Simple circular Curves

Nomenclature for Circular Curves

Simple circular Curves

POT                        Point on Tangent outside the effect of any curve

POC                        Point On a circular Curve

POST                      Point On a Semi-Tangent (within the limits of a curve)

 PI                           Point of Intersection of a back tangent and forward tangent

PC                           Point of Curvature - Point of change from back tangent to circular curve

 PT                          Point of Tangency - Point of change from circular curve to forward tangent

 PCC                       Point of Compound Curvature - Point common to two curves in the same

                                 direction with different radii

PRC                        Point of Reverse Curve - Point common to two curves in opposite directions

and with the same or different radii

L                              Total Length of any circular curve measured along its arc

 Lc                           Length between any two points on a circular curve R Radius of a circular curve

∆                              Total intersection (or central) angle between back and forward tangents

DC                          Deflection angle for full circular curve measured from tangent at PC or PT

 dc                           Deflection angle required from tangent to a circular curve to any other point on a                                 circular curve

 C                            Total Chord length, or long chord, for a circular curve

C´                            Chord length between any two points on a circular curve

T                              Distance along semi-Tangent from the point of intersection of the back and                    forward tangents to the origin of curvature (From the PI to the PC or PT)

tx                             Distance along semi-tangent from the PC (or PT) to the perpendicular offset to                any point on a circular curve. (Abscissa of any point on a circular curve                        referred to the beginning of curvature as origin and semi-tangent as axis)

ty                             The perpendicular offset, or ordinate, from the semi-tangent to a point on a                                            circular curve

E                              External distance (radial distance) from PI to midpoint on a simple circular curv 

Circular Curve Equations

Equations        Units

R=180/p * L/D                                     (M or Ft)

D =180/P * L/R                                    Degree

L = P/180 * RD                                  (M or Ft)

T = R tan D/2                                     (M or Ft)

E = [R/ (DCOS/2)]-R                         (M or Ft)

C = 2RsinD/2, = 2RsinDC                (M or Ft)

MO = R (L) 1-Cos D/2(l)                     (M or Ft)

DC = D/2                                           Degree

Dc = Lc/L (L) * D/2(l)                        (M or Ft)

C’ = 2Rsin (dc)                                  (M or Ft)

C = 2Rsin(DC)                                   (M or Ft)

Tx = R sin(2dc)                                  (M or Ft)

Ty = R [1-cos(2dc)]                           (M or Ft)

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