Ah, just noted that Chris mentions 2 section poles are a bit stronger, too. Hmm, I'm inclined for the lighter, slightly more expensive, easier to pack away carbon 3 sections.
JH,Seeing your post resurface, I took your invitation to check your figures. From what I can see, your calculations are fine, but the physics you based them on is a little wobbly IMHO. Physicists like to simplify problems down to use reliable mathematical tools to solve them – but at some point this process leads to an oversimplification and the results drift from the truth. Of course, with a complex three-dimensional shape like a Pacer Pole, you could really go to town with the moment of inertia calculation using a full tensor representation, and you have wisely chosen to do things simply, treating the pole as a point-mass located a certain distance from your pivot. Unfortunately this is a bit too drastic a simplification, and in order to improve your model, you really need a few more measurements – most importantly the total length of the poles you are comparing, and following that the length of each section and the amount of overlap.
The first improvement to the model is to think of the two cases as being uniform thin rods instead of point masses. Obviously this is a falsehood too – there are at least four sections of this rod of different densities (‘handle’, ‘upper section as far as the overlap’, ‘overlap’, ‘lower section below the overlap’ and perhaps something for the shoe if there is one… you can see this could go into as much detail as you fancy!). But thinking of it as two different uniform rods moves us a long way forward, because we start to see how the total length makes a difference. Imagine you had two rods of the same mass but made from different density materials – for example one long carbon fishing pole and one short lead pipe. Spun around their centre, the long rod clearly has a greater moment of inertia and would require more effort to accelerate (think of a tight rope walker using a long stabilising bar).
What this means to your calculations is that the relative mass of the lower section (alloy or carbon) is of less importance than you estimated because you have to consider both cases as rods of the same total length and then examine the difference.
Approximating the whole pole as a rod, we have to use the parallel axis theorem to compare the two cases. You start with the moment of inertia (MoI) of a thin rod of mass ‘m’ and length ‘L’ rotated about its centre of mass : I = (mL^2)/12. The parallel axis theorem states that the MoI of an object rotated about a pivot is equal to the MoI about the centre added to mass x displacement squared... or MoI = I_centre + mD^2. (You did the mass x displacement bit, but omitted the MoI of the rods themselves).
There is no mention of total length of the two rods, but lets say they are both 1.1m (the longer they are, the less difference the change of materials makes if all other quantities stay the same). I calculate the MoI of the two rods about the hand-pivot to be 0.079 for the alloy and 0.068 for carbon (but this doesn’t account for the fact that, if I understood your post, the poles were actually a mixture of different components?). In any case, this reduces the said difference to 16 % instead of 23% … and I don’t claim that this is accurate either – just a bit closer to the truth.
All that being said, I am very glad to see you using MoI as a rational tool in thinking about your gear. I have been harking on about it for some time, especially relating to the ultra-light obsession that puts everything on the scales but doesn’t often consider mass distribution. When you see people with ultra-light packs on their backs, but with a litre of water in each of the outer mesh pockets, you realise that they don’t appreciate the effect of MoI on their effort and comfort. Moving the water far from the the CoM of their pack ‘stiffens’ the load, making it more resistant to rotation of the torso and harder to manoeuvre. This is one of the reasons that climbers’ packs are tall and narrow, though they probably didn’t realise it!
"Of course, with a complex three-dimensional shape like a Pacer Pole, you could really go to town with the moment of inertia calculation using a full tensor representation, and you have wisely chosen to do things simply, treating the pole as a point-mass located a certain distance from your pivot. Unfortunately this is a bit too drastic a simplification, and in order to improve your model, you really need a few more measurements – most importantly the total length of the poles you are comparing, and following that the length of each section and the amount of overlap."
Funny that, I was thinking exactly the same thing but I didn't want to show off by saying it.
Though to be fair to JB, If I have to try and understand complex scientific or mathematical concepts way beyond my level of knowledge, I would have a better chance with an explanation by him than anyone else on this forum.
great minds think alike, hey ? . Perhaps I should learn to be similarly modest?
I wouldn't have taken up the subject if JH hadn't expressly asked someone to check his numbers - and as there are some on this site who openly feel that 'the science stuff is boring', they are at full liberty to ignore my post and read something more entertaining.
Frum,
that is very kind of you to say so. I am fairly sure that a large percentage of the population would find science/maths more enjoyable if it had been better explained or put into context, especially at the earliest stages of their schooling. Programmes like Horizon and Equinox as well as the natural world documentaries have a strong popular following and it is largely because they have often managed to bridge the communication gap between the scientific community and the rest of society. I enjoy trying to understand the world around me and also conveying that enthusiasm to others if they care to listen. If I tire of industry, I could well see myself re-training to teach.
John, interesting calculations and a good explanation for people like me whose grasp of maths is not, shall we say, brilliant. I wonder, though, how much difference this makes. I have again been out with a 3-part carbon fibre Pacerpole and an aluminium one and I really can't tell any difference between them in terms of how my arms and hands feel. (I agree that the carbon fibre doesn't vibrate as much, though I don't think this is significant). As a crude test to see how important it is to have the weight in the handle and not the tip try holding the poles by the tip. They swing very easily of course but you can really feel the weight of the handles.
