CALCTTLATED HORSE-POWER.] 



APPLIED MECHANICS. 



869 



F H a line drawn at a distance A F below equal to 

 1 5 Ibs. , and if we suppose steam at 30 Ibs. above atmo- 

 spheric pressure is admitted to the cylinder during half 

 the stroke, then suddenly cut off, we draw A C = 30 Ibs., 

 C D half the stroke ; take E midway in P H, and fill 



Fig. 201. 



in the hyperbolic curve D E. Then will the figure 

 A C D E B represent the best possible effect that could 

 be got under the conditions given ; for the straight line 

 A C represents the sudden rise of the pressure from that 

 of the atmosphere to 30 Ibs. above it at the beginning of 

 the stroke ; the straight line C D represents the con- 

 tinuance of that pressure during half the stroke ; the 

 curve D E indicates the gradual reduction of pressure, 

 as the steam enclosed in the cylinder expands to fill its 

 increasing capacity ; the point E midway in P H marks 

 the pressure at the end of the stroke, half that at the 

 beginning or middle, because the capacity of the cylinder 

 at the end has been doubled, while the quantity of steam 

 within it has remained constant. The straight line E B 

 marks the sudden fall of the final pressure to that of the 

 atmosphere when the exit port is opened ; and the 

 straight line B A represents the constant resistance of 

 the atmosphere to the issue of the steam during the 

 return stroke of the piston. Such might be the theo- 

 retical figure. The practical figure inscribed within it 

 must necessarily fall short, in some respects, of that which 

 is theoretically perfect. For instance, at the beginning 

 of the stroke, the port opening not suddenly, but 

 gradually, produces a curved line from K to L, the 

 piston having travelled some distance before the full 

 pressure is attained ; the gradual closing of the port or 

 expansion valve, and some diminution of pressure from 

 the cooling of the steam, or from leakage past the 

 piston, are indicated by the inclined line L M. The 

 cooling varies the expansion curve M Q from the true 

 hyperbola, and the gradual opening of the exit port 

 causes a curved turn from Q to N instead of a sudden 

 drop E B. The line N O above the line of atmospheric 

 pressure B A, indicates some additional resistance to the 

 issue of the steam dependent on limited area, or bad 

 form of opening, or leakage from the steam side of the 

 pinion, and the turn at O K marks the gradual closing 

 of the exit port, and opening of the inlet port for the 

 succeeding stroke. A careful analysis of a figure pro- 

 duced by an engine not working satisfactorily, will thus 

 point out causes of loss, and suggest means of remedy- 

 ing them, by widening the ports, readjusting the eccen- 

 tric and slide, clothing the cylinder to prevent cooling, 

 and such other arrangements as may be found advan- 

 tageous. In the hands of an experienced engineer, 

 indicator diagrams become highly suggestive of merits 

 and defects, and often furnish more information as to the 

 economical working of an engine or the reverse, than con- 

 tinued observation of its structure and action could supply. 

 CALCULATION OF POWER. In estimating the 



power of a non-condensing engine without reference to 

 its indicator figure, we may generally make a very near 

 approximation to the truth by the following mode of 

 reckoning. We assume the engine to be in fair work- 

 ing order, and fitted with an ordinary slide, cutting off 

 the steam at about f rds of the stroke ; that the 

 steam-pipe is not of great length, and well clothed 

 __ P with non-conducting material ; that the ports are 

 "j well-proportioned, and the piston and slide tight. 

 We farther suppose the piston to travel at the velo- 

 city of 200 feet per minute, which is found to be 

 practically a fair working rate ; and that a horse- 

 power, to be effective, after all allowances for fric- 

 tion, &c., should be estimated at 44, 000 Ibs. moved 

 1 foot per minute, or 220 Ibs. moved 200 feet per 

 minute. We observe the pressure in the boiler, 

 and deduct from it Jth for loss by cooling in the 

 steam-pipe and expansion in the cylinder, and 2 

 Ibs. for resistance to exit and other losses, the 

 remainder being reckoned as the mean effective 

 pressure. Multiplying this by the area of the 

 piston, and dividing by 220, we get a fair estimate 

 of the power. 



Example. An engine having a cylinder 30 

 inches in diameter, is worked at a pressure of 36 

 Ibs. in the boiler : required its power. 

 From pressure in boiler ... 30 Ibs. 

 Deduct one-fourth for cooling, <fec. 9 Ibs. 

 And for back pressure . . 2 Ibs. 11 ,, 



H 



Mean effective pressure .... 25 

 Multiply by area of 30 inches . . 707 



Divide by 220)17075 



Horse-power 80 



In general it is the business of engineers to provide 

 engines of certain powers without special reference to 

 the pressure at which they should be worked. By em- 

 ploying very high pressures, the size, weight, and cost 

 of an engine are certainly reduced ; but, on the other 

 hand, some danger is incurred, and the tear and wear 

 are considerable. By using very low pressures, again, 

 the cylinder must be large, the engine is generally cum- 

 brous and heavy, and little advantage can be taken of 

 the expansive power of the steam. We consider a 

 boiler pressure of 40 to 50 Ibs. to be a fair average on 

 which to estimate the engine-power ; and would suggest 

 the following rules for calculating the power of a given 

 engine, and the diameter of cylinder necessary to pro- 

 duce a given power. 



1. To find the power of an engine when the diameter 

 of the cylinder is given. 



Rule. Divide the diameter (in inches) by 3, and square 

 it for the horse-power. 



Example. Required the power of an engine having a 

 cylinder 15 inches in diameter. 



15 



- = 5, and 5 X 5 = 25 horse-power. 



O 



2. To find the diameter of cylinder necessary for a 

 given power. 



Kttle. Multiply the square root of the power by 3 ; 

 the product is the diameter of the cylinder in inches. 



Example. What should be the diameter of a cylinder 

 for 100 horse-power ? 



Square root of 100 = 10, and 3 X 10 = 30 inches. 



The length of stroke must depend on the number of 

 revolutions made by the crank in a given time. It is 

 convenient to assume that the piston, in engines going 

 at a fair average speed, shall travel over 200 feet per 

 minute. Sometimes it moves at the rate of 250, and 

 even exceeding 300 feet per minute ; but, upon the 

 whole, 200 is a convenient and economical speed. This 

 is the product of twice the stroke by the number of 

 revolutions ; and hence its half, 100, is the product of 

 the stroke by the number of revolutions. If, then, 

 either the length of stroke or the number of revolutions 

 be given, the other may readily be thus found : 



