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Michael J. O’Shea





Backpack Weight and the Scaling of the Human Frame, M. J. O’Shea, Phys. Teach. 52, 479 (2014)


P1000310.JPGIn working with students at Colorado Outward Bound on land sections of outward bound courses, I noticed that hikers with smaller frames were often able to carry as much weight as hikers with larger frames who were otherwise of similar fitness.  To understand this, a simple model of the human frame was created and analyzed.  This model received a large amount of publicity with articles appearing in many places, see here for a link, including The Times of London, The Daily Telegraph, Science Magazine, National Parks Traveler and Physics.Org and.  The important ingredient of this model is:

·        A hiker strength that scales as the cross-sectional area of leg muscles (assumed to scale approximately as the volume of the person to the power two-thirds)

·        A mass that is approximately proportional to the volume of the person.

An example of a plot is shown (with some assumptions, see paper) for the backpack weight, Wbp as a function of the hiker’s weight, Wh.  The dashed lines encompass a reasonable range of hiker weight.  Note that 4.54 N = 1 lb.  This model predicts a maximum backpack weight at intermediate mass (weight) of the hiker explaining with a rather simple model why there is an optimum size for backpackers.


This model will apply most closely to groups of people that are similar (same gender, same training, similar fitness) with the exception of varying size. 

It is important to realize that this is a simple model and is not designed to figure out the actual weight a person should carry since this will depend on many other factors including fitness, acclimatization to altitude etc.  The important result of this model is that there is an optimum size for backpackers and that backpackers should not assume that if they have a small frame their load should necessarily be small. 

A problem related to this work is here.