Difference between revisions of "Right Hand Wall"

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(Created page with "The right hand wall This same process can be applied to the side walls for the detector. For the sidewalls, we have approximated them as lines following the equation <center><…")
 
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The right hand wall
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This same process can be applied to the side walls for the detector.  For the sidewalls, we have approximated them as lines following the equation
 
This same process can be applied to the side walls for the detector.  For the sidewalls, we have approximated them as lines following the equation
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<center><math>r \mapsto {cot 29.5^{\circ}\ y + 0.09156, y, 0}</math></center>
 
<center><math>r \mapsto {cot 29.5^{\circ}\ y + 0.09156, y, 0}</math></center>
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<center><math>t \mapsto {cos 29.5^{\circ}\ t + 0.09156, t sin\ 29.5^{\circ} , 0}</math></center>
 
<center><math>t \mapsto {cos 29.5^{\circ}\ t + 0.09156, t sin\ 29.5^{\circ} , 0}</math></center>
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(x''
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y''
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z''
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)=(cos 6\[Degree] -sin 6\[Degree] 0
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sin 6\[Degree] cos 6\[Degree] 0
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0 0 1
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) . (x'
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y'
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z'
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)
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(x''
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y''
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z''
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)=(cos 6\[Degree] -sin 6\[Degree] 0
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sin 6\[Degree] cos 6\[Degree] 0
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0 0 1
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) . (t cos 29.5\[Degree]+0.09156
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t sin 29.5\[Degree]
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0
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)
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(x''
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y''
 +
z''
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)= (0.09156cos 6 \[Degree]+t cos 6 \[Degree]cos 29.5\[Degree]-t sin 6 \[Degree]sin 29.5\[Degree]
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t cos 6 \[Degree]sin 29.5\[Degree]+0.09156 sin 6 \[Degree]+t cos 29.5\[Degree]sin 6 \[Degree]
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0
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)
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 +
(x''
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y''
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z''
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)= (0.09156cos 6 \[Degree]+t (cos 6 \[Degree]cos 29.5\[Degree]- sin 6 \[Degree]sin 29.5\[Degree])
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0.09156  sin 6 \[Degree]+t (sin 6 \[Degree] cos 29.5\[Degree]+cos 6 \[Degree]sin 29.5\[Degree])
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0
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)
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Using the equation for y'' we can solve for t
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<center><math>y''=0.09156\  sin\ 6^{\circ}+t (sin 6 \[Degree] cos 29.5^{\circ}+cos 6 ^{\circ}sin 29.5^{\circ}) -> t=(y''-0.09156  sin 6 ^{\circ})/(sin 6^{\circ} cos 29.5^{\circ}+cos 6^{\circ}sin 29.5^{\circ})</math></center>
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Substituting this into the expression for x''
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<center><math>x''=0.09156cos 6^{\circ}+t (cos 6^{\circ}cos 29.5^{\circ}- sin 6^{\circ} sin 29.5^{\circ})=0.09156cos 6 ^{\circ}+((y''-0.09156  sin 6^{\circ})/(sin 6^{\circ} cos 29.5^{\circ}+cos 6^{\circ}sin 29.5^{\circ})) (cos 6^{\circ}cos 29.5^{\circ}- sin 6^{\circ} sin 29.5^{\circ})</math></center>
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 +
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<center><math>x''=0.09156cos 6^{\circ}+\frac{y''-0.09156  sin 6^{\circ}}{sin 6^{\circ} cos 29.5^{\circ}+cos 6 ^{\circ}sin 29.5^{\circ}} (cos 6 ^{\circ}cos 29.5^{\circ}- sin 6^{\circ}sin 29.5^{\circ})</math></center>
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<center><math>x''=(0.994522)0.09156+\frac{y''-0.09156 (0.104528) }{0.0909769+.489726} (0.865588- 0.051472)</math></center>
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<center><math>x''=(0.091058)+\frac{y''-.0095706 }{0.580703} (.814116)</math></center>
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<center><math>x''=(0.091058)+(y''-.0095706 ) (1.401949)</math></center>
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<center><math>x''=1.401949\ y''-.013417+.091058</math></center>
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<center><math>x''=1.401949\ y''+.077641</math></center>
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<pre>
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rightRotated =
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  ContourPlot[x2 == 1.401949 y + 0.077641, {y, -1, 1}, {x2, 0, 1.8},
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  Frame -> {True, True, False, False},
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      PlotLabel ->
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    "Right side limit of DC as a function of X and Y",
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  FrameLabel -> {"y (meters)", "x (meters)"},
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  ContourStyle -> Black,
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      PlotLegends -> Automatic];
 +
</pre>

