Journal of the Society of Motion Picture and Television Engineers (1950-1954)

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The Compliance of Film Loops By GERHARD SCHWESINGER The analysis of film drives may require the knowledge of the compliance of looped film, defined as the rate by which the length of looped film changes with changing film pull. In some mechanical filters for the suppression of film flutter the compliance of film loops acts in analogy to the capacitance of electrical filters. However, it is known to be highly nonlinear. As no complete information has been published on this subject, theoretical relations are derived in such form that they can be conveniently applied by the designer to U-shaped and S-shaped film loops. The results are compared with an earlier published approximation. The effect of film curling is shown to be accountable in a simple manner. I N SOME TYPES of film drives the elastic properties of looped film sections are of considerable importance. In particular, sound-film drives utilize these properties to filter out transient and periodic disturbances which by various causes may be impressed upon the steady motion of the film. An analysis of the filtering action then requires the knowledge of a relation between the film tension and the amount of slack film in a film loop, usually referred to as the elastance or, inversely, compliance of film loops. This relation has been experimentally investigated by E. D. Cook1 who pointed out its nonlinear character. The theoretical treatment of the film loop problem is mathematically more laborious than might be expected. In contribution submitted on April 8, " (rial 7ort <& < t M i I i I I .M 1 IM M I ,M H M I J I I I ' ยป 1 I Ml . \i;i If 1951, by Gerhard Schwesinger of the Sigr Corps Engineering Laboratories (F< Monmouth, N.J.), 617 Prospect Ave., r, NJ. Little Silver, herently it is a matter of analytical mechanics rather than motion picture engineering and this may explain why so far no complete information on this subject has been published for motion picture purposes. An earlier theoretical treatment is due to W. J. Albersheim and D. MacKenzie2 who derived the first two terms of a series expansion for the film slack as measured between the inflection point of an S-shaped loop and one of the drums over which the film is wound. For practical application it is desired to know the total length of slack film at a certain film tension in the loop. This information is not explicitly contained in the quoted paper. The reader might try to derive it therefrom by generalization, but he remains in uncertainty as to the validity of the result. In fact, there is no simple additive relation between (a) the total slack and (b) the partial amounts of slack as measured from the inflection point of the S-loop to the first 320 October 1951 Journal of the SMPTE Vol. 57