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The last recorded frame on each microfiche shall contain the symbol — »• (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one enposure are filmed beginning in the uppur left hand corner, left *o right and top to bottom, as many frames as required. The following diagrams illustrate the method: L'exemplaire filmA fut reproduit grAce d la gr will be 160 lbs. abso- lute, and the back pressure in low cylinder 3 lbs. absolute. The total range of pressure is therefore 157 lbs., and the corre- sponding range of temperature 221 Fahr. The object of a compound engine being to reduce cylinder condensation by dividing the range of temperature judiciously between two or more cylinders, the first step is to decide through what range of temperature each cylinder shall work. In doing this, th(» desirability of a tolerably uniform division of work beween the various cylinde^a forming the system must not be overlooked, although it cannot be considered good engineer- ing to impair the economy of t'le engine materially to accom- plish this result, as each engine of the system may be built to carry any load found desirable to put upon it. If the range of temperature is divided equally between the three cylinders in the proposed engine, the greater iuterual surface of the low cylinder would warrant the expectation of greater cylinder con- densation than in the smaller cylinder, and if so, the total con- densation can be reduced by giving the low-pressure cylinder less range of temperature and the high cylinder more. Cylinder condensation in this investigation, whether consid- ered relatively or collectively, must be made to include the CYLIN'DKR PROPORTIONS FOR COMPOUND ENGINES. 3 steam consumed in the jackets of oacli cylinder, if jackets are used. Whatever may be true in regard to the best range of temperature for each cylinder, the logic of what is to follow will apply with equal force, and therefore, for the purpose of illus- tration, it will be assumed that the temperature is to be equally divided. This will require that the high cylinder works between 160 lbs. absolute and 57 lbs., the intermediate between 57 and 16 lbs., and the low cylinder between 16 lbs. and 3 lbs. absolute pressure. B Bi B2B:iB4 Fig. 2. Fis. 3. Figs. 1, 2, and 3 represent theoretic diagrams between each of the throe divisions of pressiire mentioned. In each case " V F" represents the vacuum line, and "XX" the atmos- pheric line, and in each ease "A F'' represents the piston travel. The clearance is assumed to be ^i of the piston dis- placement, as indicated. For convenience in constructing the CYLINDER PROPORTIONS FOR COMPOUND ENGINES. curves and measuring their enclosed areaj, the following scales have been chosen : Fig. 1 Scnlo 50 lbs. to the incli, Fig. 2 " 20 Fig, 3 " 5 " In each case, ''A. B. C. DT represents a theoretically perfect diagram, so far as free expansion is concerned, because expansion is carried to the line of return pressure, and compression fills the clearance space to initial pressure. It is hardly necessary to say that the curves here shown are Mariotte curves, and not Adiabatic, as the latter are seldom used and are considered an unnecessary refinement in this investigation. The successive curves in each diagram, which follow the curves " //. C" repre- sent later points of cut-off, and they are continued beyond the limits of piston travel until thsy intersect the line of return pressure. The areas of enclosed spaces are indicated by figures. Thus in Fig. 3, the area of the theoretically perfect diagram ''A. B. C. nr is 2.68 inches, and "/i. B,. C\. C. B." is .90 inches, etc.* The next step is to determine the best point of cut-off for each cylinder. In this investigation each cylinder must be considered separately, and treated as though it was a single cylinder engine working between the limits of pressure indicated, and it may be asserted without fear of successful contradiction that if any cylinder of a compound engine is not realizing the highest econ- omy obtainable from a single cylinder engine working between its limiting pressures, then the engine as a whole is falling short of its possibilities. It is also true that if because of cylinder condensation it is not economy to expand to the line of back