APPLIED MECHANICS.] 773 . P. V. T 3000 TV. PVT. 11. Feet p see. Hours p. day. Foot-lb per sec. Foot-n, per day. MAN 1. liaising his own weight up ) stair or ladder ) 113 0-5 8 72-5 2,088,000 2. Do. do. do 10 2,G1(>,000 3. (Trend-wheel see 1) 4. Hauling up weig .twithropi: 40 0-75 (! 30 648,000 5. Lifting weights by hand .... 44 O o.-) G 24-2 522,720 (>. Carrying weights up stair.-. 143 0-13 (i 18-5 3 jy,GOO 7. Shovelling up eartli to a) height of 5 ft. 3 in >" 6 1-8 10 7-8 280,800 8. Wheeling earth in barrow i up -slope of 1 in 12 ; 3 horiz. veloc. 9 ft. per C 132 0-07.5 10 9-9 356,400 sec. (returning empty)., j 9. Pu>hing or pulling hori-)_ zontally ; capstan or oar)) 20-5 2-0 8 53 1,526,400 ( 12-5 5-0 ? 62-5) 10. Turning a crank or winch .- 18-0 2-r, 8 45 t 1,290,000 ( 20-0 14-4 2 min. 28S ) 11. Working pump 13-2 2-5 10 33 1,188,000 1 2. Hammu ing 15 f 8? J 480^000 HORSE 13. (Thoroughbred) cantering min. 22 5 , and trotting, drawing a j- meuuiiO-a.- 14-6 4 447-.-) 6,444,000 light railway carriage... ) max. i>0 ) 14. Horse (draught) drawing) cart or boat, walking....)" 120 3-6 8 432 12,441,600 160. Horizontal Transport. When men and animals carry burdens, or draw or propel loads in certain vehicles, it is difficult, and sometimes impossible, to determine the duty performed in foot pounds of work, because of the uncertainty of the amount in pounds of the resistance overcome. In this case, for the purpose of com paring performances of the same kind with each other, a unit is employed called a foot-pound of horizontal transport, meaning the conveying of a load of 1 pound 1 foot horizontally. The follow ing table, compiled from the sources referred to in sect. 159, gives some examples of the daily duty of men and horses in units of horizontal transport, L denoting the load in lb, V the velocity iu feet per second, and T the number of seconds per day of working: T L. V. 3GOO LV. LVT. lb. Feet per second. Hours per day. lb con veyed 1 font. lb con veyed 1 foot. MAN 15. Walking unloaded, trans-) port of own weight )" 140 5 10 700 25,200,000 Do. do 140 6 10 S40 30 240 000 16. Wheeling load L in two- > wheeled barrow, return- - 224 1-6 10 373 13,428,000 ingempty;V=t velocity i 1 7. Do. one-wheeled barrow, do. 135 1-6 10 225 8.100,000 18. Travelling with burden JO 2.5 7 225 5,670,000 19. Conveying burden, return-^ ing unloaded j 140 1-6 G 233 5,032,800 252 20. Carrying burden for 30 seconds only i 12fi 11-7 14742
23 1
HORSK 21. Walking wi:h cart always)^ 1500 3-C 10 5400 194,400,000 22. Trotting do. do 750 7 2 4J 0400 87,480,000 23. Walking with cart, going} loaded, returningempty; !- 1500 20 10 3000 108,000,000 V={ mean velocity ) 972 24. Carrying burden, walking... 270 3-6 10 34,992,000 25. Do. trotting... 180 7-2 7 1296 32,659,200 161. (B.) Weight of Liquids. (C.) Motion of Fluids. -In water- wheels and other hydraulic engines the weight and motion of a liquid usually act together as sources of energy. To determine the necessary loss of energy and the theoretical efficiency, we have the following formula: The power or energy exerted per second is ^ the necessary loss r the theoretical effect or useful icork per second , the tJieorctical efficiency v?-v J where Q denotes the weight of liquid which acts on the wheel or other engine per second ; H the vertical fall from the point where the liquid first begins to act directly or indirectly on the wheel or other engine to the point where it ceases to act ; l the velocity of the liquid when it begins to act ; and V 2 the least velocity, when it ceases to act, which will properly discharge the liquid, aud pre vent its accumulating so as to impede the wheel or engine. (For details as to the actual efficiency and duty aud the construc tion of hydraulic engines, see HYDROMECHANICS.) In windmills, the air, being in motion, presses against and moves four or five radiating vanes or sails, whose surfaces are approximately helical, their axis of rotation being parallel, or slightly inclined in a vertical plane, to the direction of