1859, when a company was formed for laying mains in London along the river Thames between the Tower and Blackfriars, the engineer being Sir George Bruce; but though an act of parliament was obtained, the works were not carried out. The first public hydraulic supply station was established at Hull in 1877. In 1883 the General Hydraulic Power Works, Messrs Ellington and Woodall being the engineers, were started in London, and they now form the largest system of hydraulic power transmission in existence. Works of a similar character have since been established in several other towns. The general features of hydraulic power transmissions are: (1) a central station where the hydraulic pressure is created, usually by means of steam pumping engines; (2) a system of distribution mains; (3) machines for utilizing the pressure. In cases of public supplies there is the further important matter of registration. When dealing with any practical problem of hydraulic power transmission it is of the first importance to determine the maximum demand for power, its duration and frequency. If the duration of the maximum demand is limited S and the frequency restricted - for instance, when a swing bridge has to be opened and closed only a few times in the course of a day - a small pumping plant and a large accumulator will be desirable. If the maximum demand is more or less continuous, as when hydraulic pressure is used for working a pump in a mine or a hydraulic engine in a workshop, the central station pumping engine must be capable of supplying the maximum demand without the aid of an accumulator, which may or may not, according to circumstances, be provided to serve as a regulator. A hydraulic accumulator (fig. i) ordinarily consists of a hydraulic cylinder FIG. I. Missing image Powertransmission-3.jpg and ram, the ram being loaded with sufficient weight to give the pressure required in the hydraulic mains. If a pressure of 700 lb per square inch is wanted, the weight of the ram and its load, neglecting friction, must be 700 lb for each square inch of its area, and if the cylinder is full, i.e. the ram elevated to its full extent, the accumulator is a reservoir of power, exactly as if it were a tank at the same cubical extent placed at an elevation of about 1600 ft. above the mains and connected with them. The function of accumulators in hydraulic power distribution is frequently misunderstood, and it has been urged that as in practice the size of the reservoirs of power that can be obtained by their use is small, they are of little value. An accumulator having a ram 20 in. diameter by 20 ft. stroke loaded to 700 lb is . . ? y ssy), ?.
?? .?; --,y;_ -
?? y /? G? ??? A fairly large one, but it contains only 439,740 foot-pounds of available energy. If the accumulator ram descended in one minute the horse power developed during that time would be 13.3, and until again pumped up its function would cease. Is so small a reservoir worth much ? The correct answer to this question depends upon the surrounding circumstances. In the case of any general system of hydraulic power transmission it is certain that there will be very large and frequent variations in the combined demand for power, the periods of approximate maximum rarely exceeding in the aggregate 2 or 3 hours a day (see fig. 2). Where the area of supply is very extensive there are further subsidiary variations in small sections of the area. The main features of the combined load curves are fairly constant, but the local peaks are very erratic. Such conditions are favourable to the extensive use of accumulators. When comparing the economy of hydraulic machinery which works intermittently, such as cranes and hoists, with other systems the effect of the hydraulic accumulator in reducing the maximum horse power required is often neglected. In consequence the comparison is vitiated, because the minimum cost of running a central station depends to a great extent upon the FIG. 2. maximum demand, even though the maximum may be required only during a few minutes of the day. In the hydraulic system accumulators at the central stations perform the two distinct functions of reducing the maximum load on the pumps which supply the demand, and regulating automatically the speed of the pumps as the demand varies from minute to minute. In any large system where a number of pumping units are required they also allow a sufficient interval of time to start any additional units. Accumulators connected to the mains at a considerable distance from the central station reduce the variations of pressure, and the size of mains required for a given supply of power, and therefore have a most important influence on the economy of distribution. The mechanical efficiency of hydraulic accumulators is very high, being from 95% to 98%, and they are practically indestructible. When designing central stations the aim should be to employ pumping engines of such capacity that they can be worked as nearly as possible continuously at about their maximum output; the same consideration should, in the main, determine the size of the pumping units in a station where more than a single unit is employed. With a number of units, each can be worked, when in use, at or near the most economical speed. Moreover, reserve plant is necessary if the supply of power is to be constant, and where the units are many the actual reserve required is less than where the units are few. An effect of the multiplication of power units is to increase the capital outlay; indeed, it may be stated quite generally that economy in working and maintenance cannot be obtained without a larger capital outlay than would be required for a simpler and less economical plant. A high degree of economy estimated on financial data - the ultimate base on which these practical questions rest - can only be obtained in large installations where the averaging effect of the combination of a large number of comparatively small intermittent demands for power is greatest. The term loadfactor, since it was first coined by Colonel R. E. Crompton in 1891, has come into common use as an expression of the relation between the average and the maximum output from any central source of supply. No argument is required to show that a given central station plant working continuously at its maximum speed day and night all the year round, say for 8760 hours in a year, should produce the power more cheaply per unit, not only as to the actual running cost, but also as to the capital or interest charges, than the same plant running on the average at the same speed for, say, one-third the time, or 2920 hours. In this case the load-factor 2920/8760 = 333, or 33.37 0%. The saving on the whole expenditure per unit is not in direct proportion to an increase in the load-factor, and its effect on the various items of expenditure is extremely