The Bicycle Wheel (pt. 2): Design of the Bicycle Wheel

D. PARDO: Last time, we spent most of the time talking about
individual parts and started talking about putting
everything together.
We're going to spend a bunch of time on that today.
Specifically, I'm going to start with how a wheel
supports a load.
And a basic mental model for this is you have a room and a
hub with a couple of flanges and some spokes
going down to the rim.
And you can understand a lot about how a wheel understands
loads just with that simple of a model.
It's not always correct, but it's a good place to start.

What happens when you put a load on a wheel--
if I take my fork and put some load on the wheel, there's
actually a little deflection going on down at the bottom.
Everything is made out of rubber in the
real world, as [? Yobe ?]
says, and when you put some load on the bottom, you get a
temporary flat spot on the bottom of the wheel and the
spokes down here lose some tension.
Again, it's temporary, and there is spoke tension that's
pulling up on the hub.
There's spoke tension that's pulling down on the hub, and
it's the difference in spoke tension between those that
hold the load.
So by slackening the spokes down at the bottom, but
maintaining the spoke tension up at the top, that's what's
holding the load.

Everything is in constant motion in the wheel.
It looks like a rigid body, but everything moves around a
little bit.
You can demonstrate that yourself if you happen to have
an old wheel, which has eyelets on it.
The eyelets are often made of steel.
They get rusty.
And as the wheel rolls down the road, you'll hear a click,
click, click, click, click, click, click, click or a sort
of scritchy, scritchy, scritchy, scritchy.
I have an old wheel that I just periodically apply oil to
all of the nipples, because it's annoying how noisy it is
as everything moves rolling down the road.
PIAW NA: And as soon as it starts raining, the
[UNINTELLIGIBLE] washes away.
D. PARDO: Exactly.
[LAUGHING]
There's basically three loads to consider that
the wheel is holding.
One of them is the one I just mentioned, which is a radial
load, which is the load that you have if you're just
coasting down a nice straight road.
Another one is a slide load or lateral load.
And that, usually, is pretty small, but the wheel is also
pretty weak in that dimension, so it's kind of a
balance that way.
And the third one is tortional loads.
If you have a rear wheel with sprockets on it, and you dried
it, the load has to get from the sprockets out to the tire.
Or if you have a wheel with a hub brake on it, you grab a
hold of the brake to slow down--
same thing, just going the other way.
Starting with radial loads, I mentioned the
bends a little bit.
And what's happening is the spokes down here are getting a
little shorter.
They're basically springs, so they're getting
a little bit slacker.
And as I said it's the difference in spoke tension
that holds the load that you put on it.
You can demonstrate this if you want.
If you take your bicycle, just set it there.
Pluck the spokes going around the wheel.
You can hear the--
[PLUCKING SPOKES]
D. PARDO: Tension is pretty even all around the wheel.
If you then get on the bicycle and sit down on it, or you
have your friend get on the bicycle and sit down on it and
go pluck it again, you'll notice all the ones up here
sound about the same.
But the ones down here get a little lower sound, because
they've got a little lower tension.
The load is supported mostly by the spokes that are
pointing right at the ground, a little bit less by the
spokes on either side of it, less yet by the spokes even on
other side of that.
The rim is flexible.
So when you flatten it out at the bottom, it's somewhat
stiff, so it carries some of the load around to the sides.
But it's also somewhat flexible, so it's women
limited in how far it spreads the load around.
For rims, generally like this, the load is carried over maybe
an eighth of the spokes.

For a lateral load, it's pretty much the same story.
You're pushing sideways on the rim, holding it
here, or vice versa.
Normally, the rim is nice and flat, but you can get a little
sideways blip in it if you put a side load on it.
Again, it's a transient load.
It'll straighten out again as the thing rolls along.
The story here is a little bit more complicated.
For a radial load, it's just the spokes
getting less tension.
For a lateral load, the ones that are sort of on the down
side of the force--
they're going to get less tension.
The ones that are kind of on the up side of the force are
going to get a little more tension.
Again, it's the difference and spoke tension
that's holding things.
But it's even more complicated than that, because as you
increase the spoke tension, it tends to pull the rim inward,
and as it pulls the rim inward, it spreads some of the
load around to the other spokes.
So it's the same general principle, little bit more
complicated actual behavior It's also a little bit
complicated, because the spokes for radial load--
they're pretty much in a straight line with the load
that you're applying to it.
For a lateral load, the lateral load is going side to
side like this, but the spokes are not much of an angle.
So a fairly small force applied side to side results
in a fairly large change in the tension of the spokes.
So I did a little example here, and if you put a 10
kilogram lateral force on this particular wheel-- which you
can ignore the details, but it's roughly a road wheel--
then, you wind up with about a 100 kilogram force.
Total change in the tension of the spokes where that's some
of those spokes getting tighter some of the spokes
getting looser, more so for the spokes that are near where
you're applying the load, less so for the ones on either side
of the load.
OK.
So 10 pounds sideways, 100 pounds change
in the spoke tension.
That's because it's not very well raised side to side.
Yeah, you could say, well, the bike wheels is really weak.
And either that's a terrible thing or it isn't.
Wheels don't tend to collapse very often.
If they did, we would build them with wider flanges to
support the load, but it's sort of useful to know that
they're weak.
For instance, I have a wheel that is on a tandem.
I got airborne on it lots of times,
always landed, no problem.
I just kind of rolled off the edge of a little log one time,
and the wheel collapsed, because I put a
side load on it.
When I was landing from airborne, I was
always going straight.
No problem.

