Bushwalk Australia

Modeling real-life situations is an important part of introductory physics. Here we consider the question “What is the largest weight of backpack a hiker can manage?” A quick perusal of the Internet suggests that as the weight of a healthy adult increases, the largest backpack weight Wbp also increases and should be about 25–30% of a person's body weight for a reasonably fit adult.  We show here that a careful modeling of the hiker and backpack leads to a somewhat different result, with hikers of sufficiently large (but otherwise healthy) weight not being able to carry as much backpack weight as hikers of smaller weight.

ethoen wrote:Surely it's strongly linked to a lean muscle to weight ratio of the person in question.

icefest wrote:Not quite.
The problem is that the strength of the limiting muscle/joint/tendon is determined by it's 2d cross-sectional area, making it grow by the square of the height of the person. The weight - as it's 3d - grows by the cube of the height of the person.

This means that for the same BMI, the larger person has a lower strength to weight ratio than the smaller, and that at one point her extra carrying capacity will be less than that of the smaller person.

Bubbalouie wrote:So far as I can tell from it the best weight to be is 72kg (700 Newtons from the text above it in the article).

north-north-west wrote:At what height? If I was 72kg I'd be almost as much around the middle as I am tall . .

*Some simplifications have been made, see the footnote.

1. They cite precedent to prove that strength increases to the power of 2/3 as compared to weight.
2. They then assume three possible finesses for a hypothetical ~70kg walker (able to carry 25%, 30%, or 40% of her own weight).
3. They then scale these finesses up and down to other body weights using rule 1.
4. The new possible max pack weights for each fitness level are then charted on the graph.
5. This assumes a similar BMI for all participants.

1. A 50kg walker who is quite unfit. She is comparably fit to a 70kg walker who can carry 25% of her own bodyweight. Looking at the graph where the grey line (25% fitness) and her weight (50kg) intersect gives us an estimated carrying capacity of 19kg.
2. A tall and very fit (40%) hammer thrower weighing 100kg. Following 100kg and the green line gives us a max weight of 25kg.
3. A tall and very unfit (25%) person with complete androgen insensitivity weighing 80 kg. She would be able to carry 15kg.
4. A short and fit (40%) powerlifter weighing 50kg, would be able to carry 27kg.

icefest wrote:* The original authors precedent of "all walkers are female" will be continued[/list]

GPSGuided wrote:Have they completely ignored the aerobic capacity of the individual? To carry a load for 10-20km at a reasonable pace, it's more than just the initial lift. Whilst the bones and joints keep everything up, I don't think it's that relevant for the weights we are talking about. Interesting academic exercise but there's more to consider.