file which includes the original illustrations4 ,see #cdgja-;h4htm or #cdgja-;h4zip3 7https3_/_/www4gutenberg4org_/cache_/epu b_/#cdgja_/pg#cdgja-;images4html7 or 7https3_/_/www4gutenberg4org_/files_/#cd gja_/cdgja-;h4zip7 ,images of the original pages are available through ,internet ,archive4 ,see http3_/_/www4archive4org_/details_/steam engines#jjnewyrich ---------------------------------------- ------------------ ,transcriber's note3 ,inconsistencies have not been corrected 7hyphenated vs non-hyphenated or spaced words71 except horse-power changed to horsepower and cut off to cut-off4 ,minor typographical errors have been corrected4 ,text in italics is enclosed by underscore characters as in italics4 ,subscripts are indicated by 4441 as in subscript4 ,in-line multi-line formulas have been changed to single-line formulas1 where necessary with the addition of brackets to prevent ambiguity4 ---------------------------------------- ------------------ ,machinery's ,reference ,series ,each ,number ,is a ,unit in a ,series on ,electrical and ,steam ,engineering ,drawing and ,machine ,design and ,shop ,practice ,,number #gj ,,steam ,,engines ,,contents ,action of ,steam ,engines #c ,rating and ,general ,proportions of ,steam ,engines #aa ,steam ,engine ,details #ae ,steam ,engine ,economy #cj ,types of ,steam ,engines #cf ,steam ,engine ,testing #da ,copyright1 #aiaa1 ,the ,industrial ,press1 ,publishers of ,,machinery1 #di-ee ,lafayette ,street1 ,new ,york ,city4 ,,chapter ,i ,,action ,,of ,,steam ,,engines ,a steam engine is a device by means of which heat is transformed into work4 ,work may be defined as the result produced by a force acting through space1 and is commonly measured in foot-pounds2 a foot-pound represents the work done in raising #a pound #a foot in height4 ,the rate of doing work is called power4 ,it has been found by experiment that there is a definite relation between heat and work1 in the ratio of #a thermal unit to #ggh foot-pounds of work4 ,the number #ggh is commonly called the heat equivalent of work or the mechanical equivalent of heat4 ,heat may be transformed into mechanical work through the medium of steam1 by confining a given amount in a closed chamber1 and then allowing it to expand by means of a movable wall 7piston7 fitted into one side of the chamber4 ,heat is given up in the process of expansion1 as shown by the lowered pressure and temperature of the steam1 and work has been done in moving the wall 7piston7 of the closed chamber against a resisting force or pressure4 ,when the expansion of steam takes place without the loss of heat by radiation or conduction1 the relation between the pressure and volume is practically constant2 that is1 if a given quantity of steam expands to twice its volume in a closed chamber of the kind above described1 its final pressure will be one-half that of the initial pressure before expansion took place4 ,a pound of steam at an absolute pressure of #bj pounds per square inch has a volume of practically #bj cubic feet1 and a temperature of #bbh degrees4 ,if now it be expanded so that its volume is doubled 7#dj cubic feet71 the pressure will drop to approximately #aj pounds per square inch and the temperature will be only about #aij degrees4 ,the drop in temperature is due to the loss of heat which has been transformed into work in the process of expansion and in moving the wall 7piston7 of the chamber against a resisting force1 as already noted4 ,principle of the ,steam ,engine ,the steam engine makes use of a closed chamber with a movable wall in transforming the heat of steam into mechanical work in the manner just described4 ,fig4 #a shows a longitudinal section through an engine of simple design1 and illustrates the principal parts and their relation to one another4 ,the cylinder ,a is the closed chamber in which expansion takes place1 and the piston ,b1 the movable wall4 ,the cylinder is of cast iron1 accurately bored and finished to a circular cross-section4 ,the piston is carefully fitted to slide easily in the cylinder1 being made practically steam tight by means of packing rings4 ,the work generated in moving the piston is transferred to the crank-pin ,h by means of the piston-rod ,c1 and the connecting-rod ,f4 ,the piston-rod passes out of the cylinder through a stuffing box1 which prevents the leakage of steam around it4 ,the cross-head ,d serves to guide the piston-rod in a straight line1 and also contains the wrist-pin ,e which joins the piston-rod and connecting-rod4 ,the cross-head slides upon the guide-plate ,g1 which causes it to move in an accurate line1 and at the same time takes the downward thrust from the connecting-rod4 ,the crank-pin is connected with the main shaft ,i by means of a crank arm1 which in this case is made in the form of a disk in order to give a better balance4 ,the balance wheel or flywheel ,j carries the crank past the dead centers at the ends of the stroke1 and gives a uniform motion to the shaft4 ,the various parts of the engine are carried on a rigid bed ,k1 usually of cast iron1 which in turn is bolted to a foundation of brick or concrete4 ,the power developed is taken off by means of a belted pulley attached to the main shaft1 or1 in certain cases1 in the form of electrical energy from a direct-connected dynamo4 ,illustration3 ,fig4 #a4 ,longitudinal ,section through the ,ames ,high-speed ,engine ,when in action1 a certain amount of steam 7#a_/d to #a_/c of the total cylinder volume in simple engines7 is admitted to one end of the cylinder1 while the other is open to the atmosphere4 ,the steam forces the piston forward a certain distance by its direct action at the boiler pressure4 ,after the supply is shut off1 the forward movement of the piston is continued to the end of the stroke by the expansion of the steam4 ,steam is now admitted to the other end of the cylinder1 and the operation repeated on the backward or return stroke4 ,an enlarged section of the cylinder showing the action of the valve for admitting and exhausting the steam is shown in ,fig4 #b4 ,in this case the piston is shown in its extreme backward position1 ready for the forward stroke4 ,the steam chest ,l is filled with steam at boiler pressure1 which is being admitted to the narrow space back of the piston through the valve ,n1 as indicated by the arrows4 ,the exhaust port ,m is in communication with the other end of the cylinder and allows the piston to move forward without resistance1 except that due to the piston-rod1 which transfers the work done by the expanding steam to the crank-pin4 ,the valve ,n is operated automatically by a crank or eccentric attached to the main shaft1 and opens and closes the supply and exhaust ports at the proper time to secure the results described4 ,work ,diagram ,having discussed briefly the general principle upon which an engine operates1 the next step is to study more carefully the transformation of heat into work within the cylinder1 and to become familiar with the graphical methods of representing it4 ,work has already been defined as the result of force acting through space1 and the unit of work as the foot-pound1 which is the work done in raising #a pound #a foot in height4 ,for example1 it requires #a x #a #a foot-pound to raise #a pound #a foot1 or #a x #aj #aj foot-pounds to raise #a pound #aj feet1 or #aj x #a #aj foot-pounds to raise #aj pounds #a foot1 or #aj x #aj #ajj foot-pounds to raise #aj pounds #aj feet1 etc4 ,that is1 the product of weight or force acting1 times the distance moved through1 represents work2 and if the force is taken in pounds and the distance in feet1 the result will be in foot-pounds4 ,this result may be shown graphically by a figure called a work diagram4 ,illustration3 ,fig4 #b4 ,section of ,cylinder1 showing ,slide ,valve ,in ,fig4 #c1 let distances on the line ,,oy represent the force acting1 and distances on ,,ox represent the space moved through4 ,suppose the figure to be drawn to such a scale that ,,oy is #e feet in height1 and ,,ox #aj feet long4 ,let each division on ,,oy represent #a pound pressure1 and each division on ,,ox #a foot of space moved through4 ,if a pressure of #e pounds acts through a distance of #aj feet1 then an amount of #e x #aj #ej foot-pounds of work has been done4 ,referring to ,fig4 #c1 it is evident that the height ,,oy 7the pressure acting71 multiplied by the length ,,ox 7the distance moved through71 gives #e x #aj #ej square feet1 which is the area of the rectangle ,,ycxo2 that is1 the area of a rectangle may represent work done1 if the height represents a force acting1 and the length the distance moved through4 ,if the diagram were drawn to a smaller scale so that the divisions were #a inch in length instead of #a foot1 the area ,,ycxo would still represent the work done1 except each square inch would equal #a foot-pound instead of each square foot1 as in the present illustration4 ,illustration3 ,fig4 #c4 ,a ,simple ,work ,diagram ,in ,fig4 #d the diagram1 instead of being rectangular in form1 takes a different shape on account of different forces acting at different periods over the distance moved through4 ,in the first case 7,fig4 #c71 a uniform force of #e pounds acts through a distance of #aj feet1 and produces #e x #aj #ej foot-pounds of work4 ,in the second case 7,fig4 #d71 forces of #e pounds1 #d pounds1 #c pounds1 #b pounds1 and #a pound1 act through distances of #b feet each1 and produce 7#e x #b7 7#d x #b7 7#c x #b7 7#b x #b7 7#a x #b7 #cj foot-pounds4 ,this is also the area1 in square feet1 of the figure ,y#edcba,,xo1 which is made up of the areas of the five small rectangles shown by the dotted lines4 ,another way of finding the total area of the figure shown in ,fig4 #d1 and determining the work done1 is to multiply the length by the average of the heights of the small rectangles4 ,the average height is found by adding the several heights and dividing the sum by their number1 as follows3 #e #d #c #b #a ----------------- #c1 and #c x #aj #cj square feet1 as before4 #e ,illustration3 ,fig4 #d4 ,another ,form of ,work ,diagram ,this1 then1 means that the average force acting throughout the stroke is #c pounds1 and the total work done is #c x #aj #cj foot-pounds4 ,in ,fig4 #e the pressure drops uniformly from #e pounds at the beginning to #j at the end of the stroke4 ,in this case also the area and work done are found by multiplying the length of the diagram by the average height1 as follows3 #e #j ----- x #aj #be square feet1 #b or #be foot-pounds of work done4 ,illustration3 ,fig4 #e4 ,work ,diagram when ,pressure drops ,uniformly ,the object of ,figs4 #c1 #d and #e is to show how foot-pounds of work may be represented graphically by the areas of diagrams1 and also to make it clear that this remains true whatever the form of the diagram4 ,it is also evident that knowing the area1 the average height or pressure may be found by dividing by the length1 and vice versa4 ,fig4 #f shows the form of work diagram which would be produced by the action of the steam in an engine cylinder1 if no heat were lost by conduction and radiation4 ,starting with the piston in the position shown in ,fig4 #b1 steam is admitted at a pressure represented by the height of the line ,,oy4 ,as the piston moves forward1 