Go ahead.
Scroll down.

When you're thinking about what you want to build, you
always want to build something that's at least as strong as
what you need.
So you know that's sort of the defining characteristic, or a
defining characteristic, of a wheel is
what's the load limit?
And for most intents and purposes, not all uses, but
for most of them, you can just look at what is the radial
strength limit of the wheel?
Well, what is the radial strength limit of the wheel?
It's when the spokes that are pointing down at
the ground go slack.
If I put a load on the thing, lean on it and the spokes
start going slack, then, any additional load that I put on
it isn't supported by these spokes anymore, because
they're already slack.
They can't--
they're not compression spokes.
They can't do anymore.
There will be some transfer, because for every action,
there's an equal and opposite reaction.
There will be transfer along the rim to neighboring spokes,
so you can continue applying somewhat more load on it.
Eventually, the rim is just going to buckle, because
you're asking it to support the load
across a very wide range.
Usually, before that happens, what happens is you put a
small lateral load on the wheel, and because the spokes
are loose, pointed down at the ground, there's not very much
lateral support on the rim either.
And so what tends to happen is the wheel tacos at that point.
It collapses.
If I put a load on it this way, the spokes
down here are loose.
It's not very well supported.
It starts to bend over this way.
It's kind of cantilevered across the
tight spokes over here.
And so the thing generates this potato chip shape, which
doesn't tend to be a permanent [? defirmation ?]
unless you apply a lot of load to it.
So you can often recover from it.
You can loosen up the spokes and re-true the wheel, but
it's inconvenient to have your wheel collapse in
the middle of a ride.

One of the things that you'll notice in that description is
the spreading of load.
And what that means is if you have a stiffer rim, it spreads
the load across more spokes.
And that also helps lateral strength, because what's
supporting things is side-to-side.
But if you can either increase the lateral stiffness of the
rim, or even to some degree the radial stiffness to spread
the load, it will help improve the lateral
strength at the wheel.

I also mentioned last time that skinnier spokes, which
are less stiff, can help distribute the load better,
because what happens is the rim deflects more for a given
amount of load, which spreads the load across more spokes
this way, which means you have a certain amount of--
for any given load, you have a certain
amount of leftover tension.
So that if you have a lateral load on the wheel, it won't
collapse, because it's supported by that leftover
lateral tension.

Of course, there's no free lunch, which is if you have a
stiffer rim, it's probably going to be heavier.
And if it isn't heavier, it's probably going to have thinner
brake track or something else like that to
achieve the low weight.
And if you have more flexible spokes, they'll distribute the
load better this way, which tends to build a radially
stronger wheel.
But because of the sort of funny interaction of
everything, it tends to build a laterally less strong wheel.
So there's a trade off there.
At first, you get a little bit skinnier spoke.
It's maybe no trade off at all, but as you go to a much
skinnier spoke, you might have a laterally less strong wheel.
So if you're in the habit of landing sideways and things
like that, especially if you have a history of
wheel-collapse problems, you might want to think about
stiffer spokes.

I mentioned that the load is supported by
detensioning the spokes.
So one of the things that tells you is more tension is
better, because it gives you more total load capacity
before the spokes that are pointing down go slack.
All right.
So more tension, more tension, more tension.
What's the upper limit?
Right.
I'm going to put infinite tension on my spokes.
Well, eventually, something's got to give.
Surprisingly, perhaps, spokes don't usually snap.
They are usually way too strong for the application.
There's other things that limit how lightweight of a
spoke you can make.
If you put a lot of tension, you can pull the nipple out of
the spoke bed.
You can tear the spoke out of the hub flange.
But the thing that's usually, most immediately, a limit is
that if you overtension the spokes, the wheel will start
to collapse into that classic taco shape.
And the reason that it does that is because there is a
tremendous amount of compressive load along the
rim, and the rim only has a certain amount of strength and
stiffness in that direction.
If you look at a rim that's got, let's say, just one spoke
pulling that way and one spoke pulling that way.
Well, if I've got, let's say, a 100 kilogram force in each
of these spokes, and if I just sort of make a cut here and
try and pull the two parts apiece, I'm going to have a 50
kilogram load right there.
And if I have a couple of spokes coming in at angles
that are close to that, and they're matched by a couple of
spokes at a similar angle, almost all of the spoke
tension is going to be added to that load.
Now, it's less and less as the spokes are at sharper and
sharper angles relative to that, but what you wind up
with is something close to a ton of
compressive force in a rim.
It's a pretty lightweight thing.
It weighs a few hundred grams, and it can support a ton of
load around it.
But if you go too high, what happens is that compressive
load makes it want to buckle.
And I think the place that it usually buckles is--
first--
is the hole for the valves.
So if you just gradually increase the spoke tension and
gradually increase the spoke tension, eventually what's
going to happen is the wheel starts going out of true,
because it's just starting to buckle at the valve hole.
And one of the things that happens, unfortunately, in the
industry is people sell rims, and they don't say, this is
how much tension you should build to.
I've actually seen in my life exactly one rim that had a
sticker on it saying, this is how much tension.
And there are companies that occasionally--
like if you call up Velocity and say, how much spoke
tension should I use?
They'll tell you.
But the rim doesn't come with a little piece of paper saying
this is how much tension--
or compression the rim will support.
How much spoke tension can you use?
And it certainly varies a lot.
If you have a fairly narrow section rim, then, it can
support a lot less compression than if you
have a big beefy rim.
Right.
The other thing that people commonly do is you just
discover how much it is by building the wheel up until it
starts to buckle, and then backing off a little bit.
And if you're careful about getting close gradually, then
you don't do any serious damage to the wheels.
So you can back off and have a nice true wheel but know that
you've achieved the maximum tension.
Now, this works for metal rims. In particular, it works
for aluminum rims. You don't want to do this for wood rims.
You don't want to do this for carbon fiber rims--
bunch of stuff like that, because they have different
material properties.
PIAW NA: If you build it right up to the point where it's
about to taco, isn't it more likely during use to taco?
D. PARDO: No.
It's not, because tacoing is caused by a couple of things.
One of them is the spokes going slack.
And if you have more tension, then, it's harder to get the
spokes to go slack.
The other thing that leads to tacoing is a higher amount of
compression in the rim.
But what happens, if you actually look at the spoke
tension as you apply various loads to it, is the
tension goes down.
It almost never goes up.
And so you can tension pretty close up to the limit, apply
all sorts of loads to it, and the total compression on the
rim does not increase.
So, on the one hand, more tension keeps the spokes from
going slack.
On the other hand, the loads don't tend to increase it
beyond where you put it.

