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Main
Date: 05 Nov 2007 00:50:40
From:
Subject: 1903 bicycle wheel FEA
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It turns out that the FEA for a bicycle wheel was done before 1903:
[After an impressive page of equations for an 8-spoke bicycle wheel]
"As a particular instance let W [weight] = 1000 pounds . . . Then the
stress for all the spokes except [lowermost spoke] is 76 pounds
tension, and that in [lowermost spoke] is 924 pounds compression; also
the stress in each segment of the rim is about 98 pounds compression.
It thus appears that the vertical spoke under the hub carries nearly
all the load as a compressive stress, and that as the wheel slightly
turns this is turned into a small tensile stress."
--"A Text Book on Roofs and Bridges," 5th ed., 1903, Merriman & Jacoby
p. 149-150
http://books.google.com/books?id=kBM5AAAAMAAJ&pg=PA149&dq=%22bicycle+wheel+with+stiff+spokes%22&as_brr=1&ei=yMguR4_UIZ3epQKkr63vCQ#PPA149,M1
or http://tinyurl.com/yrqx6d
Cheers,
Carl Fogel
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Date: 07 Nov 2007 09:27:37
From: bjw@mambo.ucolick.org
Subject: Re: 1903 bicycle wheel FEA
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On Nov 6, 7:05 am, unforgive...@juno.com wrote:
> On Nov 5, 3:42 pm, carlfo...@comcast.net wrote:
>
>
>
> > On 05 Nov 2007 16:21:05 GMT, jobst.bra...@stanfordalumni.org wrote:
>
> > >Carl Fogel writes:
>
> > >> It turns out that the FEA for a bicycle wheel was done before 1903:
>
> > >> [After an impressive page of equations for an 8-spoke bicycle wheel]
>
> > >> "As a particular instance let W [weight] = 1000 pounds... Then the
> > >> stress for all the spokes except [lowermost spoke] is 76 pounds
> > >> tension, and that in [lowermost spoke] is 924 pounds compression;
> > >> also the stress in each segment of the rim is about 98 pounds
> > >> compression. It thus appears that the vertical spoke under the hub
> > >> carries nearly all the load as a compressive stress, and that as the
> > >> wheel slightly turns this is turned into a small tensile stress."
>
> > >> --"A Text Book on Roofs and Bridges," 5th ed., 1903, Merriman & Jacoby
> > >> p. 149-150
>
> > >http://tinyurl.com/yrqx6d
>
> > >Unfortunately this escaped notice and the wire spoked wheel escaped
> > >mention in this work. I didn't understand how the author entered the
> > >structural parameters of the rim and spokes, but that is less
> > >important than the conclusions... that did not carry over into the
> > >world of bicycling.
>
> > >Jobst Brandt
>
> > Dear Jobst,
>
> > I'd be astonished if anyone could have dug it up back in the
> > pre-Google era. You'd have to read every engineering book back to the
> > 1890's to find that 2-page example--and it's in a book about roofs and
> > bridges, not about bicycles.
>
> > I stumbled over it while searching for references to tying and
> > soldering and thought damn, but that looks like somebody doing an FEA
> > for 8 spokes by hand instead of with a computer!
>
> > I didn't follow the equations at all--it may not even be an FEA in the
> > modern sense. But the conclusion and example tensions sure look like
> > they agree with "The Bicycle Wheel."
>
> > And that final sentence is awfully good: "It thus appears that the
> > vertical spoke under the hub carries nearly all the load as a
> > compressive stress, and that as the wheel slightly turns this is
> > turned into a small tensile stress."
>
> > Cheers,
>
> > Carl Fogel
>
> Seeing how it was a good ten years before Boris Galerkin proposed his
> weighted residual method it wasn't an FEA in any sense, modern or
> other.
It's an discretization of a continuous problem, and does appear
to be a finite element method. I think your objection is relevant
in that the discretization is ad hoc, rather than derived in a way
that assures you get an efficiently linearized problem that converges
to the solution of the original continuous problem.
Ben
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Date: 06 Nov 2007 06:05:49
From:
Subject: Re: 1903 bicycle wheel FEA
|
On Nov 5, 3:42 pm, carlfo...@comcast.net wrote:
> On 05 Nov 2007 16:21:05 GMT, jobst.bra...@stanfordalumni.org wrote:
>
>
>
> >Carl Fogel writes:
>
> >> It turns out that the FEA for a bicycle wheel was done before 1903:
>
> >> [After an impressive page of equations for an 8-spoke bicycle wheel]
>
> >> "As a particular instance let W [weight] = 1000 pounds... Then the
> >> stress for all the spokes except [lowermost spoke] is 76 pounds
> >> tension, and that in [lowermost spoke] is 924 pounds compression;
> >> also the stress in each segment of the rim is about 98 pounds
> >> compression. It thus appears that the vertical spoke under the hub
> >> carries nearly all the load as a compressive stress, and that as the
> >> wheel slightly turns this is turned into a small tensile stress."