Revision as of 03:11, 28 April 2017


This same process can be applied to the side walls for the detector. For the sidewalls, we have approximated them as lines following the equation

[math]x=cot\ 29.5^{\circ}\ y + 0.09156[/math]

Parameterizing this

[math]r \mapsto {cot 29.5^{\circ}\ y + 0.09156, y, 0}[/math]


[math]t \mapsto {cos 29.5^{\circ}\ t + 0.09156, t sin\ 29.5^{\circ} , 0}[/math]


(x y z

)=(cos 6\[Degree] -sin 6\[Degree] 0 sin 6\[Degree] cos 6\[Degree] 0 0 0 1

) . (x' y' z'

)

(x y z

)=(cos 6\[Degree] -sin 6\[Degree] 0 sin 6\[Degree] cos 6\[Degree] 0 0 0 1

) . (t cos 29.5\[Degree]+0.09156 t sin 29.5\[Degree] 0

)

(x y z

)= (0.09156cos 6 \[Degree]+t cos 6 \[Degree]cos 29.5\[Degree]-t sin 6 \[Degree]sin 29.5\[Degree] t cos 6 \[Degree]sin 29.5\[Degree]+0.09156 sin 6 \[Degree]+t cos 29.5\[Degree]sin 6 \[Degree] 0

)

(x y z

)= (0.09156cos 6 \[Degree]+t (cos 6 \[Degree]cos 29.5\[Degree]- sin 6 \[Degree]sin 29.5\[Degree]) 0.09156 sin 6 \[Degree]+t (sin 6 \[Degree] cos 29.5\[Degree]+cos 6 \[Degree]sin 29.5\[Degree]) 0

)

Using the equation for y we can solve for t

[math]y''=0.09156\ sin\ 6^{\circ}+t (sin 6 \[Degree] cos 29.5^{\circ}+cos 6 ^{\circ}sin 29.5^{\circ}) -\gt t=(y''-0.09156 sin 6 ^{\circ})/(sin 6^{\circ} cos 29.5^{\circ}+cos 6^{\circ}sin 29.5^{\circ})[/math]

Substituting this into the expression for x

[math]x''=0.09156cos 6^{\circ}+t (cos 6^{\circ}cos 29.5^{\circ}- sin 6^{\circ} sin 29.5^{\circ})=0.09156cos 6 ^{\circ}+((y''-0.09156 sin 6^{\circ})/(sin 6^{\circ} cos 29.5^{\circ}+cos 6^{\circ}sin 29.5^{\circ})) (cos 6^{\circ}cos 29.5^{\circ}- sin 6^{\circ} sin 29.5^{\circ})[/math]


[math]x''=0.09156cos 6^{\circ}+\frac{y''-0.09156 sin 6^{\circ}}{sin 6^{\circ} cos 29.5^{\circ}+cos 6 ^{\circ}sin 29.5^{\circ}} (cos 6 ^{\circ}cos 29.5^{\circ}- sin 6^{\circ}sin 29.5^{\circ})[/math]


[math]x''=(0.994522)0.09156+\frac{y''-0.09156 (0.104528) }{0.0909769+.489726} (0.865588- 0.051472)[/math]


[math]x''=(0.091058)+\frac{y''-.0095706 }{0.580703} (.814116)[/math]


[math]x''=(0.091058)+(y''-.0095706 ) (1.401949)[/math]


[math]x''=1.401949\ y''-.013417+.091058[/math]


[math]x''=1.401949\ y''+.077641[/math]


rightRotated = 
  ContourPlot[x2 == 1.401949 y + 0.077641, {y, -1, 1}, {x2, 0, 1.8}, 
   Frame -> {True, True, False, False}, 
       PlotLabel -> 
    "Right side limit of DC as a function of X and Y", 
   FrameLabel -> {"y (meters)", "x (meters)"}, 
   ContourStyle -> Black, 
       PlotLegends -> Automatic];
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