If you put it up really close to limit, you can indeed.
[? Yobe ?]
has a story about some friend who built up a wheel for new
ride, or new wheel for a ride.
And they start in Palo Alto, and they climb all the way up
to Skyline.
And they're starting to descend on the
other side of Skyline.
And the guy puts on his back brake for the first time, and
his wheel goes pwing, and it's a taco.
And it was just that little bit of extra load from putting
a brake on that caused it to taco.
He needed to have backed off just a little bit.
Instead, what he did was he built it up, and
he didn't back off.
So they loosened the spokes.
They re-trued the wheel and finished the ride.
But you'd rather not have to stop and do that.

Dishing--
and this is an example of a dished wheel--
is a wheel that has the spokes on one side at one angle and
the spokes on the other side at a different angle.
And it's most common for rear wheels where you have a big
stack of sprockets on one side, but also obviously
occurs with wheels that have hub brakes or at least have
disc brakes on them.
And dishing is great, because it lets you cram more stuff
into a given amount of space.
But it's somewhat of a disadvantage, because it
builds a weaker wheel when you do that.

One of the things that's going on when you build a dish wheel
is the spokes on the side that's very flat are at a very
large tension.
And the spokes--
here's my hub flanges--
the spokes that are on the slack side have a relatively
low tension.
So these spokes-- under a given amount of radial load--
these spokes are going to go slack.
Right.
And they're not going to be supporting the load.
Now, you do still have the spokes that are on this side,
so you're not totally lost. But if you're to thin apply a
side load to the thing, the spokes over here aren't going
to be contributing very much.
And these spokes are at a very steep angle, and so they're
not contributing very much either.
Right.
So dishing tends to build a weaker wheel.
And there's some sort of a race of tensions
and things like that.
One of the things people will do is they'll build a hub
which has narrower flange spacing in order to reduce
that angle.
And that can help sometimes, but it can only
help up to a point.
By putting the flanges together, you're still
reducing the amount of support that this provides, because
it's at a worse angle relative to sideways loads.
Right.
Another thing that people do is, and this is an example.
We passed around an offset rim last time, but I'll pass this
around again.
The spoke holes are not dead in the middle of the rim.
Instead, the spoke holes are slightly offset, so that the
spokes over here make a steeper angle, and the spokes
over here make a shallower angle.
Right.
That helps to balance the tension.
I should also say, another problem with asymmetrical
lacing like that, with dishing, is you'd like to have
lots and lots of tension.
These ones are at low tension, so you say, well, great.
I'll put these ones at yet higher tension, but you can
either pull the nipple out of the rim, pull the spoke out of
the hub flange, or one of the things that happens most
commonly is you put a wrench on the spoke nipple and try
and turn it, and it just rounds off.
Because there's too much friction, because the spoke
tension is too high.
Right.
So there are practical limits to the spoke tension that also
tend to build a weaker wheel.
rule of thumb with more than highly dished wheels is there
is no such thing as over lubrication.
If you took the spokes, and you dip it in oil, and then,
you took the nipple and you dunk it in oil, that might be
enough lubrication.

D. PARDO: So I will say, to some degree, you're just at
the mercy of component section.
You could say, for instance, well, I want to have less
wheel dish, so I'm going to buy a wheel that has fewer
sprockets on the right, but it's hard to just go out and
buy something and say, I want to have six sprockets in the
rear instead of 10.
Ten is just standard.
There's a few people-- some of the people riding observe
trials have custom-made $250.00 hubs that will take
only six sprockets, so they can build
stronger rear wheels.
But then, you have the problem of trying to buy the sprockets
that fit on it, things like that.

To some degree, you can pick and choose.
You can get a frame that has wider rear
spacings, so on, so forth.
But to some degree, you're just kind of stuck with it.
And so what that means, to some degree, is if you have
problems with wheel collapse or the wheel going out of true
regularly, you might want to buy a stiffer, albeit heavier,
rear rim in order to try and work around that.