I was really being ironic about my own, hitherto lack of grasp of the points you made and I actually found your explanations very enlightening. I also have the irritating habit of trying to poke gentle fun at just about everything and it is often not appreciated especially by the more serious minded. Physics was never a particularly weak point of mine, neither was it a particularly strong one but I haven't had to wrestle with many of its concepts and theories for some decades now and I am extremely rusty so your input really is appreciated by me. Classical explanations are so much easier to grasp and your discussion was easy to follow once I got to grips with the abbreviations.
Don't worry... I've read enough of your posts to know that it was friendly fun and not a criticism! One of the things I like about this forum is that people are generally accepted for what they have to offer. A long while ago, I used to be very active on a music forum relating to one of my other interests, but eventually I stopped posting there as it became full of puerile and quite aggressive behaviour. It's generally a civil atmosphere on here, even when people disagree, and it's fairly rare to see flaming going on - perhaps thanks to the editors who are quick to respond, but mostly due to the self-policing of a respectful online community.
For me, there has always been a deep satisfaction in coming to any understanding of how the world works. There are plenty of concepts well beyond my reach, but when I can apply the theoretical knowledge to a real-world example, it all falls into place. I come to this site to learn and discuss, and when a question arises in an area where I have some understanding, it is a pleasure to share it.
Chris,
no amount of scientific reasoning is any substitute for a field test, and in that domain, we all look to you for answers! The interesting case will arise when your experiences fly in the face of science... which would mean that it was time to revise the theories!
Thanks for that kind comment. I do find it useful to understand the scientific reasoning behind gear performance - the real scientific reasoning, that is, not the pseudo-science often pushed out in PR and advertisements. My experience has often flown in the face of the latter.
John, so sorry not to reply earlier, this is the first time I've looked at OM for a while.
Your comment "you have wisely chosen to do things simply" is not quite true - I didn't know how to do a more complex calculation, so there was no choice about it I am very pleased you've pointed me in the direction of a more accurate method, and I will be very interested to follow this up.
Those calcs I did were for the all ali and the ali/carbon poles. Pacerpole now have an all carbon pole which is considerably lighter.
Does it make a difference Chris asks. Well as you said Chris, if you swing them from the wrong end you can certainly notice the difference, and as I said before I can tell the difference between the ali/carbon and all ali. The all carbon seem weightless to me.
But apart from noticing the difference at the time, there is the question of energy expenditure over the day. When you swing the pole from the wrong end and it felt heavier (kind of) this would translate into using more energy to swing it. So reducing the moment of inertia (imagine a smaller flywheel) reduces the amount of energy used.
Also, MOI aside, if the poles are lighter, they require less energy to carry up a hill. So lighter poles score twice.
Does all this actually make any significant difference to total energy expended over a day? I don't know. If a person is shaving grams of their pack weight they certainly aught to look at this. If they carry 20kg+, then probably not.
My original post was really raising the point that some products have got to the stage where it's not really good enough to judge something just on whether it feels better or worse. Perhaps reviewers should talk to the manufacturers to help realise the significance of a design improvements.
John
Edit. Just to add that I find the three piece carbon Pacepoles brilliant. I thought I'd found a brilliant design with the earlier models and had to really grit my teeth to buy another pair; but for me, these all carbon ones are superb. I find I can walk all day at the pace I normally use for my usual evening one mile dash. 10/10.
John, interesting stuff. I do talk to manufacturers about the significance of design improvements. With Pacerpoles it seems that the introduction of carbon fibre models was due to the desire of some consumers/reviewers to have lighter poles rather than because the designer felt that this would improve the performance. It must of course require less energy to carry lighter poles. Whether this is significant or not is another matter. I can't tell the difference between the alu and carbon fibre poles in this sense where I can tell the difference between 750 gram and 1500 gram footwear for example or a 10 kilo pack and a 15 kilo pack. There are some much lighter poles around - I tried a pair a few years ago and they felt insubstantial and far harder to use than Pacerpoles. It would be interesting to see what Pacerpoles would be like with much lighter grips.
Is anyone interested in resolving some of these issues experimentally? It wouldn't be that difficult to construct an experiment using a GPS to maintain a constant speed, and a heart-rate to measure exertion and see what effect on heart-rate a different pole design, or indeed no pole at all, had.
Here is a study I found comparing different pole designs; it refers to others. The results certainly aren't clear.
If this experiment was to be of any value, you'd have to get a lot of different people to try both sets. Heart rate is a good indicator of aerobic output and follows a fairly linear relationship with power consumption up to the anaerobic threshold... but your output for a given task depends on all sorts of environmental variables (ambient temperature, humidity, sun exposure, fatigue & fitness levels, hormone balance, caffeine intake, immune system function, stress, blood glycogen availability, time of day... etc etc) that the difference in heart rate caused by changing poles would probably be lost in the noise. However, if you had a large enough sample and you did a good job in keeping other variables repeatable, you might observe a difference.
