Cayeye tire size chart for cycle computers

[Joe Riel]

Diablo Scott <[email protected]> writes:

> Paul Kopit wrote:
>
> The third is the most interesting to me. In Jobst's proposed test
> he'll ride a measured mile on his bike with the computer that has
> perfect calibration. I asked him not to concentrate too much on
> maintaining a perfectly straight line but to ride "normally". In
> normal riding we swerve around potholes and debris, we take different
> lines around corners, we vary our position relative to the edge of the
> road, we get out of the saddle and stretch or sprint - there are a
> whole host of things we do that make the path of our front wheels
> different (longer) than the straight line distance or whatever path
> GPS uses in its measurement. Since Jobst is certain of his
> calibration data, at the end of his test he'll know exactly how much
> he's deviated from a straight line by how much his computer differs
> from 1.00 miles.

It's easy to estimate an expected error.

Assume that the rider's follows a sinusoid with amplitude A and
period (length) L. The ratio that distance along the sine wave
to the period is greater one can be well approximated by

(1) dL/L ~ 1/4*(A/L)^2

The exact value is an elliptic integral.

Assume that L is equal to the development of the gear train.

(2) L = (F/R)*Dw*pi
= (52/16)(27*inch)(3.14)
~ 260 inch

The amplitude, A, is half the side to side deviation. Six inches
seems a reasonable upper bound for any reasonably competent rider.

(3) A = (6 inch)/2 = 3 inch.

Plugging into (1) gives

(4) dL/L = 1/4*(3/260)^2 = 130e-6 = 0.013%


For a 1 mile course that corresponds to

(5) dL = (130e-6)(5280 ft)(12 in/ft) = 8.4 inch


Good luck distinguishing the two.


Joe Riel

 

[Diablo Scott]

[email protected] wrote:

>
>You are asking whether the displayed distance over greater distance
>does not correspond to that over shorter distances, the instrument
>should be recalibrated to reflect the error incurred in the longer
>one. In that case you should include the small deviations used to
>make "pit" stops, grocery store stops and for dodging obstacles on the
>road. Which road will you use for this?
>
>Jobst Brandt
>
>

My only contention is that it makes more sense to calibrate to the
longer distance (a few miles) than the shorter one (a few wheel revs).
All the talk here about why there might be a difference between the two
or how much that difference might be is interesting but a side issue.

I eagerly await your HWY-1 test report.

 

[[email protected]]

Diablo Scott writes:

>> You are asking whether the displayed distance over greater distance
>> does not correspond to that over shorter distances, the instrument
>> should be recalibrated to reflect the error incurred in the longer
>> one. In that case you should include the small deviations used to
>> make "pit" stops, grocery store stops and for dodging obstacles on
>> the road. Which road will you use for this?

> My only contention is that it makes more sense to calibrate to the
> longer distance (a few miles) than the shorter one (a few wheel
> revs). All the talk here about why there might be a difference
> between the two or how much that difference might be is interesting
> but a side issue.

All the talk here was how to accurately calibrate a Cyclometer, not
whether it represented the crooked path a bicyclist takes between to
known points.

> I eagerly await your HWY-1 test report.

First it's got to stop raining so I can enjoy a ride down the coast.

These 12x36 inch white epoxy road stripes on the paved shoulder are
perpendicular to the road and are not exactly synchronous with the
nearby highway paddle markers that are numbered from the county line.
Some are ahead or behind thes markers. For legal reasons they had to
be accurately placed. In spite of that, they are no longer used since
highway patrol cars are now capable of measuring speeds to great
accuracy from a moving patrol car by using radar on the pavement to
get their own speed and to add or subtract that to the subjects
vehicle speed. Computers are great.

I watched two patrol cars traveling against and with traffic to cite
speeders along two lane part of US395 on the east of the Sierra. Two
lane highways in California, not otherwise marked, have a default
55mph limit as does HWY1 on the coast.

Jobst Brandt

 

[[email protected]]

Tom Sherman writes:

> Why not put two odometers on the bicycle, one calibrated by rollout
> and the other by riding a pre-measured distance?