AUDIENCE: Quick question.
Can you alleviate the symptoms of differences in tension by
changing the amount of lacing that you do on one side?
Like have one side that's only laced one cross versus--
D. PARDO: Not really, and here's why.
What you're dealing with, to a substantial degree, is the
elasticity of the spokes.
And you could, for instance, put twice as many spokes on
one side as on the other.
On the other hand, you could put twice as fat spokes on one
side as the other, and you'd get the same result.
But if you apply a lateral load, you're kind of in this
funny position that if the spokes over here are very
stiff, then, a fairly small lateral load is going to cause
them to detension.
And so it's not going to spread the load around
the rim very well.
On the other hand, if the spokes over here are very
flexible, then--
let's see, what's the right argument here?

You're still not getting good support from the spokes over
on the side.
I'm sorry.
I can't answer that question clearly right now, but I've
been through it before.
And the answer is basically no for some fairly complicated
interaction reasons.
But it doesn't work.
It's too bad, but it doesn't work.

One sort of amusing thing--
that wheel there has a disc brake on it and has never run
with a rim brake, but it has a rim that has
brake tracks on it.
And you would say say, well why, is that?
Why didn't you get one of those fancy rims that's
disc-specific?
And the answer is because basically nobody sells
disc-specific rims that have an offset spoke
[UNINTELLIGIBLE], which is kind of funny considering that
only single-speed bikes with disc brakes have non-dished
rear wheels.
Right.
Every other use of a disc-specific rim is dish.
Well, next year, maybe they'll fix it.
I don't know.
So that's lateral loads.
You also get the torsional loads I mentioned either from
pedaling or from using a hub brake.
For torsional loads, you want to use a tangent-spoked wheel.
I describe this as having spokes coming more or less
straight from the middle.
But if you do that and you try to apply a load to the middle,
then, there's no way for the load to get out except to kind
of wind up everything.
And it'll work, but it doesn't work very well.
It tends to have a short service life.
So what you want to instead is to run the spoke from the side
of the hub out.
And that's not perfectly tangent.
Perfectly tangent would be with this at a 90 degree angle
here, but it's pretty close.
And so when you wind up on the hub, it changes the spoke
tension relatively little in order to transmit the load out
to the rim.

In a perfect world, that load is is taken
by all of the spokes.
If I were to apply a load this way, that spoke would lose
tension, and remember, loads are carried by
difference in tension.
If I had another spoke coming out the other way, it would be
carried by increase in tension.
So half the spokes go up.
Half the spokes go down.
In practice, the two flanges are connected to each other by
a certain amount of rubber.
In the real world, everything is made of rubber.
So for the best load-sharing, you want a big fat center
section between the two flanges, so that load applied
on one side gets carried over to the other side.
Otherwise, if you don't do that, you wind up with a
quarter of the spokes have more tension.
A quarter of the spokes have less tension, and half the
spokes just don't help you transmit the load at all.

Probably the most important thing, especially for rear
wheels, is that the typical change in tension is
relatively small compared to the load that you're carrying
just to take your weight and roll straight down the road.
Here is an example climbing a 10 percent grade--
again, standard road wheel, kinds of things like that--
for a 100 kilogram bike plus rider, there's five kilograms
change in spoke tension for each of the spokes.
In contrast, if you're to put a 100 kilogram load on a
wheel, most of that 100 kilogram change in tension is
going to be carried by the spokes down near the bottom.
And a lot of it is going to be carried by a few spokes down
near the bottom.
So you'll have a lot more than five kilograms change in
tension for those bottom spokes.
So driving loads tend to be relatively small.
Go up a steeper grade, hard sprint, things like that-- you
might have slightly more than five kilogram change in spoke
tension, but it's still going to be relatively
small in most cases.
Hub brakes--
yes, go ahead.
AUDIENCE: You said dish wheels are less strong, so why would
I use dish wheels?
Is it just so they can fit components?
D. PARDO: Yeah.
So for example, I could have also built this wheel instead
of dishing it by taking the disc and
moving it further outboard.
But for reasons having-- in this case, having to do with
backwards compatibility--
they wanted to be able to sell a wheel that you could just
drop into an existing fork.
So--
AUDIENCE: [UNINTELLIGIBLE]
D. PARDO: Yeah.
You could make it wider.
It would also make it heavier.
So now, you're in a weight race, compatibility race,
weight race.
Rear wheels, same thing.
They started off wheels that were pretty much symmetrical
with one sprocket on the back, and then somebody said, I'm
going to put two back there.
Some other guy said, I'm going to put three back, and
somebody else said, I'm going to put four.
And now we're up to 10.
Right.

For hub brakes, if the maximum braking you ever did was a
tenth of a g, then, that same analysis that I just went
through holds.
Five kilograms per spoke, or if you have a good stiff
center section, half that per spoke.
100 kilogram bike plus rider.
But although, a tenth of a g is a moderately brisk
deceleration, it's not really strong.
What's the limit?
Well, if you look at a rider on a bike.

We've got two wheels, pedals.
The rider's center of gravity is up here somewhere, and it's
roughly as far behind the front wheel contact patch as
it is above the front wheel contact patch.
And what that means is the maximum deceleration that you
can get is when the back wheel is just barely starting to
come off the ground.
And because these two distances are about the same,
that's about a one g deceleration when the force
pulling down from your weight is about the same as the force
pulling forward from your deceleration.
So one g is a lot more than a tenth of a g, in fact, about
10 times as much, which means you'll see more like 55
kilogram force change in half the spokes or 25 if you're
doing a good stiff center section.
AUDIENCE: [UNINTELLIGIBLE].

