Traversing Curves

Copan's Map Checks and Map Traverses modules allow you to calculate circular curve parameters, given certain inputs. If you have the direction (i.e., azimuth or bearing) and distance from the beginning of the curve in to the centre of curvature, and the direction out from the centre to the end of curve, Copan will calculate the curve's arc length, chord length, and arc angle. Curves may be tangential or not and may be combined in sequences to form compound or reverse curves. The Map Traverses module will also calculate the centre and end of curve coordinates. (The Area and Perimeter Calculations module also can calculate curve parameters, but only if the key curve points are already in place.)

Curve Codes

Curves are assumed to be traversed in this sequence: beginning of arc, centre of circle, and end of arc. If it defines part of a curve, a point must be given an appropriate curve code:

Curve code	Meaning
`BC`	beginning of curve
`TBC`	beginning of tangential curve
`EC`	end of curve
`TEC`	end of tangential curve
`POC`	end of one curve and beginning of another (point on compound curve)
`TPOC`	tangential point on compound curve
`C`	centre of clockwise curvature
`CC`	centre of counterclockwise curvature

Note that it is the to point end of a traverse leg which must be given the relevant curve code.

Example Curves

Each of these examples shows

an annotated sketch of a curve (with points numbered in the order that they're traversed), and
the data input to, and the results listed by, the Map Trav or Map Check modules.

Although for clarity the points are all numbered consecutively, they need not be so.

Example 1: Simple Non-tangential Curve.

Traversing an example non-tangential curve: start from point 1 which is on a line but not on the curve; go to point 2 which begins the curve; go in to point 3 which is the centre of the clockwise curve; go out to point 4 which ends the curve; and go on to point 5 which is on a line but not on the curve.

Data Input
 
Point  Bearing  Distance    Curve code
1
2      N45E     50          BC
3      S20E     88          C
4      N20E     "           EC
5      S45E     50
 
 
Curve Results
 
   Beg   Cent    End      Arc   Chord   Radius    Angle
     2      3      4   61.436   60.196  88.000  + 40°00'00"

Example 2: Simple Tangential Curve.

Traversing an example tangential curve: start from point 1 which is on a line but not on the curve; go to point 2 which begins the curve; go in to point 3 which is the centre of the counterclockwise curve; go out to point 4 which ends the curve; and go on to point 5 which is on a line but not on the curve.

Data Input
 
Point  Bearing  Distance    Curve code
1
2      120      50          TBC
3      030      40          CC
4      150      "           TEC
5      060      50
 
 
Curve Results
 
   Beg   Cent    End      Arc   Chord   Radius    Angle
     2 T    3      4 T 41.888  40.000   40.000  - 60°00'00"

Example 3: Compound Tangential Curve.

Data Input
 
Point  Bearing  Distance    Curve code
1
2      070      25          TBC
3      160      80          C
4      350      "           TPOC
5      350-180  40          C
6      020      "           TPOC
7      020+180  80          C
8      030      "           TEC
9      120      25
 
 
Curve Results
 
   Beg   Cent    End      Arc   Chord   Radius    Angle
     2 T    3      4   13.963  13.945   80.000  + 10°00'00"
     4      5      6   20.944  20.706   40.000  + 30°00'00"
     6      7      8 T 13.963  13.945   80.000  + 10°00'00"

Example 4: Reverse Tangential Curve.

Data Input
 
Point  Bearing  Distance    Curve code
1
2      S60E     50          TBC
3      N30E     40          CC
4      S30E     "           TPOC
5      "        30          C
6      N30E     "           TEC
7      S60      25
 
 
Curve Results
 
   Beg   Cent    End      Arc   Chord   Radius    Angle
     2 T    3      4   41.888  40.000   40.000  - 60°00'00"
     4      5      6 T 31.416  30.000   30.000  + 60°00'00"

Curve Checks

Copan will check the following before calculating curve parameters:

The inward and outward radial distances of a curve are equal.
The inward radial direction of a beginning-of-tangential-curve is perpendicular to the preceding line or parallel to the preceding outward radial.
The outward radial direction to an end-of-tangential-curve is perpendicular to the following line or parallel to the following inward radial.

Curve Adjustments

If a traverse that contains curves is adjusted (in Map Trav), its curves are affected as follows:

For non-tangential curves, the curve chords are treated as traverse legs for the adjustment, and then the curve centres are recomputed based on the original curve radii and new curve begin-end points.
For tangential-curves, the external tangents are treated as traverse legs for the adjustment. The curve begin-end points are recomputed based on the new curve intersection points and external tangents, and then the curve centres are recomputed as above.

updated: 18-Jun-2009