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~cIntroLempor calculationSteam rate calculation
Appendix 1D
Appendix 2`izr83A@@) 2Cylinder diameter (mm)Piston stroke (mm)Wheel diameter (mm)Design speed (km/h)Number of cylindersDesign cut off (%)CALCULATED PARAMETERS,Distance travelled per wheel revolution (mm)Gas mass / steam mass, L/DThe objective of the calculation is to determine the chimney throat area, F1 and Tuyere area, F, by trial and error solution of Equation 9.KL+Trial value of chimney throat diameter (mm)From Porta's formula*Multiply throat area by exit/throat ratio.%Design steam mass flow rate, D (kg/s)Porta's equation 9Gas mass flow rate, L (kg/s)!Steam tuyere nozzle diameter (mm)Equation 9 denominator term^This spreadsheet is intended to provide a solution to Equation 9 of the following publication:
Disclaimers: ;Vary this by trial and error to maximise Tuyere nozzle sizeCoefficient, Diffuser efficiency, Equation term, Notes:#Values in black to be input by user+Values in red are calculated by spreadsheet*2 (Appendix A3 and text of Porta's paper)
0.1 (Text of Porta's paper)0.04 (Text of Porta's paper)#1.9 (Appendix A3 of Porta's paper),0.8 to 0.85 (Appendix A1 of Porta's paper.)Design speed (mm/min)&Admission pressure (% boiler pressure)3Temperature at initial pressure of compression (C)Wheel revolutions, R (rpm)=Specific volume of steam at pressure of admission, Va (m3/kg)45
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120R!First term of Phillipson equation"Second term of Phillipson equation!Third term of Phillipson equation/Steam consumption per cylinder per hour (kg/hr)(Total steam consumption per hour (kg/hr)COMMENTS PARAMETERCross sectional area x stroke!Calculated from cylinder diameterConvert units to cubic metres for convenienceEqual to wheel circumferenceConvert km/hr to mm/min8Divide design speed by distance travelled per revolution$Calculated by Phillipson Equation 618Multiply consumption per cylinder by number of cylinders
INPUT DATALocomotive GeometryOperating ParametersCylinder ParametersSteam Parameters'Calculated  From % value input by userAdmission temperature (C)EUser to input from steam tables at admission pressure and temperatureRUser to input from steam tables at pressure and temperature of initial compression%Clearance volume (% cyl swept volume)1Clearance volume, c (decimal of cyl swept volume)AVolume swept to point of cut off, v (decimal of cyl swept volume)FVolume from point of compression to end of stroke (% cyl swept volume)RVolume from point of compression to end of stroke, x (decimal of cyl swept volume) Calculated  From design cut off$Calculated  From % clearance volume&Calculated  From % compression volume%Steam consumption per minute (kg/min)#Steam consumption per second (kg/s)Alternative units (kg/min)ResultsCalculation Steps.Range suggested by Phillipson: 1920 psi (abs)Case 1Case 2Case 3Case 4_This spreadsheet is intended to provide a solution to Equation 61 of the following publication:v4 (Appendix A1 of Porta's paper.) Note that this may not be achievable in practice due to loading gauge constraints.BTypical value estimated from published indicator diagram data: 15%Exhaust System ParametersFlow Parameters#Cylinder cross sectional area (mm2)!"&Individual cylinder swept volume (mm3)$%(Individual cylinder swept volume, V (m3)&'
{(v+c)V} / Va
{(x+c)V} / Vc'Calculated  Steam mass flow rate x L/DChimney throat area, F1 (m2)Chimney exit area, Fs, (m2)$Ideal diffuser outlet area, F0, (m2)"#D2v'F1(Draught) Equation 9 denominator termSteam tuyere area, F (m2)#Calculate area from throat diameterRequired smokebox vacuum Total area of the Lempor nozzlesDDiameter of an individual Lempor nozzle  Assumes a 4 nozzle system.PROJECT DATALocomotive DescriptionDesignerDate3Mass flow rate of steam through the exhaust system.^There are various methods of determining the mass flow rate of steam, including the following:HTechnical specification of an existing locomotive with known parameters.4Experimental measurements on an existing locomotive.wNo warranties or guarantees are given as to the correctness or appropriateness of the calculations in this spreadsheet.lAll input data, and all interpretations and applications of the results, are the responsibility of the user.Locomotive Description: Designer:Date:"E. A. PHILLIPSON, 1936, "Steam Locomotive Design: Data and Formulae", Pub. Camden Miniature Steam Services, ISBN No. 0953652394" Specific volume of gas, b (m3/kg)
+ Specific volume of exhaust steam, (m3/kg)&'
