# Double Step Gearing Possibilites

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Sheldon Brown <[email protected]> wrote:
>David Damerell snipped what he was replying to and wrote:
>>There are two ways to approach this situation. One is to desire a specific cadence and to be
>>willing to allow the effort to vary to match that cadence; the other is to desire a specific
>>effort (obviously the available effort varies depending on how you feel that day and how far you
>>have to go, but at any given point it's a specific amount) and to allow the cadence to vary to
>>match that effort.
>This seems to me to be a "distinction without a difference." Indeed, if a perfect, continuously
>variable transmission existed, one would be able to maintain constant effort and cadence under all
>slope and wind conditions.

But one doesn't, and we have to compromise one or the other (or both).

>If the jumps are too large in the high cruising range, you cannot necessarily maintain the desired
>effort level. There will be situations where the desired effort in one gear will cause you to
>accelerate until you spin out of that gear, while the same effort in the next gear up won't be
>sufficient to maintain speed,

Why is this any more true in a high gear?

[Actually I don't think this, as written, is true at all; if you could spin up to a given speed in
gear n, you could always maintain it in gear n+1.]

It seems to me that the question being asked of a hypothetical drivetrain is "Does there exist any
speed between the expected minimum and maximum where the cadence is intolerable"; or "What is the
greatest variation from my optimal cadence that this drivetrain can demand?"; and that variation is
minimised by evenly spaced [1] gears.

As a concrete example, consider the 24/34 jump on the Megarange 11-34; if one was spinning the 34
at 100rpm, a shift into the 24 would take us down to 70rpm. With a more evenly spaced 7-speed,
such as an
11/13/16/19/23/28/34, the lowest one can get to after shifting up from 100rpm is 77rpm (the 16-
>13 shift).

I think the very low low gear dates from the days of fewer sprockets, when there simply had to be an
unacceptably huge gap somewhere if the overall range was not to be too small. In those cases it made
sense to have the gap at the low end because at low speeds going slightly faster to keep the cadence
acceptable demands a lesser increase in effort.
--
David Damerell <[email protected]> Kill the tomato!

"David Damerell" <[email protected]> wrote in message
news:ZXF*[email protected]...
> Sheldon Brown <[email protected]> wrote:
> >David Damerell snipped what he was replying to and wrote:
> >>There are two ways to approach this situation. One is to desire a
specific
> >>cadence and to be willing to allow the effort to vary to match that
> >>the other is to desire a specific effort (obviously the available effort varies depending on how
> >>you feel that day and how far you have to go,
but
> >>at any given point it's a specific amount) and to allow the cadence to vary to match that
> >>effort.
> >This seems to me to be a "distinction without a difference." Indeed, if a perfect, continuously
> >variable transmission existed, one would be able to maintain constant effort and cadence under
> >all slope and wind conditions.
>
> But one doesn't, and we have to compromise one or the other (or both).
>
> >If the jumps are too large in the high cruising range, you cannot necessarily maintain the
> >desired effort level. There will be situations where the desired effort in one gear will cause
> >you to accelerate until you spin out of that gear, while the same effort in the next gear up
> >won't be sufficient to maintain speed,
>
> Why is this any more true in a high gear?
>
> [Actually I don't think this, as written, is true at all; if you could spin up to a given speed in
> gear n, you could always maintain it in gear n+1.]
>
> It seems to me that the question being asked of a hypothetical drivetrain is "Does there exist any
> speed between the expected minimum and maximum where the cadence is intolerable"; or "What is the
> greatest variation from my optimal cadence that this drivetrain can demand?"; and that variation
> is minimised by evenly spaced [1] gears.
>
> As a concrete example, consider the 24/34 jump on the Megarange 11-34; if one was spinning the 34
> at 100rpm, a shift into the 24 would take us down to 70rpm. With a more evenly spaced 7-speed,
> such as an
> 11/13/16/19/23/28/34, the lowest one can get to after shifting up from 100rpm is 77rpm (the 16->13
> shift).
>
> I think the very low low gear dates from the days of fewer sprockets, when there simply had to be
> an unacceptably huge gap somewhere if the overall range was not to be too small. In those cases it
> made sense to have the gap at the low end because at low speeds going slightly faster to keep the
> cadence acceptable demands a lesser increase in effort.
> --
> David Damerell <[email protected]> Kill the tomato!

