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Scaling factors: underwater vs above water

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  • Scaling factors: underwater vs above water

    Dear colleagues:

    Because of the differences in the way light travels through air and water, films taken of swimmers
    above and below water need different scaling factors to convert 2D digitized coordinates to real
    distances. I have been asked to determine center of mass velocity profiles of members of our men's
    swim team at ASU. The pilot films I've been given were taken through an underwater window with
    both above and underwater segments visible from a single camera. The image size is small and the
    linear scale was only filmed below water (a mistake). I need to create an appropriate scaling factor for
    the above water segments. I know some of you have encountered this problem before. I'd appreciate
    hearing from some of you who have found a solution. Is there an general purpose correction factor
    that can be applied in all cases? For example, can I just assume that images are approximately 33%
    larger underwater than above water (a value based on some of Jim Hay's early work with inverse
    periscopes)? Somehow I think not, given that different underwater windows or camera enclosures
    involve different thicknesses of glass. Any help you could give would be appreciated. I'll post a
    summary of replies.

    Best regards,


    Richard N. Hinrichs, Ph.D.
    Dept. of Exercise Science
    Arizona State University