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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BS. Istanbul 2004
recording-time (time of taking a picture), which is important
during changeable weather conditions e.g. blasts of wind. In
this project, the photogrammetric method was used for checking
the tension strength.
The classical photogrammetric method consists of basic stages:
e taking a picture of the rope, usually with an orientated
phototheodolite,
e measuring the rope in the photograph (usually 6
points), transforming points’ coordinates to the rope’s
system coordinates (with a known camera
orientation),
oe rendering the shape of the rope approximate to the
catenary's model (equation 1 and figure 1),
e calculating the horizontal tension strength component
(equation 2) and, at times, also other parameters.
X-a (YX-4)
Z-b=%-(e tote + ) = k-cosh(== 23 (1)
where: | Z, X — coordinates of the rope plane,
a, b, k — catenary parameters,
e — base of natural logarithm.
F,=q-k
where: Fx - horizontal tension strength component,
k — catenary parameter,
q -unit weight of the rope [N/m].
2.2 New approach
Although the new method is based on the classical
photogrammetric, its realisation has been thoroughly modified
in this project.
Main features of the new method are as follows:
e using digital images (no-metric Kodak DCS camera
760 — 2000/3000 pixels),
e employing the photogrammetric method,
* using new technological processing for measurement
and computation, which will allow a maximal
automation of all stages,
e a large number of points (even thousands) measured
in order to determine the shape of the rope,
e using the plain projective transformation for sensor
orientation.
There are two main stages of this processing:
e terrain geodetic survey,
* both the automating and computing process.
The first stage deals with the setting out of control points,
which should be set into a vertical plane of the rope. The points
should form a polygon so that the rope is placed inside of it.
The polygon should be as regular as possible. If possible, the
control points should form a regular square-shaped pattern
throughout all of the rope-area. This guarantees a minimal
number of transformation errors.
Practical experiments show that a typical theodolite (e.g. Theo
010) is enough to set the control points into a vertical plane of
the rope. No special precision instruments are needed. Although
a large number of control points seems to be an advantage, this
task is difficult in its practical realisation. The stay-rope is
usually a very high object — several dozen meters — therefore,
setting out points around it is almost an acrobatic task. A
compromise between precision requirements and reality should
be made, although six points in one picture is a practical
minimum (a minimum of four is required for planar projective
transformation but this does not allow error evaluation).
The second stage, which constitutes the main part of my
PhD research, consists of three stages:
e measuring the rope and control points on a digital
image,
e transforming points’ coordinates from the image to
the rope plane,
e calculating the horizontal tension strength component.
At first glance it may seem similar to the stages employed in the
traditional photogrammetric method but the realisation is
entirely different. All stages of the processing are illustrated in
figure 2.
ur do DH.)
| |
Setting out and Taking a picture
surveying of control CLE LN
points
Coordinates of
control points
X- XYZ
e measuring of rope on image,
e. measuring of control points on image,
e transformation of points of rope,
e calculation of catenary parameters.
horiz. tension
strength
Repeatingof?^7 77 77—————
procedure NO Is a tension
strength
correct?
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Figure 2: Processing stages of the correction of the stay-rope
tension strength.
The terrain geodetic survey involves the setting out and
surveying of the control points. The points should be set in a
way that they can fit into the rope plane. For the sake of
simplicity, usually two of them are chosen as the upper and the
lower catch of the rope. Others are artificial control points
marked with signals placed on a tripod and on the construction
of the tower. It is of great importance to remember that the
points should be placed around the rope so that the whole
measured part of the rope is placed inside the polygon formed