pressure in a single cylinder engine, the same is true of every cylinder of a compound engii:e, it being only a question of the degree of free expansion permissible in each case. To those who believe that there ought to be no " drop " in any of the cylinders of a compound engine except the low, the foregoing will seem rank heresy. They argue that if there is " drop " in the high cylinder there is free expansion waste, and by earlier cut-off in the low cylinder the receiver pressure may be raised until the drop in high cylinder disappears, thus elimi- * For convenience of publication, the diaj^raras of Figs. 1, 2, and 3 bave been reduced in size, and therefore, while tlie areas remain relatively the same, the figures given are the actual areas of the original diagrams. CYLINDER PK0POUTIOX8 FOR COMPOUND ENGINES. natinp; free expansion and improving the economy of the system. This is a pbiusible fallacy which represents only one side of the question, the other side being that by raising the roceivor pres- sure the range of temperature is increased in the large cylinder, thereby increasing the cylinder condensation in this cylinder without effecting a corresponding reduction of condensation in the smaller cylinder. Looking at this question flora another point of view, let it bo admitted for the moment that the econ- omy of the engine will be improved by raising the receiver pres- sure until the " drop " in high cylinder disappears. Then considering the high cylinder alone, we have a diagram in which expansion is carried to the line of back pressure, which cannot be considered the most economical diagram from any engine whose internal condensation is not in proportion to the steam used, which is the recognized condition of all steam engine cylin- ders. Therefore the economy would be improved by using a cylinder of smaller diameter, with less exposed surface for con- densation and necessarily some " drop " at exhaust opening. Then if it is true that better economy will be realized by raising the receiver pressure again to eliminate the drop as before, it only requires a few successive stages of this development to dis- pense with the high cylinder altogether, completing the whole expansion in the low cylinder, and at the same time improving the economy at every step in that direction, reaching the highest economy when the low cylinder, covers^the entire range of expan- sion and the engine becomes a single cylinder engine instead of a compound. To those who still adhere to the belief that what is true of one cylinder of a compound engine is not true in any degree of the others, and that one cylinder of an engine may be wasteful in its preformance, without affecting the aggregate per- formance of the system, the reasoning of the following pages will not be convincing. To those who believe that each cylinder must realize the most economical performance for a single cylin- der working between its limits of pressure, and believe also that cylinder condensation makes it impossible to obtain this by expanding to the line of back pressure in any cylinder, the method of investigation which is to follow will be of inter- est. Referring again to Figs. 1 , 2, and 3, let us first investigate the low-pressure cylinder represented in Fig. 3 as being in some respects the most important one of the system. If 3 lbs. abso- 6 CYLIXPRR PROrORTIONS FOR COMPOUND EXfilNKS. lute ba asHumod to })e the back-prassiiro in this c^'lindor, the dia- ;,'raiu " A.Ii.CI>.'' represents full and coniploto expansion, and will correspond with the highest economy of this cylinder if there was no condensation, or if cylinder condensation was a uniform per cent, of the steam used. This diagram, carrying expansion io 3 lbs. absolute, represents a total of more than 53 expansions in the system, which is recognized as being far be- yond the economical limit. Following the successive expansion curves from " Ji,. Ji,. B,. li,,'' it will be seen that " B,." adds an area to the useful diagram of .9 inches, or more than J of the area of " A.B.C.D.,'' and the free expansion loss occasioned by this curve is only lO'/r of the useful area that has been realized. This loss is represented by the area of " C,. E,. C" Substitut- ing curve " B,. C,." for " />,. (",.," the further addition of useful area is only .78 inche ». which is accompanied by an addi- tional free expansion loss of 29r^ of this amount, and in the same manner " 7^,. C," only adds .G6 inches of area with a loss of 574, and finally " B,. C," with a useful area of only .06 inches entails a loss of Syi of this amount in consequent additional free expan- sion. As between "A*,." and "/>,." then it is not likely that an amount of cylinder condensation is -^ver found in practice that would make it economy to add this last area to the diagram with itsenormous free expansion loss and the terminal pressure of^'C^." representing 22 expansions in the system is therefore probably too high, and we must look for the best results between 22 expansions corresponding tv) " C\." and 53 expansions due to terminal " C." If the exact amount of cylinder condensation due to each of the five points of cut-oflf was known, the indicated areas of the diagrams would furnish the data necessary to determine at once the exact point of cut-off where the highest economy would be realized, and just to the extent that we are able to correctly estimate this cylinder condensation, will we be able to determine correctly the best number of expansions in each cylinder and in the system. It must be here understood that it is not intended in this paper to determine absolutely the best cylinder ratios or the best number of expansions for the conditions that have been assumed because of the lack of exact data regarding cylinder condensation, but it is the purpose of the author to show that by this method of investigation even an approximation of the cylinder condensation enables the engineer to decide the ques- CVr.lNnKU I'ROPOUTIONrt FOU (^OMI'OINl) KNCJINKS. tion of cyliiuIcirH with u coinpiirativtjly siimll limit of possihle orror, juid thin error may bo rotlucoil towiird zoro jiint in the proportion that th() truth ro^urdiuf;; cylinder condonsation is known. To illuHtrut(( the; nninnor of a])plying this knowledgo with iho uHc, of tlu) dia}^raniH o! Fij^H. 1, '-', and M, various aiiiounta of cylind(!r condonHation will bo aHHumcul and tin- probloin worked out for each eano. ]ioft)ro doin*,.," adds to the useful diagram the area of " //. //,. (\.C. JJ." equal to 2.90 inches. The free expansion of 4 lbs. at " 6',." results in a loss of useful work re])resont(^d by tho. area of " r,. h\. (\" (M|ual to I.IH inches, or about 41;^ of the former, lloferring to Fig. 1, representing the high pressure cylinder, and repeating the same calculation, the area of useful woi'k of " /?. B^. (\. C. /»'." ecpials 1.78 inches, and the drop at '* T." of 40 lbs, (lauses a loss repre- sented by " (\. h\. (['" equal to ,78 inches area, or about 41 ;o of the useful work in this case also, so that by comparing the two we see that in both cas(^s the useful areas of '" />. />^. t\. G. /?." are accompanied by a free expansion loss of about 4lr<', but in the low-pressure cylinder the terminal drop is only 4 lbs. as against 40 lbs in the high cylinder. The foregoing ought to furnish food for thought to the engi- neer who is chiefly c(m^ ' and intermediate cylr resuming the considoi assume certain quantitl. tion, and thus illustrate knowledge on this subject. • .;out preventing drop in the high '^'erring again to Fig, 8, and ' linder condensation, let us nt this C3'linder condensa er of applying more exact it, lo evident that the conditions which make late cut-off desir able are large eonJ jnsation and a constant (piantity at every point of cut-off, and the reverse conditions, viz : small condensation, varying for each point of cut-off, would call for early cut-off. In illustrating this subject two rather exti ^me conditions have been chosen, one where the cylinder condensation is assumed to be ^5f^ of the steam accounted for by the indicator at latest point of cut-off, and this amount to remain undiminished at the earlier points of cut-off, and the other condition where cjdinder condensation is assumed to be only Itvi instead of 2r"< as above, and to decrease at each of the earlier points of cut-off in the following manner : 8 CYMNDKll I'Uoroin loNH I'lHi COMPOUND KNOlNIvS, 14:2 whon ciittldK off ot /},. m " ' "i- ll;j • " n. Fif^. \ gives u graphic illuHtrati(;n of the effect on tlie economy of the h)\v cyliiuhn* picxiiUHul by the two aHHiuned conditions as to cylinder contUuisation. lleforring to Fig. ',i, the steam ac- counteil for by the indicatcjr at latest point of cut-off may be represented by tiio area of A. li,. h\. J). A. which ecpials (5.78 scpiare inches. If the staam condensed on entering the cylinder is 25;^ "f that accounted for by the indicator at latest point of cut-off it may be rej)re8entcd by 2b'^ cf the area ().7H" — l.