D. PARDO: Yeah.
Although, at a g, you tend tend to
run out of tire traction.
So you hit high loads more frequently, but you don't tend
to hit much, much higher loads.
So it's also worth noting when that happens, you had no
weight on the back wheel, but you're not
on the space shuttle.
Right?
You're still on the ground, which means that basically all
of your weight is on the front wheel.
And when you have weight on the front wheel, that means
you're detensioning the spokes that are pointing up.
Right.
So you wanted to carry load by detensioning a bunch of the
spokes to support your weight, and you also want to carry
load by detensioning, half of your spokes anyway, for the
breaking load.
And despite what I said earlier about the tension in
the spokes doesn't tend to go up, if you have a hub brake,
it does tend to go up in the spokes that are not pointed
down at the ground.
The ones pointed down at the ground, it
still doesn't go up.
What all of this means is it's much easier for a given rider
and a given rim and a given number of spokes for the
spokes to go slack.
What do you want to do?
You want to overbuild the wheels slightly compared to
what you would build if you were using rim brakes.

It's not a big deal.
Lots of people ride with hub brakes-- no problems. It's
just you want to build in that extra factor of safety knowing
that the loads in the wheels are higher as a result of
using a hub brake.
Rear wheel?
Not a problem.
What happens when you put the rear brake on is your weight
tends to pitch forward, which reduces the amount of weight
on the rear wheel, which reduces the amount of
traction, which reduces the load.
So it's very hard to get a heavy braking force on the
back wheel.
I mean, occasionally, I hang off the back of the saddle,
but that's about the best you can do.

Go ahead, and scroll.

So a lot of people will say, my spokes break.
I must need stronger spokes.

Well, I said something earlier which is actually still true
that spokes are stronger--
in some sense, stronger than they need to be for the load
that they carry.
And yet, these people are correct that
their spokes break.
It's not a spoke strength problem as such.
It's a combination of some artifacts in manufacturing and
how loads get distributed in the spoke, combined with every
time the wheel goes around, the
spokes down at the bottom--
the tension is going down, up, down, up, down, up,
down, up, down, up.
So I want to explain that in a little bit more detail.

When they make a spoke, they start with basically a
straight piece of wire, and they smash it over sideways to
make the elbow.

And when they do that, smashing over sideways, you
can imagine the spoke being divided into a bunch of layers
or a bunch of fibers.
And the ones that are the outermost part of the elbow--
it's under a lot of tension, because it's on the
outside of the curve.
And it's under so much tension that the metal
eventually just yields.
It gives up, and it takes a permanent set, which is what
you want because you want to make an elbow out of it.
But this stuff grows longer.
But the stuff closer to the middle, although, it's under
some amount of tension, it doesn't grow any longer.
And so when you let go--
after they've smashed the thing over, and they let go--
this stuff has some residual tension in it.
This part that got stretched is actually under compression
as a result of the residual tension.
So now, if I lace this thing into a wheel--
here's my hub flange.
If I lace this thing into the wheel, take it up to a nice,
high tension, this stuff here, which was under compression,
goes, to say, being neutral.
It's not carrying any tension.
It's not carrying any compression.
It's just sitting there, whereas this stuff, which is
already under some tension, is now under much more tension.
And what that means is all of the load is
concentrated there.

And this metal out here isn't really doing
you any useful good.
And that asymmetrical carrying of the load as you cycle the
thing over and over again, that means that little fiber
in the middle is getting cycled over and over again.
Say, well, you know, it's OK.
It didn't break the first time, didn't break the second
time, must be good enough.
But there's a property of metals called fatigue, and
there's a technical meaning for fatigue, which is if you
take something--
like let's say my spoke will carry 200 kilograms tension--
200 kilogram force tension.
If I put a hundred kilograms on it and stretch it and relax
it and stretch it and relax it, and I keep doing that for
a long time, it could eventually break even though
when it was new, it could take 200 kilograms force.
OK.
And that property of breaking at a lower load is fatigue.
And fatigue has this kind of funny property.
If you look at the number of cycles of load and the force
it takes to cause a failure, it's kind of like this, which
is to say: when the thing is brand new, it takes a lot of
force and if you keep stretching, relaxing,
stretching, relaxing at this force level, then, it's going
to break after that many cycles.
If you stretch and relax at a lower force level, it'll be
more cycles.
And for steel--
not for some other materials, but for steel--
there is a threshold below which
this goes out to infinity.
And spokes tend to be designed for infinity.
But if you have this fiber here that interrupts the
carrying of load, then, although the spoke as a whole
is taking this low load, that little
fiber is up here somewhere.
[SNAPS FINGERS]
D. PARDO: Whammo.
The spoke snaps.

