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I am trying to use ContourPlot to plot an implicit function. Now I have two variables (x,y) implicit function:

(b x)/a + y == ((c + d) Log[1 - (n y)/(c + d)])/m

where b/a=0.0065,c+d=-3276.26 and n=9770.6, m=9770.6x{0,60}. I can ContourPlot it y~x correctly. Physically, x is the time, y is the distance.

Actually, the y has the region {0,k}, now I want to ContourPlot it with y normalized, i.e. the x-axis is the time, y-axis is the distance y divided by k (y/k), ranges from 0 to 1. Just like this "the plot result"

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    $\begingroup$ "a,b,c,d,m and n are all known", But I do not know anything about them ? $\endgroup$ – Mariusz Iwaniuk Sep 27 '18 at 13:38
  • $\begingroup$ I have updated the parameters in the equation. Thank you for your help! $\endgroup$ – Rick Sep 27 '18 at 13:52
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    $\begingroup$ Using your numbers the expression ((c + d) Log[1 - (n y)/(c + d)])/m results in an imaginary number whenever y is greater than approximately 0.4. One is unable to plot imaginary numbers directly with Plot or ContourPlot $\endgroup$ – Jack LaVigne Sep 27 '18 at 14:10
  • $\begingroup$ Thank you for your help! $\endgroup$ – Rick Nov 11 '18 at 4:13
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Since the scaling is linear, you can simply relabel the ticks:

k = 3;
ContourPlot[x - y^2, {x, 0, 10}, {y, 0, k}, 
  Contours -> {{1, Red}, {2, Green}, {3, Blue}, {4, Purple}}, 
  ContourShading -> None, 
  FrameTicks -> {{Charting`FindTicks[{0, k}, {0, 1}], Automatic},     Automatic}]

enter image description here

Alternatively, multiply all ys by k in the first argument of ContourPlot and use {y, 0, 1} for the y range:

ContourPlot[x - (k y)^2, {x, 0, 10}, {y, 0, 1}, 
  Contours -> {{1, Red}, {2, Green}, {3, Blue}, {4, Purple}}, 
  ContourShading -> None ] 

same picture

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  • $\begingroup$ Thank you for your help! $\endgroup$ – Rick Nov 11 '18 at 4:03

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