sufficient steam is admitted to maintain the same pressure4 ,at the point ,b the valve closes and steam is cut off4 ,the work done up to this time is shown by the rectangle ,y,bb,o4 ,from the point ,b to the end of the stroke ,c1 the piston is moved forward by the expansion of the steam1 the pressure falling in proportion to the distance moved through1 until at the end of the stroke it is represented by the vertical line ,,cx4 ,at the point ,c the exhaust valve opens and the pressure drops to #j 7atmospheric pressure in this case74 ,as it is always desirable to find the work done by a complete stroke of the engine1 it is necessary to find the average or mean pressure acting throughout the stroke4 ,this can only be done by determining the area of the diagram and dividing by the length of the stroke4 ,this gives what is called the mean ordinate1 which multiplied by the scale of the drawing1 will give the mean or average pressure4 ,for example1 if the area of the diagram is found to be #f square inches1 and its length is #c inches1 the mean ordinate will be #f _/ #c #b inches4 ,if the diagram is drawn to such a scale that #a inch on ,,oy represents #aj pounds1 then the average or mean pressure will be #b x #aj #bj pounds1 and this multiplied by the actual length of the piston stroke will give the work done in foot-pounds4 ,the practical application of the above1 together with the method of obtaining steam engine indicator diagrams and measuring the areas of the same1 will be taken up in detail under the heading of ,steam ,engine ,testing4 ,definitions ,relating to ,engine ,diagrams ,before taking up the construction of an actual engine diagram1 it is first necessary to become familiar with certain terms which are used in connection with it4 ,illustration3 ,fig4 #f4 ,the ,ideal ,work ,diagram of a ,steam ,engine ,cut-off4--,the cut-off is the point in the stroke at which the admission valve closes and the expansion of steam begins4 ,ratio of ,expansion4--,this is the reciprocal of the cut-off1 that is1 if the cut-off is #a_/d1 the ratio of expansion is #d4 ,in other words1 it is the ratio of the final volume of the steam at the end of the stroke to its volume at the point of cut-off4 ,for example1 a cylinder takes steam at boiler pressure until the piston has moved one-fourth the length of its stroke2 the valve now closes and expansion takes place until the stroke is completed4 ,the one-fourth cylinderful of steam has become a cylinderful1 that is1 it has expanded to four times its original volume1 and the ratio of expansion is said to be #d4 ,point of ,release4--,this is the point in the stroke at which the exhaust valve opens and relieves the pressure acting on the piston4 ,this takes place just before the end of the stroke in order to reduce the shock when the piston changes its direction of travel4 ,compression4--,this acts in connection with the premature release in order to reduce the shock at the end of the stroke4 ,during the forward stroke of an engine the exhaust valve in front of the piston remains open as shown in ,fig4 #b4 ,shortly before the end of the stroke this closes1 leaving a certain amount of steam in the cylinder4 ,the continuation of the stroke compresses this steam1 and by raising its pressure forms a cushion1 which1 in connection with the removal of the pressure back of the piston by release1 brings the piston to a stop and causes it to reverse its direction without shock4 ,high-speed engines require a greater amount of compression than those running at low speed4 ,clearance4--,this is the space between the cylinder head and the piston when the latter is at the end of its stroke2 it also includes that portion of the steam port between the valve and the cylinder4 ,clearance is usually expressed as a percentage of the piston-displacement of the cylinder1 and varies in different types of engines4 ,the following table gives approximate values for engines of different design4 ,,table ,i4 ,,clearance ,,of ,,steam ,,engines ,type of ,engine ,per ,cent ,clearance ,corliss #a4e to #c4e ,moderate-speed #c to #h ,high-speed #d to #aj ,a large clearance is evidently objectionable because it represents a space which must be filled with steam at boiler pressure at the beginning of each stroke1 and from which but a comparatively small amount of work is obtained4 ,as compression increases1 the amount of steam required to fill the clearance space diminishes1 but on the other hand1 increasing the compression reduces the mean effective pressure4 ,initial ,pressure4--,this is the pressure in the cylinder up to the point of cut-off4 ,it is usually slightly less than boiler pressure owing to wire-drawing in the steam pipe and ports4 ,terminal ,pressure4--,this is the pressure in the cylinder at the time release occurs1 and depends upon the initial pressure1 the ratio of expansion1 and the amount of cylinder condensation4 ,back ,pressure4--,this is the pressure in the cylinder when the exhaust port is open1 and is that against which the piston is forced during the working stroke4 ,for example1 in ,fig4 #b the small space at the left of the piston is filled with steam at initial pressure1 while the space at the right of the piston is exposed to the back pressure4 ,the working pressure varies throughout the stroke1 due to the expansion of the steam1 while the back pressure remains constant1 except for the effect of compression at the end of the stroke4 ,the theoretical back pressure in a non-condensing engine 7one exhausting into the atmosphere7 is that of the atmosphere or #ad4g pounds per square inch above a vacuum1 but in actual practice it is about #b pounds above atmospheric pressure1 or #ag pounds absolute1 due to the resistance of exhaust ports and connecting pipes4 ,in the case of a condensing engine 7one exhausting into a condenser7 the back pressure depends upon the efficiency of the condenser1 averaging about #c pounds absolute pressure in the best practice4 ,effective ,pressure4--,this is the difference between the pressure on the steam side of the piston and that on the exhaust side1 or in other words1 the difference between the working pressure and the back pressure4 ,this value varies throughout the stroke with the expansion of the steam4 ,mean ,effective ,pressure4--,it has just been stated that the effective pressure varies throughout the stroke4 ,the mean effective pressure 7,m4 ,e4 ,p47 is the average of all the effective pressures1 and this average multiplied by the length of stroke1 gives the work done per stroke4 ,line of ,absolute ,vacuum4--,in the diagram shown in ,fig4 #f1 the line ,,ox is the line of absolute vacuum2 that is1 it is assumed that there is no pressure on the exhaust side of the piston4 ,in other words1 the engine is exhausting into a perfect vacuum4 ,illustration3 ,fig4 #g4 ,constructing a ,steam ,engine ,work ,diagram ,atmospheric ,line4--,this is a line drawn parallel to the line of absolute vacuum at such a distance above it as to represent #ad4g pounds pressure per square inch1 according to the scale used4 ,construction of ,ideal ,diagram ,one of the first steps in the design of a steam engine is the construction of an ideal diagram1 and the engine is planned to produce this as nearly as possible when in operation4 ,first assume the initial pressure1 the ratio of expansion1 and the percentage of clearance1 for the type of engine under consideration4 ,draw lines ,,ox and ,,oy at right angles as in ,fig4 #g4 ,make ,,or the same percentage of the stroke that the clearance is of the piston displacement2 make ,,rx equal to the length of the stroke 7on a reduced scale74 ,erect the perpendicular ,,ra of such a height that it shall represent1 to scale1 an absolute pressure per square inch equal to #j4ie of the boiler pressure4 ,draw in the dotted lines ,,ak and ,,kx1 and the atmospheric line ,,lh at a height above ,,ox to represent #ad4g pounds per square inch4 ,locate the point of cut-off1 ,b1 according to the assumed ratio of expansion4 ,points on the expansion curve ,,bc are found as follows3 ,divide the distance ,,bk into any number of equal spaces1 as shown by a1 b1 c1 d1 etc41 and connect them with the point ,o4 ,through the points of intersection with ,,bp1 as a'1 b'1 c'1 d'1 etc41 draw horizontal lines1 and through a1 b1 c1 d1 etc41 draw vertical lines4 ,the intersection of corresponding horizontal and vertical lines will be points on the theoretical expansion line4 ,if the engine is to be non-condensing1 the theoretical work1 or indicator diagram1 as it is called1 will be bounded by the lines ,,abchg4 ,the actual diagram will vary somewhat from the theoretical1 as shown by the shaded lines4 ,the admission line between ,a and ,b will slant downward slightly1 and the point of cut-off will be rounded1 owing to the slow closing of the valve4 ,the first half of the expansion line will fall below the theoretical1 owing to a drop in pressure caused by cylinder condensation1 but the actual line will rise above the theoretical in the latter part of the stroke on account of re-evaporation1 due to heat given out by the hot cylinder walls to the low-pressure steam4 ,instead of the pressure dropping abruptly at ,c1 release takes place just before the end of the stroke1 and the diagram is rounded at ,,cf instead of having sharp corners4 ,the back pressure line ,,fd is drawn slightly above the atmospheric line1 a distance to represent about #b pounds per square inch4 ,at ,d the exhaust valve closes and compression begins1 rounding the bottom of the diagram up to ,e4 ,the area of the actual diagram1 as shown by the shaded lines in ,fig4 #g1 will be smaller than the theoretical1 in about the following ratio3 ,large medium-speed engines1 #j4ij of theoretical area4 ,small medium-speed engines1 #j4he of theoretical area4 ,high-speed engines1 #j4ge of theoretical area4 ,,chapter ,,ii ,,rating ,,and ,,general ,,proportions ,,of ,,steam ,,engines ,the capacity or power of a steam engine is rated in horsepower1 one horsepower 7,h4 ,p47 being the equivalent of #cc1jjj foot-pounds of work done per minute4 ,the horsepower of a given engine may be computed by the formula3 ,,apln ,h4 ,p4 ------ #cc1jjj in which ,a area of piston1 in square inches1 ,p mean effective pressure per square inch1 ,l length of stroke1 in feet1 ,n number of strokes per minute number of revolutions x #b4 ,the derivation of the above formula is easily explained1 as follows3 ,the area of the piston1 in square inches1 multiplied by the mean effective pressure1 in pounds per square inch1 gives the total force acting on the piston1 in pounds4 ,the length of stroke1 in feet1 times the number of strokes per minute gives the distance the piston moves through1 in feet per minute4 ,it has already been shown that the pressure in pounds multiplied by the distance moved through in feet1 gives the foot-pounds of work done4 ,hence1 ,a x ,p x ,l x ,n gives the foot-pounds of work done per minute by a steam engine4 ,if one horsepower is represented by #cc1jjj foot-pounds per minute1 the power or rating of the engine will be obtained by dividing the total foot-pounds of work done per minute by #cc1jjj4 ,for ease in remembering the formula given1 it is commonly written ,,plan ,h4 ,p4 ------1 #cc1jjj in which the symbols