updated: 21-Sep-2010

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.

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.

- 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 Traverse or Map Check modules.

Also, note that, although the points are all numbered consecutively for clarity, they need not be so.

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"

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"

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"

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"

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.

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: 21-Sep-2010