THE USE OF NON-METRIC CAMERAS 97 
In a harmonic oscillation the points of interest are the endpoints of the motions, which on 
the photograph were clearly defined as the result of the reversal of the direction of motion 
(Figure 2). 
The amplitude was calculated from the coordinate differences of the endpoints of each line 
exposed by the vibrating reference points. A simple transformation formula was used, taking 
the locally determined scale factor and the inclination of the camera axis with respect to the 
wing into consideration. As a result ofthe short distances used for deriving both the amplitude 
and the scale factor from the photo coordinates, lens distortions did not have to be taken into 
consideration. An approximate value for the principal distance, derived from the nominal 
value of the focal length which was marked on the lens (158 mm), was used in the computation. 
An analysis of the accuracy of the results obtained indicated that errors in the determined 
amplitude generally did not exceed 0.2 mm corresponding to 2 to 4 per cent of the maximum 
deflections in the various mode shapes. 
DETERMINATION OF THREE-DIMENSIONAL INFORMATION 
Controlled experiment. A single camera approach was selected to determine the path and 
the orientation of a vehicle in testing various types of highway barriers?. The accuracy 
requirements in this project combined with travelling speeds of the vehicle of up to 90 
km-per-hour would require extremely precise synchronization (0.001 sec.) of the photo- 
graphic exposures if two cameras were used. It was therefore decided to base the photogram- 
metric solution on a single camera and, as the result of the required time interval of the 
photographs, a 16 mm movie camera was selected. Such a camera is generally not designed for 
precise photogrammetric operations and special precautions had to be taken to assure an 
accurate reconstruction of the bundle of projection rays. A control net was established for this 
purpose which included the precise location of the camera station, in addition to a system of 
targets behind the scene of the experiment. This net provided the necessary means for 
accurate reconstruction of the bundle of projecting rays without the need for information on 
the interior orientation of the camera. 
In order to determine the position and the orientation of the vehicle from a single photo- 
graph, it was necessary to attach a system of targets to the car, the x, y, and z coordinate of 
which had to be measured accurately. Figure 3 shows enlarged movie frames representing 
various stages of the experiment. The targets attached to the vehicle and the reference targets 
in the background can easily be identified in the photographs. 
The camera used in this project was a Millikan 16 mm movie camera with a focal length of 80 
mm and a speed of 129 frames per second. The camera was located at 86 m from the system of 
reference targets behind the scene of the experiment. Its optical axis was perpendicular to the 
plane defined by these reference targets. The image coordinates of the car targets were 
measured together with some targets of the background control target system. In practice, only 
a total of six or seven background targets, located near the car target images, were measured for 
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Fic. 2. 1 sec. exposure of wing oscillating at 65.3 cps.