Coefficient, b,Chimney exit area/chimney throat area, Fs/F1()
+Boiler pressure (MPa gauge)_"THEORY OF THE LEMPOR EJECTOR AS APPLIED TO PRODUCE DRAUGHT IN STEAM LOCOMOTIVES", L.D. PORTA, BUENOS AIRES, 1974By using this spreadsheet the user consents to take full responsibility for all costs and consequences arising directly and/or indirectly $from any application of the results.Admission pressure (MPa abs))Initial pressure of compression (MPa abs)Design draught (Pa)Required smokebox vacuum.?Calculations to determine the evaporation rate from the boiler.dThe required smokebox vacuum can similarly be determined by various methods including the following:Blast nozzle size.Chimney throat size.ITechnical specifications of an existing locomotive with known parameters.OFirst principle calculations based on the required gas flow through the boiler.Date: 1st November 2005Lempor Calculation Spreadsheet"Steam Rate Calculation SpreadsheetTuyere AreaIndividual Nozzle DiameterTrial Value from cell B40*This chart calculates values for the graphValue offset percentagejPorta's equation expresses these sizes as areas. For the user's convenience, the worksheet converts areas to diameters, on the assumption that the system comprises a single chimney with four blast nozzles. For a multiple chimney system, the user will need to compute the chimney throat and blast nozzle diameters from the area data generated by the worksheet. %The following input data is required:Caution:Note:MA trial diameter for the gas mixing chamber and the small end of the chimney.lThe "steam rate calculation worksheet" determines the steam flow rate per second through the exhaust system.TThe admission temperature should take into account the superheater if one is fitted.NSteam consumption calculations based on the cylinder volume, wheel diameter, speed, assumed cutoff, etc. This method assumes that the boiler is capable of providing the volume of steam to be consumed. The Steam Rate worksheet provides an approximate method of estimating the steam consumption rate using this philosophy. See below.dThe "Lempor Calculation" worksheet determines the following basic dimensions of the exhaust system:zFor full size locomotives, Wardale (Ref 4) and Chapelon (Ref 5) provide smokebox vacuum data for various locomotive types.The worksheet uses a method published by E. A. Phillipson (Ref 7) that requires the user to input the following information:_The detail design of the components for an actual Lempor Ejector installation requires several dimensions not calculated by this worksheet. A nonmathematical explanation of the ejector and the additional dimensions, written to assist the Live Steam enthusiast and Model Engineer, has been published by Michael Guy and is available on the web (Ref 8).Camden Miniature Steam ServicesAttention is therefore brought to the work of J.J.G. Koopmans (Ref 3) which may provide a method of calculating multiple chimney installation sizes when the values for a single chimney are known.The Ultimate Steam Page<REFERENCES & HYPERLINKSOTHER LINKSGMartyn Bane's Steam & Travel Pages: "Modern and Modernised Steam Locos"The Lempor Ejector CalculatorVValues in black to be input by user. Bold print indicates principal user input values.%/NRef 8/ Michael's Locomotive Pages: "A Lempor Exhaust Ejector for the Garratt".{Ref 7/ "Steam Locomotive Design: Data and Formulae", E.A. Phillipson, Camden Miniature Steam Services, ISBN # 09536523946Ref 6/ Michael's Locomotive Pages: "Vacuum Test Page".eRef 5/ "La Locomotive A Vapeur" Andre Chapelon, Camden Miniature Steam Services, ISBN # 0953652300mRef 4/ "The Red Devil and Other Tales from the Age of Steam" D. Wardale, Pub. By Author, ISBN # 0952999803[Ref 3/ J.J.G. Koopmans "A Theory for the Design of Multiple Exhausts for Steam Locomotives"GRef 2/ Ing. L. D. Porta's technical paper describing his Lempor Ejector0Ref 1/ Michael's Locomotive Pages: "Index page".If room is available for a tall stack (e.g. on a narrow gauge locomotive) this value may exceed 4 to accommodate the recommended 10 degree included diffuser angle and the available height. Similarly, if headroom is short, the value may be less than 4.NChemicaLogic's SteamTab Companion  a free downloadable Steam Table Calculator2EngNet Metric Conversion Calculator Selection pageEngNet Tips and Tools page/Use superheater output temperature if so fittedThe specific volume of steam is required in two places. These values can be obtained from steam tables or via the web, see "Useful Tools" below.
