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  1. #1
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    How to rationally determine the cost of a pound?

    When I pack for a tour I tend to pack more stuff than many other people, just based on anecdotal evidence I have from reading on this forum in the past. And when I've shared some details of my pack in various ways I've received comments like "why do you want to carry all that weight?". And my answer is always that I value the things I take and don't think it affects my speed or enjoyment of the ride by much.

    When we decide to take something along or not there's a kind of economic decision going on whether we think of it formally as such or not. There's the expected or potential benefit of the item, compared to the cost of taking the item. The benefit might leverage itself in various ways in terms of the pleasure or utility of the item. And the benefit might also be hypothetical as with the case of a chain repair tool that's valuable only when your chain really breaks. Or a tent, that's valuable only when you find yourself without a place to hang your hammock.

    Then, other than the benefit of the item, is the cost of it. For one, there's the bulk of the item. There's only so much room. Based on volume, anything you take will limit your ability to take other items. Or that cost might be that you have little space in reserve for temporary needs such as packing three days of food instead of two during a part of the trip where supplies will be scant.

    From reading the comments of many people I think the cost of an item that most people put at the forefront of their minds is the weight of the item. I'm calling that "the cost of a pound", and the focus of this thread.

    When we evaluate the cost of a pound that has an effect on how much enjoyment we'll get out of the tour. But are we making that decision rationally? I'm not confident that we do. It's not really that I think the ultra light folks are irrational while me, with my heavy pack am making wise choices about my trip. I really would not start this thread to gloat on how rational I am (especially since most people question my excessive pack). What I really want to get down to is how mathematics might be applied to this situation, albeit math that I'm not personally well equipped to calculate and I'm interested in hearing from those that are.

    There are many different factors to consider including the following that I've pondered:

    First, there's the cost in terms of enjoyment. In general I've found that when I'm riding on a trip I go for a certain level of effort. I'm not shooting for a certain speed. I used to do that more. But I've learned that I can't look at an incline and somehow calculate the speed that I should be able to go up it and just dial that in and pedal. Instead, I'm getting feedback from the pedals as they push back against me while I go up the hill. And pretty soon I settle into a level of effort that falls somewhere between pushing as hard as I can and spinning along as easy as pie (unless I hit first gear). Just where I fall on that scale will vary based on many many factors such as my mood, the number of miles I've already covered that day, the terrain before the hill, how long since my last meal, and many more. But my main point here is that the cost of my pack is not heavily influencing my enjoyment of the ride as long as the pack is not so heavy as to make me frequently stand on the pedals in first gear. Instead, I find a certain effort level based on how that feels to me, not based on the miles per hour.

    Then there's the cost in terms of speed. And if you're still with me, we're finally getting down to what interests me the most in terms of mathematics here and where I have unsure footing about my own rationality and want help from the mathematically inclined. What is the cost of a pound when it comes to speed? It's hard to get that "by the seat of the pants".

    Consider this example. I'm riding along on a nearly flat road at 15 mph. To rationally consider the cost to my speed of my weight, I need to know how much faster I could be going if I weighed a pound less, or ten pounds less. I don't know how to make that calculation. So instead, I look down at the speedo and I mentally calculate how fast I "think" I would be going on an unloaded bicycle. This is so subjective and I just don't trust my own judgment. My intuition (read "red flag") says that the cost is not much. On flat ground I think my speed on a loaded bicycle is nearly what it would be otherwise. I know I pay heavily in terms of acceleration! But once the cycle is accelerated to speed I'll spend most of my time cruising so the cost of acceleration is not affecting me much. But am I right that for the same level of effort I might normally go 17 mph but 15 mph loaded with 80 pounds of gear? Or is my intuition wrong and the 80 pounds reduces 17 mph to 12 mph? I don't trust myself to "look" at the situation and just know how fast I should be able to pedal a given weight at a given incline.

    I suspect, but don't know, that the cost of a pound also varies with incline. But here again I don't know what the real relationship is. I've been surprised in my experience by how little weight matters going up an incline. But here again the real effect has just been my intuitive sense of how fast I'd be going unloaded. It's hard to just go out and ride the same hills unloaded vs. loaded and make a decision that way. Accurately measuring the force I'm applying to the pedals on one ride versus another is very subjective and I think leads one to "prove" whatever case their intuition already believes in. You need to account for varying energy levels, wind, etc. With enough experiments to be statistically significant maybe you can do something here but I don't have the energy for that and would still question the conclusions I made.

