Spoke tension deflection test
carl...@comcast.net
is, hang a known weight from its midspan, and measure the spoke's
downward deflection:
tension = (length x force) / (4 x deflection)
But this measurement can be tricky to perform on a real wheel.
So I put a spoke in a vise-rig and hung two weights from its midspan
by thin wires. I also laid a thin ruler flat across the vise jaws to
serve as a reference plane when I measured the small deflection.
I used Post Office electronic weight scales and dial calipers.
Here's a view of the setup:
http://i17.tinypic.com/4bf8whi.jpg
Click on the lower right in Explorer for the full-size image.
The camera angle isn't dead level with the thin metal ruler laid a
across the jaws, but it's good enough to show the 19 lbs of weight
pulling the spoke down.
The length of the span between the vise jaws was 4.545", the two
weights together weighed 19 lbs 2.5 ounces (19.15625 lbs), and the
downward deflection was a suspiciously round 0.120", so I've
calculated the tension for 0.110, 0.120, and 0.130 inches.
(4.545 x 19.15625) / (4 x 0.110) = 212 lbs tension
(4.545 x 19.15625) / (4 x 0.120) = 195 lbs tension
(4.545 x 19.15625) / (4 x 0.130) = 180 lbs tension
Whatever the spoke's original tension was, it certainly looks as if it
must have risen to around 195 lbs.
But despite my faultless theory and careful measurements, a small
correction seems to be needed to get the correct spoke tension:
http://i18.tinypic.com/30c6a3c.jpg
:)
A real wheel may have a few smaller confounding factors hidden in it
that aren't as easily revealed.
***
So much for deceiving trusting readers as an object lesson. There are
no hidden flaws in what follows--at least no _deliberately_ hidden
flaws. Like anyone else, I may be blind to what's wrong with my
explanations.
Let's consider the relative accuracy of measuring deflections in real
wheels versus a Park gauge.
We measure a spoke in a real wheel as 280 mm from hub to rim.
(Let's use a radial wheel, so that we don't have to wonder about that
pesky bend at the spoke crossing.)
We hang a 23-pound weight from our 280 mm spoke's midspan and measure
the downward deflection as 7 mm.
Then we add a 26-pound weight and measure the deflection again, this
time as 12 mm.
We apply our spoke tension equation again:
tension = (force x length) / (4 x deflection)
(23 x 280) / (4 x 7) = 230 pounds of tension
(49 x 280) / (4 x 12) = 286 pounds of tension
There's no deflection with 0 pounds of weights, we can't tell what the
original tension was.
But it looks like a 56-lb tension increase when we add 26 lbs of
weight, so we seem to be getting two pounds of tension increase for
each pound of side force.
But this is considerably more than anyone has yet reported measuring
with a tension gauge on a real wheel.
So we simply dismiss the Park gauge as inaccurate.
But what's the margin of error in our measurements versus the Park
tool?
Again, let's ignore the length. It's 280 mm. And let's assume that our
23 and 26 pound weights total exactly 49 pounds.
But it can be tricky to measure the deflection of a spoke with a rope
or wire wrapped around its midspan in a real wheel.
Maybe the deflections really are 7.0 mm and 12.0 mm on the nose, but
what if those were a little off, say plus or minus half a millimeter?
280 mm, 23 lbs
deflection tension change
6.5 mm 248 lbs +18 (280 x 23 ) / (4 x 6.5)
7.0 mm 230 lbs 0 (280 x 23 ) / (4 x 7.0)
7.5 mm 215 lbs -15 (280 x 23 ) / (4 x 7.5)
280 mm, 49 lbs
deflection tension change
11.5 mm 298 lbs +12 (280 x 49) / (4 x 11.5)
12.0 mm 286 lbs 0 (280 x 49) / (4 x 12.0)
12.5 mm 274 lbs -12 (280 x 49) / (4 x 12.5)
Hmmm . . .
If the margin of error is +/- 0.5 mm, then our first tension is really
215~248 pounds, while our second tension is 274~298 pounds.
That would mean that the tension rise for adding the second 26-pound
weight is between 26 pounds (274-248) and 83 pounds (298-215), or
anywhere from 1-to-1 to 1-to-3.
After measuring our single spoke, we declare that the test gives us
what we wanted, that it proves that literally hundreds of spoke tests
on other wheels with a Park gauge that showed nothing better than
1-to-1 ratios must be wrong, and that our wheel must be much stiffer
than all those other wheels.
Stiffer, in fact, than a massively braced pipe-clamp rig with no spoke
crossing that achieved only a 1.5-to-1 ratio when measured with a Park
tension gauge.
Hmmm . . . let's take a look at that inaccurate Park tension gauge.
The marks on a Park tension gauge are spaced at 0.075 inches, or 1.905
mm. When applied, the Park gauge hangs as motionless as the spoke and
is fairly easy to read at a glance.
So a quarter mark on the Park tool is about 0.5 mm.
Repeated applications of the Park gauge will produce readings
consistent to within a quarter-mark or better, so a margin of error of
a quarter-mark either way seems reasonable. (More expensive tension
gauges may do even better.)
For a 2 mm round steel spoke in the 200-300 pound range (91 to 136
kgf), the Park gauge table reads like this:
Park Park extrapolated
mark kgf lbs
22.00 85 187
22.25 193
22.50 198
22.75 203
23.00 95 209
23.25 215
23.50 222 xxx
23.75 228 +/- ~7 lbs @ ~230 lbs
24.00 107 235 xxx
24.25 243
24.50 251
24.75 259
25.00 121 266
25.25 275 xxx
25.50 284 +/- ~9 lbs @ ~280 lbs
25.75 293 xxx
26.00 137 301
So the Park gauge looks accurate to +/- 7~9 lbs at the expected
tensions if read to within a quarter mark, about 0.5 mm on the scale.