in the numerator of the second member spell the word ,plan4 ,example3--,find the horsepower of the following engine1 working under the conditions stated below3 ,diameter of cylinder1 #ab inches4 ,length of stroke1 #ah inches4 ,revolutions per minute1 #cjj4 ,mean effective pressure 7,m4 ,e4 ,p471 #dj pounds4 ,in this problem1 then1 ,a #aac square inches2 ,p #dj pounds2 ,l #a4e feet2 and ,n #fjj strokes4 ,substituting in the formula1 #dj x #a4e x #aac x #fjj ,h4 ,p4 -------------------- #abc4 #cc1jjj ,the mean effective pressure may be found1 approximately1 for different conditions by means of the factors in the following table of ratios1 covering ordinary practice4 ,the rule used is as follows3 ,multiply the absolute initial pressure by the factor corresponding to the clearance and cut-off as found from ,table ,,ii1 and subtract the absolute back pressure from the result1 assuming this to be #ag pounds for non-condensing engines1 and #c pounds for condensing4 ,example #a3--;,a non-condensing engine having #c per cent clearance1 cuts off at #a_/c stroke2 the initial pressure is #ij pounds gage4 ,what is the ,m4 ,e4 ,p48 ,the absolute initial pressure is #ij #ae #aje pounds4 ,the factor for #c per cent clearance and #a_/c cut-off1 from ,table ,,ii1 is #j4ga4 ,applying the rule we have3 7#aje x #j4ga7 - #ag #eg4e pounds per square inch4 ,example #b3--;,a condensing engine has a clearance of #e per cent4 ,it is supplied with steam at #adj pounds gage pressure1 and has a ratio of expansion of #f4 ,what is the ,m4 ,e4 ,p48 ,the absolute initial pressure is #adj #ae #aee4 ,the factor for a ratio of expansion of #f 7#a_/f cut-off7 and #e per cent clearance is #j4e1 which gives 7#aee x #j4e7 - #c #gd4e pounds per square inch4 ,the power of an engine computed by the method just explained is called the indicated horsepower 7,i4 ,h4 ,p471 and gives the total power developed1 including that required to overcome the friction of the engine itself4 ,the delivered or brake horsepower 7,b4 ,h4 ,p47 is that delivered by the engine after deducting from the indicated horsepower the power required to operate the moving parts4 ,the brake horsepower commonly varies from #hj to #ij per cent of the indicated horsepower at full load1 depending upon the type and size of engine4 ,in proportioning an engine cylinder for any given horsepower1 the designer usually has the following data1 either given or assumed1 for the special type of engine under consideration3 ,initial pressure1 back pressure1 clearance1 cut-off1 and piston speed4 ,these quantities vary in different types of engines1 but in the absence of more specific data the values in ,table ,,iii will be found useful4 ,the back pressure may be taken as #ag pounds per square inch1 absolute1 for non-condensing engines1 and as #c pounds for condensing engines as previously stated4 ,,table ,,ii4 ,,factors ,,for ,,finding ,,mean ,,effective ,,pressure ---------------------------------------- --------------- ,point of ,cut-off ,percentage ------------------------------------ of ,clearance #a_/aj #a_/f #a_/d #a_/c #a_/b #c_/d ---------------------------------------- ---------- #a4ge #j4ce #j4dh #j4fj #j4gj #j4he #j4if #c4jj #j4cg #j4di #j4fa #j4ga #j4he #j4if #e4jj #j4ci #j4ej #j4fb #j4gb #j4hf #j4ig #g4jj #j4da #j4eb #j4fc #j4gc #j4hf #j4ig #i4jj #j4dc #j4ed #j4fd #j4gc #j4hf #j4ig ---------------------------------------- ---------- ,the first step in proportioning the cylinder is to compute the approximate mean effective pressure from the assumed initial pressure1 clearance1 and cut-off1 by the method already explained4 ,next assume the piston speed for the type of engine to be designed1 and determine the piston area by the following formula3 #cc1jjj ,h4 ,p4 ,a -----------------------4 ,m4 ,e4 ,p4 x piston speed ,this formula usually gives the diameter of the piston in inches and fractions of an inch1 while it is desirable to make this dimension an even number of inches4 ,this may be done by taking as the diameter the nearest whole number1 and changing the piston speed to correspond4 ,this is done by the use of the following equation4 ,first piston speed x first piston area -------------------------------------- new piston speed4 new piston area ,in calculating the effective piston area1 the area of the piston rod upon one side must be allowed for4 ,the effective or average piston area will then be 7#b;,a - a7_/#b1 in which ,a area of piston1 a area of piston rod4 ,this latter area must be assumed4 ,after assuming a new piston diameter of even inches1 its effective or average area must be used in determining the new piston speed4 ,the length of stroke is commonly proportioned to the diameter of cylinder1 and the piston speed divided by this will give the number of strokes per minute4 ,example3--,find the diameter of cylinder1 length of stroke1 and revolutions per minute for a simple high-speed non-condensing engine of #bjj ,i4 ,h4 ,p41 with the following assumptions3 ,initial pressure1 #ij pounds gage2 clearance1 #g per cent2 cut-off1 #a_/d2 piston speed1 #gjj feet per minute2 length of stroke1 #a4e times cylinder diameter4 ,,table ,,iii4 ,,pressure1 ,,clearance1 ,,cut-,,off ,,and ,,piston ,,speed ,,of ,,steam ,,engines ---------------------------------------- ----------------------------- ,initial ,clearance1 ,cut-off1 ,piston ,type of ,engine ,pressure1 ,per ,cent ,proportion ,speed1 ,feet 7,gage7 of ,stroke per ,minute ---------------------------------------- ----------------------------- ,simple high-speed #hj to #ij #d to #aj #a_/d to #a_/c #fjj to #hjj ,simple medium-speed #hj to #ij #c to #h #a_/d to #a_/c #ejj to #gjj ,simple ,corliss #hj to #ij #a4e to #c4e #a_/d to #a_/c #djj to #fjj ,compound high-speed #acj to #adj #d to #aj #a_/aj to #a_/h #fjj to #hjj ,compound medium-speed #acj to #adj #c to #h #a_/aj to #a_/h #ejj to #gjj ,compound ,corliss #acj to #adj #a4e to #c4e #a_/aj to #a_/h #djj to #fjj ---------------------------------------- ----------------------------- ,by using the rules and formulas in the foregoing1 we have3 ,m4 ,e4 ,p4 7#ij #ae7 x #j4fc - #ag #di pounds4 #cc1jjj x #bjj ,a ------------ #aib4d square inches4 #di x #gjj ,the nearest piston diameter of even inches is #af1 which corresponds to an area of #bja square inches4 ,assume a piston rod diameter of #b-a_/b inches1 corresponding to an area of #d4i square inches1 from which the average or effective piston area is found to be 77#b x #bja7 - #d4i7_/b #aih4e square inches4 ,determining now the new piston speed1 we have3 #gjj x #aib4d ----------- #fgh4e feet per minute4 #aih4e ,assuming the length of stroke to be #a4e times the diameter of the cylinder1 it will be #bd inches1 or #b feet4 ,this will call for #fgh4e _/ #b #cdj strokes per minute1 approximately1 or #cdj _/ #b #agj revolutions per minute4 ,,chapter ,,iii ,,steam ,,engine ,,details ,some of the most important details of a steam engine are those of its valve gear4 ,the simplest form of valve is that known as the plain slide valve1 and as nearly all others are a modification of this1 it is essential that the designer should first familiarize himself with this particular type of valve in all its details of operation4 ,after this has been done1 a study of other forms of valves will be found a comparatively easy matter4 ,the so called ,corliss valve differs radically from the slide valve1 but the results to be obtained and the terms used in its design are practically the same4 ,the valve gear of a steam engine is made up of the valve or valves which admit steam to and exhaust it from the cylinder1 and of the mechanism which governs the valve movements1 the latter usually consisting of one or more eccentrics attached to the main shaft4 ,illustration3 ,fig4 #h4 ,longitudinal ,section of ,slide ,valve with ,ports ,the ,slide ,valve ,fig4 #h shows a longitudinal section of a slide valve with the ports1 bridges1 etc4 ,the valve is shown in mid-position in order that certain points relating to it may be more easily understood4 ,the valve1 ,v1 consists of a hollow casting1 with ends projecting beyond the ports as shown2 the lower face is smoothly finished and fitted to the valve seat ,,ab4 ,in operation it slides back and forth1 opening and closing the ports which connect the steam chest with the cylinder4 ,steam is admitted to the cylinder when either port ,,cd or ,,dc is opened1 and is released when the ports are brought into communication with the exhaust port ,,mn4 ,this is accomplished by the movement of the valve1 which brings one of the cylinder ports and the exhaust port both under the hollow arch ,k4 ,the portions ,,dm and ,,nd of the valve seat are called the bridges4 ,it will be seen by reference to ,fig4 #h that the portions ,,oi and ,,io are wider than the ports which they cover4 ,this extra width is called the lap1 ,,oc being the outside lap and ,,di the inside or exhaust lap4 ,the object of outside lap is that the steam may be shut off after the piston has moved forward a certain distance1 and be expanded during the remainder of the stroke4 ,if there were no outside lap1 steam would be admitted throughout the entire stroke and there would be no expansion4 ,if there were no inside lap1 exhaust would take place throughout the whole stroke1 and the advantages of premature release and compression would be lost4 ,hence1 outside lap affects the cut-off1 and inside lap affects release and compression4 ,a valve has lead when it begins to uncover the steam port before the end of the return stroke of the piston4 ,this is shown in ,fig4 #i1 where the piston ,p is just ready to start on its forward stroke as indicated by the arrow4 ,the valve has already opened a distance equal to the lead1 and the steam has had an opportunity to enter and fill the clearance space before the beginning of the stroke4 ,the lead varies in different engines1 being greater in high-speed than in low-speed types4 ,illustration3 ,fig4 #i4 ,illustration showing ,lead of ,slide ,valve ,illustration3 ,fig4 #aj4 ,diagrammatical ,view of ,eccentric ,the ,eccentric ,the slide valve is usually driven by an eccentric attached to the main shaft4 ,a diagram of an eccentric is shown in ,fig4 #aj4 ,an eccentric is1 in reality1 a short crank with a crank-pin of such size that it surrounds the shaft4 ,the arm of a crank is the distance between the center of the shaft1 and the center of the crank-pin4 ,the throw of an eccentric corresponds to this1 and is the distance between the center of the shaft and the center of the eccentric disk1 as shown at a in ,fig4 #aj4 ,the disk is keyed to the shaft1 and as the shaft revolves1 the center of the disk rotates about it as shown by the dotted line1 and gives a forward and backward movement to the valve rod equal to twice the throw a4 ,illustration3 ,fig4 #aa4 ,relations of ,crank and ,eccentric ,in ,fig4 #aa let ,a represent the center of the main shaft1 ,b the crank-pin to which the connecting-rod is attached 7see ,h1 ,fig4 #a71 and the dotted circle through ,b the path of the crank-pin around the shaft4 ,for simplicity1 let the eccentric be represented in a similar manner by the crank ,ab1 and its path by the dotted circle through b4 ,fig4 #ab shows a similar diagram with the piston ,p and the valve in the positions