
How the Bicycle Wheel Carries its Load: Held Up by Downward Pull (1980) - ggreer
http://johnforester.com/Articles/BicycleEng/Wheel.htm
======
maaaats
I just finished my master's thesis on optimizing lacing patterns for bicycle
wheels using evolutionary algorithms [1]. To do that, I had to thoroughly
investigate how they work to be able to write a wheel simulator. It's quite
fascinating the forces a spoked wheel can withstand, given its simplicity and
weight.

And damn, "truing" a wheel to make the wheel round, not wobble and have equal
forces on the spokes is an art. Even done iteratively with small changes one
often end up making some part of the wheel worse when fixing one part.

[1]: [http://master.matsemann.com/](http://master.matsemann.com/)

~~~
wiredfool
Did you find any interesting dependency on the geometrical characteristics of
the rim? When I was in grad school doing my masters, I wound up spending a few
weeks playing with wheels using my FEA stuff. I found that the torsional and
lateral stability of the rim are very important when you start going to road
racing wheels with fewer spokes. (Especially as you raise the tension to get
better durability)

Also, how did you do the FEA models? Did you wind up meshing all the parts, or
did you use higher order beam elements for the spokes and rim bits?

~~~
maaaats
Since the algorithm needs to evaluate hundreds of thousands of wheels, it's
not a full-blown FEA model, as that would have taken far too long. It's
written in a real-time physics library called Bullet, and the rim can at most
be modeled as a few, infinitely stiff segments.

~~~
wiredfool
I'd bet with a good model generation, the FEA on this is completely tractable
in realtime now. It's only ~2(spokes)*6 dof, and that was doable in a second
or so on a sparc in matlab 20 years ago. But to do that, you'd need to be
doing beam elements for the spokes and rim segments, not meshing them with
smaller solid elements. (And unless you're in non-linear land in material or
geometry, a 2 node beam element with 6 dof /node is going to be an exact
solution for the spokes, and a good approximate solution for the rim as long
as the chord/arc error isn't large. ) And I've found some of the code, and
holy crap it's still on the web.
[http://www.ce.washington.edu/~soroos/matlab/501/1../wheel2.h...](http://www.ce.washington.edu/~soroos/matlab/501/1../wheel2.html)
(I'm sure I'm going to hate the 19yr ago me when I dig into that and try to
figure out what the hell I was doing based on the comments, because I only
remember the outlines of the math at this point. But... I could put this in
numpy... I need this like I need another project to suck up my time... And I'm
not sure what the me of 2034 is going to think of my code now. But that's
another story.)

The real trick with wheels from experience as a wheel builder is that all the
really interesting behavior is in the non-linear region. And you're butting
right up against that when you lace the wheels tightly. Calculating that limit
is tricky.

(Briefly, Ultimate load limit is ~ the sum of the tension in the spokes in the
loaded zone of the wheel, roughly 4 or so with the rims/spokes I was looking
at at the time. The tension limit is just under what will potato chip buckle
the rim. So there's a complex interaction between spoke stiffness, rim lateral
stiffness, and rim radial stiffness that affects performance at the load
limit. Helpfully, fatigue durability is also better with higher tension in the
spokes, since the fatigue performance goes to hell when you get stress
reversals.)

FWIW, My masters was investigating back calculating material parameters from a
dynamic pavement test based on time histories of surface loading and
displacement at known locations. I basically figured out that the error
measure that we were using was pretty smooth as the stiffness of the
subsurface layers varied and that it was possible to home in on a stiffness
profile pretty consistently if there was at least a plausible guess of what
was under there. It took a long time then though, overnight runs were common,
and we didn't have clusters then. (also, uphill both ways, through the snow) I
bet I could do it in near realtime now on my ipad, but that's a masters thesis
for someone else.

------
wiredfool
FWIW, if you're interested in this subject, the best reference is Jobst
Brandt's "The Bicycle Wheel". It's been out for 30 years or so, but it's still
the best reference.

Past that, you might want to look at Timeshenko and Geere's "Theory of Elastic
Stability", but you'd need a good university library for that one.

------
SixSigma
I'm a qualified wheel builder. It's not that difficult, just takes up to a
couple of hours per wheel. Of course, they are mostly laced by machine
nowadays.

Building your own is good fun, plus you can do specials with fancy lacing or
unusual hubs (such as hub based dynamos)

~~~
stinos
_It 's not that difficult, just takes up to a couple of hours per wheel_

Once you know how to do it properly that is. The key to that is mentioned in
the article: applying tension while building the wheel. Lots of it, in my
(borrowed) experience.

The first couple of wheels I built was before I had internet access and I just
copied the lacing pattern from an existing wheel, then tightened and trued the
wheel. It were the worst wheels I ever had and impossible to keep true (though
I was riding trials back then which does require more from wheels).

Then one day I found
[http://sheldonbrown.com/wheelbuild.html](http://sheldonbrown.com/wheelbuild.html)
and would basically put all sorts of tension on wheels while building them.
Lean on them, hammer the spokes, pull them together, smash the wheel against
the wall and so on. This, together whith experience gained from many
iterations, yields wheels which do not make the slightest sound when ridden
for the first time and stay true even under heavy circumstances (I ride
street/dirt on a 24" bmx now). As another comment mentions: wheelbuilding is
definitely some sort of an art.

~~~
wiredfool
Sheldon Brown was Awesome. Wonderful guy, full of arcane knowledge of the
corners of the bike world, mainly those corners associated with unfashionable,
interesting, reliable stuff. And he was willing to share it with anyone who
would listen.

~~~
SixSigma
And he died on my birthday :(

------
Animats
Right. This is similar to how bolted connections work. Bolted connections must
be tight enough that, when loaded with a force pulling the bolted connection
apart, the bolted surfaces still have pressure pushing them together.
Wikipedia has a good explanation of this.

~~~
analog31
Yes, and bearings too. For a bearing that will work under heavy load, the
balls have to be "pre loaded," meaning that they are actually deformed just a
bit, so they don't lose contact with the bearing races.

All of these things are examples of structures held together by springs.

------
czardoz
I wish that article had a few more diagrams to explain the concept.

Nice read though.

~~~
bliker
Just recently I made a crude simulation to compare Radial and cross lacing for
wheels.
[http://gfycat.com/ThreadbareEdibleCormorant](http://gfycat.com/ThreadbareEdibleCormorant).

I did it in response to this reddit post.
[https://www.reddit.com/r/bicycling/comments/3cxk4v/just_made...](https://www.reddit.com/r/bicycling/comments/3cxk4v/just_made_this_discovery_after_a_long_ride_to_the/)