Oh cut it out. All that is needed to do is compare the displayed
distance with the road distance using the rollout calibration number
(on one and the same instrument). These are digital devices.

Jobst Brandt

 

[Joe Riel]

Joe Riel <[email protected]> writes:

> It's easy to estimate an expected error.
>
> Assume that the rider's follows a sinusoid with amplitude A and
> period (length) L. The ratio that distance along the sine wave
> to the period is greater one can be well approximated by
>
> (1) dL/L ~ 1/4*(A/L)^2
>
> The exact value is an elliptic integral.
>
> Assume that L is equal to the development of the gear train.
>
> (2) L = (F/R)*Dw*pi
> = (52/16)(27*inch)(3.14)
> ~ 260 inch
>
> The amplitude, A, is half the side to side deviation. Six inches
> seems a reasonable upper bound for any reasonably competent rider.
>
> (3) A = (6 inch)/2 = 3 inch.
>
> Plugging into (1) gives
>
> (4) dL/L = 1/4*(3/260)^2 = 130e-6 = 0.013%
>
>
> For a 1 mile course that corresponds to
>
> (5) dL = (130e-6)(5280 ft)(12 in/ft) = 8.4 inch

Screwed up

(1) dL/L ~ pi^2*(A/L)^2

so

(4) dL/L = pi^2*(3/260)^2 = 1.3e-3 = 0.13%

For a 1 mile course that corresponds to

(5) dL = (1.3e-3)(5280)(12) = 83 inch

That is almost the circumference of the wheel,
which is the minimal resolution for many cyclometers.

Joe Riel

 

[[email protected]]

Joe Riel writes:

> For a 1 mile course that corresponds to

> (5) dL = (1.3e-3)(5280)(12) = 83 inch

> That is almost the circumference of the wheel, which is the minimal
> resolution for many cyclometers.

Since deviations from straight ahead are less than +-3 inches the
difference is even smaller for all but the least stable riders (and
ones who ride slow enough to do these gyrations).

The other is that the minimal resolution is the least significant
digit in the calibration number which is dumped into the accumulator
with each passing of the spoke detector magnet. So the resolution of
this once-around is a different from the resolution of distance
displayed although the two are inter-related.

Jobst Brandt

 

[Joe Riel]

[email protected] writes:

> Since deviations from straight ahead are less than +-3 inches the
> difference is even smaller for all but the least stable riders (and
> ones who ride slow enough to do these gyrations).
>
> The other is that the minimal resolution is the least significant
> digit in the calibration number which is dumped into the accumulator
> with each passing of the spoke detector magnet. So the resolution of
> this once-around is a different from the resolution of distance
> displayed although the two are inter-related.

Agreed. I haven't bothered with a cyclometer in years; do they show a
fixed number of digits after the decimal (giving constant precision)
or does the number of displayed digits stay fixed (giving better
precision for short distances)? Not that it matters for this case;
attempting to adjust for rider deviation from a straight line
is a pointless exercise.

Joe

 

[Tim McNamara]

I want to be confident that my computer is reasonably close- that if I
ride 50 miles per my computer, it wasn't really 48 or 53 miles. Or if
I ride a brevet of 250 miles, I'm not getting lost after 220 miles
because my computer is off by a mile.

From my experience, there are no perfectly accurate measuring systems.
Doing brevets last summer, every rider with a GPS ended up with
markedly different data for distance and accumulated climbing- 2 to 3
miles difference in distance and 300-500 feet difference in climbing.

There's nothing you can put on your bike that will slow you down as
much as a computer...

 

[john]

Tim McNamara wrote:

> There's nothing you can put on your bike that will slow you down as
> much as a computer...

Funny!

Another very misleading device is an altimeter w/o temperature
compensation. It seams like so few people realize this. Manufacturers
are able build them w/o temp. comp, and no one objects, so they keep
making them that way. Paying $80 to whatever for an altimeter sans
temp. comp. is a waste of the $$$$. I'd rather pay more & get a usable
instrument.

John

 

[[email protected]]

Joe Riel writes:

>> Since deviations from straight ahead are less than +-3 inches the
>> difference is even smaller for all but the least stable riders (and
>> ones who ride slow enough to do these gyrations).