OK.
Well, I bought this spoke this way, what do I do about it?
Stress relieving.
If the spoke is under some fair amount of tension, and I
grab ahold of a pair of spokes, and I squeeze really,
really hard, then, the tension goes up.
And when the tension goes up, this little fiber in the
middle, which is already under a lot of tension, gets to be
under so much tension that now, it lets go the way that
this one let go when they were forming the head--
or forming the elbow rather.
So this one slipped forming the elbow.
This one slipped when I overload it.
Now, the load is carried uniformly across the spoke.
I'm back down to the region that has
essentially infinite lifetime.
Problem solved.
OK.
It's a seemingly idiotic little thing.
It's just you have to go around when you're building
the wheel and squeeze really hard.
How hard do you want to squeeze?
Well, not hard enough to collapse the wheel
but pretty dang hard.
You want to squeeze hard enough that it hurts your
hands, which is why you want to bring gloves to the wheel
building class.
Or if you're not coming to the lab, when you build your own
wheels later.
You want to squeeze hard enough that it causes a little
bit of pain.
That'll tell you how hard to squeeze.
Go ahead, and do it right now.
[? PIAW NA: Yobe ?] has this great story about how he first
discovered the stress relief process.
He found this wheel builder who managed to build lots of
wheels that didn't break.
And it was this five foot tall guy, and what he did was after
he was done building the wheel, he put it on--
[INTERPOSING VOICES]
PIAW NA: And then he would flip it around.
He would walk on the spokes the other way.
And that was how he [UNINTELLIGIBLE] stress relief
[UNINTELLIGIBLE].
I don't recommend it if you're not a five foot tall tiny guy.

D. PARDO: This is easy.
Just squeeze the spokes.

Yes.
OK.
So load carrying summary.
Wheels carry loads by reducing the spoke tension.
The load limit is roughly when the spokes goes slack.
And so you can more or less figure out what the load
carrying capacity is by figuring out how much spoke
tension you have distributed across--
with a load distributed across how many spokes.
If you have a problem, or if you're designing for a problem
with wheel collapse, overbuild.
Stiffer rim, more spokes.
If you have problems with durability or radial strength,
you probably want to go with thinner spokes.
If you have a problem with lateral wheel collapse, you
probably want to go with thicker spokes.
And you want to make sure that you go through the seemingly
inconsequential little step of stress relieving, because
otherwise, you may have wheel durability problems.
I had a professor who was an enthusiastic cyclist many
years ago, and he decided to start riding
his bike into work.
So he rode for a while, and his rims wore out.
And he went down to the local bike shop, and he bought some
new wheels.
And three months later, they started popping spokes.
And after replacing six spokes or something like that, he
bought another set of wheels.
And after another three months, they
started popping spokes.
Once he had a properly stress-relieved set of wheels,
he didn't pop spokes anymore.

So I want to spend a few minutes talking about
requirements, which is to say, what are your requirements in
building a wheel?
Everybody's different.
Right.
Different riding habits, different riding terrain, all
sorts of things like that.
Some of the things you want to think about in deciding what
wheel you want to build: strength.
Do you tend to buckle wheels?
Durability.
Do you tend to wear out the brake track, or do you tend to
have other durability-related problems--
spoke bed cracking on the rim, things like that.
For most people, I will recommend not thinking too
hard about aerodynamics, but some of you may
have special needs.
Weight is always an issue for cyclists, as Mr. [? Shamono ?]
succinctly said, the principal engineering challenge for the
bicycle is that the motor is so small.
So you cannot solve problems by simply spending
more power on it.
I think aesthetics is a perfectly good thing to worry
about building wheel.
I didn't bring it this time, but last week, I brought one
with a pink rim and green flanges and things like that.
Purchase price is obviously a consideration.
It's also a consideration if your wheels might get stolen.

And operating costs is different than the purchase
cost. If you have to keep replacing the rim or hub
flanges, because they keep breaking-- things like that--
that's also an issue.
So that's sort of the space of things.
And in choosing the wheels that you want to build, you
should think about all of those things with regard to
your particular needs.
If you're doing loaded touring, that's different than
if you're trying to build the lightest possible bike for
climbing hills.
How much off road riding do you do?
How often do you crash into potholes?
What are your expectations for the wheel?
I mean some people--
when 12 months goes by, it's time for a new bicycle.
Right.
On the other hand, there's some guy who got a new bicycle
when he was 20, and at 93 or something, he stopped riding
and gave it to his local museum.

What's your risk tolerance?
I mean some people are willing to go right to the hairy edge
in order to get that last little whatever.
My general recommendation, unless you have a specific
need, is to build something that airs on the side of being
too strong, even if it's a little too heavy.
The guy who made this hub, which I passed around last
time, used to have a neighbor.
And his neighbor saw how much fun this guy was having out
riding his bike, and so he wanted to build himself a
really swift bike and go out and have a really
good time riding it.
And so he built himself a low spoke count wheel with lots of
spoke tension in it, and he was going down a hill.
And he hit the front brake really hard,
and the wheel collapsed.
And he hit his head on the sidewalk.
And a few hours later, he died.
Now, that probably won't happen to you, but it's
something to keep in mind when you're--
well, do I want to go for that last little margin--
what's your risk tolerance?

Let your experience be a guide.
If you've ever had a problem with a wheel, what was it?
How enthusiastically do you want to build around that in
your next wheel?
Again, there's a very wide range of space about rim
stiffness and brake track thickness, and number of
spokes, and the flanges and all that sort of stuff.
So a lot of these kinds of things are things that you can
work around, including, I want pink rims or
something like that.
At least one Googler I know has had problems
with that last one.
Somebody stole my wheels with shiny hubs.
You might want to think about wheels that bolt into place
instead of having quick releases, although it doesn't
help you if you have your whole bicycle stolen.
As I mentioned earlier, there is an unfortunate lack of
published information.
As I said, I saw one rim that had a sticker on it saying how
much tension.
Sometimes they'll publish it.
Sometimes they don't.
It's even more complicated if you want to worry about things
like the aerodynamics.
It's too bad.
You can measure some things.
You can measure the brake track thickness up here, but
you won't necessarily know unless you look all the way
through what the brake track thickness is down here.

