Schlumpf 29" (guni) calculations

Discussion in 'rec.sport.unicycling' started by David_Stone, Apr 28, 2006.

  1. David_Stone

    David_Stone Guest

    I went for my loop tonight, hitting 22.5 mph again despite my exhaustion
    from yestereen.

    Anyway, on my way home, I used my GPS watch to figure out some cadence
    info.

    LOW GEAR
    I found that in low gear (29"), it took me about 77 revs to hit a tenth
    of a mile, or about 770 revs per mile.

    HIGH GEAR
    It only took about 47.5 revs to reach .1m. That means about 475 revs
    per mile.

    I reached 22.5 mph (tho only for a nanosecond).

    22.5 mph means 22.5/60 miles per minute, or .375 (or 3/8) miles per
    minute. If a mile is 475 revs, then 3/8 of 475 revs per minute is a
    cadence of 178.

    Are my calcs correct? Did I really hit nearly 180 revs per minute on a
    unicycle with a 29" wheel. Jeez. That's a high cadence.


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  2. Mikefule

    Mikefule Guest

    77/47.5 = 1.62

    If your figures are correct, then the hub gears up by 62%

    That seems a lot. A Sturmey Archer hub is + 33%. I think Blue Shift
    is + 50%

    Ar you sure you've measured correctly.

    The arithmetic will be fairly simple if you can be sure of the gear
    ratio.


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  3. harper

    harper Guest

    Mikefule wrote:
    > 77/47.5 = 1.62
    >
    > If your figures are correct, then the hub gears up by 62%
    >
    > That seems a lot. A Sturmey Archer hub is + 33%. I think Blue Shift
    > is + 50%
    >
    > Ar you sure you've measured correctly.
    >
    > The arithmetic will be fairly simple if you can be sure of the gear
    > ratio.




    Mike's SA and BlueShift numbers are correct. SA three speeds go up and
    down 33% as well as 1:1. On 'Schlumpf's unicycle website'
    (http://www.schlumpf.ch/uni_engl.htm) under "technique," "technical
    data" the gear ratio is listed as 1:1.5. I believe Florian's hub is
    actually somewhat higher than that but not 1:1.62.


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  4. harper

    harper Guest

    I don't know what your true rollout is. I get

    29"xPIx77/12"/foot=584' and 584'/5280'/mile=0.11 mile

    So your 77 revs really gets you 10% farther than your cyclometer reads
    if your tire is truly 29". I think my Big Apple rolls out at 29.25"
    diameter which would make 589' in 77 revs or 0.111 mile which is pretty
    much the same thing. Three digit accuracy with rollouts and wheel
    wobble and loaded tire compression is fishy to begin with.

    Could you have miscounted (different from dismounted)? Did you ride on
    an accurately measured 0.1 mile stretch or did you rely on your
    cyclometer for the distance?

    I would question first my (own) ability to count correctly. Then I
    would question the accuracy of the cyclometer and its ability to count
    accurately which may be speed dependent. If you rode on a measured
    tenth mile course I would then question that accuracy.

    Doing this right involves some thought.


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  5. David_Stone

    David_Stone Guest

    I was fairly careful about the 77 and 47.5. I certainly can't have been
    off by 10% - that would be like miscounting 7 revs! I'll double check
    both of the #s.

    Let's suppose that the 77 was really a 76 and that the 47.5 is really
    48. Then 76/48 is 1.58, and that's pretty close to the 1.55:1 ratio
    that many of us have noted earlier about the Schlumpf hubs.

    What I'll do tonite is to check using the cyclo rather than my GPS
    watch, which is less accurate. I will also check using a longer
    distance, like maybe a half-mile.


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  6. U-Turn

    U-Turn Guest

    It looks like you are mixing apples and oranges (basically what Greg
    said). If you are using the GPS to measure speed, that is ground
    speed. The actual distance travelled to achieve that ground speed is
    what a traditional cyclometer would measure. Your cadence would have
    to be higher than that calculated from the GPS to actually achieve the
    GPS speed because of higher-frequency changes in path direction (wobble
    of various types).

    Another factor is how the GPS actually arrived at the top speed you
    mentioned. Something probably not knowable except by the engineers
    that designed that particular GPS. This includes number of averages
    and/or curve fitting of the speed data, noisy data rejection, ghost
    handling, predictive elements to the algorithm, and the like.