corresponding to the positions of the crank and eccentric in ,fig4 #aa1 and in the diagram at the right in ,fig4 #ab4 ,the piston is at the extreme left1 ready to start on its forward stroke toward the right4 ,the crank-pin ,b is at its extreme inner position4 ,when the valve is at its mid-position1 as in ,fig4 #h1 the eccentric arm ,ab will coincide with the line ,,ac1 ,fig4 #aa4 ,if the eccentric is turned on the shaft sufficiently to bring the left-hand edge ,o1 ,fig4 #h1 of the valve in line with the edge ,c of the port1 the arm of the eccentric will have moved from its vertical position to that shown by the line ,ab' in ,fig4 #aa4 ,the angle through which the eccentric has been turned from the vertical to bring about this result is called the angular advance1 and is shown by angle ,c,ab' in ,fig4 #aa4 ,the angular advance evidently depends upon the amount of lap4 ,if the valve is to be given a lead1 as indicated in ,fig4 #ab1 the eccentric must be turned still further on the shaft to open the valve slightly before the piston starts on its forward movement4 ,this brings the eccentric to the position ,ab shown in ,fig4 #aa4 ,the angle through which the eccentric is turned to give the necessary lead opening to the valve is called the angle of lead1 and is shown by angle b',ab4 ,by reference to ,fig4 #aa1 it is seen that the total angle between the crank and the eccentric is #ij degrees1 plus the angular advance1 plus the angle of lead4 ,this is the total angle of advance4 ,illustration3 ,fig4 #ab4 ,piston just beginning ,forward ,stroke ,the relative positions of the piston and valve at different periods of the stroke are illustrated in ,figs4 #ab to #af4 ,fig4 #ab shows the piston just beginning the forward stroke1 the valve having uncovered the admission port an amount equal to the lead4 ,the crank is in a horizontal position1 and the eccentric has moved from the vertical an amount sufficient to move the valve toward the right a distance equal to the outside lap plus the lead4 ,the arrows show that steam is entering the left-hand port and is being exhausted through the right-hand port4 ,illustration3 ,fig4 #ac4 ,steam ,port fully ,opened ,in ,fig4 #ac it is seen that the valve has traveled forward sufficiently to open the steam port to its fullest extent1 and the piston has moved to the point indicated4 ,the exhaust port is still wide open1 and the relative positions of the crank and eccentric are shown in the diagram at the right4 ,in ,fig4 #ad the eccentric has passed the horizontal position and the valve has started on its backward stroke1 while the piston is still moving forward4 ,the admission port is closed1 cut-off having taken place1 and the steam is expanding4 ,the exhaust port is still partially open4 ,illustration3 ,fig4 #ad4 ,valve has started on ,backward ,stroke ,illustration3 ,fig4 #ae4 ,both ,steam ,ports ,closed ,in ,fig4 #ae both ports are closed and compression is taking place in front of the piston while expansion continues back of it4 ,release occurs in ,fig4 #af just before the piston reaches the end of its stroke4 ,the eccentric crank is now in a vertical position1 pointing downward1 and exhaust is just beginning to take place through the left-hand port4 ,this completes the different stages of a single stroke1 the same features being repeated upon the return of the piston to its original position4 ,the conditions of lap1 lead1 angular advance1 etc41 pertain to practically all valves1 whatever their design4 ,illustration3 ,fig4 #af4 ,exhaust ,begins ,different ,types of ,valves ,in the following are shown some of the valves in common use1 being1 with the exception of the ,corliss1 modifications of the plain slide valve1 and similar in their action4 ,illustration3 ,fig4 #ag4 ,engine with ,piston ,valve ,double-,ported ,balanced ,valve4--,a valve of this type has already been shown in ,fig4 #b4 ,this valve is flat in form1 with two finished surfaces1 and works between the valve-seat and a plate1 the latter being prevented from pressing against the valve by special bearing surfaces which hold it about #j4jjb inch away4 ,the construction of the valve is such that when open the steam reaches the port through two openings as indicated by the arrows at the left4 ,the object of this is to reduce the motion of the valve and quicken its action in admitting and cutting off steam4 ,illustration3 ,fig4 #ah4 ,section through ,cylinder of ,engine of the ,four-valve ,type ,illustration3 ,fig4 #ai4 ,different ,types of ,corliss ,valves ,piston ,valve4--,the piston valve shown in ,fig4 #ag is identical in its action with the plain slide valve shown in ,fig4 #h1 except that it is circular in section instead of being flat or rectangular4 ,the advantage claimed for this type of valve is the greater ease in fitting cylindrical surfaces as compared with flat ones4 ,the valve slides in special bushings which may be renewed when worn4 ,piston valves are also made with double ports4 ,illustration3 ,fig4 #bj4 ,longitudinal ,section through ,corliss ,engine ,illustration3 ,fig4 #ba4 ,the ,gridiron ,valve ,four-,valve ,type4--,fig4 #ah shows a horizontal section through the cylinder and valves of an engine of the four-valve type4 ,the admission valves are shown at the top of the illustration and the exhaust valves at the bottom1 although1 in reality1 they are at the sides of the cylinder4 ,the advantage of an arrangement of this kind is that the valves may be set independently of each other and the work done by the two ends of the cylinder equalized4 ,the various events1 such as cut-off1 compression1 etc41 may be adjusted without regard to each other1 and in such a manner as to give the best results1 a condition which is not possible with a single valve4 ,gridiron ,valve4--,one of the principal objects sought in the design of a valve is quick action at the points of admission and cut-off4 ,this requires the uncovering of a large port opening with a comparatively small travel of the valve4 ,the gridiron valve shown in ,fig4 #ba is constructed especially for this purpose4 ,this valve is of the four-valve type1 one steam valve and one exhaust valve being shown in the section4 ,both the valve and its seat contain a number of narrow openings or ports1 so that a short movement of the valve will open or close a comparatively large opening4 ,for example1 the steam valve in the illustration has #ab openings1 so that if they are #a_/d inch in width each1 a movement of #a_/d inch of the valve will open a space #ab x #a_/d #c inches in length4 ,illustration3 ,fig4 #bb4 ,the ,monarch ,engine with ,corliss ,valve ,gear4--,a1 ,rod to ,eccentric2 ,b1 ,governor2 ,c1 ,reach ,rod2 ,d1 ,radial ,arm2 ,e1 ,steam ,valve2 ,f1 ,bell-crank2 ,g1 ,wrist ,plate2 ,h1 ,exhaust ,valve2 ,k1 ,dash-pot ,corliss ,valve4--,a section through an engine cylinder equipped with ,corliss valves is shown in ,fig4 #bj4 ,there are four cylindrical valves in this type of engine1 two steam valves at the top and two exhaust valves at the bottom4 ,this arrangement is used to secure proper drainage4 ,the action of the admission and exhaust valves is indicated by the arrows1 the upper left-hand and the lower right-hand valve being open and the other two closed4 ,side and sectional views of different forms of this type of valve are shown in ,fig4 #ai4 ,they are operated by means of short crank-arms which are attached to a wrist-plate by means of radial arms or rods1 as shown in ,fig4 #bb4 ,the wrist-plate1 in turn1 is given a partial backward and forward rotation by means of an eccentric attached to the main shaft and connected to the upper part of the wrist-plate by a rod as indicated4 ,the exhaust valves are both opened and closed by the action of the wrist-plate and connecting rods4 ,the steam valves are opened in this manner1 but are closed by the suction of dash pots attached to the drop levers on the valve stems by means of vertical rods1 as shown4 ,illustration3 ,figs4 #bc to #bf4 ,action of ,corliss ,valve ,gear ,the action of the steam or admission valves is best explained by reference to ,figs4 #bc to #bf4 ,referring to ,fig4 #bc1 ,a is a bell-crank which turns loosely upon the valve stem ,v4 ,the lower left-hand extension of ,a carries the grab hook ,h1 while the upper extension is connected with the wrist-plate as indicated4 ,ordinarily the hook ,h is pressed inward by the spring ,s1 so that the longer arm of the hook is always pressed against the knock-off cam ,c4 ,the cam ,c also turns upon the valve stem ,v and is connected with the governor by means of a reach rod as indicated in ,fig4 #bc and shown in ,fig4 #bb4 ,the drop lever ,b is keyed to the valve stem ,v1 and is connected with the dash pot by a rod as indicated by the dotted line4 ,this is also shown in ,fig4 #bb4 ,the end of the drop lever carries a steel block 7shown shaded in ,fig4 #bc71 which engages with the grab hook ,h4 ,when in operation1 the bell-crank is rotated in the direction of the arrow by the action of the wrist-plate and connecting-rod4 ,as the bell-crank rotates1 the grab hook engages the steel block at the end of the drop lever ,b and lifts it1 thus causing the valve to open1 and to remain so until the bell-crank has advanced so far that the longer arm of the grab hook ,h is pressed outward by the projection on the knock-off cam1 as shown in ,fig4 #bd4 ,the drop lever now being released1 the valve is quickly closed by the suction of the dash pot1 which pulls the lever down to its original position by means of the rod previously mentioned4 ,illustration3 ,fig4 #bg4 ,governor for ,corliss ,engine ,the governor operates by changing the point of cut-off through the action of the cam ,c4 ,with the cam in the position shown in ,fig4 #be1 cut-off occurs earlier than in ,fig4 #bd4 ,should the cam be turned in the opposite direction 7clockwise71 cut-off would take place later4 ,a detailed view of the complete valve mechanism described is shown assembled in ,fig4 #bf1 with each part properly named4 ,a detail of the governor is shown in ,fig4 #bg4 ,an increase in speed causes the revolving balls ,,bb to swing outward1 thus raising the weight ,w and the sleeve ,s4 ,this in turn operates the lever ,l through rod ,r and a bell-crank attachment1 as shown in the right-hand view4 ,an upward and downward movement of the balls1 due to a change in speed of the engine1 swings the lever ,l backward and forward as shown by the full and dotted lines4 ,the ends of this lever are attached by means of reach-rods to the knock-off cams1 this being shown more clearly in ,fig4 #bb4 ,the connections between the lever ,l and cam ,c are such that a raising of the balls1 due to increased speed1 will reduce the cut-off and thus slow down the engine4 ,on the other hand1 a falling of the balls will lengthen the cut-off through the same mechanism4 ,illustration3 ,fig4 #bh4 ,dash-pot for ,corliss ,engine ,illustration3 ,figs4 #bi and #cj4 ,plan and ,longitudinal ,section of ,adjustable ,piston ,mention has already been made of the dash pot which is used to close the valve suddenly after being released from the grab hook4 ,the dash-pot rod is shown in ,fig4 #bf1 and indicated by dotted lines in ,figs4 #bc to #be4 ,a detailed view of one form of dash pot is shown in ,fig4 #bh4 ,when the valve