[email protected] ( Doug Goncz ) wrote in message news:<
[email protected]>...
Dear Doug,
The curious with dialup connections should be warned that the download is 1.6mb for an animated
graph whose point still seems to be better hidden than its original URL.
Possibly your explanation below reveals something, but frankly the position changes of the red dots
on the unlabelled graph resemble minor road vibration.
In a hundred words or fewer, what's the point?
Curiously,
Carl Fogel
> Dear Andrew and Carl,
>
>
http://users.aol.com/DGoncz/Bicycle/Gearing/DoubleStepGearingPossibilities.avi
>
> (Copy, Paste, Go) (it works!)
>
> is 99 frames, now at 2 frames per second. It is designed to use the position cursor to drag left
> and right to select individual frames. I'm sorry, the first attempt was as I was rushing out the
> door to salt my mother's driveway.
>
> The patterns are generated thus:
>
> Assume a top cog of 11. Assume a bottom cog of 30-34. Generate an evenly spaced cassette of seven
> cogs. Determine the step size of the cassette. Pick a low range of 24-27. Pick a middle range
> that's two steps above the low. Pick a high range that's two steps above the middle. Vary both by
> a couple of chainwheel teeth.
>
> Analyze each front/rear combination this way:
>
> Using logarithms, compare each gear to it's nearest integer gear. Zero out the extreme positions
> like 52/34 an 24/11, six positions in all. Call this M. Create matrix J stepping the middle range
> over ONE, not two, and the high range TWO, not four. This puts the gears in opposition as you see
> them on the graph. So when you go up one on the graph, you're going up one in gear sequence. That
> is, pressing once on both index shifters at the same time in the same direction moves you one
> gear. Create D, the display matrix, with gear numbers like 1, 11, and 9.025, as J is laid out. 21
> gears, 10 duplicates, 11 distinct gears.
>
> Analyze J: for the lower two chainwheels, subtract the upper from the lower to form W. Remember
> these are already variances from integer gear positions, so this represents how accurately each
> double shifted step of one gear is made. That's 5 pairs, I think. Also square the number obtained
> forming Q. Do the same for the pairings in the upper two chainwheels.
>
> Slop it all together this way: the mean of M, which represents how closely even spacing is
> maintained, time the standard deviation of W, which represents how evenly the double lever shifts
> are distributed, times the mean of Q, which represents how accurately the double level shifts come
> to being one gear each. This is C, the rating.
>
> Do this for every cassette and chainwheel combination in the limited area of search. Sort on C.
> Display the first 99 so that first gear, second chainwheel is right about second gear, first
> chainwheel. This takes 13 coordinates. All zeroed out combination go to one, so they don't take
> any space on the graph.
>
> The first combination in the latest upload has a range of 670% and near perfect spacing. As you'll
> see by running the video, they only get worse from there, but each has its own character. Like
> some have excellent spacing which is somewhat off of integer perfection in the low range. If you
> are pushing hard, it might be good to have a predictable step there.
>
> This gearing is not for racers. The step between two gears is like a huge change in rpm and pedal
> force. This setup is designed to keep you pedaling up the steepest hill and down the other side. I
> have another worksheet modeling my ultracapacitor and motor/generator combination. This lets you
> store energy pedaling down hill, and use it on ascent. Currently the simulations are not
> encouraging.
>
> However this gearing is of use for automatic shifting. The shifter need only warn of impending up
> and down shifts, avoid the forbidden combinations, and shift, producing a predictable lurch. The
> way I see it, you're only in one gear on long hills. Most of the time, terrain changes, and you're
> shifting.
>
> I have developed a lockout to prevent the forbidden gears from being reached, and a PCB with
> buzzer that beeps when you go to the extreme second chainwheel positions, and next to extreme
> first and third chainwheel positions, so you can back off. I'm working to change the troublesome
> PCB contacts to analog slide pots with trim pots and digitizers and comparaters to do the same
> job, regardless of your indexer spacing.
>
> I selected 24-25-51 and 11-13-16-19-23-28-34, and as you can see that's not number one. But I've
> purchased the cassetes, cogs, and chainwheel. I could send the 51s back for 52s and I would have
> this setup. I purchased on the basis of a much less sophisticated graph.
>
> Now that you know the story, enjoy the video!
>
> Sorry I had to dash on that first post.
>
>
>
> My physics project at NVCC: Google Groups, then "dgoncz" and some of: ultracapacitor bicycle
> fluorescent flywheel inverter