()9". Arenn uf lucful dlu^'raiu In gquuro InuhcB. 2.. ■0 J. '', 3.{ X) 3,: » x: lO n.- .-. I.( K) \:. B J.! ti \: T. 5. JO 3. 25 s. 50 5. ■5 85 — realized. Bi B, ^ ' ^ " - — -~ hSi ■a ■fi 73 D """^ .?' Percentage of total "N "^ -°^ ^ — b, ,.£i G B, / ^ 00 A'^ / Fig. 4. Iliis last area then, under the assumed conditions, Avill be a constant loss at every point of cut-off. An additional loss by free expansion occurs at every point of cut-off later than II. These free expansio losses are represented by the indicated areas beyond the limits of piston travel, which combined with the area repreceuting condensation, and compared with the areas of useful diagram, produce the curve "J. C." (Fig. 4) in the following manner. Measurements on abscissa correspond to CYMNDKU l'HOlH)UT!ON.>-' F()|{ foMl'Ol iND K.NiUNKH. the UHofnl areas of dia^raiiiH at the five ]H)inth of ciitotl" iiuli- cntetl. Measurement*' uu ordiiiates are obtai; ■ ..'^afoUowM :* For eut-(ttl' " /r' the area of UHeful wort in 2.*^>8 iiichen, and the asHinneil eonstunt loss by condeiiHatiofi ot ].(>i) inelieK inakeH the toial area duo to the Kttiuni cnnsunuMl enual to '2.()8 inehos 4 l.()'.t ineheH " VM inches. Of thi.i amour.t the ansa r.otually realized, li.flH in(!hos, in QIM', whieh ia meaHUi-ed on ordinates and establishen the point " /j." For eutoH' " /.*„" in the same numner as before, we have useful area of, "A, n,. (',. ('. I). A." S.SS inclioH. Free exi>miHis',ive stop. Curve " D. EP is produced by the same method, the only difference bein^ that the smaller and varying condensation is assumed, thus instead of the constant area of 1.60 as assumed in curve "A. (V\ the condensation is supposed to be represented by the following aieas : .74 inches for cut-off H. .81 ' B,. .8S " " '• Ba. .95 B3. 1.03 " " " B^. These quantities are substituted for the constant quantity, 1.69 inches, used in curve "J. C." and the result is curve "z>. /-;." From an examination of these curves it appears that with the conditions assumed for curve ".-/. ^'." the highest economy is obtained at or near cut-off " /^,,."', while with the conditions which produca curve " D. K'\ the highest economy is found at or near cut-off 7i,. If the condensation assumed for either of these curves was known to be correct, then the best point of cut ff would at * This method is fully ilhiHtrated on page No. 10(57, Vol. XIV., TranHUcti'nis Americdii Society Mechanical Engineers. 10 C^T.INDER PROPORTIONS FOR COMPOUND ENfiTNKS, once jippoar, but oven without exact knowleilge an to conclen- sjition, the ran^e covered between the two assumed conditions is so great that the actual condensa<-ion wouhl pro])ably pro- duce a curve between the two, and if so^ then the terminal pressure at release in low pressure cylinder of the proposed endue, should not be less than 4 lbs. a])solute. nor more than 5 lbs., and the corresponding number of expansions of the system will not be more than 40 nor less than 32. For the purpose of keeping the low pressure cylinder as small as possible, the fewest number of expansions should be employed that promises app)-oximatoly the l)est economy, and therefore we will select 82 expiUisiouH, and the expansion curve in low pressure cylin- der will be /i., C,. Referring to Fig. 4, the lower curve assumes the greatest cylinder condensation and on this assumption B.. appears to be Arcaia of useful diagram In square Inches, a.,™ 2.75 3.00 3.2.'i 3.50 3.7.'; 4.00 4.25 4.50 4.75 2.00 5.25 5.50 5.75 85 •6 i 80 i. u u ? 75 "n "5 ™ 1 Z 05 CO B B, ■v^ \E \\ D E ^ Bi Bo \ \-i B4 -o A Fig. 5. the best point of cut-off. The condensation here assumed, if referred to the area of "^1. 7A. (IJ\ /»." will be found to equal Mi of the steam accounted for by the indicator when cutting off at "Z?,,", whi-'.i in view of the cut-off being later than 1/4 stroke and the total range of pressure m the cylinder only 13 lbs., is an altogether improbable amount. It is also equally improbable i CVLIXDER PROrORTIOXH FOR COMPOUND ENGINES. 