A Dimensional Analysis of Physical Performance and Growth in Boys

Abstract
On the assumption of geometrical similarity between young and older boys, certain functions should be expected to change with growth in a predictable way; e.g., weight and volumes as the third power of the linear dimensions, strength as the second power, etc. In an experimental group consisting of about 400 Danish school boys aged 7 to 17 a series of tests and measurements has been made. The results were split up in groups corresponding to 10-cm increases in body height, (h), averaged and plotted on log-log paper. The curves best fitting the results appeared to be straight lines, and the functions studied consequently could be expressed on the general formula y = a X hb, in which a and b are constants that can be determined. When b is compared to the predicted value of the exponent of h, it is possible to distinguish between such increases in physical capability with growth as are due to growth alone and such as are due besides to a qualitative change in the organs of the growing body. The results are discussed, and it is pointed out that especially all functions that depend on maximum muscular exertion increase with height at a much greater rate than predicted. The results point to the fact that an increasing ability to mobilize and coordinate the muscles of the body is the reason for the rapidly increasing physical capability in school boys.