But an error of the same +/- 0.5 mm on our single deflection test,
which was much harder to measure, meant an accuracy of +/- 12~18
pounds--about twice as large a margin of error.
Yet the argument is that the Park tool must be less accurate . . .
Even though it accurately measures a 190-lb weight hung from a spoke
and comes with a factory calibration stamp, with a handwritten date
and the inspector's initials:
http://i10.tinypic.com/47i07xv.jpg
Cheers,
Carl Fogel
Ron Ruff
carl...@comcast.net wrote:
> If the margin of error is +/- 0.5 mm, then our first tension is really
> 215~248 pounds, while our second tension is 274~298 pounds.
>
> That would mean that the tension rise for adding the second 26-pound
> weight is between 26 pounds (274-248) and 83 pounds (298-215), or
> anywhere from 1-to-1 to 1-to-3.
Good point Carl! I wonder if you might be interested in repeating a few
of your "side load on the spoke" tests using the pipe clamp, and also a
wheel with radial spokes (if you have one), and this time take precise
deflection measurements as well as Park gauge readings, to see if they
match... within the margin of error at least.
> Yet the argument is that the Park tool must be less accurate . . .
>
> Even though it accurately measures a 190-lb weight hung from a spoke
> and comes with a factory calibration stamp, with a handwritten date
> and the inspector's initials:
>
> http://i10.tinypic.com/47i07xv.jpg
Hey! There is no note on mine! I suspect they are skipping the
calibration step these days...
carl...@comcast.net
wrote:
Dear Ron,
Given that the Park tension gauge shows the archery-style drop or no
rise in tension for about the first twenty pounds of squeeze force, I
doubt that anything will be shown except that the fixed-point tension
equation is going to exaggerate spoke tension increases.
I can't see any good way to measure the deflection on a typical
cross-3 wheel.
The spoke starts with the ~ 4 degree crossing bend trying to
straighten out, so I'm not even sure how long people think the
effective spoke length is for L in the t = (L x F) / (4 x D)
fixed-point equation.
As the spoke is squeezed, the rim bends up to 6 mm sideways, while the
spokes slide up to 10 mm over each other at the crossing bend.
I don't know where to find a fixed point for measuring the spoke
deflection to less than half a millimeter, which seems like the outer
limits of accuracy.
I don't have a a radial wheel, which would at least eliminate the
crossing bend.
The pipe-clamp rig lacks the crossing bend, too, and would probably be
much easier to get a stable reference point. But it's so much stiffer
than any wheel that I doubt that a comparison would be useful. Squeeze
spokes on a wheel, and you can see the rim doing things next to the
brake pad. Squeeze a spoke in a pipe clamp rig with both hands, and
you just hurt your hands while trying to spot any movement at the
ends. (As far as I can tell, you can't true a pipe-clamp appreciably
by turning a spoke nipple.)
So I'm still looking into things, but so far I haven't seen any
approach that lets me measure deflection accurately enough to be
useful on my crude rigs. I'd worry that I was shading things to suit
my preconceptions.
If I seem to be too picky about the possible effects of unconscious
bias, re-read the first three sentences of the last paragraph of this
post carefully:
http://groups.google.com/group/rec.bicycles.misc/msg/051f005251748480
As for your uncalibrated Park tension gauge, it sounds as if I need to
start a thread about whether my older gauge is gaining value. :)
Cheers,
Carl Fogel
Earl Bollinger
news:1167605492....@n51g2000cwc.googlegroups.com...
Hummm...there isn't a calibration stamp on my tool either.
Yet it seems more than accurate enough for my purposes.
Do you have access to one of these super neat FSA tensometers to compare
with?
I wonder if they are a lot more accurate or only marginally more accurate.
jim beam
can gather, the park is empirically calibrated to take account of
stiffer spokes with thicker spoke gauge whereas the fsa appears not.
[its designer didn't take the spoke stiffness component into account in
their math.]
carl...@comcast.net
wrote:
>
Dear Ron,
As I mentioned in my first reply, I can't figure out a way to find a
stable reference point to measure the deflection of the bending spoke
in the cat's cradle of a wheel, at least not to measure to less than
half a millimeter while the spokes are being bent and the rim is
twisting.
I was staring at a wheel, spinning it and telling myself why this
point and that point wouldn't work.
The nearby spoke is a crossing spoke. The rim deforms. The fork gets
in the way of hanging weights, and besides, everything deforms toward
it. The hub--
The middle of the hub is pretty well fixed. It doesn't care if the
wheel turns a little this way or that as you hang weights on it,
because it turns as the spoke turns.
Some kind of doo-hickey that clamps around the hub might let you put a
wire arm out to where you plan to bend the spoke and work as a
reference point for measuring with confidence to within a quarter of a
spoke thickness.
But even the hub may not work to within half a millimeter, since the
far end of the spoke at the rim is moving laterally a couple of
millimeters.
Well, maybe after the holiday I'll stare at a wheel some more.
Cheers,
Carl Fogel
Tim McNamara
jim beam <spamv...@bad.example.net> wrote:
> Earl Bollinger wrote:
> > "Ron Ruff" <rruff...@yahoo.com> wrote in message
> > news:1167605492....@n51g2000cwc.googlegroups.com...
> >> carl...@comcast.net wrote:
> >>> If the margin of error is +/- 0.5 mm, then our first tension is
> >>> really 215~248 pounds, while our second tension is 274~298
> >>> pounds.