11 that tho actual Iosh by condeiiHation would not decrease slightly with earlier points of cut-otf, ho that in selecting 82 expansions for the propcjsod engine, it is done with the idea of using the least permissible number that will even approximate the bes* economy. Having determined that 32 expansions will be ob- tained in the proposed engine, and that "^1. /i,. 6',. C. i>." of Fig. 3, will be the diagram of low pressure cylinder, we will next proceed to investigate tho intermediate and High Pressure cylinders. Beginning with the intermediate, Fig. 2 represents a series of possible diagrams between tho pressures thu* liave been allotted to this cylinder, and Fig. 5 represents the economy of each of these points of cut-off under the two extreme conditions of con- densation that were assumed in Fig. 4. The method of locating the points on tho curves of Fig. 5 is exactly tho same as that of Fig. 4, merely substituting the areas of Fig. 2 for those of Fig. 3, and need not be again explained. Following the curves of Fig. 5, it appears that for the smallest condensation the best economy is at or near cut-off " /?,", while with the largest con- densation tho best result is with cut off somewhat later than " B." Between these two points then we must probably look for the desired point of cut off, and as before stated, if the exact condensation for each point was known it could be very quickly determined. As between this cylinder and the low v/e may assume that the condensation will be somewhat less in the smaller cylinder because of its smaller area of surface. This would be favorable to earlier cut-off, and the practical limita- tions as to size of cylinder do not interfere, as is the case of the low cylinder. On the other hand, free expansion is not a total loss in either the high or intermediate cylinder, as its super- heating effect re-evaporates a certain quantity of the moisture in the steam, thus delivering to the receiver an appreciably greater volume of steam than that accounted for by the indi- cator at exhaust opening if much " drop " occurs. For this reason, " drop " is less objectionable in these cylinders than in the low, where no such redeeming feature is found. After due consideration of these modifying influences, it is not impro- bable that about midway between li,. and B,. will approximate the best point of cut off for this cylinder, and to continue the illustration of tho proposed method, the dotted curve B,}^ 0,^ will be selected as the desired curve. 12 CYLINDER PROPORTIONS FOR COMPOUND ENGINES. Proceeding in the same manner with Fig. 1, representing the high pressure cylinder, and what has just been said about the intermediate cylinder applies to this equally as well. From a study of the curves of Fig. 6, as representing the performance of the high pressure cylinder at the various points of cut-off under the same conditions as to condensation that were assumed in Figs. 4 and 5, and keeping in mind that unlike the low cylinder no practical difficulty exists as to its size, we may with confidence select B„ as a point of cut-off that promises approximately the best results that may be obtained from this cylinder. Areas of useful diagram In square Inches. 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 Percentage of total work realized. I )^ -o^ ^S: V,^ S V- R '- ^^ Bi JB^ -- B3 ^J' . r ^C Fig. 6. We have now established the expansion curves that we desire to produce in each cylinder, and to prevent confusion Figs. 7, 8 and 9 represent diagrams from the three cylinders, in which only the desired expansion curves appear. So far, in this investigation, no attention has been paid to the compression curves further than to state at the beginning that the compression curves shown are full compression curves, which entirely fill the clearance spaces by compression, and rise without interruption to the initial pressure of the diagrams. Under no condition can these curves be the most econ .uucal, CYLINDER PROPORTIONS FOR COMPOUND ENGINES. 