Double Step Gearing Possibilites

[derbobman]

http://users.aol.com/DGoncz/Bicycle/Gearing/DoubleStepGearingPossibilites.avi

My physics project at NVCC:
Google Groups, then "dgoncz" and some of:
ultracapacitor bicycle fluorescent flywheel inverter

[mtrunnell]

If you fool around with the view (compact, perhaps) on a Windows Medi
Player, you can get a graph that looks vaguely sensible. (Our video car settings may not be up to whatever the task is.

An F and and R suggest front and rear gearing, with each followed b numbers for typical teeth that change rapidly. Meanwhile the little re dots jiggle a bit down on a wide green graph

I can't make heads or tails out of it, but perhaps there's mor concealed by my video settings or maybe a more knowledgeable bicyclis would see the point

Carl Foge

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[abbsci420]

A single speed permits a "tolerable" cadence under almost all conditions. Some of us want to spend most of our riding time at something fairly close to an "optimal" cadence.

For riders who wish to go fast, or to cope with headwinds without being slowed too much, smaller steps near the top of the range let them get up to higher speeds with less of a struggle.

At the low end of the range, close spacing is much less important. As you start to climb a hill, your pedaling cadence drops, until you must downshift or stall. There's always a slight loss of momentum involved in making a shift, and if the jumps are too small, a single jump may not be worth the loss of momentum involved.

When you get over the top of the hill, and start to accellerate up through the gears, you aren't facing much resistance as you shift out of your climbing range, and you don't tend to spend much time in any gear until you're back up to cruising speed, so largish jumps in the low range aren't a serious detriment either going up or going down. wide low, close high

Sheldon "Pear Shaped" Brown
+---------------------------------------+
+---------------------------------------+ 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

[abbsci420]

That suggests your big chainwheel is probably too big.

Back in the 5-speed days, lotsa bikes had 14-17-20... freewheels, with
52/40 chainrings. Sometimes folks would get rid of the 14 because they never used it, but I believe that they _might_ have used it if it were accessible.

It is tough to get going fast enough in 52/17 to be able to turn over a
52/14. With an intermediate step to help you accelerate, the 52/14 becomes much more useful.

I can envsion situations/terrains where this might be a good thing.

I haven't ridden in California, but my impression of it is that it's mostly either flat or mountainous.

The area I lived in in France was the opposite, high plateau cut by steep river valleys.

For such situations, tight gearing for fine tuning in flat cruising would be desirable, and a seriously high gear for descending could be useful even if it had a big jump.

For rolling terrain like my New England area, this would be less satisfactory.

Sheldon "Terrain Matters" Brown
+----------------------------------------+
+----------------------------------------+ 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

[derbobman]

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

[derbobman]

The graph shows, in increasing order of calculated rating C, gear combinations of 11 distinct gears numbered using logarithms of gear ratio scaled to the range 1 to 11 which are:

1)Close to an integer measure of perfect spacing, that is gears 1 and 11 are always integers, while 2.001 is preferred to 1.997.

2) Close to an perfect integer value of 1 in double shift changes, that is, from 2.001 to 3.003 is off by +0.002 from 1. These are the shifts that we use to get from one range to another. It is assumed we don't go to the end of a range and then double shift rear while single shifting front.

3) Close to having the same errors in 2 for every step in the same direction and magnitude.

This is accomplished in my second article in this thread with means for 1), means for 2) and standard deviation for 3) combined by multiplying without any weighting.

I want to find out ASAP if the R443 shifter recommended is actually up to this task. There aren't many front shifters that can handle it without grinding.

There's no point at all in finding the "perfect" chainwheels if there's no shifter that will handle them.

The vertical green lines on the graph are from 1 to 13. Each chainwheel has been mated with the one below so that the gear that's one higher is above its mate below. Therefore the x axis represents gear number consistently only within each row.