> >>>
> >>> That would mean that the tension rise for adding the second
> >>> 26-pound weight is between 26 pounds (274-248) and 83 pounds
> >>> (298-215), or anywhere from 1-to-1 to 1-to-3.
> >>
> >> Good point Carl! I wonder if you might be interested in repeating
> >> a few of your "side load on the spoke" tests using the pipe clamp,
> >> and also a wheel with radial spokes (if you have one), and this
> >> time take precise deflection measurements as well as Park gauge
> >> readings, to see if they match... within the margin of error at
> >> least.
> >>
> >>> Yet the argument is that the Park tool must be less accurate . .
> >>>
> >>> Even though it accurately measures a 190-lb weight hung from a
> >>> spoke and comes with a factory calibration stamp, with a
> >>> handwritten date and the inspector's initials:
> >>>
> >>> http://i10.tinypic.com/47i07xv.jpg
> >> Hey! There is no note on mine! I suspect they are skipping the
> >> calibration step these days...
> >
> > Hummm...there isn't a calibration stamp on my tool either. Yet it
> > seems more than accurate enough for my purposes. Do you have access
> > to one of these super neat FSA tensometers to compare with? I
> > wonder if they are a lot more accurate or only marginally more
> > accurate.
> >
> >
> personally, i'd trust the accuracy of the park more since, from what
> i can gather, the park is empirically calibrated to take account of
> stiffer spokes with thicker spoke gauge whereas the fsa appears not.
> [its designer didn't take the spoke stiffness component into account
> in their math.]
You've really ramped up your nastiness in the past few months, jim,
taking any opportunity you can for personal attacks. Sadly it only
demonstrates the weakness of your position. I hope that the next year
goes better for you, having watched the increasing bitterness that you
have shown over 2006.
jim beam
do /you/ see any account of spoke gauge in the formula T = FL/4d? does
it not matter? http://i18.tinypic.com/30c6a3c.jpg
but we go through the same old thing with you each and every year. you
get stuck home because of the weather, you get cabin fever, you try and
pick a personal fight on the net where you can't get hurt.
happy 2007 tim. let this be the year you learn the difference between
personal animus and technical disagreement.
Tim McNamara
jim beam <spamv...@bad.example.net> wrote:
A tensiometer that can be zeroed out on a spoke reduces this problem.
That's a basic approach in scientific measurement, n'est-ce pas? Never
having used one of Park, DT or FSA tensiometers I don't know if they can
be zeroed out. The Wheelsmith one can be.
As for spoke gauge and thickness, Jobst has referred to this in the past
in discussing how his original tensiometer was designed to avoid that
particular pitfall. He has also discussed the issue of friction binding
between the posts of the tensiometer and the spoke.
> but we go through the same old thing with you each and every year.
> you get stuck home because of the weather, you get cabin fever, you
> try and pick a personal fight on the net where you can't get hurt.
LOL. Actually, jim, if you look back you'll see that I've been quite
consistent for years. Weather's not got anything to do with it. The
past 15 years winter cycling has generally been quite good here thanks
to having had the 10-12 warmest winters on record in that time frame. I
find your lack of intellectual rigor and proneness to ad hominem just as
annoying in August as in January.
> happy 2007 tim. let this be the year you learn the difference
> between personal animus and technical disagreement.
I do know the difference, jim. Unfortunately you let your feelings
towards Jobst overwhelm your logic all too often. Your posts have
gotten increasingly hostile and bitter, aimed not at expanding the
knowledge of bicycles but solely at taking Jobst down a peg or two. You
even manage to work in attacks on Jobst into threads where those attacks
are completely irrelevant. The result is that the worth of your
contributions is near zero.
The result is that you fail to convince. With the exception of Carl
Fogel, few people if any seem to come around to your thinking in these
discussions. Why is that? Because your comments are so clearly
intended to be hurtful and this outweighs the technical merits that your
posts might have. You come across like a sullen teenager not as a
reasoned scientist. You start with ad hominem and work your way out
from there, which just undermines your position in the eyes of your
readers. And anyone who dares to question your claims just gets a
helping of invective from you. Even when Jobst agrees with you on
something you continue to hurl abuse at him.
Your posts are an interesting mish-mash. On the one hand you claim
technical knowledge. On the other hand, you distort or outright lie
about what other people say so you can "defeat" them. When your
position is challenged effectively, you start to squirm around, begin
casting out red herrings and change the subject. On one hand you
challenge the accuracy of what others write, but then you demand that
they do the experiments to prove you right instead of doing it yourself
and posting the results. You fail to have the courage to propose a
consistent, comprehensive theory of wheels and wheel building. You just
snipe away at other people. It's sad because your contributions here
could be useful and positive, but that just doesn't seem to be what you
are about.
It's the evident bitterness in your posts over a course of years that
puzzles me. I understand Jobst's tetchiness, as he's been fielding
attacks for decades over the statements in his book, in the FAQ, etc.
I've had arguments with Jobst over the past 12-13 years and have been
the recipient of a number of whacks upside the head on a number of
topics. Heck, darn near the first thing I did in the newsgroup was to
get into an argument with Jobst. Unlike you, though, I have ended up
with respect for Jobst even when we disagree.
Your negative cathexis with Jobst appears to go way beyond disagreeing
with him about technical matters, and it bleeds out into your
discussions with others. It seems to me that you have confused the
importance of *what* is right with that of *who* is right. Your ongoing
animus towards Jobst has all the hallmarks of being about who is right
rather than what it right. Your overt disrespect for Jobst, for me, and
for anyone who dares to disagree with you does you no credit.
jim beam
absolutely not. thicker spokes resist /bending/. just moving the
calibration to account for a different starting point has /nothing/ to
do with addressing bending resistance.
