Scaling of human body mass with height: the Body Mass Index revisited

TL;DR

This paper revisits the scaling laws of human body mass and waist circumference with height, using biomechanical and physiological arguments, and supports the findings with data from children in Hong Kong and Britain.

Contribution

It introduces a biomechanical framework to derive specific scaling exponents for body mass and waist circumference relative to height, refining previous models.

Findings

Body mass scales as approximately h^{8/3} in children.

Waist circumference scales as roughly h^{q} with q near 2/3.

Empirical data from children support the proposed scaling laws.

Abstract

We adapt a biomechanical argument of Rashevsky, which places limits on the stress experienced by a torso supported by the legs, to deduce that body mass $m$ of growing children should scale as the $p$th power of height $h$ with $7/3<p<8/3$. Further arguments based on stability and heat loss suggest that $p$ should be close to 8/3. The arguments are extended to suggest that waist circumference $w$ should scale as $h^q$ with $q$ near the lower end of $2/3\leq q \leq 1$. Data from Hong Kong and British children are consistent with these hypotheses.