Wheel Strength/Spokes--Part Deux
Shawn Amir
and spoke count. The following is what I believe. Please
respond if you think I am missing some thing:
(Para 4 seemed to be missing from our last discussion--thank
Jobst for raising it.)
For most rims, wheel strength is determined by the
compressive capacity of the rim. To wit, builders are
advised to add spoke tension until the rim starts to
go wavy, then back off. As this is a first level
simplification of multiple factors, one can also state
that spoke number and tension may be traded off in order
to achieve the same maximum rim compression--i.e. fewer
spokes with more tension.
However, there are a number of very important limiting
factors.
1) Triangular section rims--consider a 550g DeepV--have
extremely large compressive strengths. One would be hard
pressed to approach their compressive limits even with
48 thick spokes. More on these rims later.
2) There is a limit to how much tension a spoke can
take. More importantly, the spoke/nipple/rim juncture
will fail before the spoke snaps from static tension.
So there is a static limit on how few spokes can be
used to tension the wheel--referring to the spoke
number versus tension tradeoff in the first paragraph.
3) When in use, the bottom portion of the wheel
experiences loading. For a box section rim, this might
be as small as 40 degrees. Therefore, given 36 spokes,
4 of them will be experiencing the bulk of this
load--actually offloading since the spokes are preloaded.
It is important to have this load shared by a sufficient
number of spokes to minimize the effects, you do not
want the spokes to go slack in each rotation.
4) However, the size of the loaded arc of the rim is
determined by the bridge strength of the rim. As the
bridging strength increases, the arc will increase--limited
to about 90 degrees because of the circle's geometry. To
take the example of a 550g DeepV rim, the loaded arc
(I believe) is closer to 80 degrees. Assuming 36 spokes,
we would have the load shared by 8 spokes.
The proper perspective is to treat the wheel as a complete
system. As such there are other factors to consider, such
as spoke crossing pattern, thickness, hub flange loading,
lateral stiffness, rounded-ness, failure modes, etc.
Now for the conclusions:
A) It is indeed possible to make a very strong and very
light wheel from a box section rim with 36 spokes. Indeed
given the low bridge strength of such rims is foolish to
use fewer spokes. Spokes weigh very little and when
combined with a 350g rim and light hub (e.g. 65g AmClassic)
they can make for an amazingly light (Sub 600g) wheel that
would cost less and weigh less than the boutique alternatives.
B) Most available rims are in the 420-550g range these
days and have a triangular cross-section yielding higher
bridge strengths. These do not require 36 spokes except for
the most extreme application. Indeed, the standard lacing
for such rims (these days) is 32.
C) One may claim some aero advantage for wheels build from
deep triangular profile rims. Similarly, one may claim a
weight advantage for wheels build from the box sectioned
rims. It is debatable whether avocational cyclists benefit
from either. However, both camps energetically poo-poo the
other.
Personally, I like the look of DeepV rims. I also see no
reason to build such a rim with 36 spokes--perhaps if I gained
another 100 pounds. My feelings are that most cyclists would
benefit from building
Box-sectioned rims (350g) with 36 spokes cross 3
20mm Triangular (440g) with 32 spokes cross 3
30mm DeepV (540g) with 28 spokes cross 2
Lighter folks may use less and heavier folks more. With all
due respect to the Wagon Wheel folks, this ain't a religion.
Cheers, Shawn
PS: I welcome your comments, but please read the whole
thing before flaming.
Cesar Crusius
> There was yet another long discussion of wheel strength
> and spoke count. The following is what I believe. Please
> respond if you think I am missing some thing:
I think you are basically right. After all the discussion in that
thread, you reached the conclusion we (I and Jobst) were "preaching:"
the right wheel for the poor guy who originated the thread is a
36-spoke wheel: lightweight and durable/reliable. There is simply no
beating the "magical 36" (which turned out to be rational and not
magical, hardly surprising considering the last 100 years of bicycle
history) when these two are priorities.
Now, when you go to "deep V" and similars, then you do so, as you
hinted in your message, solely for the looks. Except for the very most
specific applications, there is no performance advantage on one type
of wheel over another (note, standard spoked wheels that is). As I
said before, if you go for the looks, then that's what you do. All the
previous discussion was summarized here and the result is that for the
"average joe" the 36 spoke is still the best "compromise" (a strong
word since as we see there is no compromise in this case), assuming
one doesn't want to look hype.
Fortunately for me, I happen to like (besides mango-cat-puke color)
box section rims. I find they to be the most elegant. This allows me
to get both "looks" (for my standards) and "rationality" (lightweight,
durable, negligible aerodynamic losses over other standard wheels, and
on top of that I climb more than I TT). If I happened to like deep V
rims, I would be in a fashion crisis.
As my only remark, regarding
> B) Most available rims are in the 420-550g range these days
That is true. Unfortunately, it is also true that they are "anodized",
"ceramic", "machined", and god knows what other B.S. necessary to sell
them to hyped crowd. As a result, they are weaker, and I strongly
believe that the light ones (400g velocity and fir, and up to 450g
maybe) still would be better with 36 spokes.
> My feelings are that most cyclists would benefit from building
>
> Box-sectioned rims (350g) with 36 spokes cross 3
> 20mm Triangular (440g) with 32 spokes cross 3
I still believe 36 from remarks above... Which in turn boils down
again to the idiocy of 32 spokes...
> 30mm DeepV (540g) with 28 spokes cross 2
I claim ignorance with respect to this one in terms of reliability.
> PS: I welcome your comments, but please read the whole
> thing before flaming.
No flames here!
Cheers,
--
Cesar Augusto Rorato Crusius o _ _ _
Stanford University __o /\_ _ \\o (_)\__/o (_)
e-mail:cru...@stanford.edu _`\<, _>(_) (_)/<_ \_| \ _|/' \/
www.stanford.edu/~crusius (_)/(_) (_) (_) (_) (_)' _\o_
He who sacrifices functionality for ease of use
Loses both and deserves neither
Jobst Brandt
>> B) Most available rims are in the 420-550g range these days
> That is true. Unfortunately, it is also true that they are "anodized",
> "ceramic", "machined", and god knows what other B.S. necessary to sell
> them to hyped crowd. As a result, they are weaker, and I strongly
> believe that the light ones (400g velocity and fir, and up to 450g
> maybe) still would be better with 36 spokes.
Check it out:
http://www.mavic.com/eng/prod/fiche/wheel/r_ksyr.htm
lists these wheels as having:
QRM SUP FORE ISO-PULS ZICRAL MAXTAL FTSL UB-CONTROL
a large part of the MAVIC special features glossary. If that doesn't
impress your friends and neighbors, it will depress your pocketbook.
But it's worth every penny of it. Just think, all this in one set of
wheels. I'll bet you can feel the difference.
Jobst Brandt <jbr...@hpl.hp.com>
Cesar Crusius
> Check it out:
>
> http://www.mavic.com/eng/prod/fiche/wheel/r_ksyr.htm
>
> lists these wheels as having:
>
> QRM SUP FORE ISO-PULS ZICRAL MAXTAL FTSL UB-CONTROL
I'll even say "sure it costs $12.123.99, but believe me, it's worth
every penny."
I just got my Sun M13 II rims I'll use to build my front wheel. Simply
6061 alloy, polished. Non-machined, non-anodized, non-bs. Of course,
they don't make it anymore! Is it the "last honest road rim?" Only
problem is that they only have eyelets (no sockets). Hope that's ok.