The chair challenge: can mechanics really tell men from women? A centre-of-mass analysis of a viral party trick

Abstract

In the "chair challenge" a person stands several foot lengths from a wall, bends forward until the head touches the wall, lifts a chair and tries to stand up. Online videos suggest that women can do this and men cannot, supposedly because women have a lower centre of mass or men have larger feet. We model the body as a planar chain of rigid segments with standard biomechanical parameters and search all postures allowed by the rules for the one that places the combined centre of mass of body and chair furthest back. As a rule of thumb, the largest toe-wall distance is roughly the trunk-plus-head length minus the distance from hip to centre of mass. For a slow, static rise this limit is 2.36 foot lengths for the male and 2.49 foot lengths for the female reference model, just short of the customary 2.5 foot lengths. The limit is set mainly by trunk-plus-head length relative to foot length, not by the height of the centre of mass; in centimetres the male model actually has more room. With the body proportions of 6068 participants in the 2012 US Army anthropometric survey, the sex difference shrinks from 0.13 to 0.03-0.05 foot lengths, half to one European shoe size. Individually, only 13% of men and 22% of women would pass statically, and predicting sex from the outcome is right in 54-68% of cases (for equal numbers of men and women), against 50% for a coin and 83% for a tape measure. Shoes, age and momentum matter more than the residual sex difference. The problem suits first-year undergraduate mechanics, combining static equilibrium of an articulated body, scaling and units, an inverted-pendulum estimate and a simple classification problem. The chair challenge is a fine demonstration of static equilibrium and a lousy sex predictor.