Which spokes support the load?

David Wagner said:

Jobst Brandt wrote, in FAQ Subject: 8c.4 Ideal Wheel Sizes:

"Two to four spokes near the ground contact point of the average wheel
support the load at any moment."

I would think that the weight load of the bicycle is transferred from the
frame to the hubs, and then through the hub to the *upper spokes* to the top
of the rim via tensile forces, and then from the top of the rim to the
bottom of the rim --- the rim being held in shape by the spokes through
tension---and then to the tires and the ground. Isn't this the correct view?

I expect that the bottom spokes have the lowest tensile force.

David Wagner

Dear David,

That's exactly what most people think. It seems perfectly
reasonable.

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

The path following the change in tension seems to go from
the ground, to the tire, to the rim, to the lowermost
spokes, and then to the hub. The other spokes behave in a
cowardly fashion and frankly act as if they'd really rather
not be involved.

Here's a nicely detailed engineering calculation table and
explanation:

http://www.achrn.demon.co.uk/astounding/ian/wheel/index.html

Beware of the common mistake of simply adding up all the
positive and negative tension changes, which leads some
people to mistakenly conclude that the upper spokes win.
They don't--an increase of 1 pound in tension on a
horizontal spoke contributes nothing to whether the hub is
being pulled up or down.

And here are actual tension measurements confirming things:

http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf

See figures 10 & 11, where the graphs show the miserable
lowermost spokes shamelessly hogging the limelight. Again,
adding up the raw tension changes (without direction) will
lead to the mistaken conclusion that the other 32 spokes are
doing more than the bottom 4 spokes, but once you realize
that many of the other 32 spokes are actually pulling at a
downward angle, this mistake can be cleared up.

The whole lower-spoke notion is almost as annoying as the
round earth theory.

Carl Fogel

Quoted message said:

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

The hub is not in the middle of the wheel, but slightly low.

The sudden loss of tension is an effect of that, indeed the hub sags _until
that happens_.

The weight of the bike is nevertheless hung from the upper spokes,
weight replacing that loss of tension from below in the force diagram.
--
Ron Hardin
[email hidden]

On the internet, nobody knows you're a jerk.

Quoted message said:

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

The hub is not in the middle of the wheel, but slightly low.

The sudden loss of tension is an effect of that, indeed the hub sags _until
that happens_.

The weight of the bike is nevertheless hung from the upper spokes,
weight replacing that loss of tension from below in the force diagram.
--
Ron Hardin
[email hidden]

On the internet, nobody knows you're a jerk.

David Wagner said:

I expect that the bottom spokes have the lowest tensile force.

David Wagner

INCOMING!

pk

David Wagner said:

I expect that the bottom spokes have the lowest tensile force.

David Wagner

INCOMING!

pk

David Wagner said:

I expect that the bottom spokes have the lowest tensile force.

David Wagner

INCOMING!

pk

Quoted message said:

Quoted message said:

"Two to four spokes near the ground contact point of the average
wheel support the load at any moment."

Quoted message said:

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

The whole lower-spoke notion is almost as annoying as the
round earth theory.

This is pretty much a semantic argument but...

It makes sense to me the the lowermost spokes experience the greatest
change in tension, intuitively. I'm fairly certain I understand the jist
of the engineering analysis (at least the results are clear to me), and I
certainly would not presume to argue with it, but does this really prove
that the wheel is being supported by the lower spokes?

The fact is that while the tension may be much lower than normal on the
bottom spokes, there is still tension, and it's tending to pull the hub
(and bicycle frame) downwards, hardly what one could reasonably consider
'providing support'. While the uppermost spokes may not be behaving any
differently from the way they did when they were spokes anywhere else on
the wheel, they are still exerting the largest components of force tending
to hold the hub and frame up against gravity, even if they require the
lower spokes to first slacken in order that that be the case. The fact
that the lowermost spokes experience the least tension only indicates to
me that they could be removed from the wheel (theoretically) and have less
impact on it's shape than would a missing spoke taken from elsewhere,
which hardly lends credibility to the idea that they are supporting the
wheel.

I think it would be fair to say that the wheel is held rigid, and the
bicycle supported, by *all* the spokes, unequally, and that the lowermost
spokes exert the greatest supportive force relative to what the spokes in
an un-loaded wheel would be doing, but I still have trouble with the
notion of the hub being supported by spokes that are clearly pulling it
downwards (IE pulling down less hard is *not* the same as pushing).

Quoted message said:

Quoted message said:

"Two to four spokes near the ground contact point of the average
wheel support the load at any moment."

Quoted message said:

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

The whole lower-spoke notion is almost as annoying as the
round earth theory.

This is pretty much a semantic argument but...

It makes sense to me the the lowermost spokes experience the greatest
change in tension, intuitively. I'm fairly certain I understand the jist
of the engineering analysis (at least the results are clear to me), and I
certainly would not presume to argue with it, but does this really prove
that the wheel is being supported by the lower spokes?