> Never
> having used one of Park, DT or FSA tensiometers I don't know if they can
> be zeroed out. The Wheelsmith one can be.
see above.
>
> As for spoke gauge and thickness, Jobst has referred to this in the past
> in discussing how his original tensiometer was designed to avoid that
> particular pitfall.
like you, he's figured out addressing the starting point, but the
fundamental issue of bending stiffness is unaddressed.
> He has also discussed the issue of friction binding
> between the posts of the tensiometer and the spoke.
indeed, but that's not in the math either.
<snip remaining self-justification>
frkr...@gmail.com
carl...@comcast.net wrote:
>
> I can't see any good way to measure the deflection on a typical
> cross-3 wheel.
>
> The spoke starts with the ~ 4 degree crossing bend trying to
> straighten out, so I'm not even sure how long people think the
> effective spoke length is for L in the t = (L x F) / (4 x D)
> fixed-point equation.
>
> As the spoke is squeezed, the rim bends up to 6 mm sideways, while the
> spokes slide up to 10 mm over each other at the crossing bend.
>
> I don't know where to find a fixed point for measuring the spoke
> deflection to less than half a millimeter, which seems like the outer
> limits of accuracy.
Let me ask again:
Do you realize that the pertinent piece of data is the angle that the
bent spoke assumes?
Have you read the material at
http://www.glenbrook.k12.il.us/gbssci/phys/class/vectors/u3l3c.html
especially problem #5 at the bottom?
The equation you're using for tension is derived from consideration of
the angles involved and their effect on force equilibrium. At least,
that's how I worked it out. The terms "L" and "D" in the equation come
from trig, specifically from the tangent of a certain angle.
Granted, angles that small are difficult to measure directly. If I
were trying to do it directly, I'd use a vernier bevel protractor, but
it's easier to measure deflection over a span. However, since it's
the angle that matters, not the span, you can use any convenient length
for the span. Just get the corresponding deflection within that span.
As an example, you might use a depth micrometer, letting the base
contact the bent spoke at the two "long" ends of the mike's base. Use
the length of the base as "L" in your equation. Use the deflection
within that length as the "D" term.
- Frank Krygowski
Tim McNamara
jim beam <spamv...@bad.example.net> wrote:
> Tim McNamara wrote:
> > In article <0Lidnfqjr7RmqATY...@speakeasy.net>,
> > jim beam <spamv...@bad.example.net> wrote:
> >
> >> do /you/ see any account of spoke gauge in the formula T = FL/4d?
> >> does it not matter? http://i18.tinypic.com/30c6a3c.jpg
> >
> > A tensiometer that can be zeroed out on a spoke reduces this
> > problem. That's a basic approach in scientific measurement,
> > n'est-ce pas?
>
> absolutely not. thicker spokes resist /bending/. just moving the
> calibration to account for a different starting point has /nothing/
> to do with addressing bending resistance.
Spokes resist bending and thicker spokes offer more resistance. In
order to accurately measure the tension of the spoke, you have to
subtract the stiffness of the spoke. You can do that readily with a
free spoke prior to measuring the tension of the spokes in the wheel,
zeroing out the tensiometer against the stiffness of the spoke.
Peter Cole
> Even though it accurately measures a 190-lb weight hung from a spoke
> and comes with a factory calibration stamp, with a handwritten date
> and the inspector's initials:
>
> http://i10.tinypic.com/47i07xv.jpg
That is impressive! What's the guaranteed accuracy?
Peter Cole
> Stiffer, in fact, than a massively braced pipe-clamp rig with no spoke
> crossing that achieved only a 1.5-to-1 ratio when measured with a Park
> tension gauge.
What were the deflections? (3rd request)
Peter Cole
> Even though it accurately measures a 190-lb weight hung from a spoke
How does it do with a 400lb weight?
Peter Cole
> After measuring our single spoke, we declare that the test gives us
> what we wanted, that it proves that literally hundreds of spoke tests
> on other wheels with a Park gauge that showed nothing better than
> 1-to-1 ratios must be wrong,
Maybe I'm misreading, but
<http://home.comcast.net/~carlfogel/download/squeeze1_tension_relative.jpg>
seems to show one spoke rose almost 90lb with a 60lb squeeze.
Tim McNamara
Peter Cole <peter...@comcast.net> wrote:
And in both cases the increase in tension is higher than the squeeze
force. At a 60 pound squeeze, the spoke tension rose to neatly 300 lbs
in both cases. And interestingly only one of the two spokes loses
tension, which suggests a flaw in measurement or methodology.
jim beam
no, that gives only one bend. a spoke in tension has three of them when
a tensiometer is used.
carl...@comcast.net
Dear Tim,
Actually, the two spokes behave consistently. One spoke loses
initially, the other stays about the same--which spoke starts out at
higher tension seems to govern things.
Even if you look at idealized, computer-generated models with
initially identical spoke tensions, you'll find that spoke tension
does not change with as much symmetry as we'd like:
http://www.astounding.org.uk/ian/wheel/index.html
Browse down to Ian's table and look at first spoke on either side of
the five bottom spokes that lose tension. It's normal to expect them
to be symmetrical, but spoke 16's raw tension change is predicted to
be 31 N, while spoke 22's raw tension change is predicted to be only
18 N, about half as much.
Real tests rarely show perfect curves. Indeed, what surprised me about
this test was how symmetrical the results were:
http://i10.tinypic.com/2njccc9.jpg
Anyway, draw a line to fit the 40 data points for each spoke here:
http://home.comcast.net/~carlfogel/download/squeeze1_tension_relative.jpg
The general trend is clear--about a 1-to-1 ratio between squeeze force
and tension increase, not 2-to-1 or 5-to-1. That was a single test run
at 5-lb increments to confirm that nothing large was being missed, not
repeated testing at a specific load.