My physics project at NVCC:
Google Groups, then "dgoncz" and some of:
ultracapacitor bicycle fluorescent flywheel inverter

[abbsci420]

I think your idea of what constitutes "perfect" spacing is fundamentally flawed.

Since drag varies in a non linear fashion with speed, the steps should be smaller at the higher end of the range. The example you give has a humungous 23% jump in the middle of the fast cruising range, the 16-13 jump. This is exactly the part of the gear range that _should_ be closest. There will be lots of road/wind conditions where the 16 is too low, but the 13 is too high.

I think the stock Shimano 11 - 13 - 15 - 18 - 21 - 24 - 34 is just about optimal for the range, given the limitation to 7 sprockets. It may look funny on paper, but I'll bet that if you were to spend some time actually riding with each of these setups, you'd wind up preferring the
Shimano arrangement.

I go into these concepts in more detail at:

http://sheldonbrown.com/gear-theory

Sheldon "GIGO" Brown
+--------------------------------------------------+
+--------------------------------------------------+ 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

[Eidolon X]

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?

[Eidolon X]

Dear Doug and Dave,

The possibilit-

-i-

-es

improve with traditional spelling.

[derbobman]

A controller board the size of a fat Magic Marker will send 4 A/D 0-5V signals and some contact closures to a Pocket PC running Java at 115,000 bps. It runs off the same 5V as the Pocket PC. The Pocket PC will send pulse width and repition rates to winch servos which position the derailers. The four signals are analog road wheel tach, capacitor voltage, altimeter, and possibly anemometer or inclinometer. The Pocket PC displays potential energy of altitude, kinetic energy of speed, and electrical energy E = 1/2 C * V^2 in the cap bank. It has a daylight readable screen but one purpose of the project is to develop self generated light sufficient to descend hillsides that can be reduced to support the full length of an uphill climb.

The automatic shifting will most likely be guided by Polar style chain tension and speed, with calculation of constant power goal suitable for distance or time, and memory of each riders preferred power/pace combination. The shifter avoids the big/big and small/small combinations.

I am currently making little progress but have much time. NVCC welcomes my project in Physics Seminar and Project, and I am checking with Va. DRS for funding for my ODU Mechanical Engineering Technology classes. I only take one class at a time so I can't get grants. DRS is also helping my build my machine shop business, drilling, tapping, milling, and sawing all materials to loose tolerances like 0.05"

Are you suggesting a step-and-a-half sequence? I like the way a double shift gives you a single step in this one. It's the same size as a single cassette step.

This produces varying power output and pacing. I admit it.

I've ordered a head (Kopf) lamp to serve as a head (tube) lamp on 6V. It seems just right for strapping to the head tube: adjustable angle from (90-72)
degrees up to 72 degrees down. LED and / or halogen. Adjustable focus for street or trail.

This is more of a running light, but there's a pedal powered generator to run it. Plenty of power for it and a 1W daylight taillight.

I'm trying lots of new idea on my bicycle. Eventually I will read where they've been tried before.

The 24-35-52 and 34-28-23-29-26-13-11 combinations give 11 distinct, 21 total,
10 repeated gears over 657% range with nearly perfect spacing. It's too be see how it feels to ride.

It's not applicable. One rides down a sloped collecting energy to be used immediately for extending the coast. Current surge limitations on the thin, light rotor preven any other use. On certain hills in my simulations, it comes out ahead. On others, the unequipped bike wins. On others, a bike with a simple flywheel wind. This was designed to be an electric flywheel.

Use motor power to add to the rider's preferred power to make that needed? Neat idea. I have a paper that says on maximum efficiency from below 60 to around
120 pedaling rpm, most efficient power goes up with pace. Not linearly, but hyperbolically.

Yes. I spoke there the last two years in PHY 298 in the fall. Would you like to be invited?

Yes, I see mopeds, scooters, and those awful powered skate wheel scooters.

My physics project at NVCC:
Google Groups, then "dgoncz" and some of:
ultracapacitor bicycle fluorescent flywheel inverter