>
> >> --"A Text Book on Roofs and Bridges," 5th ed., 1903, Merriman & Jacoby
> >> p. 149-150
>
> >http://tinyurl.com/yrqx6d
>
> >Unfortunately this escaped notice and the wire spoked wheel escaped
> >mention in this work. I didn't understand how the author entered the
> >structural parameters of the rim and spokes, but that is less
> >important than the conclusions... that did not carry over into the
> >world of bicycling.
>
> >Jobst Brandt
>
> Dear Jobst,
>
> I'd be astonished if anyone could have dug it up back in the
> pre-Google era. You'd have to read every engineering book back to the
> 1890's to find that 2-page example--and it's in a book about roofs and
> bridges, not about bicycles.
>
> I stumbled over it while searching for references to tying and
> soldering and thought damn, but that looks like somebody doing an FEA
> for 8 spokes by hand instead of with a computer!
>
> I didn't follow the equations at all--it may not even be an FEA in the
> modern sense. But the conclusion and example tensions sure look like
> they agree with "The Bicycle Wheel."
>
> And that final sentence is awfully good: "It thus appears that the
> vertical spoke under the hub carries nearly all the load as a
> compressive stress, and that as the wheel slightly turns this is
> turned into a small tensile stress."
>
> Cheers,
>
> Carl Fogel
Seeing how it was a good ten years before Boris Galerkin proposed his
weighted residual method it wasn't an FEA in any sense, modern or
other.
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Date: 05 Nov 2007 20:15:12
From:
Subject: Re: 1903 bicycle wheel FEA
|
On Mon, 05 Nov 2007 00:50:40 -0700, carlfogel@comcast.net wrote:
>It turns out that the FEA for a bicycle wheel was done before 1903:
>
>[After an impressive page of equations for an 8-spoke bicycle wheel]
>
>"As a particular instance let W [weight] = 1000 pounds . . . Then the
>stress for all the spokes except [lowermost spoke] is 76 pounds
>tension, and that in [lowermost spoke] is 924 pounds compression; also
>the stress in each segment of the rim is about 98 pounds compression.
>It thus appears that the vertical spoke under the hub carries nearly
>all the load as a compressive stress, and that as the wheel slightly
>turns this is turned into a small tensile stress."
>
>--"A Text Book on Roofs and Bridges," 5th ed., 1903, Merriman & Jacoby
>p. 149-150
>
>
>http://books.google.com/books?id=kBM5AAAAMAAJ&pg=PA149&dq=%22bicycle+wheel+with+stiff+spokes%22&as_brr=1&ei=yMguR4_UIZ3epQKkr63vCQ#PPA149,M1
> or http://tinyurl.com/yrqx6d
>
>Cheers,
>
>Carl Fogel
Here's a vastly more intimidating (and slightly earlier) set of
calculations about how loading a bicycle wheel changes spoke-tension:
http://books.google.com/books?id=4rc4AAAAMAAJ&pg=PA197&dq=%22we+assume+that+the+number+of+spokes%22&ei=bb8vR6uaMpSQsgP02rCpCQ
or http://tinyurl.com/2hgdl4
B.A. Smith's calculations run from page 197 to 203--unless you love
equations, skip to page 203.
Smith concludes that spokes on a normally tensioned and loaded wheel
will see only a slight tension increase in the spokes outside the
bottom 60 degree arc under the hub, but the five spokes under the hub
will lose tension:
"The practical result of the above investigation is that, with steel
rim and spokes of the usual proportions, if the initial tension is
about half the weight of the rider the spokes will always be in
tension, and the tension of spokes at a greater angle than about 30
degrees from the bottom is only very little increased above its
intitial value by the weight of the rider."