    Finally, what's the GPS accuracy anyway? I think it's about 1m these
    days in absolutely clear conditions with 5 satellites and no tree cover
    or surrounding buildings, with a stationary measurement over time. Or
    at least something like that. Can someone confirm or shoot that down
    (it's been a few years)? Anyhow, under typical recreational conditions,
    there's going to be plenty of measurement error to make this kind of
    calculation, which is dependent on one single measurement, essentially
    meaningless. For recreational civilian use with no controls on
    environmental or experimental conditions, treating a max speed as
    anything near truth is probably a misuse of the instrument. An average
    speed, though, taken over a reasonable time (minutes?) should be good
    under many conditions, though not all.

    I've seen people try to map single-track under less than dense leaf
    cover, and have a heck of a time trying to get a GPS to work properly.

    My measurement of the BA diameter has been just about 30", though I did
    not do a rollout on it. This was the fatter BA at about 60 psi,
    unloaded.

    Whatever the calculations, given what cadences track racers reach, and
    world-class cyclists train at, and your much shorter cranks, 178 cps is
    not an overwhelmingly high cadence to reach for a top speed.


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  7. David_Stone

    David_Stone Guest

    U-Turn wrote:
    > If you are using the GPS to measure speed, that is ground speed. The
    > actual distance travelled to achieve that ground speed is what a
    > traditional cyclometer would measure. Your cadence would have to be
    > higher than that calculated from the GPS to actually achieve the GPS
    > speed because of higher-frequency changes in path direction (wobble of
    > various types)
    > Whatever the calculations, given what cadences track racers reach, and
    > world-class cyclists train at, and your much shorter cranks, 178 cps is
    > not an overwhelmingly high cadence to reach for a top speed.


    Hey, Dave! It's always great to communicate with you. I hope all's well.
    As to your points:
    I understand that there is a discrepancy bw the GPS watch and the
    cyclo. However, they both have the same readout for my relatively long
    ride around the loop: 3.35 miles. If there were even a 1% discrepancy,
    it would show up over such a long distance. Since it doesn't, I believe
    that the two are fairly accurate. I also don't wobble very much on
    these rides -- the large wheel and my balance have kept the wobble down
    to a minimum, I think.
    178 isn't -overwhelmingly- high cadence...till you try it. Dang, it's
    a bit scary! I'm not sure I'd like to go much faster, at least not
    without more padding!


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  8. Mikefule

    Mikefule Guest

    Tip the uni upside down. Start with the crank exactly in line with the
    fork leg. Mark the tyre with chalk or tape. Turn the crank exactly 1
    revolution. How far does the wheel turn? It should be easy to tell
    whether it turns:


    - Exactly 1.5 times
    - More than 1.5 times
    - Less than 1.5 times




    Distance covered when in direct drive is a simple matter of arithmetic.
    No need to do empirical testing. Simply measure the diameter of the
    wheel and multiply by Pi.

    For comparison of distances covered in direct drive or in "overdrive",
    minor errors in measurement of the tyre (e.g. not allowing for
    distortion/pressure) won't matter, as the proportions will be the same
    whether the measurement is accurate or not.

    If you can establish the diameter of the tyre, and the ratio of the
    gear, and specify whether you want a metric or imperial calculation, I
    can do it for you.


    --
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  9. U-Turn

    U-Turn Guest

    Mikefule wrote:
    >
    > -Distance covered when in direct drive- is a simple matter of
    > arithmetic. No need to do empirical testing. Simply measure the
    > diameter of the wheel and multiply by Pi.
    >


    The effective decrease in a wheel's diameter due to the interaction of
    rider's weight, tire pressure, tire design/construction, and rim
    characteristics make this approach inadequate, Mike. There is
    significant change in diameter when the rider climbs on. Determing a
    wheel's diameter in action requires some sort of on-unicycle rollout
    approach, hopefully with at least 10 revolutions, and with anti-wobble
    control (e.g., using an overhead pipe).

    In truth, a wheel's diameter in practice will also change with speed,
    as the tire/tube move in and out of the unloaded/loaded diameters with
    inertia, but for a unicycle this would be a tertiary effect at most.

    The change in effective diameter from gear setting to gear setting will
    be a hard change, though, which is what I think you are saying, and
    could be determined from an unloaded experiment like one you are
    describing.


    David_Stone wrote:
    > I understand that there is a discrepancy bw the GPS watch and the cyclo.
    > However, they both have the same readout for my relatively long ride
    > around the loop: 3.35 miles.


    That is completely fascinating and surprising, Dave.


    David_Stone wrote:
    > 178 isn't overwhelmingly high cadence...till you try it. Dang, it's a
    > bit scary! I'm not sure I'd like to go much faster, at least not
    > without more padding!


    I agree completely. I doubt that I've been much over 150 on 150s. To
    make 178 a matter-of-fact cadence would require lots of time at high
    cadences. And 178 on a uni on a public path is hugely different than
    178 on a track bike in a velodrome.