For me the big advantage of having close spaced gears in the "level cruise" range is I spend a lot
of time there. As the result that sort of spacing gives me maximum "efficiency" - i.e. I spend the
greatest part of the ride near my preferred cadence. Additionally, the places/times I'm likely to be
using the gear extremes often have varying gradient, so by the time I'm in the "perfect" gear the

At the risk of going off topic - don't circuit racers (you know those roundy-roundy type racing cars
they have in the US) have exactly the type of gearing that Sheldon likes? Hugh Fenton

Sheldon Brown wrote:
> Some of us want to spend most of our riding time at something fairly close to an "optimal"

I read some of this thread and I'm a bit surprised. Robert Chung has analyzed some power meter data
and empirically shown that cadence is not the real goal of optimization. It's torque. See his page
at http://mywebpage.netscape.com/rechung/wattage/. The appropriate links are under "Data Analysis"
and those links are broken right now. I hope he's reading this NG, since a quick google and yahoo
search didn't give me his addy (too many Robert Chungs out there).

The analyses of gear ratios in this thread seems fundamentally flawed, since the cadence is used as
the optimization goal. I don't know how the conclusions would change; that requires a bit more
thought. Maybe I'll think about that while I'm on the bike tonight...

Dave dvt at psu dot edu

Hugh Fenton <[email protected]> wrote: [Gear spacing]
>For me the big advantage of having close spaced gears in the "level cruise" range is I spend a lot
>of time there.

Now this is an interesting point (but this doesn't quite suggest close spacing at the very top end,
but rather just below it, on the assumption that you have some gears for pedalling downhill or with
strong tailwinds).
--
David Damerell <[email protected]> Distortion Field!

dvt wrote:
> See his page at http://mywebpage.netscape.com/rechung/wattage/.

The links appear to be operative now. They didn't work yesterday, and last night there was a graphic
missing. Read the section "Can I use power to find my optimum cadence," then move on to "The
components of power." Very interesting stuff, IMO.

Dave

>From: meb [email protected]

> Is your shifting microprocessor controlled, mechanical, analog electro-mechanical?

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"

>If micro, you should still be able to program a non repetitive gear selection step sequence.

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.

>Otherwise, you might need set up ratio combinations to give a repetitive shift sequence as you step
>through the gears.

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.

>Also, I think youâ€™ll find you will you change ratios on downhills because your speed is not
>constant.

There are a few high gears in there.

>What is your top speed with electric boost?

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.

> I find on my electric bikes, tight ratios are less critical since the motor supplements enough
> torque to give you a broad range of acceptable pedal ratios.

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.

>Are you at the Annandale campus of NVCC?

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

>Iâ€™m located in Arlington and have come accross fewer than ten electrics in the DC area.

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

Originally posted by Doug Goncz
>From: meb [email protected]
Snip

>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.

I was suggesting even smaller steps at the high ratios, and broader steps at the lower electric speeds. Identical spacing is not that beneficial in ratios because of the nonlinear drag effect. That issue will be amplified with a bike that has electric assist because the added electric torque reduces ratio criticality in the electric speed range, extra weight creating more load when not having electric available such as exceeding the speed of the electrics.

Snip

>>What is your top speed with electric boost?
>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.

> >I find on my electric bikes, tight ratios are less critical since the motor supplements enough
>> torque to give you a broad range of acceptable pedal ratios.

>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.

That’s standard practice on electric bikes, in Europe and Japan it is mandated the electric drive not operate unless the pedals are moving.

I was asking about top speed for the flats. As indicated, while in the electric speed range, the ratio differences can be very broad since the motor supplements the pedalling enough that you need add less torque. Consequently you could use fewer ratios in the electric range and increase the number of ratios above the max electric speed for fine adjust.

>>Are you at the Annandale campus of NVCC?

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

Are you presenting this as lecture once each fall or are you a staff/faculty/grad student teaching the class? I’d be interested in seeing the presentation if my schedule fits at that time. Is your bike in a lab at the school? I will take a half day seminar at the school on 4/14.

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