All that said, you can make some educated guesses.
You can also look to other people for experience.
Now, this is a little bit more complicated in the sense that
you don't necessarily know how to judge somebody else's
experience.
If you go, and you look, and you say, well, this particular
part has had lots and lots of failures.
Well, that's a good sign to stay away.
On the other hand, if you say, well, maybe
this is a good rim.
So I go, and I look.
And I say, what's other people's experience with it?
Well, maybe nobody has failures with it, because
nobody's using it.
I've also seen a lot of cases where there is what I'll call
observation error where somebody says, oh, you know, I
built this thing, and it's totally bump proof for a 50
kilogram rider, But what about for a 100 kilogram rider?
I know some people who are much more than
100 kilogram riders.
If you carry groceries on your rack or something else that's
heavy, it doesn't stand up to go over bumps the way that you
probably do.
Even if you don't think about it, you probably stand up to
go over bumps.
It might not.
Correspondingly, do they?
Do you?
It's not just what are their experiences.
It's what's the relationship between your experience and
their experience.
So that's a little bit of an iffy way to do things, but
given the lack of published data, it's basically just
something that you have to do.
So I think it's a good idea to sit down and say, well, what
are my requirements?
What absolutely does this wheel have to do?
I think it's also a good idea to sit down and say, well,
what are the things I want it to do?
I mean, obviously, you want it to be free.
Obviously, you want it to weigh zero
grams, things like that.
But you can write down some of the things that are important
to you, and you can rank it in order to--
when you've got to shop for stuff--
say, what are the features I want to look for in the
components that build up the wheel?
And how does that relate to what I want to do?
And you might want to split up some of your rankings, like
you might say, well, it's really important to me that it
weighs under 1450 grams. It's not a requirement, but it'd be
really, really nice.
On the other hand, I don't care as much--
it'd be nice if it's under 1400 grams, but I'd rather
have a [? narrow ?] section rim than save those last few
grams, as example.
Right.

Then, I think what you want to do is gather together some of
the component information, and you'll be saying, well, do I
want to use this rim?
Or do I want to use that rim?
And you can, on paper, build up a wheel.
And you can say, well, this rim has a deeper section, but
it weighs more.
And you can compare this hypothetical wheel that you're
going to build against what your requirements are and what
your preferences are.
And when it finally comes time to choose, you probably will
have looked at so many things so carefully that you're
basically looking at a couple wheels that are relatively
close, and they're both good solutions to your problem.
So don't actually sweat the last little bit, because
anything you choose is probably going to be good.

So end of that section, any questions before we move on?
AUDIENCE: What about rim eyelets?
D. PARDO: Yeah.
The rim eyelets are a really good idea.
AUDIENCE: What are they?
D. PARDO: They are a small tubular piece of metal that's
basically smashed into place.
It's a grommet.
It's run through the spoke hole, and then, it's smashed
over on either side.
And it's usually made out of something like
chrome-plated brass.
Although, from the conversation about rust
earlier, you might notice that some of them are
also made of steel.
And there's a couple reasons why they're good idea.
One is they spread the load out some around the spoke
hole, and so you're less likely to have problems with
the rim cracking in the spoke bed.
Another reason they're a good idea is because chromed brass
has lower friction than aluminum.
And when you're going to true the wheel, it's nice to not
have to fight that.
And that's especially true--
I recommend brass spokes for most situations.
But if you really have to save that last gram and want to
build with aluminum spokes, what you're
going to find out--
PIAW NA: You mean aluminum nipples?
D. PARDO: Sorry, aluminum nipples.
Yes.
Aluminum nipples.
You're going to find out that as you tighten things, you'll
have terrible galling and it gets very
hard to turn the nipple.
And you tend to round off the nipple unless you're pretty
careful about it, especially if you try and to build up a
high-tension wheel.

They're a really great idea, but on the other hand, there's
relatively few rims these days that are available with them.
And so to some degree, you're going to be looking at a set
of rims versus another set of rims. And if you want to get
some, for instance, that have an offset spoke bed, I don't
think you can buy a rim with an offset spoke bed that
eyelets on it.

Ultimately, what you care about is the durability of the
rim, and there are rims that have a relatively thick
aluminum spoke bed, so you can work around that.
And if you use chrome-plated brass nipples, you'll have
less problems with galling, so on, so on and so on.

Lacing.
This is a tangent-spoke spoke wheel.
I guess I didn't bring in a radially-spoked wheel.
Radial is OK for a front wheel, which has a rim brake
and tends to be a little bit lighter.
But cross-spoking or tangent-spoking is much more
common for both rear wheels and for disc brakes.
And it's also common even if there's not a torque load,
because to some degree, the overlapping spokes support
each other in carrying load.
And because if you get a broken spoke, it doesn't tend
to flop around the way that it does if you get a broken spoke
with a radially-laced wheel because then, there's nothing
holding the spoke in place.
It's not a cosmic difference, but it is a reason that a lot
of wheels get built up with cross in the front, even
though you don't technically need it.
It's occasionally possible to get things built up, so that
you have the same length spoke for the left side of the front
wheel, the right side of the front wheel, the left side of
the rear wheel, the right side of the rear wheel.
And that's nice, especially if you're going to be out riding
around and want to carry a spare spoke with you instead
of carrying one of each different length of spoke with
you or something like that.