>> The other is that the minimal resolution is the least significant
>> digit in the calibration number which is dumped into the
>> accumulator with each passing of the spoke detector magnet. So the
>> resolution of this once-around is a different from the resolution
>> of distance displayed although the two are inter-related.

> Agreed. I haven't bothered with a cyclometer in years; do they show
> a fixed number of digits after the decimal (giving constant
> precision) or does the number of displayed digits stay fixed (giving
> better precision for short distances)? Not that it matters for this
> case; attempting to adjust for rider deviation from a straight line
> is a pointless exercise.

Well that depends on which unit. The AVO45 reads in 0.01 Km's and
others with 0.1, but in 100 miles that is unimportant because it dumps
about 2096mm per revolution of the wheel into the accumulator for a
700x25 tire. So in 100 Km about 47710 times that number in Km's is
displayed so the trailing bits are out of the picture.

Jobst Brandt

 

[Bob Flumere]

On 14 Jan 2006 02:57:01 GMT, [email protected] wrote:

>Tom Sherman writes:
>
>> Why not put two odometers on the bicycle, one calibrated by rollout
>> and the other by riding a pre-measured distance?
>
>Oh cut it out. All that is needed to do is compare the displayed
>distance with the road distance using the rollout calibration number
>(on one and the same instrument). These are digital devices.
>
>Jobst Brandt


Has it occured to anyone that the cyclometer is supposed to measure
how far the bike went and not how far the road did?

Jeeeze.. enough already.

 

[Johnny Sunset]

Bob Flumere wrote:
> On 14 Jan 2006 02:57:01 GMT, [email protected] wrote:
>
> >Tom Sherman writes:
> >
> >> Why not put two odometers on the bicycle, one calibrated by rollout
> >> and the other by riding a pre-measured distance?
> >
> >Oh cut it out. All that is needed to do is compare the displayed
> >distance with the road distance using the rollout calibration number
> >(on one and the same instrument). These are digital devices.
> >
> >Jobst Brandt
>
>
> Has it occured to anyone that the cyclometer is supposed to measure
> how far the bike went and not how far the road did?
>
> Jeeeze.. enough already.

For the price of a second odometer (typically 1 to 3% of the cost of a
quality bicycle) one can have both pieces of information, even if Jobst
Brandt does not appreciate the humor of my deliberate facetiousness.

--
Tom Sherman - Fox River Valley

 

[[email protected]]

Bob Flumere writes:

>>> Why not put two odometers on the bicycle, one calibrated by
>>> rollout and the other by riding a pre-measured distance?

>> Oh cut it out. All that is needed to do is compare the displayed
>> distance with the road distance using the rollout calibration
>> number (on one and the same instrument). These are digital
>> devices.

> Has it occurred to anyone that the cyclometer is supposed to measure
> how far the bike went and not how far the road did?

I didn't catch the method you prefer from this but it seems that the
precise (rollout) method is what you advocate as I do.

> Jeeeze.. enough already.

That what I say!

Jobst Brandt

 

[[email protected]]

Tom Sherman writes:

>>>> Why not put two odometers on the bicycle, one calibrated by
>>>> rollout and the other by riding a pre-measured distance?

>>> Oh cut it out. All that is needed to do is compare the displayed
>>> distance with the road distance using the rollout calibration
>>> number (on one and the same instrument). These are digital
>>> devices.

>> Has it occurred to anyone that the cyclometer is supposed to measure
>> how far the bike went and not how far the road did?

>> Jeeeze.. enough already.

> For the price of a second odometer (typically 1 to 3% of the cost of
> a quality bicycle) one can have both pieces of information, even if
> Jobst Brandt does not appreciate the humor of my deliberate
> facetiousness.

I think you need to look in your manner of expression for the answer
to that. As a comedian, your style at times requires the vaudeville
stage hand to come out with the "LAUGH" sign or your intended humor
will be lost.

will not do, such symbols having been over used for diverse
meanings. It's like Sandy's "Bonne route!" that doesn't mask his
perpetual state of pique.

