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.