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La séance du 24 juillet 1956, à 9 heures (e) 1 
P. 0. Fagerholm: 
Mechanical Radial 
Triangulation. 
(Pubi. IIIF1) 
Czerski 
La session est ouverte à 9 heures 05. 
Le président donne la parole à M. P. O. Fagerholm (Suède), pour la présen 
tation de sa communication: »A Study of Mechanical Radial Triangulation». 
Résumé: 
Mechanical radial triangulation (MRT) of different types is widely used and 
mainly for approximate mapping. Its popularity for such purposes depends 
l:o on very limited and simple instrumentation 
2: o on low requirements on experience and training of personnel 
3: o on fastness and 
4: o on limited demands on geodetic controls as a consequence of its being a 
block-method. 
Dutch numerical radial triangulation showed many years ago high precision 
and the American trials at Beltsville and elsewhere showed surprisingly good 
results with rather simple mechanical radial triangulation. 
In the author’s thesis »A study of Mechanical Radial Triangulation and some 
related problems in modern mapping», (1952, referred in Photogrammetria 
1952/53—2 by Roelofs) a complete analysis of the sources of error in radial 
triangulation and MRT was made and a precision type of MRT called PMRT 
proposed. It was shown e.g. l:o that the magnitude of tip and tilt and their 
influence on the accuracy was very limited; 2: o that the influence of topography 
was overestimated, could be reduced and decreased with decreasing negative 
scale; 3: o that several sources of error could be reduced to a magnitude which 
could be disregarded, and 4: o that the mechanical arrangements could be modi 
fied with a decrease of the mean square error to about one third. Several tests of 
the mechanical accuracy of the method confirmed the author’s opinion that 
PMRT was applicable to medium and small scale mapping with high demands 
on accuracy and a very sparse geodetic control net or new types of control 
quantities as isolated basis, radar fixes etc. 
It was also found that the interior or local error within a region (e.g. 5X5 km) 
due to rather limited correlation errors (showing up as small displacements of 
such a region) were of much lower magnitude than the coordinate error deter 
mined from the grid. This is in favour of the MRT. 
All types of radial triangulation compared with stereotriangulation have the 
disadvantage not to give z-coordinates. Due to the higher demands on vertical 
than horizontal accuracy in maps and a trend toward higher photography 
altitude, terrestrial levelling is often carried through for the horizontalizing of 
each plotting-model. When accuracy specifications permit, short bridgings or 
radar profiles are used. 
It is not a question of »either-or» when discussing stereotriangulation and 
MRT, only a question of profiting from the advantages of a correct MRT or 
PMRT for certain types of mapping. 
Instrumentation for PMRT and for simple MRT, designed by the author, 
will be shown in connection with the VIII Congress of Photogrammetry. 
Analyse de la triangulation radiale mécanique 
La triangulation radiale mécanique (TRM) a jusqu’à présent surtout été employée pour des 
travaux approximatifs ou à petite échelle, où la demande de précision est modeste. Pour des motifs 
différents ce groupe de méthodes n’a pas été accepté pour les travaux de précision. 
Dans sa thèse »A study of mechanical radial triangulation and some related problems in modern 
mapping», publiée en 1952, l’auteur donne une analyse des problèmes et rend compte des résultats 
1 Pendant cette session une communication par M. Z. Czerski, Pologne, intitulée »Über das 
optimale Richtungszentrum bei der Radialtriangulation» est aussi lue par titre seulement. Voir 
publication III: C 1.