Trig & RTS7.0 Notes for Pike Design & Construction

Model Railroader Layouts and layout building
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Note Calculator is calc.exe

RTS 7.0TM is rts.exe

AtlasTM HO Code 83 Components used

Quick Trig Review

Given Triangle a,b,c with the right angle at b

Co-ordinates let A=0,0) è B(b,0), C(b,c), let α = angle at A, where East=0º, counter-clock wise

Let lgt ç length, hyp ç hypotenuse, oppçside opposite, adj ç side adjacent

Sin(α) = lgt(line b,c)/lgt(line a,c) = opp/hyp

Cos(α) = lgt(line a,b)/lgt(line a,c) = adj/hyp

Tan(α) = lgt(line b,c)/lgt(line a,b) = opp/adj = Sin(α)/Cos(α)

Cot(α) = lgt(line a,b)/lgt(line b,c) = adj/opp = 1/Tan(α)

Of course hyp2=adj2+opp2, Note X2 is X^2 key on Calc

Sin(α) = opp/hypè opp = Sin(α) * hyp è hyp = opp / Sin(α)

Cos(α) = adj/hyp è adj = Cos(α) * hyp è hyp = adj / Cos(α)

Tan(α) = opp/adj è opp= Tan(α) * adj è adj = opp/ Tan(α)

lgt(length of track), α (angle to horizontal), run(distance →), ris(rise or distance↑)

run = adj = Cos(α) * lgt

ris = opp = Sin(α) * lgt

αº = ArcTan(opp/adj) or Tan-1(opp/adj) or InvTan(opp/adj) check INV box on Calc

Let β = 90º - α, è Sin( β) = Cos(α), Cos(β) = Sin(α)

Note β = angle at B or angle where North=0º, clock wise

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Uh, thanks?

3

xPD,

I am not sure where you are going with all this but if you are wanting geometrical accuracy down to three decimal places then RTS is not the software for you. You need to be using true CAD based packages like Cadrail (http://www.sandiasoftware.com/) or 3rd PlanIt (http://www.trackplanning.com/3pi.htm). RTS started out a long time ago as a general purpose Atlas Snap Track layout package. Even though it has expanded over time it is still a general purpose package. After all it is freeware. It still does a good job of putting together rough plans.

On one of your exercises you wanted to make a double crossover with a 2 inch spacing. You can’t do that with Atlas components. You would have to use a prebuilt double crossover such as the one available from Walthers/Shinohara. Atlas components make a double crossover with a three inch spacing and an overall length of 26 inches.

I am using up all my old Atlas parts in my staging area so I happen to have put one together:

Again, I am not sure where you are headed but I hope this helps.

-John