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The Dancing Chain, by Frank Berto
John McGraw wrote:
I'd use log log paper to day to know where my cross over redundant gears are, if I could find the graph paper. Any suggestions on where to find it would be deeply appreciated. John Google "Graph paper software" and you'll find several programs that will print the stuff out. But these days, when I want to do a gear chart, I use a spreadsheet package. Depending what you need, you may find it better to set up an extra column containing the logarithm of the gear inches, but simply plotting the gear inches on a logarithmic axis may be fine. -- --------------------+ Frank Krygowski [To reply, remove rodent and vegetable dot com, replace with cc.ysu dot edu] |
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Frank Krygowski wrote in message ...
John McGraw wrote: I'd use log log paper to day to know where my cross over redundant gears are, if I could find the graph paper. Any suggestions on where to find it would be deeply appreciated. John Google "Graph paper software" and you'll find several programs that will print the stuff out. But these days, when I want to do a gear chart, I use a spreadsheet package. Depending what you need, you may find it better to set up an extra column containing the logarithm of the gear inches, but simply plotting the gear inches on a logarithmic axis may be fine. okay, i don't understand the origianl need for log plots of gear inches. i've seen how the spacing of gears on a single chainring for a typical bike is somewhat logarithmic. perhaps you'd want the gears across the entire range to be lined up on the log plot as a magical ideal, but that seems pretty arbitrary. i don't see how a log plot helps you elimintate duplicate gears in a way that you couldn't do on a linear plot, or even by simply eyeballing the gear chart. -Amit |
#3
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Amit wrote:
okay, i don't understand the origianl need for log plots of gear inches. i've seen how the spacing of gears on a single chainring for a typical bike is somewhat logarithmic. perhaps you'd want the gears across the entire range to be lined up on the log plot as a magical ideal, but that seems pretty arbitrary. i don't see how a log plot helps you elimintate duplicate gears in a way that you couldn't do on a linear plot, or even by simply eyeballing the gear chart. The key is that on a log plot, equal percent changes show up as equal distances between points. If you felt that each gear change should have the same effect (say, reducing your gear ratio by 5%) then you could plot different cog combinations until you achieved equal spacing on a log plot. If you felt you wanted greater spacing in the low gears and finer spacing in the high gears, you could verify that as well. If you plotted things on a linear scale, or just looked at the number of gear inches, you might think shifting from a 100 inch gear to a 95 inch gear would feel the same as shifting from a 30 inch to a 25 inch. But in practice, the former is a fine adjustment, the latter is a pretty big jump. Of course, many people rode far, fast and long without giving this a thought. It all depended on how much you were into the technology and the numbers. -- --------------------+ Frank Krygowski [To reply, remove rodent and vegetable dot com, replace with cc.ysu dot edu] |
#4
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Frank Krygowski wrote: Amit wrote: okay, i don't understand the origianl need for log plots of gear inches. i've seen how the spacing of gears on a single chainring for a typical bike is somewhat logarithmic. perhaps you'd want the gears across the entire range to be lined up on the log plot as a magical ideal, but that seems pretty arbitrary. i don't see how a log plot helps you elimintate duplicate gears in a way that you couldn't do on a linear plot, or even by simply eyeballing the gear chart. The key is that on a log plot, equal percent changes show up as equal distances between points. If you felt that each gear change should have the same effect (say, reducing your gear ratio by 5%) then you could plot different cog combinations until you achieved equal spacing on a log plot. If you felt you wanted greater spacing in the low gears and finer spacing in the high gears, you could verify that as well. If you plotted things on a linear scale, or just looked at the number of gear inches, you might think shifting from a 100 inch gear to a 95 inch gear would feel the same as shifting from a 30 inch to a 25 inch. But in practice, the former is a fine adjustment, the latter is a pretty big jump. Of course, many people rode far, fast and long without giving this a thought. It all depended on how much you were into the technology and the numbers. -- --------------------+ Frank Krygowski [To reply, remove rodent and vegetable dot com, replace with cc.ysu dot edu] It's not as important today as 20+ more years ago, when 5 or 6 speeds were all that were available. It's also not at all difficult to do if log paper is used. What I was saying is that it's still a good way look at ones gearing. So far spread sheets baffle me. They sure don't look like any math I've ever done. Also my peculiar mind has to see or imagine seeing something in order to understand it. Words just float around in empty space. Happy Holidays, John |
#5
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Amit wrote:
Frank Krygowski wrote in message ... John McGraw wrote: I'd use log log paper to day to know where my cross over redundant gears are, if I could find the graph paper. Any suggestions on where to find it would be deeply appreciated. John Google "Graph paper software" and you'll find several programs that will print the stuff out. But these days, when I want to do a gear chart, I use a spreadsheet package. Depending what you need, you may find it better to set up an extra column containing the logarithm of the gear inches, but simply plotting the gear inches on a logarithmic axis may be fine. okay, i don't understand the origianl need for log plots of gear inches. i've seen how the spacing of gears on a single chainring for a typical bike is somewhat logarithmic. When changing gears, the difference your legs feel is a "percent change difference"; so the problem by definition is a geometric sequence. A geometric sequence, which is exponential, of course becomes linear when transformed by the log function. This is where the utility of log-paper comes in, although I've never bothered myself. perhaps you'd want the gears across the entire range to be lined up on the log plot as a magical ideal, but that seems pretty arbitrary. Well sort of--it isn't a law, nor is it exactly