One of the of things to think about when you're building up
a tangent-spoked wheel is some of the spokes come out of the
hub and go--
let's see--

come out of the hub and go sort of forward in the sense
they go in the direction of rotation.
Some of them come out from the same location on the flange
and go backwards.
So you have some choice about whether the ones going forward
have the head out or head in.
And you furthermore have some choice about whether the ones
on this side of the wheel are done the same way, symmetrical
with the ones over here, or whether it's a mirror image.

For the most part, it doesn't make much of a difference.
There's a little bit of a difference, potentially, that
if you apply a load and the spokes that are getting less
tension in them are all kind of coming in like this a
little bit, and the ones that are getting more tension are
all kind of coming in like this a little bit, you can get
a little bit of lateral motion in the rim.
But it tends to be pretty small.

A more significant consideration, in some cases
anyway, is what happens with the rear wheel if the chain
comes off the innermost sprocket and drops into the
space between the sprocket and the spokes.
You basically have two choices here.
One of them is the spokes are going to come out and go back.
Or they're going to come out, and
they're going to go forward.
And If you had a rear wheel that was like this where they
come out and go back and the chain drops into that area,
the chain is a little rough on the sides, and so it's going
to kind of grab on to one of the spokes.
And it'll get pulled down into that gap,
which you don't want.
On the other hand, if you start to coast, it will tend
to get pushed back out of that gap.
If the spokes are the other way where the spoke comes out
and then goes that way, then, it won't tend to jam in.
But if you coast, it will tend to jam in.
Sorry.
It won't tend to jam in when you pedal, but it will tend to
jam in when you coast.
It's been my personal experience that you're better
off having it not jam in when you coast. So you know there
is some risk that it really gets pounded in there, because
it comes off under chain tension.
That's been my personal experience that you're better
off-- you sort of notice when it comes off, and so it
doesn't tend to get jammed in.
But when things start going wrong, you tend to coast. You
could also use a spoke protector, but
that's pretty unpopular.
AUDIENCE: Could I make that, or is that [UNINTELLIGIBLE]?
D. PARDO: The lightest one I've seen probably weighs at
least 20 grams, and cyclists will typically pay a dollar to
save a gram.
So basically, you have to pay an extra few dollars, and then
your bicycle gets $20 less valuable.

OK.
So on to assembly.
When you actually want to put things together-- oops.
I think we're out of of time, so we'll do
assembling in the class.
I will send out a piece of mail to everybody with links
to the various pages, so you can go look at the notes.
PIAW NA: OK.
Those of you who are going for the hands-on workshop.
Make sure you read part two about assembly
before showing up.
That will help everything go much faster.
And once again, that section is 9:00 in the
morning next Tuesday.
This is a test of how badly you want to learn
how to build a wheel.
So--
D. PARDO: Or how well you want to build a wheel.

AUDIENCE: Who makes that stand?
D. PARDO: I think it's a Minoura.
I don't know that it has any brand
indication on it anywhere.
This is the stand, I think, Piaw learned to
build wheels on.
PIAW NA: That's correct.
D. PARDO: And he liked it so much he went out, and he
bought a different brand.

PIAW NA: It's two different brands.
AUDIENCE: Safety glasses, what do you require?
Like just any kind of goggles?
Or are there some specifics that you--
D. PARDO: Oh.
Ideally, you have something that's got good
impact-resistant whatever in it.
Chances are, almost anything is good enough.
When spokes break--

well, first of all, it's fairly rare.
And second of all, when they break, they don't weigh very
much, so they don't get launched with
rifle-bullet velocity.
They just get launched with modest velocity.
So you're mostly trying to keep
something out of your eye.
But it's not like you're trying to keep a
bullet out of your eye.
AUDIENCE: So plastic goggles should be sufficient.
D. PARDO: Oh yeah.
Probably what you're wearing right now.

PIAW NA: If you don't need glasses,
then you should wear--
AUDIENCE: I actually discovered, last weekend, that
glasses aren't good enough at least for little bits of wood
flying out from a drill, which will bounce off your
cheek and go in.
I don't know if you've got little bits of metal flying
off a spoke.
D. PARDO: Typically not.
And they also don't tend to be at like molten metal
temperatures and things like that.

AUDIENCE: Speaking of flying spokes, are you going to be
providing rim tape for the workshop?
PIAW NA: I plan to have rim tape for my wheel.
D. PARDO: Well, I'm planning to use something.
I'm not necessarily going to bring it for the workshop.
AUDIENCE: So people who are [UNINTELLIGIBLE]
should bring rim tape.
D. PARDO: You can put it on later.
AUDIENCE: Well, at the same time, if you have a spoke
that's under high pressure and the actual--
it's exposed to your eyes, then--
D. PARDO: Oh, I see.
PIAW NA: It's a good safety precaution to apply rim tape
before you add a ton of tension.
D. PARDO: I think the biggest increment in safety, though,
is wearing something over your eyes.
Doesn't hurt.
Good idea, but the biggest increment is probably wearing
something over your eyes.

OK.
PIAW NA: Thank you very much.