Here's what collecting hundreds of repeated readings can do:
http://home.comcast.net/~carlfogel/download/squeeze1_calibrate.jpg
Stretch it out to fill the screen, and the blue line of data is about
as wiggly as the other graph.
The blue line shows the average for multiple tests just to calibrate
the tool when one post was on a 1.8 mm midspan and the other post was
on a 2.0 mm nipple end. As I recall, there were several data points
for each 0.1 step from 20.0 to 26.0 on the Park scale. (It turns out
that the result is always a little higher than just averaging straight
2.0 mm and straight 1.8 mm spokes.)
The yellow and red lines are from the Park table. The green line is a
simple average of the two. Note that the blue line averaging hundreds
of actual readings waves about as much as the single-wheel tests
instead of staying precisely between the yellow and green lines.
That's real-world variation.
But initial tension does keep dropping for one spoke in a squeezed
pair, while the other spoke stays the same. After the initial odd
behavior at 5 to 20 lbs of squeeze force, both start climbing. It
happens on wheel after wheel.
As for claims that some wheel must see twice as much tension increase
as other wheels, someone may someday apply a tension gauge to a real
wheel and find that its spokes gain two pounds of tension per pound of
squeeze force over a reasonable range of forces and a reasonable
number of tests.
They could be out there, but I never measured such a wheel.
What surprised me was how low the measured tension increases were. I'd
been led to expect much higher increases by conjectures on RBT.
But a spoke in a massively braced pipe-clamp rig achieves only 1.5
pounds of tension increase per pound of squeeze force.
It could be that the real advantage of the pipe-clamp rig is the lack
of a springy spoke crossing. If so, it's likely that no one wheel is
appreciably stiffer in the face of spoke-squeezing.
Unfortunately, radial-spoked wheels are so rare that I have little
hope of anyone testing them.
The bottom line is that I'll be surprised if someone finds a wheel
that registers a 100-lb tension increase on a tension gauge with a
50-lb squeeze force, or 120 lbs with a 60-lb squeeze.
Anyone can mail me a wheel for testing, and I'll pay to ship it back.
I'd love to find a wheel that behaved significantly differently when I
put a tension gauge on it.
Cheers,
Carl Fogel
b...@mambo.ucolick.org
> So I put a spoke in a vise-rig and hung two weights from its midspan
> by thin wires. I also laid a thin ruler flat across the vise jaws to
> serve as a reference plane when I measured the small deflection.
>
> The length of the span between the vise jaws was 4.545", the two
> weights together weighed 19 lbs 2.5 ounces (19.15625 lbs), and the
> downward deflection was a suspiciously round 0.120", so I've
> calculated the tension for 0.110, 0.120, and 0.130 inches.
>
> (4.545 x 19.15625) / (4 x 0.110) = 212 lbs tension
> (4.545 x 19.15625) / (4 x 0.120) = 195 lbs tension
> (4.545 x 19.15625) / (4 x 0.130) = 180 lbs tension
>
> Whatever the spoke's original tension was, it certainly looks as if it
> must have risen to around 195 lbs.
>
> But despite my faultless theory and careful measurements, a small
> correction seems to be needed to get the correct spoke tension:
>
> http://i18.tinypic.com/30c6a3c.jpg
>
> :)
>
> A real wheel may have a few smaller confounding factors hidden in it
> that aren't as easily revealed.
>
> So much for deceiving trusting readers as an object lesson. There are
> no hidden flaws in what follows--at least no _deliberately_ hidden
> flaws. Like anyone else, I may be blind to what's wrong with my
> explanations.
This is clever but a somewhat misleading example
because the supports of your test rig were only 4.5" apart.
That is ~115 mm, while when hanging weights from a
spoke in a wheel, the spoke is supported at its ends
about 280 mm apart.
The reason this is a big deal is that the deflection of an
untensioned beam under a side load goes as the length
of the beam cubed. However, the deflection of a tensioned
rope (rope = the limit of zero stiffness against bending)
goes linearly with the length. So if you test a shorter span,
it exaggerates the importance of the bending stiffness.
In formulae, the bending deflection is w = FL^3 / (48*E*I)
where F is the side load force, L is the beam length, E is
the modulus of elasticity and I is the moment of inertia of
the beam (spoke).
The deflection of the tensioned rope is w = FL / (4*T)
where T is the tension.
If you had done this with the vise jaws 280mm apart, the
deflection would have been (280/115)^3 = 14.4 times
larger or about 43mm. Applying the tension equation
would have yielded an estimate of about 30 lbs tension.
This is still erroneous since the spoke wasn't tensioned.
It's a lot less erroneous than ~180 lbs though.
Another way of arriving at that number is that because
the deflection from bending goes as L^3 and the deflection
against tension goes as L, their relative importance goes
as L^2. Thus one expects your setup to exaggerate the
pseudo-tension estimate by about (280/115)^2 = 5.9
over the full-length case.
I appreciate that the reasons you set the jaws only 115mm
apart were likely limitations of the size of the vise, the length
of the spoke, and the need to keep the spoke from falling
through. However, it is important when doing experiments,
to keep the theory close at hand. Theory without experiment
is vacuous; experiment without theory is blind.
