When backpacking, it pays to be small

Rex, I will put my Nepalese Sherpa up against your Outward Bound student, and we will see who makes the carry.

–B.G.–

The guy is a turkey. It goes to show what happens when an academic strays out of his very narrow area of knowledge.

The load limit is an approximation, for sure, but it has nothing to do with your muscles or your strength. It has everything to do with your bones and especially the cartiledge disks in your spine. It should be rigorously applied to kids and teenagers, as their bones and cartiledge and ligaments have not matured yet. Damage the spine when young and they may have a lifetime of pain.

Sigh
Cheers

Body weight goes up as the cube, while muscle and bone cross-section only as the square.

Approximation, other things being equal, etc.

–MV

Dang, there is another thread recently about the same thing. looking…

"but it has nothing to do with your muscles or your strength. It has everything to do with your bones and especially the cartiledge disks in your spine."

I think "nothing" is a bit strong. I agree that stress on structure is the most important consideration for establishing a rule-of-thumb pack weight limit, but the strength issue is real, at least when there are uphills involved. Completely apart from pack weight limits, tall hikers have harder work to do getting the same pack weight (as a percentage) up the mountain.

This is really a no-brainer. Volume doesn't scale linearly with length, and neither do inertial forces and such. That affects all kinds of activities. That's why you never see 7-foot sprinters or running backs.

>"Body weight goes up as the cube, while muscle and bone cross-section only as the square."

+1

I do a math lecture about scaling entitled, Why you don't want to be the "50-foot-tall woman".

To paraphrase Peter Parker's uncle, "With great size comes great need to eat, poop and cool." Also, one is proportionally weaker.

Math Problem: Carol used 64 times more paint to paint the larger of two cubes. How many of the small cubes would fit in the larger cube?

Ken, Here is the thread you were thinking of It pays to be small from10/24/14

"That's why you never see 7-foot sprinters or running backs."

I agree with you, although there are exceptions to every rule. Usain Bolt is HUGE by sprinter standards and just happens to be the fastest person who ever lived.

An interesting article from a few days ago:

http://www.insidescience.org/blog/2013/07/25/using-physics-and-other-factors-explain-usain-bolts-speed

Ryan

…

But us big ones can still take your lunch money.

"Math Problem: Carol used 64 times more paint to paint the larger of two cubes. How many of the small cubes would fit in the larger cube?"

Is 21.3 correct?

(I figured: surface-to-volume ratio of a cube is 3:1, so divide 64 by 3.)

That's what you think Craig :)

"I agree with you, although there are exceptions to every rule. Usain Bolt is HUGE by sprinter standards and just happens to be the fastest person who ever lived."

Bolt is an alien, and you don't see him backpacking, either.

Hi Katherine

Nope. Sorry.

Also, the surface/volume ratio is not 3:1 – sorry about that too.
To explain: consider a cube of unit dimension. It has a volume of 1. Each face has an area of 1, and there are 6 faces.

Cheers
PS: neat problem, David.

"The load limit is an approximation, for sure, but it has nothing to do with your muscles or your strength. It has everything to do with your bones and especially the cartiledge disks in your spine."

Not following you Roger. You're saying the limit of what someone can carry in a backpack is determined by spinal cartiledge?

512, right?

Scott has it.

Since their areas (paint usage) differ by a factor of 64, their linear dimensions differ by a factor of 8. Each face, being 8x longer on its two sides, 8×8, has 64x more area.

Volume (how many small cubes can be held) is length to the third power – height x width x depth. Each side is 8 times larger, so 8x8x8 = 512.

Note that this relates to the original discussion as: the larger cube is 8X bigger, 64X "stronger", but 512X heavier.

–MV

ah well, fun to try, as the rest of my day is word-centric.

Yes, strength of bone goes as the cross section L^2 (L is linear size) where as weight goes as L^3. This is why elephants need relatively fat legs and birds are fine with thin.

Muscle strength can be more complicated. The NUMBER of muscle fibers goes as L^2, but the total strength should scale somewhat as the length of the fibers since there are more motor proteins over the muscle fiber length. So this is more than enough (perhaps) to explain the size discrepancy of sprinters with the small-is-better observation. Overall however, all other thing being equal, strength per unit mass for more static, endurance-type activities should scale as gamma = L^2/3, so smaller is usually better for endurance activities. For more dynamic activity the effective exponent goes up, gamma >2/3 (in other words penalty for being bigger is less due to compensating factors). An argument can be made that in the dynamics case (sprinting, jumping) the exponent is close to unity (no size bias), and this explains the often noticed interesting factoid that a human can jump as high as a mouse can jump as high as a flea. For falling damage you totally have to go back to gamma = 2/3 which is why you can drop your hamster off the roof an it will hardly notice.

Of course if you are a endurance-based hunter (or lunch money stealer) you have to be big enough to bring down you prey, or like dogs/wolves, have enough friends to help you out.

The type of scaling stuff was first explicitly mentioned in terms of mathematical laws by Galileo in his "Two New Science", to be distinguished from "Two World Systems" – the one that got him in hot water with the Vatican douchebags. I used to teach that the first day of my freshman physics course.

The little guy has the advantage up to a certain point. Think of it as a parabola. When the payload gets heavy enough (all other thing being equal) the bigger guy takes over. A pony doesn't pull the same load as a Clydesdale. There's a reason why in Nam the biggest guy in the squad carried the M-60.

But with light loads going up a steep gradient, heck yea, the little guy has the advantage for sure.

If you make the little guy carry the same stuff (i.e. that does not scale in weight as L^3) such as when you make him carry the the M-60, or anything standardized that is a significant fraction of his own weight, then that is NOT all things being equal in that case. Scaling laws like this only work when, as a simplified example, if you took a picture of the little guy and his load and the big guy and his load and blew up the little guy pic they look the same.

Of course in reality (unfortunately as a little guy I know this all too well) the usual picture looks like a little guy with a huge pack, and the big guy with a small (though exactly the same) pack. So scaling violated. So can still suck to be the little guy under those conditions.

I think the little guy should just explain to his Sargent that the laws of physics dictate that the weight he should carry should scale as the weigh ratio to the big guy to the 2/3 power. I'm sure the sargent will understand, and his innate sense of cosmic justice will prevail, and that he will allow the little guy carry less. NOT! :-o

"Bolt is an alien, and you don't see him backpacking, either."

I think his powers are more pharmaceutical in nature. Lol

Ryan

"If you make the little guy carry the same stuff"

However, at the time, I weighed only about 130 pounds, and I had to carry the AN-PRC-25 radio, which weighed about 25 pounds fully loaded. I had nobody to complain to, since I was the E-5.

–B.G.–