It seems to me the answer to this would make a big difference in what spokes
and tension to use.   If the spoke bed is the limiting factor, you'd run the
same tension and spokes on both sides of the front wheel and the drive side
of the rear (assuming the same rim).  The non-drive side would have lower
tension (due to dish) and you could get away with thinner spokes there.

However, if the rim yielding due to overall compression is the limiting
factor, then you would use higher tension on the drive side of the rear than
on the front wheel to get the rear wheel up to the same overall tension as
the front.  You may then need to use thicker spokes on the drive side to
take the increased loads during wheelbuilding and use.  Again, you could use
thinner spokes on the non-drive side.

If the answer depends on the rim, what about a single-eyelet, double-cavity
rim like the Mavic 517 or Bontrager Mustangs?

Thanks for any analysis or experiences you can share...

    Ryan Campbell
    Software Engineer
    University of Washington

Jobst Brandt      <jbra...@hpl.hp.com>

There is a book on this at your local bicycle shop.  I can recommend it.

Jobst Brandt      <jbra...@hpl.hp.com>

I believe that, for an older road rim design such as the MA series from
Mavic, where, for a given cross section area (rim weight), the walls
were fairly thick by modern standards due to limitations on the extrusions
they could get at the time I think. These sections were shorter and
narrower, which makes them less rigid laterally and radially.  They
also have fairly strong spoke beds when socketed (double eyelets) because
of the thick walls and small section. The limit on spoke tension may well
be based on the yield point of the rim section in bending.  One could, if
one really cranked up the tension, make the wheel unstable and very prone
to folding with a little lateral knock.

With Open 4 and Open Pro sections this might no longer be a good idea.
In those sections Mavic has taken the extrusion process a little farther.
Many of the walls are thinner (though the actual spoke bed is thick)
and the section is "larger" for a given rim weight. Even though they
are socketed (double eyelets), many of the failures I observe in shop
recycling bins are due to spoke bed failures, usually drive side rear
spokes.

The socketing reinforcement scheme is the only alternative for road
rims because they are so narrow.

The elasticity of the spoke is an issue as well.  If one were to ignore
spoke loads on the rim and the spoke loads themselves, and try to build
the wheel with the highest possible lateral strength, a stiff spoke is
best (all else being equal).  For a given tension, the stiffer spoke
makes the assembly stiffer and stronger laterally.  But it is not without
a cost.  Spoke fatigue failure is more likely.  And, the stiff spoke
increases the local load around the nippl in the rim when the wheel
is loaded dynamically.

Butted spokes are better in both respects.  The butting makes the spoke
slightly less stiff, so, when built to the same initial tension as the
plain gauge spoke, the load around the nipple will increase more slowly
as a function of rim displacement.  Good for the spoke, good for the rim,
small loss of lateral strength.

Heavily butted spokes like the Revolution makes these characteristics
more pronounced.  It is not easy to build to the same initial tension
as is possible with 14 gauge unbutted spokes though, so there is a small
strength reduction because of that.  And, the lower spoke rigidity in
tension reduces the lateral strength of the wheel more as well.

Whether a road wheel built with these and a modern light section rim like
the Open Pro holds up in a given application is a matter of the loads
applied to it.  I doubt they would be a good idea as the one and only wheels
for a large rider who rides hard and often.  They might be fine for a lighter
rider or as a race day set.

Modern MTB rims are very stiff laterally and radially because they have
big sections (width and height and a large "box") and very thin walls.
The discussion of why this works, why this type of section is stiff is
similar to the one used to explain the properties of large diameter
thin wall aluminum frames like a Klein.  The rims are very strong as
well when bending strength is considered, if they are made from an
aluminum alloy that has decent mechanical properties.  This is what
mavic 217/517 and CrossMax rims are like.  Bontrager Valiants and Mustangs
too (I have an inside track on the latter   ;-).

But, because of the thin walls that support the spoke loads on the rim
at the nipple seat, these rims are prone to fatigue failure in that area.
Field experience with 217s indicates this strongly.

One can see that a rim can be designed to be stiff when considered as a
beam, analyzing the cross section only.  Large section modulii in
both directions. It is also easy to understand that the rim can be
weak in a given local area, looking at bending and shearing loads on the
spoke bed near the nipples for example.  There are also some internal
stresses between and around spoke holes that can lead to a fatigue
failures in practice.  Thin walled light section rims are tougher
to design because of this.

But that's the design compromise that makes the newer rims a little
different than the older style, thicker wall rim.  It raises the short
term performance characteristics at the cost of fatigue strength (and
brake wall wear replacement intervals).

While the socketing reinforcement scheme is the only alternative for road
wheels because the section is so narrow.  MTB rims can use inner walls
to reinforce the spoke bed area on a thin light rim.

