# Full text: Transactions of the Symposium on Photo Interpretation

```WORKING GROUP 2
MARKOVIODIMITRIJEVIC-PETROVIC
131
The error of the radial triangulation-sketchmaster process is a function of
many factors, such as, for instance, relative height of triangulation points,
relations of flying height, relief, focal length, and others. It will be useful to
avoid this step in the statistical drainage analysis, especially in mountainous
regions. This can be avoided by analysing the prints themselves, and not the map.
In this case, only one group of errors remains - the errors due to central
projection, and they can be mathematically predicted.
The central projection of a non-horizontal line does not have the same
pitch, direction or length as the line itself. If the line has a pitch azimuth
v = v r -\-[x, and a length m (orthogonally projected as mi, centrally as m'), its
projection will have an azimuth v r -\~n' (where v r is the azimuth of the radial
line r, which passes through the projected point A', ¡x the horizontal angle be
tween this line and mi, and ¡x the horizontal angle between line r and m'), and
a length m'. The differences between ¡x and ¡x, and between m and m' are
functions ol the focal length/, the radial distance of the projected point A' (r),
the pitch a and length m of the line, and the angle between r and m' (/a). These
relations are shown in fig. 1. From the photographs ¡x' can be read off, as can
m', r and/ The key-datum is therefore the pitch angle a, so we shall assume
that it is known for the further theoretical treatment.
Bearing deformation
Fig. 1 shows the relation:
As fx = [x—<5, the true azimuth can be found knowing r, / and ¡x . For
varying values of these parameters, the change of ò has the form of a sinusoid
of a variable amplitude but of constant wave length. The graphical solution
of equation (2) is given in fig. 2.
In a statistical treatment, the stream bearings are divided into classes with
intervals of 10°. The exact position of each datum in its class has no importance;
thus the measurement errors must be so small that a large number of data
could not pass into an adjacent class. If we know that the error in field dip-
measurements is about 2-3° and assume that the measurements on the photo
graphs cannot be more accurate, we could adopt 3° 36' (1% of 360°) as the
maximum permissible error. By introducing this value into equation (2) we get:
(i) For a given a, the error will be, for every ¡x in the permitted limits,
within a circle with its centre at the principal point and radius:
A r m\
(1)
sin ò sin Cp
where: cp — 180°—//, mi = m cos a and Ah — m sin a
r
Also : Ar = — m sin a
r
By substitution we obtain: sin <5 = — tan a sin /x'
or
(2)
```

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