Here are the bottom 7 spokes, showing the tension changes indicated by
the table just above the conclusion. The initial spoke tension is 100
lbs and rises or falls to 0.xxx * 200 lbs. (The other spokes all rise
slightly to 0.522 in the theoretical wheel.)
hub
spokes
/
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Date: 05 Nov 2007 16:21:05
From:
Subject: Re: 1903 bicycle wheel FEA
|
Carl Fogel writes:
> It turns out that the FEA for a bicycle wheel was done before 1903:
> [After an impressive page of equations for an 8-spoke bicycle wheel]
> "As a particular instance let W [weight] = 1000 pounds... Then the
> stress for all the spokes except [lowermost spoke] is 76 pounds
> tension, and that in [lowermost spoke] is 924 pounds compression;
> also the stress in each segment of the rim is about 98 pounds
> compression. It thus appears that the vertical spoke under the hub
> carries nearly all the load as a compressive stress, and that as the
> wheel slightly turns this is turned into a small tensile stress."
> --"A Text Book on Roofs and Bridges," 5th ed., 1903, Merriman & Jacoby
> p. 149-150
http://tinyurl.com/yrqx6d
Unfortunately this escaped notice and the wire spoked wheel escaped
mention in this work. I didn't understand how the author entered the
structural parameters of the rim and spokes, but that is less
important than the conclusions... that did not carry over into the
world of bicycling.
Jobst Brandt
|
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Date: 05 Nov 2007 13:42:53
From:
Subject: Re: 1903 bicycle wheel FEA
|
On 05 Nov 2007 16:21:05 GMT, jobst.brandt@stanfordalumni.org wrote:
>Carl Fogel writes:
>
>> It turns out that the FEA for a bicycle wheel was done before 1903:
>
>> [After an impressive page of equations for an 8-spoke bicycle wheel]
>
>> "As a particular instance let W [weight] = 1000 pounds... Then the
>> stress for all the spokes except [lowermost spoke] is 76 pounds
>> tension, and that in [lowermost spoke] is 924 pounds compression;
>> also the stress in each segment of the rim is about 98 pounds
>> compression. It thus appears that the vertical spoke under the hub
>> carries nearly all the load as a compressive stress, and that as the
>> wheel slightly turns this is turned into a small tensile stress."
>
>> --"A Text Book on Roofs and Bridges," 5th ed., 1903, Merriman & Jacoby
>> p. 149-150
>
> http://tinyurl.com/yrqx6d
>
>Unfortunately this escaped notice and the wire spoked wheel escaped
>mention in this work. I didn't understand how the author entered the
>structural parameters of the rim and spokes, but that is less
>important than the conclusions... that did not carry over into the
>world of bicycling.
>
>Jobst Brandt
Dear Jobst,
I'd be astonished if anyone could have dug it up back in the
pre-Google era. You'd have to read every engineering book back to the
1890's to find that 2-page example--and it's in a book about roofs and
bridges, not about bicycles.
I stumbled over it while searching for references to tying and
soldering and thought damn, but that looks like somebody doing an FEA
for 8 spokes by hand instead of with a computer!
I didn't follow the equations at all--it may not even be an FEA in the
modern sense. But the conclusion and example tensions sure look like
they agree with "The Bicycle Wheel."
And that final sentence is awfully good: "It thus appears that the
vertical spoke under the hub carries nearly all the load as a
compressive stress, and that as the wheel slightly turns this is
turned into a small tensile stress."
Cheers,
Carl Fogel
|
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Date: 07 Nov 2007 07:37:48
From: Luns Tee
Subject: Re: 1903 bicycle wheel FEA
|
In article <tevui39aqcvpeaaul9hi0so3hupa9528jc@4ax.com >,
<carlfogel@comcast.net > wrote:
>>> --"A Text Book on Roofs and Bridges," 5th ed., 1903, Merriman & Jacoby
>>> p. 149-150
>>
>> http://tinyurl.com/yrqx6d
>I didn't follow the equations at all--it may not even be an FEA in the
>modern sense. But the conclusion and example tensions sure look like
>they agree with "The Bicycle Wheel."
Nice find!
The pages you cite just re-use analysis done a bit earlier in
the book; see pp132-134. The analysis starts with a ferris wheel, and
then extends the results found for that to a model of a bicycle wheel.
It is a proper FEA, but is somewhat deficient, being a planar
truss model rather than a frame model. That is, the model assumes that
each segment of rim is in pure compression, with no bending moments at
their ends (e.g. free swivelling joints connecting each piece of
the rim to the next and the spoke ends).
The model is a reasonable one for a ferris wheel (where the
wheel's perimeter is constructed of individual straight members). As
applied to a bicycle wheel, this models the rim as having essentially
no vertical stiffness, and the conclusions drawn are only valid for that
scenario.
This is not to say that the conclusion (bottom spoke does the
work) is not also true for a vertically stiffer rim, but rather that
the analysis does not tell one way or the other for that case.
-Luns
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