Useful Tools wThe authors of this worksheet have no connection with the following companies but have found these pages to be helpful.CONTACT INFORMATIONlemporcalculator@ca.inter.net5The authors would like to thank the following people:=Nigel Day for kindly answering a number of emailed questions.2Joe Dunham for MS Excel consulting to Michael Guy.+LEMPOR EXHAUST SIZING CALCULATION WORKSHEET STEAM RATE CALCULATION WORKSHEETThe engine geometry. The locomotives cylinder bore and stroke, wheel diameter and the number of cylinders used. Assumes all cylinders are of the same diameter.#_The operating parameters. The maximum speed of the locomotive and the designed maximum cutoff.#`The cylinder parameters section allows "tweaking" clearance volume etc to suit specific designs.#]The steam parameters section accepts boiler and cylinder admission pressures and temperature.#Admission pressure (MPa gauge)7Calculated  add atmospheric pressure to gauge pressured Input Data column shows terms {b, etc} as used by Porta and units (m3/kg) as used in this workbook. !
EF
0 Specific volume of steam/gas mixture, 1 (m3/kg)+,
Rev 1.1Nov 16 2005Numerical Calculation CheckLocomotive DataSAR Modified 25NCSAR Modified 19DSource of dataND Wardale, The Red Devil and Other Tales from the Age of Steam, Tables 26 & 27ND Wardale, The Red Devil and Other Tales from the Age of Steam, Tables 19 & 20,Steam flow rate through blast nozzle (kg/hr)+Steam flow rate through blast nozzle (kg/s)!Total chimney choke area, F1, cm2+,  Total chimney choke area, F1, m2+, Total chimney exit area, Fs, cm2+,Total chimney exit area, Fs, m2+,Fs/F1+*+$Total blast nozzle tip area, F, cm2 "#*#Total blast nozzle tip area, F, m2 !"*Design smokebox vacuum, PaLempor Calculator OutputDiscrepancy, %Model Locomotive DataChimney Choke Chimney exit
Stack typeStraight73mmMixing chamber or petticoatNon38mm102mmBlast nozzle typeSingle hole 3/8"
57mm water
51mm water127mm water% Change38mm x 76mmBlast pipe backpressure%Above manometer range of 178mm water.R. Marsh Romulus Case 1Modified Romulus Case 2Modified Romulus Case 34hole diverging @ 9deg. 1/4" diameter holes.
APPENDIX 1TThis workbook is copyright Richard Stuart & Michael Guy, all rights reserved 2005.PComparison between asdesigned draft and Lempormodified draft from track tests.5Existing Locomotive believed true to original design.DWith Lempor Ejector as calculated by the spreadsheet without tuning.310 degree taper Lempor Ejector with mixing chamber.FWith same ejector chimney but original sized single hole blast nozzle.Track Test ResultsMaximum Draft at 1214 km/hr.Not measured, assumed to be similar to case 3.6Units (kg/s) Enter this value in Lempor sheet cell B36rSteam flow through the exhaust system per second. Take the value from Steam Rate Sheet line 66.5Lower than case 3, but not quantified during testing.hCase 1 is based on SAR modified 25NC, case 2 on SAR 19D. Case 3 for 71/4" gauge Romulus miniature loco.
Disclaimers: The authors hope that this workbook will be of interest and of use to the model engineering community worldwide. If you use it to build or modify a model or indeed, a fullsized locomotive, we would be interested to hear about it and to see your photographs.Your feedback, photographs and suggestions for improvements or corrections are requested and welcomed at this email address:ACKNOWLEDGEMENTSOTrevor Heath for kindly offering to host this work on his Livesteaming.com site#The smokebox vacuum for model engineering scale locomotives is much lower than full size. Experimental data from measurements on two 7.25" gauge locomotives with conventional exhaust systems has been published by Michael Guy (Ref 6). 735 Pa may be used as a starting point for large models.8A web page documenting these track test results is here.ENote regarding Line 33: Chimney exit area/chimney throat area, Fs/F1.Engine speed, valvegear cutoff and steam "specific volume" input numbers make a real difference to the sheet output steam consumption figure in line 66. If the "Lempor calculation sheet" results are to be meaningful, these inputs must be realistic and accurate.Imperial conversions lb/secondinchesInch H2O71/4" gauge Romulus.R. MarshNovember 20th 2005)Y*+[>`./M0N1wD3 4t5!\7
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Attention is drawn to the disclaimers printed on the Lempor and Steam Rate calculation worksheets.
It is considered that others in the live steam community will have the knowledge and experience to make corrections and improvements to the spreadsheet. Such corrections and improvements are welcomed, provided that all revised versions of the spreadsheet are clearly marked to identify changes and avoid confusion between versions, and that all improvements are freely shared within the live steam model engineering community. Initial releases of the workbook will have protection turned on and passworded to prevent accidental changes. If you wish to try to make improvements or alter the math for your own purposes, please contact us at the address below for an open version.< (%w&V~~
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The workbook is split into the following sheets:
 Introduction.
