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Chainage Equations
Chainage Equations allow you to add or subtract a
constant from a certain chainage range to accommodate
long and short chainages (chainage intervals longer and
shorter than the actual interval used).
Chainage Equations can be used to adjust for changes in
a designed road (i.e. curve radius change) where only a
certain section needs to be redone in terms of plotting
etc., or to force a particular chainage to a required
coordinate when a particular chainage needs to
fall on the centerline of an intersecting road for
example.
A start chainage, stop chainage and constant to apply to
that chainage range have to be specified. The result
will be that vertical and horizontal alignments, as well
as the resultant volume calculations, will take into
account the long or short chain at the start and/or end
of the specified stretch.
Within the stretch itself generated points will be named
by the original chainage name, but will be coordinated
at the correct (adjusted) position. |
How do Chainage Equations work?
User Interface
Select [Tools] [Chainage Equation] from the
Roads menu to display the following dialog:
Note that the chainage constant used here has been
exaggerated in order to illustrate the function. The
constant is usually much smaller than this and should
NEVER be greater than the chainage interval.
The chainage Equation +5.00 will be applied to the
chainages greater than chainage 200 up to and
including chainage 300.
Horizontal Alignment
The chainages that will be affected (given a 10m
chainage interval) are: 210, 220, 230, 240, 250, 260,
270, 280, 290 and 300 as indicated by the following
diagram.
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The chainage labels 210 to 300 will now be
physically situated at chainage x + 5, thus creating a long
chainage (15m long) between chainage 200 and 210 and a short
chainage (5m long) between 300 and 310. A negative chainage
equation would cause a short chainage between 200 and 210
and a long chainage between 300 and 310.
Please note that only the labels of the affected chainages
are “incorrect” and that the correct physical chainage
values will be used for quantities.
Vertical alignment and Edge Levels
The physical vertical alignment within the chainage equation
chainage ranges will be kept unchanged. Internally, the
chainage equations will be subtracted in order to calculate
the levels at the correct physical position. The calculated
levels at these chainages might differ, because of the
altered positions of these chainages (Chainage 210 is
actually situated at physical chainage 215). Illustrated
below is a long section of the road with and without the
chainage equations.
As you can see the physical alignment remains the same and
will not be shifted by the chainage equation.
Practical Example
General
It is often necessary to change the horizontal alignment by
altering one of the radii of a road after production
drawings have been submitted, which will cause the last
chainage of the road to increase or decrease.
To avoid issuing a complete set of new drawings, we can
apply a chainage equation from the affected ECC to the end
of the road, in which case we only need to issue new
drawings for the affected horizontal curve.
Load the Tutor.cdp project from the Examples folder and
select the first road as the active road. We will be
changing the curve 2 radius from 20m to 30m.
Determining the chainage equation
- Before you alter the radius in the Horizontal alignment
spreadsheet, locate a chainage that will remain the same
after the change. In this case, we will use chainage 150.
- Determine the coordinates for chainage 150 by selecting
[Index] [list Chainage Records]. Set the Start and End
chainages to 150 and press OK.
The coordinates of chainage 150 will now be listed in the
Output Window. If you cannot see your Output Window, select
[Window] [Toggle Output Window]. Write the coordinate down.
- Now, select [Alignment] [Horizontal] [Edit Alignment] and
alter the radius for curve 2 from 20 to 30 and coordinate
the alignment.
- We now need to calculate the new chainage of the old
chainage 150. Select [Alignment] [Horizontal] [Point
Chainage], you will be prompted to: “Indicate position for
chainage calculation”. Press the U key and type in the
coordinates of the old chainage 150 separated by a space,
and press Enter. An information box with the calculated
chainage will appear:
- The chainage equation must be calculated as follows:
Constant = Chg – Old Chg
-2.567 = 147.433 – 150.00
- Select [Tools] [Chainage Equation] and enter in the
following to create a short chainage between chainage 140
and 150:
- Coordinate the Horizontal alignment and run all the other
calculations to finish the road design.
Vertical Alignment and Edge Levels
Because the Horizontal alignment has actually been shortened
by 2.567m and, as we stated earlier, the vertical alignment
and Edge control are not affected by the chainage equations,
we need to shift all the VPIs and Edge level control points
after chainage 150 by adding the chainage equation (-2.567)
to the chainages of those VPIs and edge control points.
Hint
It is a good idea to copy the original road to another roads
file so that you can compare the levels and coordinates with
the changed alignment. This way it is easy to see the effect
of the chainage equations on your coordinates and levels.
Click Print Results to have the final results
displayed, saved to a file or printed.
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Last Updated:
April 26, 2006
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