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MathGroup Archive 2005

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Re: legend scaling

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54476] Re: [mg54446] legend scaling
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Mon, 21 Feb 2005 03:44:44 -0500 (EST)
  • References: <20050220154315.PYDF5415.lakermmtao08.cox.net@smtp.east.cox.net>
  • Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup,

Following Bob Hanlon's suggestion, I came up with the following modifications:

imgscale = 1.1
ImageSize -> 600 imgscale, LegendSize -> {1.6, 0.5} imgscale^-1,
LegendPosition -> {-.8 imgscale^-1, -1.25 imgscale^-(GoldenRatio^-2)}

My method essentialy takes the LegendSize that is known to work and
scales it with the inverse of the new image scale. This does not work
properly at image sizes much smaller than 600 because the width of my
legend *text* begins to be wider than the picture.

The LegendPosition is set to that it will be centered as the
LegendSize changes, but will remain a fixed distance below the graph.
x scaling in the LegendPosition comes into play because the control
point for the LegendPosition is in the bottom left corner of the
legend. The LegendPosition y scaling is an empirical relation; it does
not work for drastic changes in image scale -- this is one area for
improvement.

Regards,

On Sun, 20 Feb 2005 10:43:15 -0500, Bob Hanlon <hanlonr at cox.net> wrote:
> 1. Use a LegendLabel so that you can shorten the individual legends.
> 2. Scale the LegendSize and LegendPosition with the ImageSize.
> 3. Wrap the y AxesLabel
> 
> If this is not what you want it should at least suggest an approach.
> 
> Bob Hanlon
> 
> imSize = 400;
> EngineTorqueVsEngineSpeedData =
>     Transpose[{# 2?/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 -> {{"Rolling", "", "Radius"},
>       {"Final", "Drive", "Reduction", "Ratio"}}]
> TopGearNVRatio =
>     EngineTorqueVsEngineSpeedData[[-1, 1]]/CarSpeedAtTopEngineSpeed /.
>       TransmissionReductionRatio -> 1;
> Needs["Graphics`"];
> MultipleListPlot[
>     Append[#, Level[#, {Length@Dimensions@#} - 1] &@
>                             ReplaceAll[#, Line[pts_] :>
>                                 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 -> 1/1000, s -> 1/3600} /.
>               TransmissionReductionRatio -> 1) &@Map[
>                 ReleaseHold@ReplacePart[Function[{CarSpeedDummyVariable},
> Null],
>               Apply[{Hold[
>               CarSpeedDummyVariable /. EngineSpeed -> #1], \
> DrivelineEfficiency[TransmissionReductionRatio] #2} &,
>               EnginePowerVsEngineSpeedData, {1}], 2], CarSpeed, {2}],
>     PlotJoined -> True,
>     SymbolShape -> Append[#, None] &@
> 
>                      Take[#, \
> Length[RollingRadius]*Length[FinalDriveReductionRatio]]
> &@Apply[PlotSymbol[#1,
>                    Filled -> #2] &, #, {1}] &@Flatten[#, 1] &@
>       Outer[List, {Box, Diamond, Star, Triangle}, {True, False}], PlotLegend \
> -> Append[#, "Road Load"] &@Level[
>         Outer["Radius: " <> ToString[#1 /. m -> 100 cm] <>
>               ", Ratio: " <> ToString[#2] &,
>           RollingRadius, FinalDriveReductionRatio], {2}],
>     ImageSize -> imSize,
>     LegendSize -> {450, 300}/imSize,
>     LegendPosition -> {-250, -5/8imSize - 320}/imSize,
>     LegendSpacing -> -.3,
>     LegendTextSpace -> Automatic,
>     LegendLabel -> "     Rolling Radius & \nFinal Drive Reduction Ratio",
>     AxesLabel -> {"Speed\n(kph)", "Power\n(kW)"},
>     PlotLabel -> "Top Gear Power Curves and Road Load"];
> 
> >
> > From: Chris Chiasson <chris.chiasson at gmail.com>
To: mathgroup at smc.vnet.net
> > Date: 2005/02/20 Sun AM 12:10:48 EST
> > To: mathgroup at smc.vnet.net
> > Subject: [mg54476] [mg54446] legend scaling
> >
> > 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[*){2.95,3.5
> 5,
> >       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
> >
> >
> 
> 


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


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