I didn't know how much spokes bend around each other where they cross,
so I cut two straight spoke sections and taped them to the rim side of
of some outer spokes on the drive and non-drive side of an 8-speed hub
on a Performance 700c 32-spoke rim:
http://i18.tinypic.com/3ym7bz4.jpg
Click on the lower right in Explorer to see things full-size.
The ends of the cut lengths of reference spoke are at the bottom of
the white paper and are marked with yellow tape. The upper ends of the
reference spokes are taped out of sight above the top of the picture.
You can get an exaggerated idea of the bend where spokes cross by
looking just above and to the right of the "263.71° caption, where a
blurry inner spoke is coming from the hub toward the viewer and then
bending away to the right.
The real spokes are bending around the spokes that they cross. Since
the forest of spokes may be confusing, here's a crude ASCI diagram:
upper rim
\\ //
\\ //
_\\______________________//__________top of picture
\\ //
\\ //
\\ // <--where real spokes bend around
/ \ / \ other real spokes
/ \ / \
/ \ / \
real ref ref real
nds spoke spoke ds
spoke yellow yellow spoke
flange------hub----------flange sprockets
bend about 4.6° bend about 3.7°
An onscreen protractor measured the red lines drawn down the left
sides of the four spokes, but of course any camera angle and parallax
will confuse things slightly at such tiny angles. (I think that the
tendency is to minimize the angles.)
I expect that someone could easily improve on my snapshot.
Posters who bend elbows and nipples might offer some pictures of bent
and unbent spoke ends. It would be interesting to see what angles and
changes are actually involved. I'd be glad to run raw pictures through
a paint program, add lines, and measure angles.
Here's a free Windows screen protractor, the little brother of a
version with six more measuring tools:
http://www.markus-bader.de/MB-Ruler
Cheers,
Carl Fogel