Again, based on what I know of rim manufacturing processes and extrusion
processes, older rims were limited in the minimum wall thickness that
was possible by the extrusion practice.  That has changed.  It might have
also been a cost thing as well, with the market for "cost is no object
extruded stuff" in a lot of markets (not just bike rims) big enough now
to allow this type of operation to exist commercilly out side of the
aerospace biz.  Dunno.  It's what happened anyway.

I am anticipating (!) some discussion of all this since it seems to go
against the other opinions offered, but I don't think it is inconsistent
with those in primciple.  It just requires an extension of those ideas,
to include a rim with a different section and new properties.  If you make
the walls of the rim continuously thinner and the section larger it's
clear that, at some point,you can't ignore spoke bed loads and subsequent
fatigue failures, even with reinforcement schemes.  That's the point at
which these rims are.

Brake wall wear, crash damage, and rock dings are all very likely ways
a rim can come to it's end before it breaks at the spoke bed though.
Unlike a road wheel (with the exception of brake wall wear in wet weather),
the fuse is burning from a lot of different directions on an MTB wheel.
Because of that, it is reasonable to risk breaking a rim at the spoke
bed (or design a rim that will break at the spoke bed) to get the
other properties IF AND ONLY IF those properties are an advantage.
Racers like wheels like this.  They are light, strong, and it doesn't
matter if they don't last forever at the spoke bed because they can
be replaced ofen enough to avoid mechanical failures in a race.  Many
recreationl riders will be okay with this tyoe of rim too, because they
will die a cruel, untimely death (the rims, not the riders at least not
from the POV I am writing this from now ;-) in some other way before the
spokes pull through.

They are not that many riders who really NEED them though.  A heavier rim
with thicker walls is easier for everyone to deal with in almost every
respect, is stronger on the trail, and lasts longer too.  The difference
in performance to a recreational rider between a 450g + rim and a 400 gram
rimm is small but the difference in durability on the trail is big. Mavic
makes some rims like this (forgot the numbers), and we do too. Mavericks,
Corvairs etc.  These come on low cost bikes.

Of course, the light section rims also make wheels that are more attractive
and easier to sell, so most popular rims are that way.  These are the
only ones that get attention from the press as well.

Ceramic coating takes out the brake wall wear mechanism and ups the ante
on spoke bed strength.  That's why we use DT Revolutions all around on
the lite wheelset - to buy field service time in that area.  The rims are
strong enough laterally to give up a little strength in that respect to
gain fatigue life.

Again, you can pick the properties in the wheel you are after and decide
spoke tension/gauge accordingly.  Some tricks:  14/15 on the drive side
of the wheel and 14/17 elsewhere makes a light wheel with a little more
lateral strength and pretty good spoke bed life.  14 plain everywhere
makes a stiffer stronger wheel at the expense of fatigue strength, the
other end of the spectrum.  In the NW mud, brake wall wear rates are pretty
high, so that makes some of your decisions easier unless you are running a
coated rim.

Keith Bontrager

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The Mustang rims are a little different than the 517/217 box
section, single eyelet rims.

(Best ascii version - sorry if the spacing is messed up)

Mavic standard box rim

  __                 __
  |                   |
  |                   |
  |                   |
  |___________________|
  |                   |
  |                   |
   |                 |
    |_______________|
           ||
           ||
           ||
           ||
          spoke

Mustang extra inner walls to reinforce the spoke bed
around the nipple seats:

front
  __                  __
  |                    |
  |                    |
  |                    |
  |____________________|
  |    |          |    |
  |    |          |    |
   |   |          |   |
    |__|__________|__|
            ||
            ||
            ||
            ||
          spoke

Valiant and Mustang rear ASYM
  __                  __
  |                    |
  |                    |
  |                    |
  |____________________|
  |      |             |
   |     |             |
    |    |            |
     |___|___________|
              ||
              ||
              ||
              ||
            spoke

There is no room for the second inner wall with the
spoke shifted over.

It is reasonable to question whether this method of reinforcement
is better than a double eyelet (the sockets Jobst refers to) in
a standard box section rim.

I believe it is (imagne that).  The section is well reinforced
because of the integral character of the reinforcement wall.
It is part of the extrusion.  The sockets are fit into the rim
and require (due to mounting requirements and tolerance
accumulation) some deflection of the rim inner walls to bear
much of the load. The cups are also not shaped very well to
support the load.

This has shown to be very effective iin testing and in the field.

These are small details though and the best test is that of time.
The triple cavity rim has done well so far. I am willing to gamble
that it will continue in this respect.

To show how close this is (and show how the fatigue of the spoke bed
is a function of initial static stresses from spoke tension) we had
some Mustang ASYM rear rims that were over sanded around the welded
joint.  The wall was sanded 0.2 to 0.3mm thinner than the spec.  The
location next to the seam put the flaw at one of the drive side
pulling spokes when the wheel was built.  These rims had
a very short fuse in service, with a fatigue failure at the thin
spoke bed wall in several months of hard service...

Cheers,

Keith Bontrager

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