variable. The influence is greatest on the capital charges, and it has no influence at all, or may even have a detrimental effect, on some items; for instance, the cost of repairs per unit of output may be increased by a high loadfactor. Its effect on the coal consumption depends very much on the kind and capacity of the boilers in use; on whether the engines are condensing or non-condensing; on the hours of work of the engine staff, &c. The economic value of the load-factor is of great importance in every installation, but its influence on the cost of supply varies at each central station, and must be separately determined. There is a load-factor peculiar to each use for which the power is supplied, and the whole load-factor can only be improved by the combination of different classes of demands, which differ in regard to the time of day or season at which they attain their maximum. It is in this respect that the great economy of a public distribution of power is most apparent, though there is also, of course, a direct economy due simply to the presumably large size of the central stations of a public supply. Demands for power of every kind have unfortunately a tendency to arise at the same time, so that in the absence of storage of power there seems no prospect of the load-factors for general supply of power in towns exceeding, in the most favourable conditions, 40%. The load-factor of most public hydraulic power supplies is considerably under 30%. It is questionable, however, whether a very high load-factor conduces to economy of working expenses as a whole in any general supply of energy. The more continuous the supply during the twenty-four hours of the day the greater is the difficulty of executing repairs, and the greater the amount of the reserve plant required. In all central station work where fluctuating loads have to be dealt with it is most important that there should be ample boiler power. In a comprehensive system of power supply demand arises in a very sudden and erratic manner, and to meet this by forcing the boilers involves greater waste of coal than keeping steam up in sufficient reserve boilers. For this purpose boilers with large water capacity, such as the Lancashire, are preferable to the tubular type, if sufficient space is available. Superheated steam and also thermal storage are advantageous. Feed water heaters or economizers should always be used, all steam and feed pipes should be carefully protected from radiation, and the pipe flanges should be covered; in short, to secure good results in coal consumption every care must be taken to minimise the stand-by losses which are such serious items in central station economy when the load-factor is low. Though hydraulic power has the peculiar advantage, as regards coal consumption, that it is the speed of the engines which varies with an intermittent demand, nevertheless at the London stations it has been found that during a year's working only from 60 to 75% of the coal efficiency of trial runs of the engines can be obtained - i.e. at least 25% of the coal is wasted through the stand-by losses and through the pumping engines having to run at less than full power. Missing image Powertransmission-4.jpg Missing image Powertransmission-5.jpg To determine the scale on which a central station plant should be designed is frequently a difficult matter. The rate of growth of the expected demand for the power is an important factor, but it has been clearly established that the reduction of working expenses resulting from the increase of size of an undertaking proceeds in a diminishing ratio. Increase in output is in fact sometimes accompanied by more than a proportionate increase of expenses. During recent years there have been causes at work which have raised considerably the price of labour, fuel, other items of expense, and the law of the " diminishing ratio " has been masked. On the diagram (fig. 3) of the costs of the London undertaking and the amount of power supplied, have been plotted points marking the total expenses of each year in relation to the output of power. These points for the years 1884-1899, and for output of from 50 to 700 million gallons followed approximately a straight line. Since 1899, however, though the output has increased from 708 millions to 1040 million gallons, the costs per unit of output have been always considerably above the preceding periods. The details of the London supply given in table I partly explain this by the relatively high price of fuel, but an equally important factor has been the rise in the local rates, which in the period1899-1909have risen from 2d. up to 3d. per moo gallons. If the cost of fuel, rates and wages had remained constant the plotting of expenses in relation to output would have been approximately along the extension of the line AB. This line cuts the vertical axis at A above the origin 0, and the line OA indicates the minimum amount of the expenses, and by implication the initial size of the first central station erected in London. The curve in this diagram gives the cost per moo gallons. Whether it is more economical to have several smaller stations in any particular system of power transmission, or a single centre of supply, is mainly governed by the cost of the mains and the facilities for laying them in the area served. No general rule can, however, be formulated, for it is a question of balance of advantages, and the .t...m.e, ¦ ¦ ¦¦¦¦¦¦¦¦¦¦¦¦i¦¦¦¦¦ ' 'SS ' '? ' '?1¦¦ ¦¦¦¦¦ /i¦ ¦¦¦¦¦ ¦¦¦¦¦ t° ¦%¦¦¦¦ 111¦/iM¦¦¦¦¦¦¦¦ ¦¦¦ ¦¦¦¦ FIG. 3. solution must be obtained by consideration of the special circumstances of each case. It has been found desirable as the demand for the power and the area within which it is supplied has enlarged, not only to increase the number of central stations but also their capacity. The first pumping station erected was installed with 4 pumping engines of 200 h.p. each. The pumping capacity of this station has been increased to 7 units. The station at Rotherhithe completed in 1904 has 8 units together 1600 h.p., and the plant at the new station at Grosvenor Road has 8 units equalling 2400 h.p. The pumping stations are situated about 3 m. apart and concurrently with the increase in their size it has been found desirable to introduce a system of feeder mains (see below). There are in all five central stations at work in connexion with the public supply of hydraulic power in London, having an aggregate of 7000 i.h.p. All the stations and mains are connected together and worked as one system. There are 14 accumulators with a total capacity of 4000 gallons, most of them having rams 20 in. diameter by 23 ft. stroke. The pumping engines are able together to deliver 11,000 gallons per minute Details of the London supply are given in fig. 3 and in table . TABLE I.
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