Shoe weight equivalent to weight on back

Hi Art, originally I think this came from an army study, though I can't point you to it, nor can I even remember what era it was. Hopefully someone here can. Even so, apparently they never learned in that institution that putting 90 lbs on you back is exactly like putting 90 lbs on your back.

As a physicist I'd say that the science behind it, such as it was, was probably based on the work (weight X distance = energy expended) done lifting the boots/weight. This is the only thing simple enough – and therefore probably too simple – to even be susceptible to a semi-pat answer. This is energy expended that no hiking style or technique can overcome. Technically the muscles are doing work on the microscopic scale just standing up, but it is more efficient.

If I had to guess I'd say either the 5:1 figures come from a somewhat shaky quantitative argument based on mechanical work, or on an empirical test with a shaky numerical interpretation of the result. Probably it is the former – some general in the army probably suggested they hire an "egghead" to figure this out. The egghead just wanted the money, and this is incompatible with saying "it depends", or "its complicated", so he did a back of the envelope calculation (see below) and came of with the 5:1. An example of the calculation: if the weight was in your pack it would displace(bounce) about 1 inch per stride where it would get lifted 5 inches per stride on you feet. This leaves out a tremendous number of variables but as is is basically correct assuming everything else is equal. If I wanted to get a bit more analytic I might get into the geometry of the stride, etc. depending on how much money I could squeeze out of the general. I'd bet the "bounce" here is somewhat variable in different people, but you could for example look at movies of people walking wearing packs and get some average numbers there.

However, the basic result is VERY true. You have to do a lot more mechanical work carrying any weight on you shoes that you would on your back. On that the physics (not to mention experience) is overwhelmingly clear.

Previous discussion here might be useful: http://www.backpackinglight.com/cgi-bin/backpackinglight/forums/thread_display.html?forum_thread_id=18358

Yeah, I think I remember that thread. There are a lot of tantalizing references there (and a few off piste things as well) but it is inconclusive as to the original source, and serves as an illustration of how confused the "source" of this number is. This number was reference in 1st Ed of The Complete Walker, so anything later than early 60's does not have priority. Maybe some Roman general said it somewhere.

I do like the O2 consumption rate measurement – probably as accurate as it can get. 6.4.

This blog presents a summary of the ratio

Thanks everyone. this is good stuff. As a physiology guy, I like the O2 consumption research. The physics are interesting, I am sure it depends on the person. A hiker who shuffles vs a marching band stride might make a big difference.
Art

There is also a energy efficiency curve validated both physiologically and in term of similar simple physical models that shows each person has a most energetically efficient stride length.

https://en.wikipedia.org/wiki/Effect_of_gait_parameters_on_energetic_cost

This is something we also all know intuitively – and that it is much less tiring to hike with someone that matches your optimal speed, even when you are well below your aerobic capacity.

BTW, it would be real interested to see if some of those shoe weight studies how well the ratio they measured physiologically match my back-of-the-envelope guesstimate of R = height of shoe lift divided by the height difference of pack/head/torso at top and bottom of the stride. They would have to redo with a camera I guess.

It’s odd that no one as actually calculated the energy required to move the shoes. It’s basically mass x acceleration x distance problem. Mass and distance are givens, where acceleration would have to be determined based on how fast the shoe is accelerated from the stopping point of each step.

Basically acceleration will not play a significant role, if any, in this particular problem. This is what a physicist would call a highly dissipative system – one that depend more on friction than momentum – there are relatively insignificant acceleration/inertial forces. The kinetic energy is nil in comparison to the potential energy. The system is governed mostly by static forces and the 2nd law of thermodynamics. For example no energy is recovered from dropping the shoe back down barring some Rube-Goldberg style springy shoes that appear now and then, and those don't magically convert the spring back into metabolic energy. So the energy to move the shoe each stride is to a good approximation just weight times distance vertically lifted. If you want you can think of the swinging part as a pendulum that expends very little energy by comparison with the lift.

Guess I should get out my calculator and calculate how many calories this is – remember that the "cals" you see on food are actually kcals in the mks physics units. Maybe they should have caloric ratings on hiking shoe boxes next to the size! "Based on an average shoe lift of 4.5 inches these shoes will require X cals per stride".:-)

Vertical energy is probably minimal compared to horizontal energy. When walking one one lifts the foot only slightly as compared to forward movement. Acceleration does come into play as Force=mass x acceleration. The shoe is at rest and stopped at the start of every step. One has to apply force to get the shoe to move forward. The greater the mass of the shoe the more force required to accelerate at the same speed.

One source of this claim is part of an MSc thesis in Human and Applied Physiology, done at London University, 1982. The paper was published in the journal Ergonomics by S J Legg and A Mahanty. The reference is Ergonomics 1986 Vol 29 No 3, pp 433-438 . They found a factor of 7x for VO2 increase.

With a name like Legg, what else would he be studying? And yes, they were associated with the Army.

Cheers

The physics is certainly fun to ponder, but go with the direct measurements of humans in controlled trials. Oxygen consumed = the answer.

Now folks around here are going to be 'tuning' their shoes by cutting every other lug off, using 1 mm spectra laces, cutting grab loops off, ordering custom cottage industry cuben tongues, etc.

I'm an engineer, not a physicist, but I'm not completely buying the argument against the significance of horizontal movement. I base this mainly on experience, but as someone who moves relatively fast, I think there's a noticeable difference between light trail runners and heavier boots in the effort it takes just to take quick strides. Maybe it's all vertical lift for slower walkers, I don't know.

All that said, I think the single most important factor in choosing a feet/back ratio is easy math: 5.0

"Vertical energy is probably minimal compared to horizontal energy. "

Ugh…I'm not going to get into a debate with people about their *opinion* about some the applicability of Newton's 2nd law, while at the same time they are cancelling out his law of gravity. Gravity does the work to move the foot forward in many cases, on the forward stride the lower leg acts a bit like a pendulum to lowest order approximation – in that approximation zero work done by the human.

This is why I try to remember not to do this, but I never learn. LOL

Jones, Bruce H.; Toner, Michael M.; Daniels, William L. and Knapik, Joseph J. “The energy cost and heart-rate response of trained and untrained subjects walking and running in shoes and boots (abstract).” US Army Research Institute of Environmental Medicine via Defense Technical Information Center. 1983. (July 6, 2012) http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA131420

Now we have to bring moment of inertia into the calcs! Joking aside, the intent of my original post was that I was surprised that no one has calculated this out from a physic's problem perspective. It'd be interesting to see as there's so many different items to take into consideration.

What I find very interesting is in one of the studies mentioned by Jorgen Johansson in the blog Willie linked to. They tested boots versus shoes with added weight to equal the boots – and found that the shoes with added weight apparently required less energy than the boots, and suggested that the stiffness of the boots was also causing a greater expenditure of energy.
This makes intuitive sense and it would be interesting to see this confirmed in other studies.