Jobst Brandt

 

[Sandy]

Dans le message de news:[email protected],
[email protected] <[email protected]> a
réfléchi, et puis a déclaré :
> Tom Sherman writes:
>
>>>>> Why not put two odometers on the bicycle, one calibrated by
>>>>> rollout and the other by riding a pre-measured distance?
>
>>>> Oh cut it out. All that is needed to do is compare the displayed
>>>> distance with the road distance using the rollout calibration
>>>> number (on one and the same instrument). These are digital
>>>> devices.
>
>>> Has it occurred to anyone that the cyclometer is supposed to measure
>>> how far the bike went and not how far the road did?
>
>>> Jeeeze.. enough already.
>
>> For the price of a second odometer (typically 1 to 3% of the cost of
>> a quality bicycle) one can have both pieces of information, even if
>> Jobst Brandt does not appreciate the humor of my deliberate
>> facetiousness.
>
> I think you need to look in your manner of expression for the answer
> to that. As a comedian, your style at times requires the vaudeville
> stage hand to come out with the "LAUGH" sign or your intended humor
> will be lost.
>
> will not do, such symbols having been over used for diverse
> meanings. It's like Sandy's "Bonne route!" that doesn't mask his
> perpetual state of pique.
>
> Jobst Brandt



Doesn't make you a better person, does it. Good to get it out, though.
Read anything good lately ? Read anything lately ?
Do you renew the laurels regularly, or does a service have a maintenance
contract.

More appropriate to most of your posts, the following excisable sig line :

--
Les faits relatés ici ne sont que pure fiction, et ne sauraient être
utilisés ou rapprochés d'une situation réelle existant ou ayant
existée

 

[Paul Kopit]

On Fri, 13 Jan 2006 11:41:43 -0800, Diablo Scott
<[email protected]> wrote:

>What percent error do you find between the rollout calibration and the
>corrected number from GPS?

Little deviation but if there is any, the GPS usually indicates that a
lower setting for the wheel size should be used...usually <1%.

 

[Benjamin Lewis]

Diablo Scott wrote:

> [email protected] wrote:
>
>> Are you suggesting that in a straight ahead level mile I cannot
>> control the line enough to get an accurate reading? I suspect you
>> haven't tried riding on such a route, especially with a good tailwind
>> that often prevails on the Coast Highway in that direction.
>> Jobst Brandt
>
> I'm suggesting that in real riding situations, the total distance
> travelled as measured along the actual path of the tire's contact patch
> (which is what you'd have with a "perfectly" calibrated computer),
> doesn't necessarily correspond to the actual sum of straight line
> distances between boundry points (which I contend is what you {I} really
> want to know).

Just to butt in, it's certainly not what *I* want to know. I want to know
how far *I* went, including when I'm on a brevet with cue sheet.

Your preferred distance function is really the perimeter of the convex hull
formed by the points in your journey, or did I not understand correctly
what you meant by boundary points?

--
Benjamin Lewis

Now is the time for all good men to come to.
-- Walt Kelly

 

[Diablo Scott]

Benjamin Lewis wrote:

> Diablo Scott wrote:
>
>>I'm suggesting that in real riding situations, the total distance
>>travelled as measured along the actual path of the tire's contact patch
>>(which is what you'd have with a "perfectly" calibrated computer),
>>doesn't necessarily correspond to the actual sum of straight line
>>distances between boundry points (which I contend is what you {I} really
>>want to know).
>
>
> Just to butt in, it's certainly not what *I* want to know. I want to know
> how far *I* went, including when I'm on a brevet with cue sheet.
>
> Your preferred distance function is really the perimeter of the convex hull
> formed by the points in your journey, or did I not understand correctly
> what you meant by boundary points?
>

Yes, you understand what I meant by my description and I think that's
similar to how you would describe what GPS does. But you missed the
underlying reason for my preference: I want my odometer to match the cue
sheet and so do you. So when I found that my rollout calibration
resulted in a distance reading higher than the measured and stationed
course, I recalibrated. Unless you do too, yours might not (assuming of
course the cue sheets are "accurate" - GPS?).