 Lempor exhaust sizing calculation. (Use this sheet to design the ejector once you know the steam flow rate)
 Steam mass flow rate calculation. (Use this sheet to estimate the steam flow rate of your engine)
 Appendix 1 of explanatory notes, cautions and hyperlinks.
 Appendix 2, tables of locomotive data used in calculation verifications.<(&
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%0<&CONDITIONS OF USE
Attention is drawn to the disclaimers printed on the Lempor and Steam Rate calculation worksheets.
It is considered that others in the live steam community will have the knowledge and experience to make corrections and improvements to the spreadsheet. Such corrections and improvements are welcomed, provided that all revised versions of the spreadsheet are clearly marked to identify changes and avoid confusion between versions, and that all improvements are freely shared within the live steam model engineering community. Initial releases of the sheet will have protection turned on and passworded to ensure clean downloads. If you wish to try to make improvements or alter the math for your own purposes, please contact us at for an open version.<0(%w&%&%>@8887;;yK1/ Michael's Locomotive Pages_parentyKRhttp://home.ca.inter.net/~mguy/index.htm@@yK/6/ Michael's Locomotive Pages Vacuum Test Page_parentyKthttp://home.ca.inter.net/~mguy/vacuum_testing_romulus.htmFFyK Camden Miniature Steam Services_parentyK8http://www.camdenmin.co.uk/d==yKX3/ J.J.G. Koopmans "A Theory for the Design of Multiple Exhausts for Steam Locomotives"_parentyKhhttp://www.trainweb.org/tusp/koopmans/koopmans.html4<<yKD2/ Ing. L. D. Porta's technical paper describing his Lempor Ejector_parentyK`http://www.trainweb.org/tusp/lempor/lempor.htmlGGyKThe Ultimate Steam Page_parentyKPhttp://www.trainweb.org/tusp/index.htmlFBByKI8/ Michael's Locomotive Pages: A Lempor Exhaust Ejector for the Garratt._parentyKhhttp://home.ca.inter.net/~mguy/A Lempor Exhaust.htmHHyK#Martyn Bane's Steam & Travel Pages_parentyKzhttp://www.martynbane.co.uk/modernsteam/modernsteamlocos.htmOOyKEngNet Tips and Tools page._parentyK\http://www.engnetglobal.com/tips/default.aspxQQyK4EngNet Metric Conversion Calculator Selection page._parentyKZhttp://www.engnetglobal.com/tips/convert.asp`SSyKOChemicaLogic's SteamTab Companion  a free downloadable Steam Table Calculator_parentyKvhttp://www.chemicalogic.com/steamtab/companion/default.htm
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<A Note regarding these results.
Separate work was done to check the steam flow output against David Wardale's results. The steam flow output given by the steam rate sheet cannot be used directly because about 17.5% of the steam generated by the 25NC was tapped off for the feedwater heater and GPCS.
This means that the steam flow output should be about 7.8kg/s to match Wardale's 6.43kg/s through the blast nozzles.< >@*7yK.A web page documenting these results is here.yKthttp://home.ca.inter.net/~mguy/vacuum_testing_romulus.htm
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՜.+,D՜.+,X PXdlt
e IntroLempor calculationSteam rate calculationAppendix 1Appendix 2WorksheetsX
X5=% A I _PID_HLINKSDM_Links_Updated_AdHocReviewCycleID_EmailSubject
_AuthorEmail_AuthorEmailDisplayName_PreviousAdHocReviewCycleID _ReviewingToolsShownOnceANH,%mailto:lemporcalculator@ca.inter.netf
;http://www.chemicalogic.com/steamtab/companion/default.htmU\ http://www.engnetglobal.com/tips/convert.aspVC.http://www.engnetglobal.com/tips/default.aspxS=http://www.martynbane.co.uk/modernsteam/modernsteamlocos.htm5k4http://home.ca.inter.net/~mguy/A Lempor Exhaust.htm/3(http://www.trainweb.org/tusp/index.html`0http://www.trainweb.org/tusp/lempor/lempor.html.c4http://www.trainweb.org/tusp/koopmans/koopmans.htmlfehttp://www.camdenmin.co.uk/^:http://home.ca.inter.net/~mguy/vacuum_testing_romulus.htmG)http://home.ca.inter.net/~mguy/index.htm^:http://home.ca.inter.net/~mguy/vacuum_testing_romulus.htmorBSPREADSHEETRICHARD.STUART@woodside.com.auStuart, Richard R.srtua
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~Root Entry FٮEWorkbook[Revision LogSummaryInformation(DocumentSummaryInformation8