Ben
b...@mambo.ucolick.org
> carl...@comcast.net wrote:
>
> > So I put a spoke in a vise-rig and hung two weights from its midspan
> > by thin wires. I also laid a thin ruler flat across the vise jaws to
> > serve as a reference plane when I measured the small deflection.
>
> because the supports of your test rig were only 4.5" apart.
> That is ~115 mm, while when hanging weights from a
> spoke in a wheel, the spoke is supported at its ends
> about 280 mm apart.
>
> The reason this is a big deal is that the deflection of an
> untensioned beam under a side load goes as the length
> of the beam cubed. However, the deflection of a tensioned
> rope (rope = the limit of zero stiffness against bending)
> goes linearly with the length. So if you test a shorter span,
> it exaggerates the importance of the bending stiffness.
>
> In formulae, the bending deflection is w = FL^3 / (48*E*I)
> where F is the side load force, L is the beam length, E is
> the modulus of elasticity and I is the moment of inertia of
> the beam (spoke).
Following up my own post, I think that the situation is actually
a bit worse. Carl, I don't understand how you got a spoke
to deflect by only 0.12 inches while hanging 20lb from it.
When I try it with a regular spoke, it bends way more than
that with less weight. For those of you who want to skip
the blather, visit
http://www.ucolick.org/~bjw/misc/rbt/spokebending.html
to see how you can measure this without even a bench vise.
Wait a minute, looking at your picture the spoke is unusually
short and thick. Goddamnit, Fogel, that is a 3mm or 3.5mm
motorcycle spoke, isn't it? No wonder it doesn't bend much.
I know you were trying to be cute with this demonstration, but
that is perilously close to scientific fraud, or at least bullshit.
Let us assume, for a moment, that you are not just trying
to score points and are interested in this subject. We can
use the beam bending formula above, w = FL^3 / (48*E*I)
to figure out how much a spoke resists bending due to its
stiffness as compared to tension.
Consider a BICYCLE spoke of diameter 1.8mm. It has moment
of inertia I = pi r^4/4 = 0.52 mm^4. Typical stainless steel has
modulus E ~ 200 kN/mm^2. I take a spoke that is supported
at two points L = 270 mm apart and hang a 0.5 kg weight from
it, so F = 4.9 N. I predict the spoke will bend by 20 mm.
Please see
http://www.ucolick.org/~bjw/misc/rbt/spokebending.html
to see that this prediction works, to about 10%.
If I take this w=20mm displacement and try to erroneously
infer a tension from it, T = FL/4w, I get about 15 N or 1.5 kgf.
This is quite small compared to typical wheel tensions,
which shows that when you measure over a span of the
entire length of the spoke, bending stiffness is negligible
compared to typical spoke tensions.
Carl, I wrote this up and took the web page photos before
realizing that you'd probably fudged and used a 3-3.5mm
spoke for your little demo, and if I had known that, I might
not have bothered.
Ben
Peter Cole
Nicely done. It's a nuisance to have to go to the bother of actual
measurements with photos, etc., but I guess it's the only way to
convince those who regard statics as a devious conspiracy. Devious is as
devious does.
Peter "flat earth" (nyuk nyuk nyuk) Cole
Tim McNamara
jim beam <spamv...@bad.example.net> wrote:
I see your what you're saying there, one bend at each contact point when
the spoke is under tension and only one bend (at the center contact
point) with a free spoke. There is also the issue of friction binding
at the contact points as well, which is also affected by spoke
thickness. Hmmm. I'll have to ponder that. Looks like you've proven
Jobst right that most spoke tensiometers are more or less useless for
absolute tension measurement.
jim beam
was an exercise in irony and to illustrate that spoke thickness can
matter...
Tim McNamara
carl...@comcast.net wrote:
> On Mon, 01 Jan 2007 20:30:54 -0600, Tim McNamara
> <tim...@bitstream.net> wrote:
>
> >In article <H5-dnTTUbK8dPQTY...@comcast.com>,
> > Peter Cole <peter...@comcast.net> wrote:
> >
> >> carl...@comcast.net wrote:
> >>
> >> > After measuring our single spoke, we declare that the test gives
> >> > us what we wanted, that it proves that literally hundreds of
> >> > spoke tests on other wheels with a Park gauge that showed
> >> > nothing better than 1-to-1 ratios must be wrong,
> >>
> >> Maybe I'm misreading, but
> >> <http://home.comcast.net/~carlfogel/download/squeeze1_tension_relat
> >> ive .jpg> seems to show one spoke rose almost 90lb with a 60lb
> >> squeeze.
> >
> >And in both cases the increase in tension is higher than the squeeze
> >force. At a 60 pound squeeze, the spoke tension rose to neatly 300
> >lbs in both cases. And interestingly only one of the two spokes
> >loses tension, which suggests a flaw in measurement or methodology.
>
> Dear Tim,
>
> Actually, the two spokes behave consistently. One spoke loses
> initially, the other stays about the same--which spoke starts out at
> higher tension seems to govern things.
No, Carl, they behave quite differently. One loses tension initially
and the other does not, according to your graph. That is not
"consistent," not even close.
> Even if you look at idealized, computer-generated models with
> initially identical spoke tensions, you'll find that spoke tension
> does not change with as much symmetry as we'd like:
>
> http://www.astounding.org.uk/ian/wheel/index.html
>
> Browse down to Ian's table and look at first spoke on either side of
> the five bottom spokes that lose tension. It's normal to expect them
> to be symmetrical, but spoke 16's raw tension change is predicted to
> be 31 N, while spoke 22's raw tension change is predicted to be only
> 18 N, about half as much.