Again, the reasons for the difference and the magnitude of the
difference are interesting topics for discussion, but if your goal is to
match odometer readings with cue sheets and mileage markers, calibrate
to the longer standard. Sheldon calls this "fine tuning" on his
calibration page.

 

[Sandy]

Dans le message de news:[email protected],
Diablo Scott <[email protected]> a réfléchi, et puis a déclaré :
> Benjamin Lewis wrote:
>
>> Diablo Scott wrote:
>>
>>> I'm suggesting that in real riding situations, the total distance
>>> travelled as measured along the actual path of the tire's contact
>>> patch (which is what you'd have with a "perfectly" calibrated
>>> computer), doesn't necessarily correspond to the actual sum of
>>> straight line distances between boundry points (which I contend is
>>> what you {I} really want to know).
>>
>>
>> Just to butt in, it's certainly not what *I* want to know. I want
>> to know how far *I* went, including when I'm on a brevet with cue
>> sheet. Your preferred distance function is really the perimeter of the
>> convex hull formed by the points in your journey, or did I not
>> understand correctly what you meant by boundary points?
>>
>
> Yes, you understand what I meant by my description and I think that's
> similar to how you would describe what GPS does. But you missed the
> underlying reason for my preference: I want my odometer to match the
> cue sheet and so do you. So when I found that my rollout calibration
> resulted in a distance reading higher than the measured and stationed
> course, I recalibrated. Unless you do too, yours might not (assuming
> of course the cue sheets are "accurate" - GPS?).
>
> Again, the reasons for the difference and the magnitude of the
> difference are interesting topics for discussion, but if your goal is
> to match odometer readings with cue sheets and mileage markers,
> calibrate to the longer standard. Sheldon calls this "fine tuning"
> on his calibration page.

Not being overly interested in the expense of one of these GPS thingies, I
can't figure out what they do, if not give you mileage and position. Why
would you care what a separate bike computer says, if you trust in the GPS.
Don't they offer the same info as a bike computer ?
--
Bonne route !

Sandy
Verneuil-sur-Seine FR

 

[Benjamin Lewis]

Diablo Scott wrote:

> Benjamin Lewis wrote:
>
>> Diablo Scott wrote:
>>
>>> I'm suggesting that in real riding situations, the total distance
>>> travelled as measured along the actual path of the tire's contact patch
>>> (which is what you'd have with a "perfectly" calibrated computer),
>>> doesn't necessarily correspond to the actual sum of straight line
>>> distances between boundry points (which I contend is what you {I}
>>> really want to know).
>> Just to butt in, it's certainly not what *I* want to know. I want to
>> know how far *I* went, including when I'm on a brevet with cue sheet.
>> Your preferred distance function is really the perimeter of the convex
>> hull formed by the points in your journey, or did I not understand
>> correctly what you meant by boundary points?
>>
>
> Yes, you understand what I meant by my description and I think that's
> similar to how you would describe what GPS does. But you missed the
> underlying reason for my preference: I want my odometer to match the cue
> sheet and so do you.

In that case I didn't understand you; that's certainly not what the convex
hull I mentioned measures.

Also, that's *not* what I want. I want my computer to give me a reasonably
accurate reading of the distance I've traveled. Ideally, the cue sheet
will approximately match my odometer, but the match always gets off a
little. I don't turn my computer off every time I take a side jaunt to a
restaurant, restroom, etc.

In any case, I'm not convinced that the GPS measurements of road distances
are any more precise than measurements by bicycles; I suspect they're
significantly less so.

> Again, the reasons for the difference and the magnitude of the difference
> are interesting topics for discussion, but if your goal is to match
> odometer readings with cue sheets and mileage markers, calibrate to the
> longer standard.

I get significantly better precision in my rollout measurements than my
cycle computer allows (I can only enter rim circumference to the nearest
centimeter, but can accurately measure to within a mm or so). I could, of
course, use this additional measurement precision to obtain a corrective
factor for my computer's readout, but readings within the +/- 0.25% accuracy
given by the 1 cm calibration limit are already good enough for my
purposes.

--
Benjamin Lewis

Now is the time for all good men to come to.
-- Walt Kelly