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June 1947 16 AND 8-MM SPROCKET STANDARDS 499
amount of this change is slight. On any but very freshly perforated film, it only counteracts some of the normal shrinkage that occurs with aging. For projectors and most cameras and printers, pitches longer than permitted by the standard need not be considered. However, film, like all materials, has a modulus of elasticity governing its elongation under tension. The elongation is negligible for the forces applied in ordinary cinematographic apparatus. But there is an apparent elongation that is particularly evident when 16-mm film is run on a sprocket with a single row of teeth. ^ This effect is caused both by the local distortion of the film at the perforation that carries the load and by the elongation of the film between perforations. The extent of the distortion depends upon the amount of tension on the film. Tension at a drive sprocket causes appreciable trouble and should be kept to a minimum. It is probably not necessary to take this distortion into consideration in the initial design, but it is well to keep it in mind so that if difficulty occurs when the sprocket is driving fresh film, the effect of the film tension on its pitch can be properly evaluated, and the circular pitch of the sprocket can be increased accordingly.
Minimum Pitch of Film. — The major factor to be considered in determining the minimum film pitch is simply the maximum shrinkage that is likely to be encountered. The permissible error in perforating is minus 0.0005 inch, which corresponds to 0.17 per cent shrinkage. Unprocessed film used in a camera or printer rarely exceeds 1.0 per cent shrinkage, and this is a satisfactory figure for •Smax. f°r most equipment using unprocessed film. In projectors and other equipment using processed film, a shrinkage of 1.5 per cent should be accommodated. The greater average age of such film and varying conditions of storage account for the increase.
Summary. — The above derivation applies to 16-mm film, but the principles involved are applicable to 8-mm film.
The formulas listed below show the basis of computation for 8-mm and 16-mm sprockets. The root diameter D, in inches, of the surface on which the film lies, is
_ 0.006
in each case, where N is the number of teeth. This diameter may be a part of the sprocket or a fixed guiding surface.