    --
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  10. Mikefule

    Mikefule Guest

    U-Turn wrote:
    > The effective decrease in a wheel's diameter due to the interaction of
    > rider's weight, tire pressure, tire design/construction, and rim
    > characteristics make this approach inadequate, Mike.





    Of course, but assume that the radius is not going to change by more
    than 1 cm (seems reasonable on a tyre pumped up for speed riding):

    Radius of a 28" (for example) is 35.56 cm.

    Thus the error would be 1/35.56 = 2.8%.

    For normal every day purposes, I can live with under 3% error on the
    speedo on my unicycle. It's likely to be more accurate than my car or
    scooter.

    In reality, I'd expect the deformation on my own 28 to be somewhat less
    than 1 cm, and the error to be proportionately reduced.


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  11. joemarshall

    joemarshall Guest

    I've not had time to measure it properly, but by Mikes brief test, I
    think it's more than 1.5:1 and significantly less than 1.75:1

    The Schlumpf bike bottom bracket 'Speed-drive' is 1.65:1, maybe it's
    the same as that, although I'd guess it's lower than that.

    Joe


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  12. David, did you manage the 22.5mp/h on a flat road? And was there any
    wind?
    I've done 33.1km/h on flat with wind but I can't get above 30km/h in
    the velodrome.. More questions! What size cranks are you using and
    what's your cruising speed? That's enough for now..

    Cheers

    Dustin

    P.S. I want a guni


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  13. David_Stone

    David_Stone Guest

    DustinMichels wrote:
    > David, did you manage the 22.5mp/h on a flat road? And was there any
    > wind? ... I've done 33.1km/h on flat with wind but I can't get above
    > 30km/h in the velodrome.. More questions! What size cranks are you
    > using and what's your cruising speed?


    My top speed (achieved on consecutive nights) was on the same stretch of
    DOWNHILL. The hill ends, and then there is a nice flat stretch where I
    maintained a speed ranging from 20-22 mph for a minute. I also don't
    think I could reach a speed of 20 in a velodrome -- the downhill helped
    considerably. My fastest speed on a flat was about 18.5. I've also
    noticed that it takes a while to hit top speed, tho maybe I haven't
    tested that enough. My cranks are 127mm. I don't have a 'cruising
    speed' because I so rarely get to ride on long, flat straightaways. I
    think that the top speed I've maintained for even a few minutes was
    about 16 or 17. I think it's possible I could maintain 16 for an hour
    in a velodrome, but I'd have to train for that one a little.


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  14. Mikefule

    Mikefule Guest

    Assuming a 29 inch wheel

    29 inch diameter x Pi = circumference of 91.12 inches.

    A mile = 1,760 yards.

    X36 = 63,630 inches to the mile

    63,636 / 91.12 = 695.34 revolutions to the mile.

    1 mile an hour = 695.34 / 60 = 11.59 rpm.

    10 miles per hour = 115.90 rpm.

    Assume gearing up of 1.65 and in overdrive, 115.90 rpm = 16.5 mph.

    Or, 115.90 / 16.5 shows that 7.02 rpm = 1 mph.

    22 mph = 7.02 x 22 = 154.44 rpm, which is brisk but not unachievable.


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  15. Klaas Bil

    Klaas Bil Guest

    On Fri, 28 Apr 2006 22:26:23 -0500, David_Stone wrote:

    >Are my calcs correct? Did I really hit nearly 180 revs per minute on a
    >unicycle with a 29" wheel. Jeez. That's a high cadence.


    I tweaked my roadride.xls calculation and on my setup I would need 173
    revs/min to reach 22.5 mph (which I can't, BTW). That's with a 3%
    wobble. If you say you have less wobble, you'll need somewhat less
    rpm, up to 5 rpm less, so probably 168 - 170 rpm. The discrepancy with
    your calculation will be because of the indirect measurement, probably
    mostly in the GPS inaccuracy.

    If you want to know cadence, why not measure cadence? Have a stopwatch
    in your hand, rev up, count every second right foot down (so I mean
    only the even ones, not the odd ones), like this:

    "0
    and that is then 1
    and that is then 2
    ....
    and that is then 10."

    Start the stopwatch at 0, stop it at 10 (that's 100 revolutions), and
    do the calculation.

    For the record:

    The high gear ratio of the Schlumpf uni is exactly 1 : 17/11, or about
    1 : 1.5455.

    The gear ratio of Frank Bonsch's unicycle is 1 : 1.5833.
     