acheivable with only rational fractions available. But the rule of thumb is to determine what increments feel good (for example, I choose 6 gStep 9% as desirable), and try to approximate from that specification. Once that is determined, synthesis starts from there--although we are obviously constrained by what actual hardware is available. Some folks do choose to intentionally distort this rule by "stretching the lows," for example. That is, they figure they only need to "bail out" on a rare basis, and don't wish to sacrifice step size. As the number of speeds increases, obviously there are less trade offs. i don't see how a log plot helps you elimintate duplicate gears in a way that you couldn't do on a linear plot, or even by simply eyeballing the gear chart. There is no presumption to eliminate duplicates, except for certain designs. Obviously the so-called "half-step" *requires* interleaving (half-steps are rarely used anymore). For the so-called "crossover," the point is to actually have a duplicate available. IOW, the same percentage step is available whether you cross to other ring, or change only the back. Nowadays, a lot of the duplicate gear concern is awash with 9sp and 10sp cassettes. It just doesn't matter for the most part. (Funny how 9&10sp cassettes have helped obsolete log-paper. Whodda thunk?) |
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Quoth Frank Krygowski:
The key is that on a log plot, equal percent changes show up as equal distances between points. If you felt that each gear change should have the same effect (say, reducing your gear ratio by 5%) then you could plot different cog combinations until you achieved equal spacing on a log plot. If you felt you wanted greater spacing in the low gears and finer spacing in the high gears, you could verify that as well. If you plotted things on a linear scale, or just looked at the number of gear inches, you might think shifting from a 100 inch gear to a 95 inch gear would feel the same as shifting from a 30 inch to a 25 inch. But in practice, the former is a fine adjustment, the latter is a pretty big jump. That would be true if we cycled in a vacuum, opposed by linear frictional resistances only. However, the non-linearity of air resistance cancels this out to a considerable extent. See: http://sheldonbrown.com/gear-theory.html#progression Sheldon "Pear Shaped" Brown +------------------------------------------+ | The lower your gear, the more of your | | riding time will be spent going uphill. | +------------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide http://captainbike.com http://sheldonbrown.com |
#7
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Sheldon Brown wrote:
Quoth Frank Krygowski: The key is that on a log plot, equal percent changes show up as equal distances between points. If you felt that each gear change should have the same effect (say, reducing your gear ratio by 5%) then you could plot different cog combinations until you achieved equal spacing on a log plot. If you felt you wanted greater spacing in the low gears and finer spacing in the high gears, you could verify that as well. If you plotted things on a linear scale, or just looked at the number of gear inches, you might think shifting from a 100 inch gear to a 95 inch gear would feel the same as shifting from a 30 inch to a 25 inch. But in practice, the former is a fine adjustment, the latter is a pretty big jump. That would be true if we cycled in a vacuum, opposed by linear frictional resistances only. However, the non-linearity of air resistance cancels this out to a considerable extent. See: http://sheldonbrown.com/gear-theory.html#progression Sheldon "Pear Shaped" Brown This may sound like a quibble, but: my descriptions of "fine adjustment" and "pretty big jump" are correct. The adjustments are as I describe them, 5% in one case, 17% in the other. What the person is adjusting _for_ is another matter. I'm aware, of course, of the variation in air resistance with speed. That's the reason for the "If" beginning my paragraph above, and the reason for my saying "If you felt you wanted greater spacing in the low gears and finer spacing in the high gears, you could verify that as well." It's perfectly logical to prefer the latter. My intent is not to act as a proponent for either scheme. My intent is to point out why log graph paper is a useful tool when designing either scheme. -- Frank Krygowski [To reply, remove rodent and vegetable dot com. Substitute cc dot ysu dot edu] |
#8
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Sheldon Brown wrote:
That would be true if we cycled in a vacuum, opposed by linear frictional resistances only. However, the non-linearity of air resistance cancels this out to a considerable extent. Why do you presume the speed changed (or anything else)? |
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Sheldon Brown wrote:
See: http://sheldonbrown.com/gear-theory.html#progression Hmmm. Within that same page, I disagree with much of the stuff you've written in this topic: http://sheldonbrown.com/gear-theory.html#cadence, but particularly with this: "For the cyclist who wants to maximize efficiency, there is a particular combination of cadence and resistance that will produce the most power with the least stress on the body. [...] The idea of gears is to select the gear in which this combination of cadence and resistance is met. Depending on the wind, grade and surface conditions, your speed may be faster or slower, but theoretically your legs should always be pushing against the same resistance, and spinning the cranks at the same cadence." -- Still a proud member of the reality-based community. |
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On Tue, 7 Dec 2004 10:36:30 +0100, "Robert Chung"
wrote: Sheldon Brown wrote: See: http://sheldonbrown.com/gear-theory.html#progression Hmmm. Within that same page, I disagree with much of the stuff you've written in this topic: http://sheldonbrown.com/gear-theory.html#cadence, but particularly with this: "For the cyclist who wants to maximize efficiency, there is a particular combination of cadence and resistance that will produce the most power with the least stress on the body. [...] The idea of gears is to select the gear in which this combination of cadence and resistance is met. Depending on the wind, grade and surface conditions, your speed may be faster or slower, but theoretically your legs should always be pushing against the same resistance, and spinning the cranks at the same cadence." And I disagree with you, so? it might be helpful if you explained what/why you disagree with the above. It makes sense to me. Life is Good! Jeff |
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