The fact is that while the tension may be much lower than normal on the
bottom spokes, there is still tension, and it's tending to pull the hub
(and bicycle frame) downwards, hardly what one could reasonably consider
'providing support'. While the uppermost spokes may not be behaving any
differently from the way they did when they were spokes anywhere else on
the wheel, they are still exerting the largest components of force tending
to hold the hub and frame up against gravity, even if they require the
lower spokes to first slacken in order that that be the case. The fact
that the lowermost spokes experience the least tension only indicates to
me that they could be removed from the wheel (theoretically) and have less
impact on it's shape than would a missing spoke taken from elsewhere,
which hardly lends credibility to the idea that they are supporting the
wheel.

I think it would be fair to say that the wheel is held rigid, and the
bicycle supported, by *all* the spokes, unequally, and that the lowermost
spokes exert the greatest supportive force relative to what the spokes in
an un-loaded wheel would be doing, but I still have trouble with the
notion of the hub being supported by spokes that are clearly pulling it
downwards (IE pulling down less hard is *not* the same as pushing).

Jacobe Hazzard said:

I think it would be fair to say that the wheel is held rigid, and the
bicycle supported, by *all* the spokes, unequally, and that the lowermost
spokes exert the greatest supportive force relative to what the spokes in
an un-loaded wheel would be doing, but I still have trouble with the
notion of the hub being supported by spokes that are clearly pulling it
downwards (IE pulling down less hard is *not* the same as pushing).

superposition much?

David Wagner said:

Jobst Brandt wrote, in FAQ Subject: 8c.4 Ideal Wheel Sizes:

"Two to four spokes near the ground contact point of the average wheel
support the load at any moment."

I would think that the weight load of the bicycle is transferred from the
frame to the hubs, and then through the hub to the *upper spokes* to the top
of the rim via tensile forces, and then from the top of the rim to the
bottom of the rim --- the rim being held in shape by the spokes through
tension---and then to the tires and the ground. Isn't this the correct view?

I expect that the bottom spokes have the lowest tensile force.

The spoke or spokes immediately adjacent to or at the contact point
with the ground will have the greatest reduction in tension at any
given time as the wheel is rolling under load, and the two immediately
past that spoke or spokes will have the greatest tension, though their
increase in load will not be anywhere near the magnitude of the
reduced tension on the contact-point spokes.. It is because this in
the case - that the greatest *change* in tension from the unladen
state is in those contact-point spokes - that these spokes are said to
be bearing the load. This seems counterintuitive, but if you look at
the cyclic change in spoke loading during wheel rotation and the
instantaneous load on the remaining spokes, you will also see that it
is definitely not the case that the upper spokes are the ones with the
greatest tensile load at that point, so it is demonstrably and
obviously incorrect to state that the hub hangs from the upper spokes
under load. Some transfer of the load occurs to many of the spokes,
in a variety of directions, but nowehere is the change as great as in
the contact-patch spoke(s), and in a properly tensioned wheel, nowhere
does the spoke tension increase due to loading approach the magnitude
of the unloaded tension.

The wheel is a complex system. Its function is highly interdependent,
and not as simple as it might appear.
--
Typoes are a feature, not a bug.
Some gardening required to reply via email.
Words processed in a facility that contains nuts.

Ron Hardin said:

[email hidden] wrote:

[snip]

Quoted message said:

The hub is not in the middle of the wheel, but slightly low.

The sudden loss of tension is an effect of that, indeed the hub sags _until
that happens_.

[snip]

Dear Ron,

In relation to what does the hub sag, and how much?

Do you have a link to a description?

I was under the impression that the hub stayed put, and that
only the bottom of the rim deflected inward.

Curiously,

Carl Fogel

Quoted message said:

Quoted message said:

Dear David,

That's exactly what most people think. It seems perfectly
reasonable.

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

No its not, the lower spoke loses tension because the rim distorts.

The reduction in lower spoke tension is a consequence of the wheel structure
supporting the load not the source of support to the hub.

Imagine the position when there is no spoke immediately below the hub. How
is it supported then? (have look at the wheel here and imagine that wheel
with the "gap" at the bottom:
http://www.wheelmasters.be/nl/wielen/Rolf%20Prima%20Vigor.htm

or this one:

http://www.kinisibikes.com/rolf/rearc630.jpg

pk

In article <[email hidden]>,
[email hidden] says...

Quoted message said:

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

To "A bicycle wheel stands on its spokes.", I would add,
"Tug of war teams lose by pushing on the rope".

;-)

Rick

PK said:

Quoted message said:

Quoted message said:

Dear David,

That's exactly what most people think. It seems perfectly
reasonable.

Unfortunately, engineering theory and actual tension
readings of the spokes show that not much happens except
when a pre-tensioned spoke passes under the hub--at which
point it loses tension dramatically, which is effectively
the same as compression.

No its not, the lower spoke loses tension because the rim distorts.

The reduction in lower spoke tension is a consequence of the wheel structure
supporting the load not the source of support to the hub.