  16. David_Stone

    David_Stone Guest

    Klaas Bil wrote:
    > If you want to know cadence, why not measure cadence? Have a stopwatch
    > in your hand, rev up, count every second right foot down (so I mean
    > only the even ones, not the odd ones), like this: ...
    >
    > Start the stopwatch at 0, stop it at 10 (that's 100 revolutions), and
    > do the calculation.


    Hey, I have to say that at my top speed, flying down a hill where a
    misstep could mean a trip to hospital, I can hardly imagine counting
    strokes. However, I did count cadence on my Coker at about 21 mph on
    that same hill, where I hit a cadence of about 200. The difference is
    that the Coker rides more securely -- a fall isn't quite as dangerous
    -- so I felt safer in paying att'n to cadence. And anyway, I can't rely
    on counting because my cadence is going to vary over the time it takes
    me to count out revs. In addition, unless I count for a long time, I
    may add or subtract a rev, which in a short distance will alter my
    overall cadence.



    > The high gear ratio of the Schlumpf uni is exactly 1 : 17/11, or about 1
    > : 1.5455.


    Where'd you get that 17/11? That's a weird fraction, but it certainly is
    about how much I've calculated the shift to be.


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  17. joemarshall

    joemarshall Guest

    I have one of these radar speed signs near my house. I'm not sure how
    accurate it is but it's a great way of knowing how fast you're going.
    http://www.nwpwr.com/traffic_sig/speed_signs.htm

    I'm okay to get to 19mph either on the Schlumpf or the Coker, but I'm
    still not sure if I've passed it going faster than 20mph on either
    (I've had higher figures on the coker but I think a car interfered). I
    think the Schlumpf will be first if I do it, just because I'm commuting
    on that at the moment. It's a bit hard to use the sign, as sometimes it
    doesn't catch you, and often there are cars in the way, and there's
    only about 100m of slightly downhill to accelerate up to it.

    I did some RPM tests too, on the flat, with a smooth surface, doing
    120rpm is fine, and 100rpm is easy-tastic normal cruising speed. 120rpm
    is about 16mph I believe.

    Joe


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  18. Klaas Bil

    Klaas Bil Guest

    David_Stone wrote:
    > Hey, I have to say that at my top speed, flying down a hill where a
    > misstep could mean a trip to hospital, I can hardly imagine counting
    > strokes. However, I did count cadence on my Coker at about 21 mph on
    > that same hill, where I hit a cadence of about 200. The difference is
    > that the Coker rides more securely -- a fall isn't quite as dangerous
    > -- so I felt safer in paying att'n to cadence. And anyway, I can't rely
    > on counting because my cadence is going to vary over the time it takes
    > me to count out revs. In addition, unless I count for a long time, I
    > may add or subtract a rev, which in a short distance will alter my
    > overall cadence.
    >
    > Where'd you get that 17/11? That's a weird fraction, but it certainly
    > is about how much I've calculated the shift to be.



    I have counted rpm's easily at 160 rpm using my method (on a 20"). I
    actually find that I can go faster if I count. Like yours, my cadence
    varies over time, but my counting can keep up.

    For the 17/11, I first counted like a 100 revs with the unicycling
    hanging from the ceiling to get a decimal number, then I did some math
    to find an almost matching fraction with not too high numbers, because
    I figured that there must be some exact fraction there. Then I checked
    and it turned out to be exact. Must have to do with the number of teeth
    on the sun and planet cogs.


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  19. harper

    harper Guest

    David_Stone wrote:
    >
    > Where'd you get that 17/11? That's a weird fraction, but it certainly
    > is about how much I've calculated the shift to be.




    A simple planetary gear system with fixed sun and driven planets has a
    gear ratio of 1:1+S/R where S is the number of teeth in the sun gear
    and R is the number of teeth in the ring gear. The fraction 17/11, also
    written 1+6/11, suggests that the ratio of the number of teeth in the
    sun gear to the ring gear is 6/11.

    Florian's hub has 6 planet gears which means that both the number of
    teeth in the sun and ring gears must be evenly divisible by 6 in order
    to mesh. My guess is that the sun gear has 36 teeth and the ring gear
    has 66 teeth. This could be made small and rugged.

    The gear diameters must add such that two planet diameters plus one sun
    diameter fit into one ring diameter. The difference between the ring
    and sun gears is 30 teeth so that each planet gear would have 15 teeth.
    This is a workable combination for any number of gear pitches which
    could be determined if you knew the diameter of any one of the gears.

    That's my guess. His ring gear has 66 teeth, his sun gear has 36 teeth,
    and his planet gears have 15 teeth each. This is where the 1:17/11
    ratio comes from.


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