    Math is not the end of the story. But it's an important part of the story. What I mean there is that once you know the cost to your speed, you have to consider the "cost" of a mile per hour. In other words, how much will your actual enjoyment of the trip be influenced on the basis of averaging 12 mph instead of 15 mph? For me, very little. On some days when I'm trying to make a specific destination that day, maybe it matters a lot. But it's easy to be deceived here because whatever speed you can attain, there's always a higher speed that would let you cover more miles. How much this means to enjoying a tour is entirely in question.

    I'm not trying to investigate these trade-offs at extremes. By pushing yourself to absolute limits in terms of weight or volume it's easy to see that the tour can be substantially improved by reducing the load. You don't need math for that. But then when we get into the middle ground between being very spartan or having a variety of luxuries around, I'd like to learn more about how the volume/weight really affects things. For example I could watch videos on my iPhone at night. But it has a real small screen and my iPad is more enjoyable for that. Given the cost of weight and volume of the iPad and the amount of time I carry it versus use it at night, should I take it? I don't feel equipped to make that decision rationally but I still make it nonetheless.

    Who's out there that finds these questions interesting as I do? Who has other perspectives on what trade-offs should be considered when deciding what to pack? And most importantly, who has the understanding of math required to calculate the real effect on the speed of the bicycle at a given weight and incline? I find that most intimidating.

  2. #2
    Long Distance Cyclist Machka's Avatar
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    1) When I travel, the weight of the bicycle + bicycle box + all the gear has to fall within the airline restrictions.

    If I'm flying with Qantas, I've got a restriction of 32 kg per item, and I can carry 2 items. Other airlines have tighter restrictions. Some restrict you to a weight of 23 kg per item ... so that's usually the number I work with.

    So after I've weighed the bicycle and the box ... whatever is left is what I've got to work with.

    That is a very real cost, in monetary terms, of what you bring. If what you bring exceeds the limits, you pay.




    2) My own personal guideline is to bring no more than half my body weight. Bicycle + All The Gear should add up to no more than half my body weight. From my experience, when I go over half my body weight, I struggle and the tour loses its enjoyment. I struggle cycling up hills, I struggle pushing the bicycle up hills, and I struggle during the off-the-bike lifting and carrying portions of the tour. Half my body weight puts me well within the 23 kg * 2 item limit ... so that's good too.




    3) I mentioned the off-the-bike lifting and carrying portions of the tour above ... our tours are rarely the type of tour where we wheel the bicycles down the driveway and set off, then camp the whole time. Our tours usually involve flights, trains, ferries, hotels, hostels, and all sorts of things. When you've got to haul stuff around an airport or train station ... when you've got to dash from one platform to another in a train station ... when you've got to carry it all from the airport or train station to a hotel ... when you've got to haul it all up flights of stairs to your room ... you start to appreciate the idea of carrying less. In fact, you start entertaining ideas of mailing it all back home and travelling with a toothbrush and a towel.






    You mention enjoyment ... and yes, that's a factor. I want to go as light as possible, because that is more enjoyable. But not too light that I'm missing a key element.

    You mention speed ... I don't care about that. I rarely travel with an itinerary so tight that I have to reach a certain place by a certain date. All I know is that if my stuff weighs too much I find it very difficult to get up hills. And, as mentioned above, I have a pretty good idea where that line is for me.






    As for specifically what I bring ... that list of stuff has been refined through years of cycling, years of camping, and lots of cycletouring. But, of course, it still goes through changes before each tour.

  3. #3
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    All very reasonable Machka. And hitting the right mark, like you say, is mostly about previous experience. For me, most of my tours are in fact starting at the end of my driveway. But I get your points. All those factors are important.

    My interest in the math side is probably somewhat academic. I don't expect it to deliver a recipe for my behavior. But I'd like to be influenced by it.

    Edit: I think half your weight is an interesting idea. At that level my pack is only a "little" heavy. (Weight 150, pack 80). No, I re-read what you said. Mine is very heavy since I'm not counting the weight of the bicycle there.
    Last edited by Walter S; 12-21-13 at 05:05 AM.

  4. #4
    Long Distance Cyclist Machka's Avatar
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    Quote Originally Posted by Walter S View Post
    Edit: I think half your weight is an interesting idea. At that level my pack is only a "little" heavy. (Weight 150, pack 80).
    I count everything: my bicycle + panniers and other bags + all the gear <= half my weight.

    So in your case (which is pretty close to mine) if your bicycle + panniers and other bags comes in at 30 lbs ... that would leave 45 lbs for all the gear (tent, sleeping stuff, clothing, cooking stuff, etc.).


    But I have found that when I carry more than that in a desire to have a bit more luxury with me, the enjoyment level drops off quickly, and I regret my packing decisions.

