Geometric Design - Spiral Curve Design
Spiral curves (aka transition or easement curves) are generally used to provide a gradual transition in curvature from a straight section of road to a curved section (or from tangents to circular curves). Figure 1 shows the placement of spiral curves in relation to circular curves. Figure 2 shows the components of a spiral curve. Spiral curves are necessary on high-speed roads from the standpoint of comfortable operation and gradually bringing about the full superelevation? of the curves. A spiral should be utilized with a circular curve with a superelevation? of 3% or greater. Spiral curves were developed for locomotives and are still used widely today in the industry.
Figure 1: The Placement of a Spiral Curve
Figure 2: Components of a Spiral Curve
- SCS PI = Point of intersection of main tangents.
- TS = Point of change from tangent to spiral curve.
- SC = Point of change from spiral curve to circular curve.
- CS = Point of change from circular curve to spiral curve.
- ST = Point of change from spiral curve to tangent.
- LC = Long chord.
- LT = Long tangent.
- ST = Short tangent.
- PC = Point of curvature for the adjoining circular curve.
- PT = Point of tangency for the adjoining circular curve.
- Ts = Tangent distance from TS to SCS PI or ST to SCS PI.
- Es = External distance from the SCS PI to the center of the circular curve.
- Rc = Radius of the adjoining circular curve.
- Dc = Degree of curve of the adjoining circular curve, based on a 100 foot arc (English units only).
- D = Degree of curve of the spiral at any point, based on a 100 foot arc (English units only).
- l = Spiral arc from the TS to any point on the spiral (l = ls at the SC).
- ls = Total length of spiral curve from TS to SC.
- L = Length of the adjoining circular curve.
- θs = Central (or spiral) angle of arc ls.
- ∆ = Total central angle of the circular curve from TS to ST.
- ∆c = Central angle of circular curve of length L extending from SC to CS.
- p = Offset from the initial tangent.
- k = Abscissa of the distance between the shifted PC and TS.
- Yc = Tangent offset at the SC.
- Xc = Tangent distance at the SC.
- x and y = coordinates of any point on the spiral from the TS.
Equations to use:
- Iowa Department of Transportation
- Hickerson, T.F., Route Location and Design. 2nd ed. (New York: McGraw-Hill, Inc., 1964), pg 168.