is opened1 the rod attached to lever ,b1 ,figs4 #bc and #bd1 raises the piston ,p1 ,fig4 #bh1 and a partial vacuum is formed beneath it which draws the piston and connecting rod down by suction as soon as the lever ,b is released1 and thus closes the valve suddenly and without shock4 ,the strength of the suction and the air cushion for this piston are regulated by the inlet and outlet valves shown on the sides of the dash pot4 ,engine ,details ,figs4 #bi to #cg show various engine details1 and illustrate in a simple way some of the more important principles involved in steam engine design4 ,illustration3 ,fig4 #ca4 ,a ,typical ,cross-head ,illustration3 ,figs4 #cb and #cc4 ,methods ,commonly ,used for ,taking ,up ,wear in a ,connecting-rod ,a partial cross-section of an adjustable piston is shown in ,fig4 #bi1 and a longitudinal section of the same piston in ,fig4 #cj4 ,the principal feature to be emphasized is the method of automatic expansion employed to take up any wear and keep the piston tight4 ,in setting up the piston a hand adjustment is made of the outer sleeve or ring ,r by means of the set-screws ,,aa4 ,ring ,r is made in several sections1 so that it may be expanded in the form of a true circle4 ,further tightness is secured without undue friction by means of the packing ring ,p which fits in a groove in ,r and is forced lightly against the walls of the cylinder by a number of coil springs1 one of which is shown at ,s4 ,as the cylinder and piston become worn1 screws ,a are adjusted from time to time1 and the fine adjustment for tightness is cared for by the packing ring ,p and the coil springs ,s4 ,the points to be brought out in connection with the cross-head are the methods of alignment and adjustment4 ,a typical cross-head is shown in cross and longitudinal sections in ,fig4 #ca4 ,alignment in a straight line1 longitudinally1 is secured by the cylindrical form of the bearing surfaces or shoes1 shown at ,s4 ,these are sometimes made ,v-shaped in order to secure the same result4 ,the wear on a cross-head comes on the surfaces ,s1 and is taken up by the use of screw wedges ,w1 shown in the longitudinal section4 ,as the sliding surfaces become worn1 the wedges are forced in slightly by screwing in the set-screws and clamping them in place by means of the check-nuts4 ,illustration3 ,fig4 #cd4 ,outboard ,bearing for ,corliss ,type ,engine ,illustration3 ,fig4 #ce4 ,inner ,bearing and ,bed of ,corliss ,engine ,the method commonly employed in taking up the wear in a connecting-rod is shown in ,figs4 #cb and #cc4 ,the wear at the wrist-pin is taken by the so called brasses1 shown at ,b in the illustrations4 ,the inner brass1 in both cases1 fits in a suitable groove1 and is held stationary when once in place4 ,the outer brass is adjustable1 being forced toward the wrist-pin by a sliding wedge which is operated by one or more set-screws4 ,in ,fig4 #cb the wedge is held in a vertical position1 and is adjusted by two screws as shown4 ,the arrangement made use of in ,fig4 #cc has the wedge passing through the rod in a horizontal position1 and adjusted by means of a single screw1 as shown in the lower view4 ,with the arrangements shown1 tightening up the brasses shortens the length of the rod4 ,in practice the wedges at each end of the rod are so placed that tightening one shortens the rod1 and tightening the other lengthens it1 the total effect being to keep the connecting-rod at its original length4 ,a common form of outboard bearing for an engine of the slow-speed or ,corliss type is illustrated in ,fig4 #cd4 ,the various adjustments for alignment and for taking up wear are the important points considered in this case4 ,the plate ,b is fastened to the stone foundation by anchor bolts not shown4 ,sidewise movement is secured by loosening the bolts ,c1 which pass through slots in the bearing1 and adjusting by means of the screws ,s4 ,vertical adjustment is obtained by use of the wedge ,w1 which is forced in by the screw ,a1 as required4 ,the inner bearing and bed piece of a heavy duty ,corliss engine is shown in ,fig4 #ce4 ,the bearing in this case is made up of four sections1 so arranged that either horizontal or vertical adjustment may be secured by the use of adjusting screws and check-nuts4 ,engines of the slide-valve type are usually provided either with a fly-ball throttling governor1 or a shaft governor4 ,a common form of throttling governor is shown in ,fig4 #cf4 ,as the speed increases the balls ,w are thrown outward by the action of the centrifugal force1 and being attached to arms hinged above them1 any outward movement causes them to rise4 ,this operates the spindle ,s1 which1 in turn1 partially closes the balanced valve in body ,b1 thus cutting down the steam supply delivered to the engine4 ,the action of a throttling governor upon the work diagram of an engine is shown in ,fig4 #ch4 ,let the full line represent the form of the diagram with the engine working at full load4 ,now1 if a part of the load be thrown off1 the engine will speed up slightly1 causing the governor to act as described1 thus bringing the admission and expansion lines into the lower positions1 as shown in dotted lines4 ,illustration3 ,fig4 #cf4 ,common ,form of ,throttling ,governor ,the shaft governor is used almost universally on high-speed engines1 and is shown in one form in ,fig4 #cg4 ,it consists1 in this case1 of two weights ,w1 hinged to the spokes of the wheel near the circumference by means of suitable arms4 ,attached to the arms1 as shown1 are coil springs ,c4 ,the ends of the arms beyond the weights are connected by means of levers ,l to the eccentric disk4 ,when the engine speeds up1 the weights tend to swing outward toward the rim of the wheel1 the amount of the movement being regulated by the tension of the springs ,c4 ,as the arms move outward1 the levers at the ends turn the eccentric disk on the shaft1 the effect of which is to change the angle of advance and shorten the cut-off4 ,when the speed falls below the normal1 the weights move toward the center and the cut-off is lengthened4 ,the effect of this form of governor on the diagram is shown in ,fig4 #ci4 ,the full line represents the diagram at full load1 and the dotted line when the engine is under-loaded4 ,illustration3 ,fig4 #cg4 ,shaft ,governor for ,high-speed ,engine ,,chapter ,,iv ,,steam ,,engine ,,economy ,under the general heading of steam engine economy1 such items as cylinder condensation1 steam consumption1 efficiency1 ratio of expansion1 under- and over-loading1 condensing1 etc41 are treated4 ,the principal waste of steam in the operation of an engine is due to condensation during the first part of the stroke4 ,this condensation is due to the fact that during expansion and exhaust the cylinder walls and head and the piston are in contact with comparatively cool steam1 and1 therefore1 give up a considerable amount of heat4 ,when fresh steam is admitted at a high temperature1 it immediately gives up sufficient heat to raise the cylinder walls to a temperature approximating that of the entering steam4 ,this results in the condensation of a certain amount of steam1 the quantity depending upon the time allowed for the transfer of heat1 the area of exposed surface1 and the temperature of the cylinder walls4 ,during the period of expansion the temperature falls rapidly1 and the steam being wet1 absorbs a large amount of heat4 ,after the exhaust valve opens1 the drop in pressure allows the moisture that has collected on the cylinder walls to evaporate into steam1 so that during the exhaust period but little heat is transferred4 ,with the admission of fresh steam at boiler pressure1 a mist is condensed on the cylinder walls1 which greatly increases the rapidity with which heat is absorbed4 ,the amount of heat lost through cylinder condensation is best shown by a practical illustration4 ,one horsepower is equal to #cc1jjj foot-pounds of work per minute1 or #cc1jjj x #fj #a1ihj1jjj foot-pounds per hour4 ,this is equivalent to #a1ihj1jjj _/ #ggh #b1eej heat units4 ,the latent heat of steam at #ij pounds gage pressure is #hha heat units4 ,hence1 #b1bej _/ #hha #b4i pounds of steam at #ij pounds pressure is required per horsepower1 provided there is no loss of steam1 and all of the contained heat is changed into useful work4 ,as a matter of fact1 from #cj to #ce pounds of steam are required in the average simple non-condensing high-speed engine4 ,there are three remedies which are used to reduce the amount of cylinder condensation4 ,the first to be used was called steam jacketing1 and consisted in surrounding the cylinder with a layer of high-pressure steam1 the idea being to keep the inner walls up to a temperature nearly equal to that of the incoming steam4 ,this arrangement is but little used at the present time1 owing both to the expense of operation and to its ineffectiveness as compared with other methods4 ,the second remedy is the use of superheated steam4 ,it has been stated that the transfer of heat takes place much more rapidly when the interior surfaces are covered with a coating of moisture or mist4 ,superheated steam has a temperature considerably above the point of saturation at the given pressure2 hence1 it is possible to cool it a certain amount before condensation begins4 ,this has the effect of reducing the transfer of heat for a short period following admission1 and this is the time that condensation takes place most rapidly under ordinary conditions with saturated steam4 ,this1 in fact1 is the principal advantage derived from the use of superheated steam1 although it is also lighter for a given volume1 and therefore1 a less weight of steam is required1 to fill the cylinder up to the point of cut-off4 ,the economical degree of superheating is considered to be that which will prevent the condensation of any steam on the walls of the cylinder up to the point of cut-off1 thus keeping them at all times free from moisture4 ,the objections to superheated steam are its cutting effect in the passages through which it flows1 and the difficulty experienced in lubricating the valves and cylinder at such a high temperature4 ,the third and most effective remedy for condensation losses is that known as compounding1 which will be treated under a separate heading in the following4 ,multiple ,expansion ,engines ,it has been explained that cylinder condensation is due principally to the change in temperature of the interior surfaces of the cylinder1 caused by the variation in temperature of the steam at initial and exhaust pressures4 ,therefore1 if the temperature range be divided between two cylinders which are operated in series1 the steam condensed in the first or high pressure cylinder will be re-evaporated and passed into the low-pressure cylinder as steam1 where it will again be condensed and re-evaporated as it passes into the exhaust pipe4 ,theoretically1 this should reduce the condensation loss by one-half1 and if three cylinders are used1 the loss should be only one-third of that in a simple engine4 ,in actual practice the saving is not as great as this1 but with the proper relation between the cylinders1 these results are approximated4 ,engines in which expansion takes place in two stages are called compound engines4 ,when three stages are employed1 they are called triple expansion engines4 ,compounding adds to the first cost of an engine1 and also to the friction1 so that in determining the most economical number of cylinders to employ1 the actual relation between the condensation loss and the increased cost of the engine and the friction loss1 must be considered4 ,in the case of power plant work1 it is now the practice to use compound engines for the large sizes1 while triple expansion engines are more commonly employed in pumping stations4 ,many designs of multiple expansion engines are provided with chambers between the cylinders1 called receivers4 ,in engines of this type the exhaust is frequently reheated in the receivers by means of brass coils containing live steam4 ,in the case of a cross-compound engine1 a receiver is always used4 ,in the tandem design it is often omitted1 the piping between the two cylinders being made to answer the purpose4 ,the ratio of cylinder volumes in compound engines varies with different makers4 ,the usual practice is to make the volume of the low-pressure cylinder from #b4e to #c times that of the high-pressure4 ,the total ratio of expansion in a multiple expansion engine is the product of the ratios in each cylinder4 ,for example1 if the ratio of expansion is #d in each cylinder in a compound engine1 the total ratio will be #d x #d #af4 ,the effect of a triple-expansion engine is sometimes obtained in a measure by making the volume of the low-pressure cylinder of a compound engine #f or #g times that of the high-pressure4 ,this arrangement produces a considerable drop in pressure at the end of the high-pressure stroke1 with the result of throwing a considerable increase of work on the high-pressure cylinder without increasing its ratio of expansion1 and at the same time securing a large total ratio of expansion in the engine4 ,in the case of vertical engines1 the low-pressure cylinder is sometimes divided into two parts in order to reduce the size of cylinder and piston4 ,in this arrangement a receiver of larger size than usual is employed1 and the low-pressure cranks are often set at an angle with each other4 ,another advantage gained by compounding is the possibility to expand the steam to a greater extent than can be done in a single cylinder engine1 thus utilizing1 as useful work1 a greater proportion of the heat contained in the steam4 ,this also makes it possible to employ higher initial pressures1 in which there is a still further saving1 because of the comparatively small amount of fuel required to raise the pressure from that of the common practice of #hj or #ij pounds for simple engines1 to #abj to #adj pounds1 which is entirely practical in the case of compound engines4 ,with triple expansion1 initial pressures of #ahj pounds or more may be used to advantage4 ,the gain from compounding may amount to about #ae per cent over simple condensing engines1 taking steam at the same initial pressure4 ,when compound condensing engines are compared with simple non-condensing engines1 the gain in economy may run from #cj to #dj per cent4 ,,table ,,iv4 ,,steam ,,consumption ,,of ,,engines ---------------------------------------- ----------------- ,pounds of ,steam per ,indicated ,horsepower per ,hour ,kind of ,engine ------------------------------- ,non-condensing ,condensing ---------------------------------------- ---------------- ,high-speed #cb #bd ,simple ,medium-speed #cj #bc ,corliss #bh #bb ,high-speed #bf #bj ,compound ,medium-speed #be #ai ,corliss #bd #ah ---------------------------------------- ---------------- ,steam ,consumption and ,ratio of ,expansion ,the steam consumption is commonly called the water rate1 and is expressed in pounds of dry steam required per indicated horsepower per hour4 ,this quantity varies widely in different types of engines1 and also in engines of the same kind working under different conditions4 ,the water rate depends upon the cylinder losses1 which are due principally to condensation1 although the effects of clearance1 radiation from cylinder and steam chest1 and leakage around valves and piston1 form a part of the total loss4 ,table ,,iv gives the average water rate of different types of engines working at full load4 ,the most economical ratio of expansion depends largely upon the type of the engine4 ,in the case of simple engines1 the ratio is limited to #d or #e on account of excessive cylinder condensation in case of larger ratios4 ,this limits the initial pressure to an average of about #ij pounds for engines of this type4 ,in the case of compound engines1 a ratio of from #h to #aj is commonly employed to advantage1 while with triple-expansion engines1 ratios of #ab to #ae are found to give good results4 ,illustration3 ,fig4 #ch4 ,action of ,throttling ,governor on ,indicator ,diagram ,illustration3 ,fig4 #ci4 ,effect of ,shaft ,governor on ,indicator ,diagram ,illustration3 ,fig4 #dj4 ,increasing ,power of ,engine by ,condensing ,illustration3 ,fig4 #da4 ,decreasing ,steam ,consumption by ,condensing ,the thermal efficiency of an engine is the ratio of the heat transformed into work to the total heat supplied to the engine4 ,in order to determine this1 the absolute temperature of the steam at admission and exhaust pressures must be known4 ,these pressures can be measured by a gage1 and the corresponding temperatures taken from a steam table1 or better1 the temperatures can be measured direct by a thermometer4 ,the absolute temperature is obtained by adding #dfa to the reading in degrees ,fahrenheit 7,f474 ,the formula for thermal efficiency is3 ,t#a - ,t#b ----------------- ,t#a in which ,t#a absolute temperature of steam at initial pressure4 ,t#b absolute temperature of steam at exhaust pressure4 ,example3--,the temperature of the steam admitted to the cylinder of an engine is #cdj degrees ,f41 and that of the exhaust steam #bbj degrees ,f4 ,what is the thermal efficiency of the engine8 7#cdj #dfa7 - 7#bbj #dfa7 ,thermal efficiency ------------------------- #j4ae 7#cdj #dfa7 ,the mechanical efficiency is the ratio of the delivered or brake horsepower to the indicated horsepower1 and is represented by the equation3 ,b4 ,h4 ,p4 ,mechanical efficiency -------- ,i4 ,h4 ,p4 in which ,b4 ,h4 ,p4 brake horsepower1 ,i4 ,h4 ,p4 indicated horsepower4 ,all engines are designed to give the best economy at a certain developed indicated horsepower called full load4 ,there must1 of course1 be more or less fluctuation in the load under practical working conditions1 especially in certain cases1 such as electric railway and rolling mill work4 ,the losses1 however1 within a certain range on either side of the normal load1 are not great in a well designed engine4 ,the effect of increasing the load is to raise the initial pressure or lengthen the cut-off1 depending upon the type of governor4 ,this1 in turn1 raises the terminal pressure at the end of expansion1 and allows the exhaust to escape at a higher temperature than before1 thus lowering the thermal efficiency4 ,the effect of reducing the load is to lower the mean effective pressure4 7,see ,figs4 #ch and #ci47 ,this1 in throttling engines1 is due to a reduction of initial pressure1 and in the automatic engine to a shortening of the cut-off4 ,the result in each case is an increase in cylinder condensation1 and as the load becomes lighter1 the friction of the engine itself becomes a more important part of the total indicated horsepower2 that is1 as the load becomes lighter1 the mechanical efficiency is reduced4 ,effect of ,condensing ,so far as the design of the engine itself it concerned1 there is no difference between a condensing and a non-condensing engine4 ,the only difference is that in the first case the exhaust pipe from the engine is connected with a condenser instead of discharging into the atmosphere4 ,a condenser is a device for condensing the exhaust steam as fast as it comes from the engine1 thus forming a partial vacuum and reducing the back pressure4 ,the attaching of a condenser to an engine may be made to produce two results1 as shown by the work diagrams illustrated in ,figs4 #dj and #da4 ,in the first case the full line represents the diagram of the engine when running non-condensing1 and the area of the diagram gives a measure of the work done4 ,the effect of adding a condenser is to reduce the back pressure on an average of #aj to #ab pounds per square inch1 which is equivalent to adding the same amount to the mean effective pressure4 ,the effect of this on the diagram1 when the cut-off remains the same1 is shown by the dotted line in ,fig4 #dj4 ,the power of the engine per stroke is increased by an amount represented by the area enclosed by the dotted line and the bottom of the original diagram4 ,assuming the reduction in back pressure to be #aj pounds1 which is often exceeded in the best practice1 the gain in power by running condensing will be proportional to the increase in mean effective pressure under these conditions4 ,for example1 if the mean effective pressure is #dj pounds when running non-condensing1 it will be increased to #dj #aj #ej pounds when running condensing1 that is1 it is #ej_/dj #a4be times as great as before4 ,therefore1 if the engine develops #ajj ,i4 ,h4 ,p4 under the first condition1 its final power will be increased to #ajj x #a4be #abe ,i4 ,h4 ,p4 under the second condition4 ,fig4 #da shows the effect of adding a condenser and shortening the cut-off to keep the area of the diagram the same as before4 ,the result in this case is a reduction in the quantity of steam required to develop the same indicated horsepower4 ,the theoretical gain in economy under these conditions will run from about #bh to #cj per cent for simple1 and from #bj to #bb per cent for compound engines4 ,the actual gain will depend upon the cost and operation of the condenser which varies greatly in different localities4 ,,chapter ,v ,,types ,,of ,,steam ,,engines ,there are various ways of classifying steam engines according to their construction1 the most common1 perhaps1 being according to speed4 ,if this classification is employed1 they may be grouped under three general headings3 ,high-speed1 from #cjj to #djj revolutions per minute2 moderate-speed1 from #ajj to #bjj revolutions2 and slow-speed1 from #fj to #ij revolutions2 all depending1 however1 upon the length of stroke4 ,this classification is again sub-divided according to valve mechanism1 horizontal and vertical1 simple and compound1 etc4 ,the different forms of engines shown in the following illustrations show representative types in common use for different purposes4 ,the ,ball engine1 as shown in ,fig4 #db1 is a typical horizontal single valve high-speed engine with a direct-connected dynamo4 ,it is very rigid in design and especially compact for the power developed4 ,the valve is of the double-ported type shown in ,fig4 #b1 having a cover plate for removing the steam pressure from the back of the valve4 ,the piston is hollow with internal ribs similar to that shown in ,fig4 #bi1 and is provided with spring packing rings carefully fitted in place4 ,the governor is of the shaft type1 having only one weight instead of two1 as shown in ,fig4 #cg4 ,illustration3 ,fig4 #db4 ,the ,ball ,engine ,the ,sturtevant engine shown in ,fig4 #dc is a vertical high-speed engine of a form especially adapted to electrical work4 ,engines of this general design are made in a variety of sizes1 and are often used on account of the small floor space required4 ,in the matter of detail1 such as valves1 governors1 etc41 they do not differ materially from the high-speed horizontal engine4 ,fig4 #dd illustrates a moderate-speed engine of the four-valve type4 ,these engines are built either with flat valves1 or with positively driven rotary or ,corliss valves1 the latter being used in the engine shown4 ,it will be noticed that the drop-lever and dash-pot arrangement is omitted1 the valves being both opened and closed by means of the wrist-plate and its connecting rods4 ,this arrangement is used on account of the higher speed at which the engine is run1 the regular ,corliss valve gear being limited to comparatively low speeds4 ,all engines of this make are provided with an automatic system of lubrication4 ,the oil is pumped through a filter to a central reservoir1 seen above the center of the engine1 and from here delivered to all bearings by gravity4 ,the pump is attached to the rocker arm1 and therefore easily accessible for repairs4 ,the standard ,harris ,corliss engine shown in ,fig4 #de1 is typical of its class4 ,it is provided with the girder type of frame1 and with an outboard bearing mounted upon a stone foundation4 ,the valve gear is of the regular ,corliss type1 driven by a single eccentric and wrist-plate4 ,the dash pots are mounted on cast-iron plates set in the floor at the side of the engine1 where they may be easily inspected4 ,the governor is similar in construction to the one already described1 and shown in ,fig4 #bg4 ,the four engines so far described are simple engines1 the expansion taking place in a single cylinder4 ,figs4 #df to #dh show three different types of the compound engine4 ,illustration3 ,fig4 #dc4 ,the ,sturtevant ,vertical ,engine ,the engine shown in ,fig4 #df is of a type known as the tandem compound4 ,in this design the cylinders are in line1 the low-pressure cylinder in front of the high-pressure1 as shown4 ,there is only one piston rod1 the high-pressure and low-pressure pistons being mounted on the same rod4 ,the general appearance of an engine of this design is the same as a simple engine1 except for the addition of the high-pressure cylinder4 ,the governor is of the shaft type and operates by changing the cut-off in the high-pressure cylinder4 ,the cut-off in the low pressure cylinder is adjusted by hand to divide the load equally between the two cylinders for the normal load which the engine is to carry4 ,illustration3 ,fig4 #dd4 ,moderate ,speed ,engine of the ,four-valve ,type ,the engine shown in ,fig4 #dg is known as a duplex compound4 ,in this design the high-pressure cylinder is placed directly below the low-pressure cylinder1 as indicated1 and both piston rods are attached to the same cross-head4 ,the remainder of the engine is practically the same as a simple engine of the same type4 ,illustration3 ,fig4 #de4 ,the ,harris ,corliss ,engine ,fig4 #dh shows a cross-compound engine of heavy design1 built especially for rolling mill work4 ,in this arrangement two complete engines are used1 except for the main shaft and flywheel1 which are common to both4 ,the engine is so piped that the high-pressure cylinder exhausts into the low-pressure1 through a receiver1 the connection being under the floor and not shown in the illustration4 ,one of the advantages of the cross-compound engine over other forms is that the cranks may be set #ij degrees apart1 so that when one is on a dead center the other is approximately at its position of greatest effort4 ,selection of an ,engine ,the selection of an engine depends upon a number of conditions which vary to a considerable extent in different cases4 ,among these may be mentioned first cost1 size and character of plant1 available space1 steam economy1 and utilization of the exhaust steam4 ,the question of first cost is usually considered in connection with that of operation1 and items such as interest and depreciation are compared with the saving made through the saving in steam with high priced engines4 ,illustration3 ,fig4 #df4 ,the ,skinner ,tandem ,engine ,illustration3 ,fig4 #dg4 ,american ,ball ,duplex ,compound ,engine ,the principal use of the stationary engine is confined to the driving of electric generators and the furnishing of motive power in shops and factories4 ,for the first of these uses1 in cases where floor space is limited1 as in office buildings1 and where the power does not exceed about #ajj ,i4 ,h4 ,p41 the simple non-condensing high-speed engine is probably employed more than any other type4 ,for larger installations1 a saving may usually be made by the substitution of the moderate-speed four-valve engine4 ,the question of simple and compound engines in this class of work depends largely upon the use made of the exhaust steam4 ,in winter time the exhaust is nearly always utilized in the heating system1 hence steam economy is not of great importance1 and the simple engine answers all purposes at a smaller first cost4 ,in localities where the heating season is comparatively short and fuel high1 there is a decided advantage in using compound engines on account of their greater steam economy when operated within their economical range as regards load4 ,illustration3 ,fig4 #dh4 ,the ,monarch ,corliss ,engine ,in large central plants where low cost of operation is always of first importance1 it is common practice to use the best class of compound condensing engines of moderate or low speed4 ,those equipped with some form of ,corliss valve gear are frequently found in this class of work4 ,in the generation of power for shops and factories1 where there is plenty of floor space1 low-speed engines of the ,corliss type are most commonly used4 ,when space is limited1 very satisfactory results may be obtained by using the moderate-speed four-valve engine4 ,in deciding upon an engine for any particular case1 the problem must be studied from all sides1 and one be chosen which best answers the greatest number of requirements4 ,,chapter ,,vi ,,steam ,,engine ,,testing ,the principal information sought in the usual test of a steam engine is3 #a4 ,the indicated horsepower developed under certain standard conditions4 #b4 ,the friction of the engine1 from which is determined the mechanical efficiency4 #c4 ,the steam consumption per indicated horsepower4 #d4 ,the general action of the valves4 #e4 ,the pressure conditions in the cylinder at different periods of the stroke4 ,the ultimate object of an efficiency test is to determine the foot-pounds of work delivered by the engine per pound of coal burned in the boiler furnaces4 ,the general method of finding the pounds of dry steam evaporated per pound of coal has been treated in ,,machinery',s ,reference ,series ,no4 #fg1 ,boilers1 under the head of ,boiler ,testing4 ,in the present case it is1 therefore1 only necessary to carry the process a step further and determine the foot-pounds of work developed per pound of steam4 ,the apparatus used in engine testing1 in addition to that used in boiler testing1 consists of a steam engine indicator and reducing device for taking diagrams1 and a planimeter for measuring them afterwards4 ,if the test is made independently of the boiler test1 a calorimeter for measuring the amount of moisture in the steam should be added to the outfit4 ,it has already been shown how a diagram may be made to represent graphically the work done in a steam engine cylinder during one stroke of the piston4 ,the diagrams shown thus far have been theoretical or ideal cards constructed from assumed relations of the pressure acting and the distance moved through by the piston4 ,an indicator is a device for making a diagram of what actually takes place in an engine cylinder under working conditions4 ,such a diagram shows the points of admission1 cut-off1 and release1 and indicates accurately the pressures acting upon both sides of the piston at all points of the stroke4 ,a common form of steam engine indicator is shown in ,fig4 #di4 ,it consists of a cylinder ,c which is placed in communication at ,e with one end of the engine cylinder by a proper pipe connection1 provided with a quick opening and closing cock or valve4 ,the cylinder ,c contains a piston1 above which is placed a coil spring of such strength that a given pressure per square inch acting upon the lower side of the piston will compress the spring a definite and known amount4 ,extending through the cap or head of cylinder ,c is a stem attached to the piston below1 and connected by suitable levers with a pencil point ,p4 ,the arrangement of the levers is such that a certain rise of the piston causes the point ,p to move upward in a vertical line a proportional amount4 ,the springs used above the piston vary in strength1 and are designated as #bj-pound1 #dj-pound1 #fj-pound1 etc4 ,a #bj-pound spring is of such strength that a pressure of #bj pounds per square inch1 acting beneath the piston in cylinder ,c1 will raise the pencil point #a inch4 ,with a #dj-pound spring1 a pressure of #dj pounds per square inch will be required to raise the pencil #a inch1 and so on for the other strengths of spring4 ,the hollow drum ,d rotates back and forth upon a vertical stem at its center1 its motion being produced by the string ,h1 which is attached by means of a suitable reducing motion to the cross-head of the engine4 ,the return motion to the drum is obtained from a coil spring contained within it and not shown4 ,the paper upon which the diagram is to be drawn is wound around the drum ,d1 and held in place by the spring clip ,f4 ,in taking an indicator card1 the length of stroke must be reduced to come within the limits of the drum1 that is1 it must be somewhat less than the circumference of drum ,d4 ,in practice1 the diagram is commonly made from #c to #d inches in length4 ,there are a number of devices in use for reproducing the stroke of the engine on a smaller scale4 ,the most accurate consists of a series of pulleys over which the cord passes on its way from the cross-head to the indicator drum4 ,the indicator is connected with the engine cylinder by means of special openings tapped close to the heads and either plugged or closed by means of stop-cocks when not in use4 ,in some cases two indicators are used1 one being connected to each end of the cylinder1 while in others a single indicator is made to answer the purpose by being so piped that it can be connected with either end by means of a three-way cock4 ,after the indicator is connected and the cord adjusted to give the proper motion to the drum1 a card is attached1 after which the three-way cock is opened and steam allowed to blow through the indicator to warm it up4 ,the cock is now closed and the pencil pressed against the drum to get the so-called atmospheric line4 ,the cock is again opened1 and the pencil pressed lightly against the drum during one complete revolution of the engine4 ,the cock is then thrown over to connect the indicator with the other end of the cylinder and the operation is repeated4 ,illustration3 ,fig4 #di4 ,steam ,engine ,indicator ,the indicator card obtained in this way is shown in ,fig4 #ej4 ,it is sometimes preferred to take the diagrams of the two ends on separate cards1 but it is simpler to take them both on the same one1 and also easier to compare the working of the two ends of the cylinder4 ,the analysis of a card for practical purposes is shown in ,fig4 #ea4 ,suppose1 for example1 that the length of the diagram measures #c4f inches2 the distance to the point of cut-off is #a4b inch2 and the distance to the point of release is #c4c inches4 ,then1 by dividing #a4b by #c4f1 the cut-off is found to occur at #a4b _/ #c4f #a_/c of the stroke4 ,release occurs at #c4c _/ #c4f #j4ib of the stroke4 ,compression begins at 7#c4f - #j4e7 _/ #c4f #j4hf of the stroke4 ,the diagrams shown in ,figs4 #ej and #ea are from non-condensing engines1 and the back-pressure line is therefore above the atmospheric line1 as indicated4 ,the indicator diagram gives a means of determining the mean effective pressure1 from which the power of the engine can be found from the previously given equation ,,apln ,i4 ,h4 ,p4 ------4 #cc1jjj ,the method of determining the mean effective pressure is as follows3 ,first measure the area of the card in square inches1 by means of a planimeter 7an instrument described later71 and divide this area by the length in inches4 ,this gives the mean ordinate2 the mean ordinate1 in turn1 multiplied by the strength of spring used1 will give the mean effective pressure in pounds per square inch4 ,for example1 suppose that the card shown in ,fig4 #ea is taken with a #fj-pound spring1 and that the area1 as measured by a planimeter1 is found to be #b4f square inches4 ,dividing the area by the length gives #b4f _/ #c4f #j4gbb inch as the mean ordinate1 and this multiplied by the strength of spring gives a mean effective pressure of #j4gbb x #fj #dc4c pounds per square inch4 ,illustration3 ,fig4 #ej4 ,a ,typical ,indicator ,diagram ,in practice1 diagrams taken from the two ends of the cylinder usually vary more or less1 due to inequalities in the valve action4 ,again1 the effective area of the piston on the crank end is less than that on the head end1 by an amount equal to the area of the piston rod4 ,for these reasons it is customary to compute the mean effective pressure of all the cards separately1 and take1 for use in the formula1 the average of the various computations4 ,the corrected value of the piston area is1 as already stated1 equal to 7#b;,a - a7_/#b1 in which ,a is the area of the piston1 and a the area of the piston rod4 ,substituting these values for ,a and ,p in the formula1 together with the length of stroke and average number of revolutions per minute1 the indicated horsepower is easily computed4 ,in making an ordinary test1 diagrams are taken from both ends of the cylinder at #aj-minute intervals for several hours1 depending upon the accuracy required4 ,the revolutions of the engine are counted for two or three-minute periods each time a pair of cards are taken1 or still better1 an automatic counter is used for the run1 from which the average number of revolutions per minute may be determined4 ,illustration3 ,fig4 #ea4 ,diagram for ,illustrating ,method of ,computation ,the friction of the engine is determined by taking a pair of cards while running light1 that is1 with the belt thrown off1 or the engine uncoupled1 from the dynamo1 if part of a direct-connected outfit4 ,the friction load is then computed in horsepower from the indicator cards1 and subtracted from the indicated horsepower when loaded4 ,thus we obtain the delivered or brake horsepower4 ,the delivered horsepower divided by the indicated horsepower gives the mechanical efficiency4 ,this may be expressed in the form of an equation as follows3 ,i4 ,h4 ,p4 - friction loss ------------------------ mechanical efficiency4 ,i4 ,h4 ,p4 ,planimeter ,the planimeter is an instrument for measuring areas in general1 and especially for measuring the areas of indicator cards4 ,some forms give the mean effective pressure directly1 without computations1 by changing the scale to correspond with the spring used in the indicator4 ,a planimeter of this type is shown in ,fig4 #eb4 ,the method of manipulating this instrument is as follows4 ,set the arm ,,bd equal to the length of the card ,,ef1 by means of the thumb screw ,s1 and set the wheel at zero on the scale1 which must correspond to the spring used in the indicator4 ,next1 place the point ,d at about the middle of the area to be measured1 and set point ,c so that the arm ,,cb shall be approximately at right angles with ,,bd4 ,then move ,d to the upper left-hand corner of the diagram1 and with the left hand move ,c either to the right or left until the wheel comes back exactly to the zero point on the scale2 then press the point firmly into the paper4 ,now1 go around the outline of the diagram with point ,d from left to right1 finishing exactly at the starting point4 ,the mean effective pressure may now be read from the scale opposite the edge of the wheel4 ,when very accurate results are required1 the tracer point ,d may be passed over the diagram several times1 and the reading divided by the number of times it is thus passed around4 ,with short cards1 #c inches and under in length1 it is best to make the arm ,,bd twice the length of the card1 and go around the diagram twice1 taking the reading directly from the scale as in the first case4 ,determining ,steam ,consumption ,when it is desired to determine accurately the water rate of an engine1 a boiler test should be carried on simultaneously with the test upon the engine1 from which the pounds of dry steam supplied may be determined as described in ,,machinery',s ,reference ,series ,no4 #fg1 ,boilers4 ,knowing the average weight of steam supplied per hour for the run1 and the average indicated horsepower developed during the same period1 the water rate of the engine is easily computed4 ,sometimes the average cylinder condensation for a given type and make is known for certain standard conditions4 ,in this case an approximation may be made from an indicator diagram which represents the average operation of the engine during the test4 ,illustration3 ,fig4 #eb4 ,general ,construction of ,planimeter ,a diagram shows by direct measurement the pressure and volume at any point of the stroke1 and the weight of steam per cubic foot for any given pressure may be taken directly from a steam table4 ,the method1 then1 of finding the weight of steam at any point in the stroke is to find the volume in cubic feet1 including the clearance and piston displacement to the given point1 which must be taken at cut-off or later1 and to multiply this by the weight per cubic foot corresponding to the pressure at the given point measured on the diagram4 ,as this includes the steam used for compression1 it must be corrected1 as follows1 to obtain the actual weight used per stroke4 ,take some convenient point on the compression curve1 as ,q1 in ,fig4 #ec2 measure its absolute pressure from the vacuum line ,,ox and compute the weight of steam to this point4 ,subtract this weight from that computed above for the given point on the expansion line1 and the result will be the weight of steam used per stroke4 ,the best point on the expansion line to use for this purpose is just before release1 both because the maximum amount of leakage has taken place1 and also because of the re-evaporation of a portion of the steam condensed during admission4 ,the actual computation of the steam consumption from an indicator diagram is best shown by a practical illustration4 ,example--,let ,fig4 #ec represent a diagram taken from the head end of a #af x #cj-;inch non-condensing engine1 running at a speed of #aej revolutions per minute2 the card is taken with a #fj-pound spring2 the clearance of the engine is #f per cent2 the average cylinder condensation is #bj per cent of the total steam consumption2 the diameter of the piston rod is #c inches4 ,illustration3 ,fig4 #ec4 ,diagram for ,calculating ,steam ,consumption ,measuring the card with a planimeter shows the mean effective pressure to be #dh4b pounds4 ,the area of the piston is #bja square inches2 the area of the piston rod is #g square inches2 hence1 the average piston area 77#b x #bja7 - #g7_/b #aih square inches1 approximately4 ,then #aih x #dh4b x #b4e x #cjj ,i4 ,h4 ,p4 ---------------------- #bag4 #cc1jjj ,in ,fig4 #ec1 ,,gh is the atmospheric line2 ,,ox is the line of vacuum or zero pressure1 drawn so that ,,go #ad4g pounds on the scale2 and ,,oy is the clearance line1 so drawn that ,,on #j4jf ,,nx4 ,the line ,,pq is drawn from ,,ox to some point on the compression line1 as at ,q4 ,from ,c1 a point on the expansion line1 just before release1 the line ,,cf is drawn perpendicular to ,,ox4 ,the following dimensions are now carefully measured from the actual diagram 7not the one shown in the illustration71 with the results given3 ,,ox #c4ga ,,op #j4db ,,nx #c4ej ,,cf #j4ha ,,of #c4bj ,,qp #j4ha ,on the indicator diagram1 being taken with a #fj-pound spring1 all vertical distances represent pounds per square inch1 in the ratio of #fj pounds per inch of height4 ,the stroke of the engine is #cj inches or #b4e feet4 ,the length of the diagram ,,nx is #c4e inches2 hence1 each inch in length represents #b4e_/c4e #j4ga feet4 ,from the above it is evident that vertical distances in ,fig4 #ec must be multiplied by #fj to reduce them to pounds pressure per square inch1 and that horizontal distances must be multiplied by #j4ga to reduce them to feet4 ,making these reductions gives3 ,,ox #b4fc feet4 ,,op #j4cj foot4 ,,nx #b4di feet4 ,,cf #dh4f pounds4 ,,of #b4bg feet4 ,,qp #dh4f pounds4 ,as a card from the head end of the cylinder is taken to avoid corrections for the piston rod1 the area is #bja square inches or #a4d square foot4 ,with the above data the volume and weight of the steam in the cylinder can be computed at any point in the stroke4 ,when the piston is at ,c1 the volume is #a4d x #b4bg #c4ah cubic feet4 ,when the piston is at ,q1 the volume is #a4d x #j4cj #j4db cubic foot4 ,from a steam table the weight of a cubic foot of steam at #dh4f pounds absolute pressure is found to be #j4aaf pounds4 ,therefore1 the weight of steam present when the piston is at ,c is #c4ah x #j4aaf #j4cfi pounds4 ,the weight of steam present when the piston is at ,q is #j4db x #j4aaf #j4jdi pound4 ,that is the weight of steam in the cylinder at release is #j4cfi pound1 and the weight kept at exhaust closure for compression is #j4jdi pound4 ,the weight exhausted per stroke is therefore #j4cfi - #j4jdi #j4cb pound4 ,the number of strokes per hour is #aej x #b x #fj #ah1jjj1 from which the steam accounted for by the diagram is found to be #ah1jjj x #j4cb #egfj pounds1 or #egfj _/ #bag #bf4e pounds per indicated horsepower per hour4 ,if the cylinder condensation for this type of engine is #bj per cent of the total steam consumption1 the water rate will be #bf4e _/ #j4h #cc4a pounds per indicated horsepower per hour4 ,in the present case it has been assumed1 for simplicity1 that the head- and crank-end diagrams were exactly alike1 except for the piston rod4 ,ordinarily1 the above process should be carried out for both head and crank ends1 and the results averaged4