Gain ratio and other methods of gear comparison

Discussion in 'Cycling Equipment' started by Byron Sheppard, Nov 26, 2003.

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  1. I recently read Sheldon Brown's intriguing proposal for a universal system of gear comparison which
    he calls "gain ratio" (name attributed to someone else. see http://www.sheldonbrown.com/gain.html).
    What do others think of it and why hasn't the system gained more "traction" in the cycling world.
    Or has it?

    As an engineer, I am attracted to the unit-less-ness of it, though I haven't yet figured out whether
    that is actually useful, for reasons mentioned below.

    It also raised some other interesting questions. In my own little cycling universe, I have always
    compared gear combinations by calculating the front/back ratio and multiplying it by the wheel
    circumference, usually in inches. Thus I have discovered that I reinvented the notion of
    "development in inches" rather than meters. Contrary to Sheldon's claim that this method is
    cumbersome because it involves multiplying the wheel diameter by an irrational number, I found it
    easy because the wheel circumference is usually in my notes having been directly measured and
    entered into my computer (though usually in mm's). Then I whip up a spreadsheet table that allows me
    to compare the number of inches traveled per crank revolution with each ratio, which is then easily
    compared between bikes with different gearing, tire, and wheel combinations.

    Sheldon raises a valid technical point about the error introduced by ignoring differences in crank
    length, but I only have four bikes and they all have the same crank length, whether on road or off.
    So this would seem to be a problem only if you have as many bikes as Sheldon does, a problem I'm
    sure we'd all love to have. (or perhaps for those naïve enough to have road and mountain bikes with
    the same crank length)

    I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    good is this number, except purely for the sake of comparison, and why did it become so popular? It
    seems only vaguely related to inches actually traveled (through a proportion of pi) which doesn't
    give it much intuitive value.

    I guess I like comparing inches traveled, rather than gain ratios or gear inches, because then I
    know the magnitudes of the numbers compared have some physical meaning.

    So my question to the group is: what method of comparing gear ratios have others found
    useful and why?

    fire away, byron

    BTW, for the record, I love Sheldon's site. I have learned a great deal about cycling from him
    (including especially how to build my own wheels; the last great mechanical cycling mystery solved)
    and always promote the site to others. It is a great service to our sport. Thanks, Sheldon!
     
    Tags:


  2. David Kerber

    David Kerber Guest

    In article <BBE9A1E8.16BEF%[email protected]>, [email protected] says...

    ...

    > I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    > discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    > good is this number, except purely for the sake of comparison, and why did it become so popular?
    > It seems only vaguely related to inches actually traveled (through a proportion of pi) which
    > doesn't give it much intuitive value.

    It supposedly comes from being equivalent to the size of the wheel of an "ordinary" (one of those
    old-time bikes with the huge front wheel and small rear) which one might ride, and which had the
    pedals connected directly to the wheel.

    --
    Dave Kerber Fight spam: remove the ns_ from the return address before replying!

    REAL programmers write self-modifying code.
     
  3. Byron Sheppard wrote:

    > I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    > discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    > good is this number, except purely for the sake of comparison,

    It _is_ purely for the sake of comparison...why else would you want to calculate a gear value? ;-)

    > and why did it become so popular? It seems only vaguely related to inches actually traveled
    > (through a proportion of pi) which doesn't give it much intuitive value.

    This is explained in my Bicycle Glossary at:

    http://sheldonbrown.com/gloss_g.html#gearinch

    Sheldon "http://sheldonbrown.com/glossary" Brown +-----------------------------------------+
    | When I cannot sing my heart, | I can only speak my mind... | --John Lennon |
    +-----------------------------------------+ 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
     
  4. Art Harris

    Art Harris Guest

    Byron Sheppard wrote:

    > I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    > discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    > good is this number,

    That goes back to the days of the penny farthings (high wheelers). Those were direct drive, and a
    bigger wheel covered more distance for each pedal revolution.

    The "gear inches" calcuation gives you the equivalent wheel diameter of a high wheeler.

    Art Harris
     
  5. Byron Sheppard <[email protected]> wrote in message news:BBE9A1E8.16BEF%[email protected]...
    > I recently read Sheldon Brown's intriguing proposal for a universal system of gear comparison
    > which he calls "gain ratio" (name attributed to someone else. see
    > http://www.sheldonbrown.com/gain.html). What do others think of
    it
    > and why hasn't the system gained more "traction" in the cycling world. Or has it?

    Hate to say it , cos Sheldon has a great site, but I don't like it since it takes no account of gain
    variation as the knee opens nor muscle function effects.

    It doesn't work for max power effort gear selection according to a scientific test.

    Personal experience tells me a 17 sprocket on a 190 crank feels harder than a 19 sprocket on a 170
    although the gain remains the same.

    > So my question to the group is: what method of comparing gear ratios have others found useful
    > and why?

    Just divide chainring size by sprocket size - simpler than anything else for a given crank/wheel
    setup, though the question rarely arises.

