Spiral Geometry
Spiral Geometry
- Basic spiral properties:
- Radius changes uniformly from infinity at TS to the radius of the circular curve at the SC. So, it’s degree of curve DS changes uniformly from 0o to D at the SC.
- Average degree of curve is D/2.
- In circular curves, L = (I/D) 100 ft, or I = LD stations
- similarly, DS= Ls (D/2) DS and D in deg, L in stations
- Spiral angles at any point is proportional to the square of the distance Lp from TS to the point. DP = DS
- In Fig 25-15, M is the mid point of the spiral, Lp = Ls/2 but DM is not = (DS /2).Since D changes uniformly, degree of the curve = D/2 at M. But D changes uniformly, so the average degree of curvature between TS and M is (D/2)/2 = D/4
- Then, DM = ( Ls/2) (D/4) = (Ls D/8) = DS /4
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