The problem with scientific experimentation on this kind of question is the more rigorous the experiment, the less it resembles real life usage. If you did this on a treadmill with test subjects rigged up to monitor VO2 consumption, you would have the best chance of noticing the difference in effort. This is the kind of setup used to work out how much difference a heavy boot makes to energy consumption... but a treadmill doesn't really help to analyse the suitability of kit to a rough mountain terrain, and ultimately that is the only test we are interested in.
In the end, I suspect that a mass & MoI saving of this scale would only really be observable in 'perceived energy', user comfort and (possibly) in the development (or absence) of long-term overuse injury like tendonitis!
"I do talk to manufacturers about the significance of design improvements. With Pacerpoles it seems that the introduction of carbon fibre models was due to the desire of some consumers/reviewers to have lighter poles rather than because the designer felt that this would improve the performance."......Chris
I don't have the article that sparked this thread, but judging by the opening sentence, John Manning got the wrong end of the stick [groan] in his review, and Pacerpole might have had a different opinion.
I say "might" because you say Pacerpole weren't convinced of a performance improvement, which rather puts a damper on my cheerleading. I wonder if they expect a performance improvement with the all carbon poles.
"I can't tell the difference between the alu and carbon fibre poles in this sense where I can tell the difference between 750 gram and 1500 gram footwear for example or a 10 kilo pack and a 15 kilo pack."
Yes, these are much bigger differences in weight too.
"There are some much lighter poles around - I tried a pair a few years ago and they felt insubstantial and far harder to use than Pacerpoles."
Yes, my early trials with other poles only reinforced my view that treking poles were a stupid design.
As we've said before, the Pacerpole design is so functional that some extra weight is worth it.
...
Perhaps the interesting thing is as John B pointed out - there are many areas where a closer analysis (than just weight) might show a small performance increase.
This might be in the way we use our gear as well as the way it is designed and manufactured.
For instance, how much energy is wasted by walking with a bobbing up and down motion.
At every step energy is used to raise the weight of the pack say 40 or 50mm.
If one could learn to walk keeping the pack at a constant height, one wouldn't have to all that lifting. (In theory it doesn't take any energy to keep an object at a constant height, but it does take energy to raise it, and that energy isn't recoverable in a pack on back situation).
Or perhaps you can already tell the backpackers in a busy street by their smooth level walk (and a glazed far away look in their eyes).
this is one of the reasons that I like carrying my Macpac Glissade - the pivoting waist belt means that your hips can move without having to lift or twist the pack. I am fairly sure that a lot of other manufacturers have taken this on, but I've had my Glissade for a decade and don't see myself replacing it anytime soon!
I have spent some time trying to improve my economy of movement whilst running - I am very far from a natural runner and when I first took up running as a regular activity, I didn't even appreciate that there was a technique to be learned. I can't say that I have made that much of an improvement, but on the flat I know that I can run further and faster for the same energy expenditure. It's not just down to cardiovascular fitness (I was already CV fit from rowing) - it is largely the result of improved economy of motion and muscular adaptation. Walkers, and especially trekkers with a heavy pack, could benefit from the same kind of focus on technique.
Of course, movement on the flat is very different from climbing & descending hills. In the various articles I have read, it seems that 10-20% of bodyweight can be carried on the flat without severe penalty in terms of effort. Most of the leg swing movement is energy-conserving pendulum swing and much of the lifting of the centre of mass is achieved by elastic return from the tendons - both of which work OK with additional load. Kangaroos are the natural masters of elasticity.
But as soon as you try to climb with that weight, the effort can go up enormously. What is less obvious is what, asides from carrying less weight, can we do about it!
Going through my extensive email correspondence with Pacerpole's designer I can find nothing to suggest she expects any performance improvement with carbon poles. I do think they were introduced because alu Pacerpoles were criticised, especially in the USA, as being too heavy. I think these criticisms ignored the point you make that it's not just weight reduction that can improve performance. I can understand why Pacerpole felt the need to respond with carbon poles. Any benefit to carbon other than weight reduction seems to be a bonus rather than an intention.
I suppose we should remeber that walkers are out to enjoy themselves rather than win a race, and also not all walkers are interested in expending minimal energy - some walkers are keen to use more energy (calories).
But if walking all day I find it more enjoyable to use less energy, so it is important, and on a multi day trip more so.
Chris, I don't remember Pacerpole saying much about this sort of performance increase either, but then, they do seem very modest people. And lets face it, for many people the jump from regular treking pole to ali Pacerpole is a much bigger jump than from ali Pacerpole to carbon Pacerpole.
Another thing I meant to add about the all carbon Pacerpole is that they are much easier to position than the ali or ali/carbon Pacerpoles. I mean that when you are on roughish ground and want to position the end of a pole in a precise place quickly, the lower moment of inertia allows you to do this more easily. Imagine a treking pole with a heavy weight on the end to see how much more imprecise/slower this is.
. Perhaps I should learn to be similarly modest?
I am very pleased you've pointed me in the direction of a more accurate method, and I will be very interested to follow this up. 