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    Quote Originally Posted by Machka View Post
    I count everything: my bicycle + panniers and other bags + all the gear <= half my weight.

    So in your case (which is pretty close to mine) if your bicycle + panniers and other bags comes in at 30 lbs ... that would leave 45 lbs for all the gear (tent, sleeping stuff, clothing, cooking stuff, etc.).


    But I have found that when I carry more than that in a desire to have a bit more luxury with me, the enjoyment level drops off quickly, and I regret my packing decisions.
    Forgive me, I made two edits to that and should probably have just entered another reply. My bicycle alone (no panniers or anything added) is 40 lbs. Then I pack 80 lbs. onto it for a total of 120 lbs. Half my body weight is 75 pounds, so it looks like I'm 15 lbs. past your limit.

  6. #6
    Long Distance Cyclist Machka's Avatar
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    Quote Originally Posted by Walter S View Post
    Forgive me, I made two edits to that and should probably have just entered another reply. My bicycle alone (no panniers or anything added) is 40 lbs. Then I pack 80 lbs. onto it for a total of 120 lbs. Half my body weight is 75 pounds, so it looks like I'm 15 lbs. past your limit.
    I think you mean 45 lbs past my limit.

    And, of course, that's my limit ... the one that I've found works for me. Other people feel comfortable hauling around a lot more than that.

  7. #7
    Garlic
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    Your analysis looks good, but it's a little long.

    You say that once you accelerate to cruising speed, you need little effort to maintain that speed. That's true if you have perfect cadence. But if you're like me and you don't, you need greater force twice every crank revolution to accelerate your load. That adds up.

    There's another factor: Whether you can actually carry the load or not. (Sorry, I didn't read every word of your long post, so forgive me if you did cover this.) Some of us, as we age or get hurt, find we can simply no longer carry what we did in our younger days, and we must greatly lighten our loads to continue just getting on the bike. This might require a large, radical shift, beyond considering the marginal "cost" of an individual item. Deciding to take the leap to carrying a tarp and a quilt and not cooking are examples. Going rackless is another. Or even switching from camping to inns.

  8. #8
    Senior Member Thulsadoom's Avatar
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  9. #9
    Long Distance Cyclist Machka's Avatar
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    Quote Originally Posted by andrewclaus View Post
    Or even switching from camping to inns.
    That's one of the reasons I like hub-and-spoke tours ... I can cycle light because everything is back at HQ.

  10. #10
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    Quote Originally Posted by andrewclaus View Post
    Your analysis looks good, but it's a little long.

    You say that once you accelerate to cruising speed, you need little effort to maintain that speed. That's true if you have perfect cadence. But if you're like me and you don't, you need greater force twice every crank revolution to accelerate your load. That adds up.

    There's another factor: Whether you can actually carry the load or not. (Sorry, I didn't read every word of your long post, so forgive me if you did cover this.) Some of us, as we age or get hurt, find we can simply no longer carry what we did in our younger days, and we must greatly lighten our loads to continue just getting on the bike. This might require a large, radical shift, beyond considering the marginal "cost" of an individual item. Deciding to take the leap to carrying a tarp and a quilt and not cooking are examples. Going rackless is another. Or even switching from camping to inns.
    You seem to be assuming that I'll try to maintain the same speed when loaded vs. unloaded. I don't even know what that speed would be. I'm maintaining the same level of effort. So I think your comment about how I'll have to push harder every rev is not correct is it? I can just go slower instead.

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    Also, I've noticed that if I have a day when I'm hanging around the same town (perhaps early for a train) I'll go ride around unloaded. At first I'm amazed at how easy it is and I feel liberated. But then after a while I settle down into the same level of effort that I'm used to all the time. So I don't ride around all day with a much bigger smile on my face. On an emotional level I feel about the same as always. This also contributes to my feeling that the weight does not matter much.

  12. #12
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    Quote Originally Posted by Thulsadoom View Post
    Excellent. I'm giving this a careful look. Thanks

  13. #13
    Senior Member SmallFront's Avatar
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    I just discovered the problem of hills and weight pertaining to cadence the other day.

    I am not a spinner, I tend to stand up in a heavier gear rather than sit down in a lighter gear. At first I thought "well, people say you can only push down with platform pedals", and as I have platform pedals I first thought I would have to live with it.

    Then I realised that when sitting down, I don't just push down. I have spikes on my platform pedals for a reason and since I have the pedal axle under the ball of my foot I actually push forward and pull to the rear as well. Now, I can't pull up with platforms, but I don't need to, as when one of the feet is in that position, the other is in the "push down" position. This is most evident when I have things in the cargo box, that aren't tied-down - such as my daughter, lol.