>
> Real tests rarely show perfect curves. Indeed, what surprised me
> about this test was how symmetrical the results were:
>
> http://i10.tinypic.com/2njccc9.jpg
>
> Anyway, draw a line to fit the 40 data points for each spoke here:
>
> http://home.comcast.net/~carlfogel/download/squeeze1_tension_relative.
> jpg
>
> The general trend is clear--about a 1-to-1 ratio between squeeze
> force and tension increase, not 2-to-1 or 5-to-1. That was a single
> test run at 5-lb increments to confirm that nothing large was being
> missed, not repeated testing at a specific load.
Your own graph shows a non-1:1 ratio.
http://home.comcast.net/~carlfogel/download/squeeze1_tension_relative.jpg
Why don't you believe your own data?
Reality periodically confounds expectations.
> But a spoke in a massively braced pipe-clamp rig achieves only 1.5
> pounds of tension increase per pound of squeeze force.
1.5:1 != 1:1
> It could be that the real advantage of the pipe-clamp rig is the lack
> of a springy spoke crossing. If so, it's likely that no one wheel is
> appreciably stiffer in the face of spoke-squeezing.
It's not the spoke crossing, or at least not mostly the spoke crossing.
It's the rim flex- radially if squeezing opposing pairs and to a much
greater degree laterally if you're only squeezing one pair.
> Unfortunately, radial-spoked wheels are so rare that I have little
> hope of anyone testing them.
>
> The bottom line is that I'll be surprised if someone finds a wheel
> that registers a 100-lb tension increase on a tension gauge with a
> 50-lb squeeze force, or 120 lbs with a 60-lb squeeze.
You might not see a 2:1 ratio, but you've demonstrated a better than 1:1
ratio in your own experiments. And you've shown that a 60 lb squeeze
can raise the spoke tension to some 300 lbf in a fairly typically built
wheel. That's about 1334.5 Newtons.
carl...@comcast.net
<tim...@bitstream.net> wrote:
[snip]
Dear Tim,
Yes, the spoke _pair_ behaves consistently.
As you begin to squeeze the _pair_, one spoke remains at the same
tension. The other spoke loses tension.
Again, which spoke loses tension and which stays the same seems to
depend on which starts out at higher tension.
Cheers,
Carl Fogel
Luns Tee
jim beam <spamv...@bad.example.net> wrote:
>personally, i'd trust the accuracy of the park more since, from what i
>can gather, the park is empirically calibrated to take account of
>stiffer spokes with thicker spoke gauge whereas the fsa appears not.
>[its designer didn't take the spoke stiffness component into account in
>their math.]
The conversion charts for FSA tensiometers are generated the
same way as the park instrument - by measurements on a tensile tester.
The charts are not based on the FL/4d equation that some people here
seem to have issues with.
-Luns
Tim McNamara
carl...@comcast.net wrote:
> On Tue, 02 Jan 2007 09:14:24 -0600, Tim McNamara
> <tim...@bitstream.net> wrote:
>
> >In article <25ijp2d91i1cf3b4o...@4ax.com>,
> > carl...@comcast.net wrote:
> >
> >> On Mon, 01 Jan 2007 20:30:54 -0600, Tim McNamara
> >> <tim...@bitstream.net> wrote:
> >>
> >> >In article <H5-dnTTUbK8dPQTY...@comcast.com>,
> >> > Peter Cole <peter...@comcast.net> wrote:
> >> >
> >> >> carl...@comcast.net wrote:
> >> >>
> >> >> > After measuring our single spoke, we declare that the test
> >> >> > gives us what we wanted, that it proves that literally
> >> >> > hundreds of spoke tests on other wheels with a Park gauge
> >> >> > that showed nothing better than 1-to-1 ratios must be wrong,
> >> >>
> >> >> Maybe I'm misreading, but
> >> >> <http://home.comcast.net/~carlfogel/download/squeeze1_tension_re
> >> >> lat ive .jpg> seems to show one spoke rose almost 90lb with a
> >> >> 60lb squeeze.
> >> >
> >> >And in both cases the increase in tension is higher than the
> >> >squeeze force. At a 60 pound squeeze, the spoke tension rose to
> >> >neatly 300 lbs in both cases. And interestingly only one of the
> >> >two spokes loses tension, which suggests a flaw in measurement or
> >> >methodology.
> >>
> >> Dear Tim,
> >>
> >> Actually, the two spokes behave consistently. One spoke loses
> >> initially, the other stays about the same--which spoke starts out
> >> at higher tension seems to govern things.
> >
> >No, Carl, they behave quite differently. One loses tension
> >initially and the other does not, according to your graph. That is
> >not "consistent," not even close.
>
> [snip]
>
> Dear Tim,
>
> Yes, the spoke _pair_ behaves consistently.
>
> As you begin to squeeze the _pair_, one spoke remains at the same
> tension. The other spoke loses tension.
>
> Again, which spoke loses tension and which stays the same seems to
> depend on which starts out at higher tension.
You're squeezing a pair of spokes with markedly different initial
tensions? Why?
carl...@comcast.net
b...@mambo.ucolick.org wrote:
> Following up my own post, I think that the situation is actually
> a bit worse. Carl, I don't understand how you got a spoke
> to deflect by only 0.12 inches while hanging 20lb from it.
> When I try it with a regular spoke, it bends way more than
> that with less weight. For those of you who want to skip
> the blather, visit
> http://www.ucolick.org/~bjw/misc/rbt/spokebending.html
> to see how you can measure this without even a bench vise.
