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THE ACCURACY OF PHOTOGRAMMETRIC CONTOUR LINES
AND THE AMERICAN C-FACTOR
by
Prof. Dr. R. Finsterwalder.
Contour lines are in many cases an essential result of photogrammetric work.
In order to prove the value of this result it is necessary to find out and check
the accuracy of photogrammetric contour lines.
The mean error in height mn of contour lines is
(1a) m = a + b tgy
the mean error in plan m1 of contour lines is
(1b) mi —b t a ctgy
In the case of photogrammetry *a" is the mean error of a point in height,
b is the mean error in plan, y is the angle of slope of ground.
1. General determination of a and b.
One gets a easily from the mean error m, — 0,015 mm), which is due to
the stereoscopic measuring of image coordinates. By differentiating the funda-
mental, equation of the normal case h — bf : p we get
(2) a b. f - Mp
In (2) h is the flying height, f the calibrated focal length, b the length of
base, p the horizontal parallax.
For h:p —3:1 and f — 200 mm we get a = 0,22%¢0 h and in a similar
way b —0,15?/oo h *). Both values are valid for I.O. instruments.
Thus we have
(3a) Mn 0,22°/00 h + 0,15% 00 h. I9 y
(3b) mu = 0, 15%o h T 0,22% 0 h. cto y
As the amount of y is usually small, practice has chiefly to consider the
value a — 0,22?/,, h.
The formulas 3a and 3b give the accuray of contour lines in a general man-
ner for I.O. instruments. They have been proved in practice since long time.
2. The practical way for evaluating a and b.
In practice we can obtain the values a and b for a contour plan if we have
very accurate control points on the terrain or, better still, contour lines which
are constructed with a higher degree of accuracy. We can compare them with
the countour lines to be proved point by point, from a number of about 100-200
suitably chosen points we get the values a and b by simple adjustement.
May I show an example. We have a contour plan worked out on an old
1) See for instance Finsterwalder, R., Photogrammetrie. Verl. W. de Gruyter, Berlin 1952. S.
282-287.
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