    In any case, I am currently "retraining" myself to have a more "smooth" cadence, which works, but I have to be concentrating on it because I am not used to it.

    As for camping gear, I am not a weight weenie, but I do have an awful lot of lightweight gear (titanium etc.). I think of it as having reasonably lightweight gear allows me to bring more per pound. So if my sweet spot is, say, 35lbs, I can carry a larger tent, a better sleeping pad, a better sleeping bag, proper tools (I think I'm through with small bike multitools), and the necessary items for a good cup of coffee. Or, hell, more water.

    If I went with heavier stuff, I would simply have to cut out a lot of items. I have yet to actually tour on my cargo bike, but I have tried packing my stuff on it, and I drive my daughter around on a daily basis, often with quite a bit of shopping added up and down hills constantly.
    Last edited by SmallFront; 12-21-13 at 06:38 AM.

  14. #14
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    Do you enjoy going fast or do you enjoy getting there? I know a couple people that refer to their touring bikes as the carbon or titanium bikes that they use for credit card touring. To them it is a touring bike because it has a rack and a rack top bag. They are shocked that I would tour on a bike that is 10 or more pounds heavier than theirs, even more shocked that I would carry a tent and sleeping bag and cooking gear. It becomes a factor of what type of touring you prefer.

    Part of the equation is the tools and spares that would not be needed in an ideal world. But we do not live in an ideal world and suffer untimely equipment failures. If I lose a day because I need something that I do not have to get rolling, to me that is a disaster. Others on this forum have suggested that such events are to be cherished, as it gives you an opportunity to get to know the kind people that went out of their way to help them.

    And what is the probability of bad weather vs the probability that you will lug around clothing that you rarely or never wore on a trip? And, would you prefer to shiver for a day to reduce your gear weight?

    My point is that each person will have a different philosophy on the importance of light weight vs the importance of having more stuff along.

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    Sorry for being flip, but this sure seems like an awfully long post that could be summed up in just a few words: different strokes for different folks.

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    Senior Member SmallFront's Avatar
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    Dengidog, yes, it is a question of different strokes for different people, but for a given bike, at least in theory,it ought to be possible to quantify the wattage needed to propel a bike up a given incline. and also how it helps down a hill. It's a bit geeky, but I totally see where he is coming from, and I applaud the curiosity - even if it comes down to trial and error of what is comfortable and what is the good compromise of weight vs. comfort for the individual.

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    This thread weighs too much Enjoy your ride.

  18. #18
    Garlic
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    Quote Originally Posted by Walter S View Post
    You seem to be assuming that I'll try to maintain the same speed when loaded vs. unloaded. I don't even know what that speed would be. I'm maintaining the same level of effort. So I think your comment about how I'll have to push harder every rev is not correct is it? I can just go slower instead.
    Force = mass x acceleration. Speed is not an issue. Any time you accelerate, no matter your speed (or more correctly, velocity), increased mass requires increased force.

    This is the kind of stuff that runs through my engineer brain on those long days on the bike.

  19. #19
    Senior Member SmallFront's Avatar
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    Thank you, I knew there was a simple formula somewhere. Now throw in air resistance and a bit of an incline, as well as wind puffs, and we're in business!

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    Quote Originally Posted by andrewclaus View Post
    Force = mass x acceleration. Speed is not an issue. Any time you accelerate, no matter your speed (or more correctly, velocity), increased mass requires increased force.

    This is the kind of stuff that runs through my engineer brain on those long days on the bike.
    My original post (and I agree it is long) openly accepts that acceleration is dramatically affected by weight. As stated though, that is not particularly important to me since I spend a lot more time just riding down the road at a given speed than I do accelerating.

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    I couldn't read all of this, but i think part of what you were wondering is how to calculate the difference in speed based on weight, taking into consideration the incline.

    Here's a calculator:
    http://bikecalculator.com/veloUS.html
    ...

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    Quote Originally Posted by valygrl View Post
    I couldn't read all of this, but i think part of what you were wondering is how to calculate the difference in speed based on weight, taking into consideration the incline.

    Here's a calculator:
    http://bikecalculator.com/veloUS.html
    That's interesting. Thanks. I'd like to see the math. Not that I'm totally qualified to evaluate it but...otherwise the validity of the calculations are in question. I looked at the http://en.wikipedia.org/wiki/Bicycle_performance link too which spells out all the math but there's a good bit of disagreement there about it too. So I'm less sure how important it is to see the math really! But in a broad sense I am seeing confirmation about my belief that weight does not affect speed "very much".