>
> Wait a minute, looking at your picture the spoke is unusually
> short and thick. Goddamnit, Fogel, that is a 3mm or 3.5mm
> motorcycle spoke, isn't it? No wonder it doesn't bend much.
> I know you were trying to be cute with this demonstration, but
> that is perilously close to scientific fraud, or at least bullshit.
[snip]
> Carl, I wrote this up and took the web page photos before
> realizing that you'd probably fudged and used a 3-3.5mm
> spoke for your little demo, and if I had known that, I might
> not have bothered.
>
> Ben
Dear Ben,
Glad that you decided to test things and figured them out.
:) <--symbol used to hint in original post at deception
"So much for deceiving trusting readers as an object lesson."
--further hint in original post that all was not as it seemed
Yes, that's the same old 165 mm motorcycle spoke whose picture and
dimensions have appeared in previous posts on RBT:
http://groups.google.com/group/rec.bicycles.tech/msg/4d550ee1e11d41c5
Here, it poses next to its little brother:
http://home.comcast.net/~carlfogel/download/spokes.jpg
Like you, I've known the embarrassment of making detailed calculations
based on what turned out to be mistaken assumptions.
:)
Cheers,
Carl Fogel
b...@mambo.ucolick.org
> b...@mambo.ucolick.org wrote:
>
> > the blather, visit
> > http://www.ucolick.org/~bjw/misc/rbt/spokebending.html
> > to see how you can measure this without even a bench vise.
> >
> > Wait a minute, looking at your picture the spoke is unusually
> > short and thick. Goddamnit, Fogel, that is a 3mm or 3.5mm
> > motorcycle spoke, isn't it? No wonder it doesn't bend much.
> > I know you were trying to be cute with this demonstration, but
> > that is perilously close to scientific fraud, or at least bullshit.
>
> > realizing that you'd probably fudged and used a 3-3.5mm
> > spoke for your little demo, and if I had known that, I might
> > not have bothered.
>
>
> :) <--symbol used to hint in original post at deception
>
> "So much for deceiving trusting readers as an object lesson."
> --further hint in original post that all was not as it seemed
Don't weasel, Carl. It's unattractive. A smiley is not a license
to dissemble. You inserted the 3.5mm spoke (which is ~9 times
stiffer than a 2.0mm spoke) into a discussion of the importance
of bending stiffness in bicycle wheel spokes because it made a
more striking picture and gave an outlandishly large tension
estimate.
> Yes, that's the same old 165 mm motorcycle spoke whose picture and
> dimensions have appeared in previous posts on RBT:
> http://groups.google.com/group/rec.bicycles.tech/msg/4d550ee1e11d41c5
> Here, it poses next to its little brother:
> http://home.comcast.net/~carlfogel/download/spokes.jpg
>
> Like you, I've known the embarrassment of making detailed calculations
> based on what turned out to be mistaken assumptions.
>
> :)
Actually, I'm not embarrassed about anything. I am gratified
that my not-very-detailed calculation and the experiment agree
on the bending of bicycle spokes, but I'm not terribly surprised.
However, I do regret my error of judgment in taking your interest
in this subject to be serious.
Ben
carl...@comcast.net
<b...@mambo.ucolick.org> wrote:
Dear Ben,
If you miss something as plain as that picture, that smiley, and the
explicit statement, "So much for deceiving trusting readers as an
object lesson," then you missed the point.
Feel free to pout.
Cheers,
Carl Fogel
frkr...@gmail.com
carl...@comcast.net wrote:
> Dear Ben,
>
> Glad that you decided to test things and figured them out.
>
> :) <--symbol used to hint in original post at deception
FWIW:
For some of us, this entire discussion is similar to discussing
mechanical perpetual motion machines with a bright 16-year-old.
We _know_ there can be no such machine, because it would violate many
well-proven laws of physics. Consequently, we have little interest in
tracking through the minute details of his reasoning. We're
speed-reading. A humorously deceptive "test" photo doesn't necessarily
look obvious, smiley or no, and can confuse matters.
Some of us admire the boy's initiative, but we wish he would learn some
basic concepts. Like those at
http://www.glenbrook.k12.il.us/gbssci/phys/class/vectors/u3l3c.html
We can help with the trigonometry, if necessary.
"A coupla months in the laboratory can save a coupla hours in the
library."
- Frank Krygowski
P.S. ;-)
Michael Press
<u1nmp2li1bi9quv28...@4ax.com>,
carl...@comcast.net wrote:
> If you miss something as plain as that picture, that smiley, and the
> explicit statement, "So much for deceiving trusting readers as an
> object lesson," then you missed the point.
>
> Feel free to pout.
You were deceptive. Now you are spiteful and
provocative.
Fun is fun. Misrepresenting a laboratory procedure is
serious.
--
Michael Press
not pouting
Peter Cole
> carl...@comcast.net wrote:
>> If you miss something as plain as that picture, that smiley, and the
>> explicit statement, "So much for deceiving trusting readers as an
>> object lesson," then you missed the point.
>>
>> Feel free to pout.
>
> You were deceptive. Now you are spiteful and
> provocative.
>
> Fun is fun. Misrepresenting a laboratory procedure is
> serious.
I think Carl was just delivering a sermonette, "Appearances can be
Deceiving", although I think he gave what amounted to a counter-example.
The (attempted) point was that there is more to spoke tension than meets
the eye, since what meets the eye apparently contradicted his
unimpeachable tensiometer.
He seems to be rethinking all that.
Stay tuned.