Dimensional analysis revisited

Abstract

The applicability of dimensional analysis (DA) is discussed in relation to the metabolic scaling laws. The evolution of different theories of biological similarity has shown that the calculated reduced exponents (b) of Huxley's allometric equation are closely correlated with the numerical values obtained from the statistical analysis of empirical data. Body mass and body weight are not equivalent as biological reference systems, since in accordance to Newton's second law, the former has a dimension of a mass, while the latter should be dimensionally considered as a force (W = MLT-2). This distinction affects the coefficients of the mass exponent (a). This difference is of paramount importance in microgravity conditions (spaceflight) and of buoyancy during the fetal life in mammals. Furthermore, the coefficients (ß) of the length dimension, and (g) of the time dimension do not vary when mass or weight are utilized as reference systems. Consequently, the "specific metabolic time," that results from the ratio of basal oxygen consumption and body mass or body weight yields the "biological meaning" of the time dimension, which is of fractal nature.

Keywords

• Dimensional analysis
• Allometric scaling
• Theories of biological similarity
• Body mass
• Body weight