    Andrew Bradley
     
  6. Pete Biggs

    Pete Biggs Guest

    Byron Sheppard wrote:
    > I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    > discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    > good is this number, except purely for the sake of comparison

    That's the numbers are usually used for. Eg. to compare existing gears to various different
    possibilities.

    > , and why did it become so popular?

    Because it's simple and produces nice chunky numbers that are easy to remember.

    > It seems only vaguely related to inches actually traveled (through a proportion of pi) which
    > doesn't give it much intuitive value.

    It's pretty obvious what 27" means (on a road bike with approx 27" wheels).

    > So my question to the group is: what method of comparing gear ratios have others found useful
    > and why?

    None - except when I have a go with others when vaguely curious about different cranks.

    ~PB
     
  7. Dave Kahn

    Dave Kahn Guest

    Byron Sheppard <[email protected]> wrote in message news:<BBE9A1E8.16BEF%[email protected]>...

    > What do others think of it and why hasn't the system gained more "traction" in the cycling world.
    > Or has it?

    Consider competitions in which riders are limited to a maximum gear ratio. In road racing in the UK
    this is generally applied to young riders. A wily rider, or his coach, could defeat the gear limit
    by using shorter cranks. This is both unfair and potentially harmful to the developing athlete. If
    the limit were expressed as a gain ratio this would not be possible. Why hasn't it caught on? I
    can't think of a reason other than that we're just set in our ways.

    > I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    > discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    > good is this number, except purely for the sake of comparison, and why did it become so popular?
    > It seems only vaguely related to inches actually traveled (through a proportion of pi) which
    > doesn't give it much intuitive value.

    The high performance racing bike of its brief day was the ordinary, or penny-farthing. If you wanted
    a higher gear you needed a bigger front wheel. Your top gear was limited by the size of wheel you
    could perch above and still pedal. When people started riding chain drive bicycles it was natural to
    express the gear size in way that allowed a direct comparison with the ordinary. So riding a 90"
    gear would be equivalent to riding an ordinary with a 90" diameter wheel - an improbable beast. As
    you say, "gear inches" are only really good for comparison.

    > I guess I like comparing inches traveled, rather than gain ratios or gear inches, because then I
    > know the magnitudes of the numbers compared have some physical meaning.

    It's a very good point.

    --
    Dave...
     
  8. Pete Biggs

    Pete Biggs Guest

    Pete Biggs wrote:
    > Byron Sheppard wrote:
    >> I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    >> discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    >> good is this number, except purely for the sake of comparison
    >
    > That's the numbers are usually used for. Eg. to compare existing
    ^^^^ what
    > gears to various different possibilities.

    ~PB
     
  9. Matt O'Toole

    Matt O'Toole Guest

    "Andrew Bradley" <[email protected]> wrote in message
    news:[email protected]...

    > Just divide chainring size by sprocket size - simpler than anything else for a given crank/wheel
    > setup, though the question rarely arises.

    Ah, but wheel setups in particular vary a lot -- like between my road, mountain, and beach
    cruiser bikes.

    I like the idea of distance traveled per crank revolution, but I admit I think in gear inches.

    Matt O.
     
  10. Bruce

    Bruce Guest

    But any distance value is a real number. And since there are infinitly more real then rational
    numbers the distance is almost certainly irrational, so when Sheldon includes two distances - wheel
    radius and crank length - he doesn't remove that issue.

    For simiplicity perhaps staying with pure integers would be best, so a 38-16 is just that, a 38-16.
    And to compare two gears, say the 38-16 and 50-21 you could just multiply the first of the first by
    the second of the second and compare that to the first of the second times the second of the first.

    38*21 = 798 50*16 = 800 so the 50-21 is slightly larger.