    If I believe the calculator, the effect of weight is small indeed. Probably less than I would have guessed. I increased the weight of the bicycle from 22 lbs. to 120 lbs. That dropped the speed from 15 mph to 14.07 mph. Then to decrease the weight of the cycle from 120 lbs. to 100 lbs., the speed improves from 14.07 mph to 14.26 mph. So to shave 20 lbs. off my pack improves my speed by so very little.

    Then on hills the effect is small too. For a 150 lb. rider with a 120 lb. bicycle on a 7% grade at 150 watts the speed is 3.79 mph. Then this rider shaves 20 lbs. off the load and can go 3.52 mph. That's a bigger hit percentage wise on the hills, but still not much to complain about if we're not racing. That tells me that pouring over my pack to find 20 pounds to get rid of is not doing a lot for me (according to this calculator).

    I suppose the place this hurts the most on hills though is when you get onto the smallest cog. It's hard to ride much slower than 3.5 mph so if 20 lbs. makes the difference between 3.25 and 3.5 then you may be talking about riding vs. walking (or of course the need to temporarily increase effort a lot which is no big deal unless it's super-long hill).

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    You do notice a speed difference but mostly you notice a difference in terms of strength/endurance. You will seem to go slower when loaded as compared to unloaded simple because you aren't maintaining the same endurance level...as long as all you do is train unloaded. Had it happen to me last year. I could 160 mile days back to back without any trouble...unloaded but once I added the load on and also added the factor of setting up/breaking down camp each day and finding places to camp/food/water it started to really put a big hinderance in the numbers of miles I could each day. I ended up averaging more like 120 miles a day when I was on the trip. Sure I was also comparing June/July unloaded to August/September loaded so I had fewer hours of daylight each day as well. My speed didn't really drop that much, with an extra 35 pounds but I did have to get used to riding with the load which took some time.

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    I got the feeling reading your article that you're looking for a simple cost/benefit ratio. Therefore, I think the foray into Newtonian physics (mass, acceleration, gravity) and fluid dynamics (air resistance) isn't necessary. The cost of a given pound is going to be inherently personal and subjective. So, why not just assign some subjective factors to weight and volume and play around with factors? Even if you get a little bit complicated, such as increasing the factors exponentially over a base weight or max weight limit, you'd still be comfortably within 7th grade algebra. Pop a few formulas in Excel and you could investigate your model to no end by adding items and tinkering with the parameters/factors.

    On the benefit side of the equation, I'd be tempted to use the exact opposite of the common risk assessment rationale. I'm not an expert in risk management, but I've seen people apply it to projects a few times. They typically apply exponential factors to the probability of an occurrence and the impact of that occurrence and multiply the two to determine the risk factor. In other words, assign 1, 3, or 9 to both the probability and the impact and multiply. E.g. The probability that a Sasquatch emerges from from the woods to flip me off and call me names is very low as is the impact; "Sticks and stones, Bigfoot. Sticks and stones.") Therefore, 1 times 1 = risk factor of 1. Contrast that with a hike through bear country where the probability of encountering a pissed-off bear is high and the impact of that encounter is very high (he kicks my ass). I'd want to mitigate that risk with bells and spray.

    To morph risk into your benefit, you could assign the probability of using an item while on tour times the impact of using it or the impact of not having it available. E.g. The probability of using water is very high and the impact of not having it available is very high, ergo, you bring water. The probability of using an electric juicer is low and the impact of not having it available is very low, ergo, you might not be able to justify the cost.

    Being a computer nerd, I am interested in this topic. Not because I believe it would yield results any better than gut feel and experience. But interested because it sounds like a fun project and there is a probability that a little surprise pops out of it. Let us know if you pull something together.

  25. #25
    djb
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    another believer in the "old bike+stuff= 1/2 your body weight" adage, just like Machka, when I get past that the enjoyment just goes downhill.

    I only read of this rough calculation a few years ago but when I figured it out for myself, it pretty much was spot on for my real world experiences and the lessons learned from taking too much crap.
    bike 30 lbs + about 40 lbs = 1/2 of me at 140 lbs.
    The 40 lbs magic number is pretty much what I've learned is the amount camping, cooking stuff etc comes to for the things I own and decide to take. It is always going to be a bit more with extra food or water, but its certainly in the ballpark for my target weight, and having toured in fairly mountainous regions, its what works for me---of course we also then get into what gearing works for a given weight and gradient of hills one is going up (but thats a whole other kettle of fish).

    *re: your "level" road comment, it has been very astutely noted by Doug64 that a perfectly level road is pretty darn uncommon in real life compared to all the ups and downs we suddenly notice when riding a bike with 40lbs of stuff on a bike, let alone 80lbs.

    As you say though, whatever works for you.

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