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PLANE OF MOVING PART
CAMERA LENS
PLANE OF FILM
/Z\
D
w%
a
a
D
_Z
J
10mm 16mm
Fig. 3. Relationship between object and image.
through the moving part, parallel to the camera lens, has to be considered.
Reduction of image in camera: This defines the proportions of image to object dimensions (see Fig. 3). It can be expressed in terms of the width of field, w, which is covered by the effective width of the film, the latter being approximately 0.4 in. for the 16-mm film and 0.2 in. for the 8-mm film. The reduction itself then becomes 0.4/w and 0.2/w, respectively.
Exposure time of one frame and film velocity: The image travel per frame changes in proportion to the exposure time, i.e., in the inverse ratio to the film velocity (assuming a constant ratio of exposure time to frame time) .
With one type of high-speed motion picture camera the permissible image travel during exposure time, which still guarantees sharp pictures, is 0.002 in. This means approximately 0.010-in. image travel per frame, since the exposure time is about one-fifth of the frame time. The film velocity, therefore, must be greater than a certain lower limit, Vmin, in order to obtain sharp pictures. This means that the beginning of the film, moving with velocities less than V,,,in during exposure, cannot produce records meeting all requirements.
Based on an image travel of 0.010 in. per frame, the following formulae are obtained for the minimum film velocity (compare with chart for selecting speed given by Eastman Kodak Co.) :
16-mm film:
Vmin = 12 • — ft/SCO
(11)
Vmin = 480 • — frames/sec (12)
8-mm film:
3 — ft/sec (11')
Vmiu = 240 • — frames/sec (12') \v
For example: When a machine part moving with a maximum velocity v* = 40 ft/sec has to be photographed on 16mm film within a field 10 in. wide, only film velocities greater than 48 ft/sec or 1920 frames/sec will guarantee sharp pictures. For 8-mm film, the film velocity must be greater than 12 ft/sec or 960 frames/sec, with the same velocity of machine part and width of field assumed.
3. Conclusion
The correct film velocity to be chosen for recording lies within a range where the lower limit is determined by claiming sharp pictures, while the upper limit is prescribed by the time to be recorded and possibly by the illumination required to obtain a suitable exposure. The acceleration characteristic of film run, illustrated in Fig. 2, should be known for each camera under various operating conditions.
Description of Slide Rule
Since the above formulae involve only multiplications and divisions, a slide rule based on logarithmic scales seems to be the best approach to a mechanical computer.
The slide rule developed consists of three parts, the body, the slide and the
June 1951 Journal of the SMOTE Vol.56