13 unless it has baen shown that the best economy is obtained by expanding fully to the line of back pressure, as B. C. (Figs. 1, 2 and 3). Following the law relating to compression curves, suggested in Vol. XIV. of the Transactions of the American Society of Mechanical Engineers, page 1070, the curves //. F. have been produced as the compression curves in each case that correspond with the expansion curves that have been adopted. The completed diagrams, then as sought to be produced, are •t ^ Scale: 50 '^ M. E. P. 65.65 .-.El Fig. 7. represented by full lines in Pigs. 7, 8 and 9. The next step is to ascertain the ratio of cylinders which will produce these respective diagrams, and to do this the diagrams must be com- pared as to the relative volumes of steam which tliey indicate. A very convenient graphical method for doing this is the fol- lowing.* * The author is indebted to his son, B. C. Ball, meniher of the class of '95 at Stevens Institute of Technology, for this method, which is believed to have been original with him.— F. H, B. 14 CYLINDER PR0PP:HTI0XS FOR COMPOUND ENGINES. First, continue the compression curves //. F. of Figs. 8 and 9 to the line of highest pressure of each diagram, as shown. Next continue the expansion curves of Figs. 7 and 8 to the intersection of the line of lowest pressure of each diagram as shown. Assuming that the lengths of these diagrams representing the piston travel are the same, and that the line G. B.^ in Fig. 9 rep- resents the same pressure as the line //. /^ (Fig. 8), it is only necessary to compare the length of the line G. B- with H. E^j,, and \A Scale: 20 '^ JI. E. P. 24,46 HP Fig. 8. the inverse ratio will be the ratio sought. Thus, in this case, the line G. //, measured, with a scale of 100 to the inch, meas- ures 92, and in the same manner //. E^^ measures 368, therefore 868 = 4 the ratio of the intermediate to low cylinder will be By the same method G. Z?, (Fig. 8) measures 104, find IL Fa (Fig. 7) = 342, and therefore the ratio of high to intermediate 848 cylinders will be ' .^ = 3 3. Reviewing these figures we have the ration of high to inter- mediate 3.3, and of intermediate to low 4, and consequently of high to low 13.2. .\ CYLINDER PROPORTIONS FOR COMPOUND ENGINES. 15 It sometimes may be more convenient in measuring cylinder ratios by the method just described to extend both the com- pression and expansion curves of the lower diagram upward to .1 the line of terminal pressure of the next higher diagram, and use this line for measuring the ratios. The result will be the same in either case. If these ratios are used, and the valves of each cylinder are set to give the steam distribution indicated, the actual diagrams 16 CYLINDEK PROPORTIONS FOR COMPOUND ENGINES. from the engine will approximate very closely to those of Figs. 7, 8 and 9, excepi as they may be slightly modified by 'cylinder condensation. Where steam-jackets are used the loss by cylin- der condensation after cut-off in high-pressure cylinder is largely restored by heat from the jackets, so that frequently no allow- ance need be made in the ratios of cylinders for this loss. With unjacketed cylinders a progressive deficiency will appear in each successive diagram of the system as compared with the theoretical diagrams, unless an allowance is made in the cylinder ratios to compensate for the progressive loss occa- sioned by condensation in the cylinders. Continuing the study of the diagrams of Figs. 7, 8 and 9, the same diagrams appear in Fig. 10, reduced to the scale of the high-pressure diagram, and in Fig. 11 they are reduced m length to correspond with the respective cylinder ratios, thus representing the total expansion referred to the low-pressure cylinder. CYLINDKR PROPORTIONS FOR CO >f POUND ENGINES. 1" The mean eflfective pressures of these diagrams are as follows : High cylinder 65.65 U)s. Intermediate cylinder 34.46 lbs. Low cylinder 7.05 lbs. Or, referred to the low cyliiicjer, as follows : High cylinder 4.96 lbs. Intermediate cylinder 6.10 lbs. Low cylinder 7.55 Iba. Total 18.61 lbs. These figures show a progressive increase of indicated work in each cylinder from the high to the low. A more even division of work would be obtained by decreas- ing the range of pressure in the low cylinder, and increasing the range in the high. It has already been suggested that because of the relatively larger area of surface of the low cylinder a modification of this kind would probably reduce the total con- 2 18 CYLINDKll I'ROI'OUTIONS FOH COMPOINI) KN