the wind. The best form arid proportions for windmill sails, as determined experimentally by Smeaton, are as follows (see fig. 36): Angle of each sail with the plane of rotation at DE = 18 ; Bo. do. do. at BC = 7; OD = J of whip OA ; bar DE = OA ; bar BC = ^OA ; AC-DE. 162. (D.) Heat. In sect. 157 the three factors into which the efficiency of an engine moved by heat can be resolved have already been stated. The efficiency of the furnace and boiler in steam-engines varies from 4 to 85. It may be considered that the loss of heat to the extent of 15 by the chimney is necessary in order to produce a sufficient draught ; any loss beyond this is waste. The theoretical efficiency of the steam, or other elastic fluid, which serves as the mechanism for converting heat into me chanical energy, is regulated by a law which will now be explained. Heat acts oil bodies in two ways to elevate temperature and make the bodies hotter, and to produce mechanical changes. Heat employed in producing mechanical changes disappears or becomes latent, as it is termed, and can be reproduced by reversing those mechanical changes. When a cycle of mechanical changes, ending by the restoration of the body to its original condition, produces mechanical energy, heat disappears to an amount equal to that which would be generated by employ ing the mechanical energy in overcoming friction, that is to say, a British unit of heat (or one degree Fahr. in one Ibof liquid water) for every 772 foot-pounds of energy (being the constant already mentioned in sect. 115 as Joule s equivalent). This is called the conversion of heat into mechanical energy. The efficiency of the fluid in a heat-engine is the proportion which the heat converted into mechanical energy bears to the whole heat received by the water or other fluid ; and the theoretical or maximum value of that efficiency depends solely upon the respective tempera tures at which the fluid receives heat and rejects the unconverted heat, according to the following law : let ^ represent the tempera ture at which the fluid receives heat, and t 2 the temperature at which it rejects the unconverted heat, as measured from the absolute zero, that is, from a point 493 2 Fahr. or 274 C. below the temperature of melting ice (temperatures so measured are called absolute temperatures} ; then the maximum theoretical efficiency of the icater or other fluid in a steam-engine or other hcat-enyine is h-** ......... (88). The necessary loss of heat by the fluid is tjt^ of the whole heat received by it ; and any loss beyond this is waste. The theoretical efficiency of the steam in ordinary steam-engines seldom exceeds - th ; the greatest actual efficiency is about th ; the efficiency in good ordinary engines is about O l or 08, and in bad and wasteful engines O OJ, or even less. (For details see STEAM-ENGINE.) 163. (E.) Electricity and Magnetism. Electricity developed by chemical action in a galvanic battery has been to a small extent used to produce mechanical energy by alternately magnetizing and unmagnetizing soft-iron bars. The data for determining the actual efficiency of such engines are deficient. Their theoretical efficiency depends on the following law demonstrated by Joule : Let y 1 denote the strength of the electric current which would be developed in the conducting wire of the battery if there were no iron bar to be magnetized ; y z the strength to which the current is reduced by the reaction of the iron bar, tending to induce a contrary current. Then the theoretical efficiency of the engine is (89). 7i The proportion of the energy expended which is necessarily lost is 7-J/7,, and is employed iu producing heat in the conducting circuit. This law is exactly analogous to that of the theoretical efficiency of heat-engines given in equation 88. There is reason to believe that electromagnetic engines are cap able of a higher efficiency than heat-engines ; but the greater cost of the materials consumed renders them much less economical com
mercially. (W. J. M. 11.)