Heat engineering; a text book of applied thermodynamics for engineers and students in technical schools . little change in steam effect of clearance surface as shown by Heinrich has beenmentioned on p. 209. General practice, however, is to cut theclearance to a minimum so as to increase the area of the indicatorcard for a given displacement and to make the steam loss due toimproper compression with different cut-offs as small as possible. BEST POINT OF COMPRESSION The effect of compression is very slight as is shown theoreticallyand by the tests of Heinrich but to determine the
Heat engineering; a text book of applied thermodynamics for engineers and students in technical schools . little change in steam effect of clearance surface as shown by Heinrich has beenmentioned on p. 209. General practice, however, is to cut theclearance to a minimum so as to increase the area of the indicatorcard for a given displacement and to make the steam loss due toimproper compression with different cut-offs as small as possible. BEST POINT OF COMPRESSION The effect of compression is very slight as is shown theoreticallyand by the tests of Heinrich but to determine the best point THE STEAM ENGINE 231 theoretically several methods may be used. The amount ofcompression to be used with any given cut-off may be found bythe following construction of Stumpf. In Fig. 107 the initialpressure is pi, and the back pressure pb, the curves are rectangularhyperbolae. With the dimensions given on the card, Area = pi f- PiD [I + -] loge z — Dpb[l — x] + 1 pbD[l + X] l0ge l + X I It is desired to eliminate x in terms of the volume of steam takenfrom the boiler, that is, xD. xD. Fig. 107.—Stumpf s method of finding compression Dpb(l - x) = Dpb[l + I] - Dpb[l + x] = DpJLl + 1]- DVl[l + 1 x] and pbD(l + x) log l-±* = PlD(l+ }~x) loge A_!L^ 1^ area _ p\~D = 7 + Pill + + p,[z+±]log.^-pJl + Z] ~ + l r Vl[l+--x] log. [t + h*[ Vi Suppose now that the volume, xD, of working steam re-mains constant and there is a change in the point of cut-off. 232 HEAT ENGINEERING The relation which gives maximum work under this change withconstant volume of working steam is given by equating thederivative to zero. rf() n , . l+l [7^ly+l l + l 1 + --x + Vi - Vi log* 2i Pid + l x) 1 1+-- xr Pi log, l + l X- + l r l + l -+1 I + Pi log, l+x1 Pi , l + x - = Pi log, -r (80) or the point of cut-off divides a line from the end of the card tothe axis of volume in the same proportion as the clearance di-vides a line to the axis of volume from the point of compr
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