updated: 21-Sep-2010

 Copan for Windows

Traversing Curves

Contents
  1. Codes
  2. Examples
  1. Checks
  2. Adjustments

Copan's Map Check and Map Traverse modules allow you to calculate circular curve parameters, given certain inputs. If you have the azimuth (or bearing) and distance (or radius) from the beginning of the curve in to the centre of curvature, and the bearing out from the centre to the end of curve, Copan will calculate the curve's arc length, chord length, and arc angle (deflection angle or delta angle). Curves may be tangential or not and may be combined in sequences to form compound or reverse curves. The Map Traverse module will also calculate the centre and end of curve coordinates.

The Area and Perimeter Calculation module also can calculate curve parameters, if the key curve points are already in place. In this case, because it is an inverse traverse, you don't enter the bearing and distance of the curve radials; they are part of the output.

1. 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 point of connection (end of one curve and beginning of another)
TPOC tangential point of connection
C centre of clockwise (right) curve
CC centre of counterclockwise (left) curve

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

2. Example Curves

Each of these examples shows In the case of the Inverse Map Trav module, assuming the points are already on file, the input would consist of point numbers and curve codes but not bearings or distances.

Also, note that, although the points are all numbered consecutively for clarity, 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 anticlockwise 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.

Traversing an example compound tangential curve: start from point 1 which is on a line but not on a curve; go to point 2 which begins the first curve; go in to point 3 which is the centre of the first curve; go out to point 4 which ends the first curve and begins the second curve; go in (the opposite direction) to point 5 which is the centre of the second curve; go out to point 6 which ends the second curve and begins the third curve; go in (the opposite direction) to point 7 which is the centre of the third curve; go out to point 8 which ends the third curve; and go on to point 9 which is on a line not a curve. All three curves are clockwise.

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.

Traversing an example reverse tangential curve: start from point 1 which is on a line but not on a curve; go to point 2 which begins a counterclockwise curve; go in to point 3 which is the centre of the first curve; go out to point 4 which ends the first curve and begins the second curve; go (in the same direction) in to point 5 which is the centre of the a clockwise curve; go out to point 6 which ends the second curve; and go on to point 7 which is on a line not a 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"

3. Curve Checks

Copan will check the following before calculating curve parameters:

4. Curve Adjustments

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

updated: 21-Sep-2010