Seems little fellas (and gals) have a real advantage with ca

[Bubbalouie]

http://scitation.aip.org/content/aapt/journal/tpt/52/8/10.1119/1.4897584

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.

[vicrev]

Have to be a Mathmatician to go for a walk now.............

[GPSGuided]

Good rationale to transfer more load to the smallest person in the party...

[vicrev]

Or, the dumbest.........

[north-north-west]

Trust me, in practice it's not that simple.

Maybe it's just that smaller people are tougher and less likely to whinge . . .

[ethoen]

Surely it's strongly linked to a lean muscle to weight ratio of the person in question.
i.e. Full Metal Jacket's Private Pyle is going to struggle more carrying the same weight up a mountain as say Charlie's Angel's Alex Munday

[icefest]

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

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]

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.

They did use some pretty extreme examples for the bigger people that have trouble "In particular, students of mass over 100 kg (220 lb) who are not overweight according to their BMI (Body Mass Index) struggle to carry the same amount of weight as 60-kg (132-lb) students". That's a person of 2m tall (or about 6'7") at the very top end of the healthy weight range.

In any case this graph shows what you describe (though I can't help some extra markers would have made it easier to read): http://scitation.aip.org/content/figure/aapt/journal/tpt/52/8/10.1119/1.4897584.f2

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). So 72kg & 1.7-1.85m, the shorter end having the greater cross sectional area so being naturally stronger.

The whole cube thing makes sense (really you neatly summed up the whole article in that one comment). That said, individual fitness varies immensely, I am very inclined to think that lean mass (given the variability of peoples bf%) & more importantly muscle & tendon conditioning would be far more important factors in weight carrying capacity in 90% of cases.

Really I just thought this was interesting that the difference was so pronounced for people. I'd not have expected tall people at a given BMI to be at any disadvantage, this demonstrates this assumption isn't so.

Last edited by Bubbalouie on Sun 26 Oct, 2014 9:56 am, edited 1 time in total.

[north-north-west]

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).

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

[Bubbalouie]

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

1.7-1.85m (BMI 21-25), the shorter end having the greater cross sectional area so being naturally stronger as ice-fest pointed out.

Cross sectional area of the muscle & bone naturally being most important.

I think muscle composition is hugely important though, at the end of a season I'm way fitter than the start re. pack carrying & I'm the same weight & BF% year round.

[icefest]

Here's my explanation of the maths:

*Some simplifications have been made, see the footnote.

The mathemagicians steps:

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.

Using this you can read the following graph:


Analysis:
The curves on the graph indicate that the peak carrying capacity lies at a lighter weight and height for unfit people - the grey line (from the leftward progression of the mode).
The difference in carrying capacity decreases with additional fitness (the curves are wider as you go higher up).

Some examples:

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.

If we compare 1 and 3, both unfit, we see that the shorter (and lighter) person can carry 4kg more than the other.
If we compare 2 and 4, both very fit, we see that there is only 2 kg difference.


Footnote:
* For this it is assumed that:

gravity= 10ms*-2
1kg = 10Newton
The original authors precedent of "all walkers are female" will be continued

[GPSGuided]

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.

[north-north-west]

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

Which makes a nice change.

[icefest]

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.

You are right that aerobic capacity doesn't follow the ^2/3 rule.

They attempt to account for that by comparing similar fitnesses.

[Tortoise]

Wonder if Aarn packs would have the same result.

[Taurë-rana]

I can certainly carry more further with an Aarn pack.
I was once told by an experienced bushwalker that it was height that made a difference, not weight - you can carry more if you are taller.
I can carry about 18kg on long walks when I am fit, but I tried 22kg and although I manage to carry it up and down a small mountain, I could tell that it was way too much for my body to carry very far without breaking down. I'm 5' and 53kg.

[vicrev]

I just like to walk,admire the scenery,listen to the birds,meet fellow walkers,just enjoy......I don't want to worry if my pack is too heavy, according to graphic mumbo jumbo(is to me) about size etc.,wether my pack is 10k/30k & too heavy for my height/weight.......I carry what I'm comfortable with......just for the number crunchers,there doesnt seem to be any mention about a persons age(unless I've missed it),is there a difference between a 20yr & 80yr in pack carrying capability ?......like to see a graph on that............... ....Vicrev

[corvus]

I weigh up to 70kg stand 170cm age 67 with normal BDI, my ideal pack weight is around 17 kg however in reality it is often much heavier so I just put up with it not so long ago I whilst doing a food drop into Pelion I even toted a 30 kg load got to the stage that half way I needed to get a mate to lift the pack onto my back would not even contemplate that load now .