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Transition Curves

Clothoid curves

posted Mar 1, 2015, 7:00 PM by Javad Taghia

The arc length is equal to its curvature. 
K = arclength = |0 t INT (dx/dt ^2 + dy/dt ^ 2) dt

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Calculate the arc length from parametric eq x(t) y (t)

posted Mar 1, 2015, 6:54 PM by Javad Taghia

x(t) = f (t)
y(t) = g(t)
0 < t < pi
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arc lenght = |0 pi INT( dx/dt ^2 + dy/dt ^ 2) dt

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Euler Transition Curves

posted Mar 1, 2015, 6:44 PM by Javad Taghia

theta = s^2 / 2 r L
x = s - s^5 / 40 r^2 L^2
y = s^3 / 6 r L - s ^7 / 336 r^3  L^3
c = (h, k)
h = x - r sin theta
k = y + r cos theta


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