The spiral definition you choose determines how spirals will be computed throughout this survey. The spiral definition is stored with the survey.
You can set the spiral definition in any of the spiral dialogs or in the Definitions tab of the Survey Information dialog.
Modern highways use spiral equations based on arc definition (degree of curve is the change of direction in 100 units along the arc of the spiral as opposed to 100 units along a chord). You may see this spiral referred to as a 'clothoid', 'Euler', 'American' or 'transition' spiral.
These equations derive the spiral using a Taylor expansion series in which a point along the spiral is a function of and derived from the distance along the spiral. For transitional spirals in which both ends of the spiral have a radius other than zero, TPC uses the equations from "Route Surveying and Design", Meyer & Gibson, 5th Edition, Appendix B. If one end of the spiral has a radius of zero (a tangent spiral), TPC simplifies these equations down to the four most significant terms of the spiral equation. This gives excellent results and is much faster.
TPC includes multiple chord spiral definitions. The basic assumption in all of them is that where the degree of curve (for the circular curve) does not exceed 8 degrees and the spiral angle does not exceed 15 degrees, the measurement of the spiral by its chords gives good results. The equations are simplified by assuming that for any very small angle (i), sin(i) = i. In a flat spiral, the deflection angle from the tangent to a point on the spiral is a very small angle so this simplification holds true. For sharp spirals, these equations are not as accurate.
TPC does not make any attempt to compute 10 equal chords for a railroad spiral, it just uses the railroad equations to compute the position of any point required on the spiral.
In the case of a simple spiral (two spirals on either side of an embedded curve) the distance from the original PI to the points of tangency at the beginning and end of the adjoining spirals are computed much the way they are for a highway spirals, accounting for the throw or offset of the curve portion needed to fit the spirals.
This is the traditional 10-chord railroad spiral.
This definition is sepecific to the UP and BNSF railroads in the wester US. They are referenced on www.wa-ccs.org/reference/reference.html. Look for the 'Spiral Curve Calculator' at the bottom of the page. The Excel spreadsheet lists the formulas but not all the assumptions.
If you require an additional spiral definition, contact TPC tech support firstname.lastname@example.org.
Choose from Spiral Angle or Chord Ratio.
A basic relationship of spirals is sl = 2 * radius * spiralangle(rad) where radius is the sharp end of the spiral. TPC computes the spiral angle of the center line, then use it along with the new radii of the offset spiral to compute the spiral length of the offset spiral.
Approiximates Hickerson formulas by applying the ratios of the chords to the spiral lengths. Two chords are computed, one for the centerline spiral and one for the offset spiral. The ratio of the spiral lengths will match the ratio of these chords.