    -Bruce

    As far as "Byron Sheppard" <[email protected]> wrote in message
    news:BBE9A1E8.16BEF%[email protected]...
    > I recently read Sheldon Brown's intriguing proposal for a universal system of gear comparison
    > which he calls "gain ratio" (name attributed to someone else. see
    > http://www.sheldonbrown.com/gain.html). What do others think of
    it
    > and why hasn't the system gained more "traction" in the cycling world. Or has it?
    >
    > As an engineer, I am attracted to the unit-less-ness of it, though I
    haven't
    > yet figured out whether that is actually useful, for reasons mentioned below.
    >
    > It also raised some other interesting questions. In my own little cycling universe, I have always
    > compared gear combinations by calculating the front/back ratio and multiplying it by the wheel
    > circumference, usually in inches. Thus I have discovered that I reinvented the notion of
    "development
    > in inches" rather than meters. Contrary to Sheldon's claim that this
    method
    > is cumbersome because it involves multiplying the wheel diameter by an irrational number, I found
    > it easy because the wheel circumference is usually in my notes having been directly measured and
    > entered into my computer (though usually in mm's). Then I whip up a spreadsheet table that allows
    > me to compare the number of inches traveled per crank revolution
    with
    > each ratio, which is then easily compared between bikes with different gearing, tire, and wheel
    > combinations.
    >
    > Sheldon raises a valid technical point about the error introduced by ignoring differences in crank
    > length, but I only have four bikes and they all have the same crank length, whether on road or
    > off. So this would seem to be a problem only if you have as many bikes as Sheldon does, a problem
    > I'm sure we'd all love to have. (or perhaps for those naïve enough to have road and mountain bikes
    > with the same crank length)
    >
    > I always thought I must be calculating what everyone else called "gear inches" and was baffled to
    > discover that that term actually refers to the gear ratio times the wheel diameter. What the heck
    > good is this number, except purely for the sake of comparison, and why did it become so
    popular?
    > It seems only vaguely related to inches actually traveled (through a proportion of pi) which
    > doesn't give it much intuitive value.
    >
    > I guess I like comparing inches traveled, rather than gain ratios or gear inches, because then I
    > know the magnitudes of the numbers compared have
    some
    > physical meaning.
    >
    > So my question to the group is: what method of comparing gear ratios have others found useful
    > and why?
    >
    > fire away, byron
    >
    >
    > BTW, for the record, I love Sheldon's site. I have learned a great deal about cycling from him
    > (including especially how to build my own wheels;
    the
    > last great mechanical cycling mystery solved) and always promote the site
    to
    > others. It is a great service to our sport. Thanks, Sheldon!
     
  11. Erik Brooks

    Erik Brooks Guest

    Byron Sheppard asked:
    > I recently read Sheldon Brown's intriguing proposal for a universal system of gear comparison
    > which he calls "gain ratio" (name attributed to someone else. see
    > http://www.sheldonbrown.com/gain.html). What do others think of it and why hasn't the system
    > gained more "traction" in the cycling world. Or has it?
    >
    I'm another big fan of Sheldon's, and I've thought a bit about this gain ratio idea, but I don't
    personally have any datapoints about it, so take my comments with a _block_ of salt.

    It seems to me that the crank length is very important to power output at low cadence, and not very
    important at higher cadence. The gear ratio would be important at both hi and low cadence.

    If my gut feel analysis has any validity, then the gain ratio approach would be somewhat analagous
    to torque readings in a gas engine, and the gear ratio approach is more similar to horsepower
    readings. Of course, the riders strength affects actual power more than any bike parts.

    just a thought....
     
  12. "Matt O'Toole" <[email protected]> wrote in message news:<[email protected]>...
    > "Andrew Bradley" <[email protected]> wrote in message
    > news:[email protected]...
    >
    > > Just divide chainring size by sprocket size - simpler than anything else for a given crank/wheel
    > > setup, though the question rarely arises.
    >
    > Ah, but wheel setups in particular vary a lot -- like between my road, mountain, and beach
    > cruiser bikes.

    Yes, for people building different wheel-size bikes from scratch either gear inches "development" or
    gain are useful ballparks, though not as easy to work out mentally.

    But different size wheels usually mean different applications. I used mostly 57X12 to 50X21 on my
    last racing bike. I've never considered what that would be on my mtb - hard work i reckon.

    I like the sound of a beach cruiser bike, is that for sand or something?

    Andrew Bradley
     
  13. Ron Hardin

    Ron Hardin Guest

    You can actually get a real ratio by dividing the (for some reason used) gear inches by the crank
    length in inches.

    Then it doesn't matter what bicycle you have. Same ratio means same pedal force, on an uphill say.
    --
    Ron Hardin [email protected]

    On the internet, nobody knows you're a jerk.
     
  14. Ron Hardin wrote:
    > You can actually get a real ratio by dividing the (for some reason used) gear inches by the crank
    > length in inches.
    >
    > Then it doesn't matter what bicycle you have. Same ratio means same pedal force, on an uphill say.

    That's what Gain Ratio is. You calculate it with any unit system you like-inches, meters, furlongs,
    micro-light-years...

    Sheldon "http://sheldonbrown.com/gain" Brown +----------------------------------------------------+
    | I admit that reason is a small and feeble flame, | a flickering torch by stumblers carried in the
    | | star-less night, -- blown and flared by passion's | storm, -- and yet, it is the only light. |
    | Extinguish that, and nought remains. | -- Robert Green Ingersoll |
    +----------------------------------------------------+ 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
     
  15. Tom Sherman

    Tom Sherman Guest

    Andrew Bradley wrote:
    >
    > Just divide chainring size by sprocket size - simpler than anything else for a given crank/wheel
    > setup, though the question rarely arises.

    This may work fine for road bike riders who now almost always use ISO 622-mm (700C) wheels and tires
    that typically range from 19-28 mm in width (so wheel circumferences vary only slightly) but it does
    not work for internally geared hubs, multi-speed BB's (Schlumpf), compound drives, small
    drivewheels, or some combination of these.

    Tom Sherman - Planet Earth
     
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