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legend scaling

• To: mathgroup at smc.vnet.net
• Subject: [mg54446] legend scaling
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sun, 20 Feb 2005 00:10:48 -0500 (EST)
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup,

Below, I have attached code that is part of one of my homework
assignments in my powertrain class. The code contains all input
statements up to and including a graph I am working on. I mapped
steady state 100% throttle engine power to top gear vehicle speed for
different drivetrain configurations. I superimposed the road load
power onto the same graph. My concern is with the legend below the
graph. If I change the ImageSize->600 argument in the last command,
the legend box becomes larger or smaller. How do I make sure that no
matter what size I choose for the ImageSize, that the legend always
stays nicely wrapped around the legend text? Thank you in advance for
your valuable time.

EngineTorqueVsEngineSpeedData=
    Transpose[{# 2\[Pi]/60 (rad)/s&/@{1000,1400,2100,2800,3500,4200,4900,5300,
            5700},{61.0,67.6,73.7,78.5,80.9,77.3,76.2,73.3,68.7} kg m^2/s^2/
            rad}];
EnginePowerVsEngineSpeedData={#1,#1 #2}&[Sequence@@#]&/@
      EngineTorqueVsEngineSpeedData;
EnginePowerVsEngineSpeed=
    MapAt[Evaluate,(Interpolation[{#1 (rad/s)^-1,#2 (kg m^2/s^3)^-1}&[
                      Sequence@@#]&/@
                  EnginePowerVsEngineSpeedData][# (rad/s)^-1]kg m^2/s^3&),1];
DrivelineEfficiency[TransmissionReductionRatio_]=
    1-(0.06+TransmissionReductionRatio^1.5/100);
FinalDriveReductionRatio=(*Interval[{Min[#],Max[#]}&@Rationalize[*){2.95,3.55,
      3.73}(*]]*);
RollingRadius=(*Interval[*){300/1000 ,310/1000}(*]*) m;
RollingResistanceCoefficient=0.015;
CoefficientOfDrag=0.335;
Area=2 m^2;
g=9.81 m/s^2;
CurbWeight=g 1350 kg;
AirDensity=100000/(286.9*298.15) (kg/m^3);
RoadLoadPower=
    Function[{CarSpeed,GradeAngle},
      CarSpeed*(1/2*AirDensity*CarSpeed^2*CoefficientOfDrag*Area+
            RollingResistanceCoefficient*CurbWeight*Cos[GradeAngle]+
            CurbWeight*Sin[GradeAngle])];
N[DesiredTopSpeed=140 km/h*1000 m/km/(3600 s/h)];
Outer[Times,RollingRadius,
    1/rad/TransmissionReductionRatio/FinalDriveReductionRatio];
CarSpeed=Outer[Times,RollingRadius,
      EngineSpeed/rad/TransmissionReductionRatio/FinalDriveReductionRatio];
CarSpeedAtTopEngineSpeed=
    CarSpeed/.EngineSpeed->EngineTorqueVsEngineSpeedData[[-1,1]];
TypeBTopSpeedDifference=DesiredTopSpeed-CarSpeedAtTopEngineSpeed;
LastGearReductionRatioSolution=
    Map[Solve[# ==0,TransmissionReductionRatio][[1]]&,
      TypeBTopSpeedDifference,{2}];
DisplayLastGearReductionRatio=
    Array[junk,Drop[Dimensions[LastGearReductionRatioSolution],-1]+1];
DisplayLastGearReductionRatio[[
      Sequence@@(Range[
                2,#]&/@(Drop[
                  Dimensions[LastGearReductionRatioSolution],-1]+1))]]=
    TransmissionReductionRatio/.LastGearReductionRatioSolution;
DisplayLastGearReductionRatio[[Range[2,#]&[Length[RollingRadius]+1],1]]=
    RollingRadius;
DisplayLastGearReductionRatio[[1,
      Range[2,#]&[Length[FinalDriveReductionRatio]+1]]]=
    FinalDriveReductionRatio;
DisplayLastGearReductionRatio[[1,1]]="4th Gear";
TableForm[DisplayLastGearReductionRatio//N,
  TableHeadings\[Rule]{{"Rolling","","Radius"},{"Final","Drive","Reduction",
        "Ratio"}}]
TopGearNVRatio=
    EngineTorqueVsEngineSpeedData[[-1,1]]/
        CarSpeedAtTopEngineSpeed/.TransmissionReductionRatio\[Rule]1;
Needs["Graphics`MultipleListPlot`"]
MultipleListPlot[
  Append[#,Level[#,{Length@Dimensions@#}-1]&@
                          ReplaceAll[#,Line[pts_]\[RuleDelayed]List/@pts]&@
                      First@Block[{$DisplayFunction=Identity},
                          ReleaseHold[#]]&@
                  Hold[Plot[
                      RoadLoadPower[CarSpeed*1000 m/(3600 s),0]/.kg m^2/s^3->
                            W/.W->1/1000,{CarSpeed,0,160}]]]&@
            Level[#,{2}]&@(#/.kg m^2/s^3->W/.W->1/1000/.{m\[Rule]1/1000,
                s\[Rule]1/3600}/.TransmissionReductionRatio\[Rule]1)&@
    Map[ReleaseHold@
        ReplacePart[Function[{CarSpeedDummyVariable},Null],
          Apply[{Hold[CarSpeedDummyVariable/.EngineSpeed\[Rule]#1],
                DrivelineEfficiency[TransmissionReductionRatio] #2}&,
            EnginePowerVsEngineSpeedData,{1}],2],CarSpeed,{2}],
  PlotJoined\[Rule]True,
  SymbolShape\[Rule]Append[#,None]&@
                Take[#,Length[RollingRadius]*
                    Length[FinalDriveReductionRatio]]&@
            Apply[PlotSymbol[#1,Filled\[Rule]#2]&,#,{1}]&@Flatten[#,1]&@
    Outer[List,{Box,Diamond,Star,Triangle},{True,False}],
  PlotLegend\[Rule]Append[#,"Road Load"]&@
    Level[Outer[
        "Rolling Radius: "<>ToString[#1/.m\[Rule]100 cm]<>
            ", Final Drive Reduction Ratio: "<>ToString[#2]&,RollingRadius,
        FinalDriveReductionRatio],{2}],ImageSize\[Rule]600,
  LegendSize\[Rule]{1.6,0.5},LegendPosition\[Rule]{-.75,-1.25},
  LegendSpacing\[Rule]-.3,LegendTextSpace\[Rule]Automatic,
  AxesLabel\[Rule]{"Speed (kph)","Power (kW)"},
  PlotLabel->"Top Gear Power Curves and Road Load"]

Regards,
-- 
Chris Chiasson
Kettering University
Mechanical Engineering
Graduate Student
1 810 265 3161

• Follow-Ups:
  • Re: legend scaling
    • From: Chris Chiasson <chris.chiasson@gmail.com>