Imagine the position when there is no spoke immediately below the hub. How
is it supported then? (have look at the wheel here and imagine that wheel
with the "gap" at the bottom:
http://www.wheelmasters.be/nl/wielen/Rolf%20Prima%20Vigor.htm

or this one:

http://www.kinisibikes.com/rolf/rearc630.jpg

pk

Dear PK,

Not having such a wheel handy, I'll stick to imagining--I
imagine that the lower pre-tensioned spokes lose tension.

I can't imagine a pre-tensioned wheel in which there are no
lower spokes.

The gap that you mention seems to be simply wider than the
gaps in a 36-spoke wheel.

What do you imagine happens to the spoke tension when such a
low-spoke-count wheel is loaded?

Carl Fogel

David Wagner said:

Jobst Brandt wrote, in FAQ Subject: 8c.4 Ideal Wheel Sizes:
"Two to four spokes near the ground contact point of the average wheel
support the load at any moment."

It is the case that the greatest change in tension is in the bottom
spokes, far greater than the increase in the other spokes.

You can verify that with a tensionmeter.

Conversely, the semantic argument is utterly unproductive.
--
David Damerell <[email hidden]> flcl?

Carl Fogel said:

Quoted message said:

The hub is not in the middle of the wheel, but slightly low.

Quoted message said:

Quoted message said:

The sudden loss of tension is an effect of that, indeed the hub
sags (until that happens).

Quoted message said:

In relation to what does the hub sag, and how much?

Quoted message said:

Do you have a link to a description?

Quoted message said:

I was under the impression that the hub stayed put, and that only
the bottom of the rim deflected inward.

Let's state a frame of reference. In the case of "the Bicycle Wheel"
and Gavin's analyses, the axle or center of the wheel is the reference.
It is the easiest one to use because it is independent of load and
torque.

I think the use of superposition may help some people visualize this
better because by this method spoke tension can be removed from the
problem entirely, only to be reintroduced after the analysis is
complete for those who have problems with compressed thin columns.

Finite element analyses ignore compression and tension and distribute
spoke loads purely by external forces and elasticity of the elements
of the structure. That is how these graphs are generated.

I didn't think it was time for this discussion, it usually appearing
only once per year.

Jobst Brandt
[email hidden]

David Damerell said:

David Wagner said:

Jobst Brandt wrote, in FAQ Subject: 8c.4 Ideal Wheel Sizes:
"Two to four spokes near the ground contact point of the average wheel
support the load at any moment."

It is the case that the greatest change in tension is in the bottom
spokes, far greater than the increase in the other spokes.

You can verify that with a tensionmeter.

Conversely, the semantic argument is utterly unproductive.

.... and is thus perfectly at home on usenet.

--
Benjamin Lewis

Although the moon is smaller than the earth, it is farther away.

David Damerell said:

Quoted message said:

"Two to four spokes near the ground contact point of the average
wheel support the load at any moment."

Quoted message said:

It is the case that the greatest change in tension is in the bottom
spokes, far greater than the increase in the other spokes.

Quoted message said:

You can verify that with a tensionmeter.

By the way, it's a tensiometer.

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=tensiometer

Quoted message said:

Conversely, the semantic argument is utterly unproductive.

That may be if you fail to define your terms. Those who have read
"the Bicycle Wheel" instead of taking someone else's word for what it
says know that the terms are defined and the reason for using the
metaphor "stand" explained. How is it that this subject elicits so
much energy from the UK, regularly? I can only conclude that the book
is not readily available there so this is all based on hearsay.

Jobst Brandt
[email hidden]

David Wagner said:

Jobst Brandt wrote, in FAQ Subject: 8c.4 Ideal Wheel Sizes:

"Two to four spokes near the ground contact point of the average
wheel support the load at any moment."

I would think that the weight load of the bicycle is transferred
from the frame to the hubs, and then through the hub to the *upper
spokes* to the top of the rim via tensile forces, and then from the
top of the rim to the bottom of the rim --- the rim being held in
shape by the spokes through tension---and then to the tires and the
ground. Isn't this the correct view?

I expect that the bottom spokes have the lowest tensile force.

Ooooooooohhhhhaaarrrrggghhhh here we go again. ;-) Nope, that isn't a
correct description. You could save us a lot of time and read one of
the several hundred post threads from the past 15 years via Google
(click on groups, navigate to rec,bicycles.tech and search for
something like "wheel support load spokes"😉. Also, you could read
"The Bicycle Wheel" by Jobst Brandt, which includes finite element
analysis and lots of descriptions. There's also information readily
available on the Web, including other FEAs. Try also Sheldon
"Encycleopedia" Brown's Web site (www.sheldonbrown.com) and somewhere
in there is bound to be an informative discussion of this topic.

The short answer is that a wheel is a prestressed or pretensioned
structure, and supports the load through the compression of the
roughly four spokes below the hub. You can test it for yourself by
plucking spokes like a guitar string at various points on a wheel
unloaded and then while a load is applied- the ones where you can hear
the greatest change in pitch are the ones holding up the load.