Finally got here!
What I'm about to write is pretty much my conclusion on this topic.
I've still got plenty more material, but I've been writing about ヌポーク and such just to get to this point.
As usual, it's ridiculously long.
Regarding the left-right difference in spoke tension on rear wheels,
last time I wrote about correction methods when viewing the wheel from front-to-back.
The answer was offset rim and high-low flange,
but today it's about viewing the wheel from left to right.
In this diagram I'm drawing ヌポーク radial spokes,
When viewing from the side, the extension line of spokes in a radial lacing
(the red dashed line in the diagram above) passes through the hub center.
I'll call this the "radial line" from now on.
You could also think of it as a line segment derived from a circle's radius.
The word "radial line" exists in amateur radio circles too,
but that's completely unrelated. It's my own invention.
Next, let me consider the case of 4-cross lacing with ヌポーク and反ヌポーク.
This is what the radial line looks like from the hub hole of ヌポーク.
To make it clearer, I removed反ヌポーク and left only ヌポーク.
The most direct way a spoke coming from the hub pulls the rim
is when the spoke overlaps the radial line (radial lacing).
From there, as tangent lacing increases in cross count and spokes
deviate further from the radial line, spoke tension loss occurs.
Spoke tension (how taut the spoke is)
can be measured by observing deflection the way shown in the diagram above.
Thicker spokes deform less easily (deflect less),
so technically it's not a unique measurement method,
but since there's no other way, we measure it like this.
↑This diagram shows the rim and hub at 90° to each other,
which is weird, but please don't nitpick that.
When you tighten the nipple, spoke tension increases.
(the red arrow in the diagram above)
At the same time, the nipple's neck digs into the rim.
(the blue arrow in the diagram above)
If you keep raising spoke tension indefinitely from here,
one of the four components—rim, nipple, spoke, or hub—will break
and the wheel becomes unusable.
If the hub is weak, the hub flange tears.
I haven't seen this happen during assembly,
but there are real examples of it happening after time has passed following radial lacing.
This is the least likely of the four to occur.
If the spoke is weak, it breaks at the neck where it's bent.
This also rarely happens during assembly, but spoke breakage from fatigue
during wheel use does happen.
When truing a well-used wheel, sometimes the spoke snaps at the neck
with a crack the moment you tighten the nipple.
This is the most likely of the four to occur.
If the nipple is weak, a crack develops all the way around
where the nipple's neck digs into the rim, and the spoke slips out.
This is the second most common failure.
Amateurs often call this "spoke breakage" too.
Since there's damage in the spoke area requiring repair,
it's not wrong, really.
Nipples come in brass and aluminum materials.
It's commonly thought that the lighter aluminum is more prone to this.
It's true that aluminum nipples have their corners rounded more easily
when assembling a wheel,
but I'm not sure the tensile strength is actually weaker than brass.
From my personal experience, aluminum seems stronger once assembled,
but since my theoretical basis for this is weak, I won't state it as fact.
If aluminum were stronger, it would mean (for the user, not the wheel builder)
weight reduction with no risk.
If the rim is weak, it breaks like in the diagram above.
(The text got so long you probably can't see the diagram anymore.)
Sometimes this happens from age and use,
but with rims having low tensile strength at spoke holes,
it can happen during assembly too.
I'd like to say carbon rims are weaker than aluminum at this,
but lately some aluminum rims or better can take the same spoke tension,
so it's hard to generalize.
Rim manufacturers set spoke tension upper limits
specifically to prevent this.
Here I'll express spoke tension asST,
and the force trying to break through the rim by the nipple asRK.
SpokeTension for ST and
RimKui (break through) for RK.
Back to a diagram like the opening: when tensioning spokes
with 100 ST in radial lacing, let's say 100 RK of pull is generated on the rim.
Manufacturers are concerned with RK regarding rim breakage,
but since RK can't be measured (except maybe by specialized testing labs),
normally we measure ST using the method described earlier.
Next, consider achieving 100 RK of pull with 4-cross lacing.
4-cross spokes pull at an angle away from the radial line,
so there's loss in pulling force. To achieve 100 RK despite that,
you'd need to tension beyond 100 ST.
The diagram shows 120 ST, but that's not the exact value.
It's definitely more than 100 ST, just a rough estimate.
If a manufacturer says "don't assemble beyond 100 ST,"
you'd assemble at 100 ST max with 4-cross too,
but the RK would then be maybe 80 RK.
What's important here is that with the same RK, radial lacing
requires lower spoke tension than tangent lacing.
Everything I've written so far has been to make this one point.
RK directly relates to vertical wheel stiffness, but since rim manufacturers
specify the ST limit, when tensioning to the max ST limit,
the highest RK occurs with 0-cross (radial lacing).
"Radial lacing makes vertically stiff wheels" is no myth.
Moving from there through 2→4→6→8-cross tangent lacing,
the RK increase per 1 ST decreases due to loss from deviation off the radial line.
↑The spokes colored blue in this image are 8-cross ヌポーク,
nearly perpendicular to the radial line.
Almost tangent to the circle (hub flange). "Tangent" lacing
means tangent line lacing, literally.
Here's what hub hole counts are possible for 0-8 cross lacing.
I'll use y≦4/x. Yeah, so convenient.
When viewing wheels front-to-back, I usually intend to draw from straight behind,
but this time it's from above.
The perspective is sharp, you know. But
that has nothing to do with Sharp (the company).
If Sharp designed a bicycle wheel,
they'd probably add Plasmacluster technology to it.
Imagine a wheel built on a hub with Plasmacluster generator
rolling by, and blowing エヘン bugs (coughing bugs) from the front.
Thanks to negative ions,
the エヘン bugs became clean.
Not that the bugs matter (then why mention them?),
but let me look at a wheel without tires from above.
Assume the valve hole is at the top.
I'll use the magic knife from ヌポーク Part 1 (→here) to
slice through this wheel. Carefully avoiding rim spoke holes,
I'll cut the hub straight in half.
The direction forward is obviously from the sprocket side shown,
and both sides are radial laced for clarity (laugh).
This time I'll just open it without flattening it.
Like a clam opened to maximum.
Viewing that from the brake zone side of the rim cut, not the cut face itself,
gives you the diagram above.
As I said before, rear wheels have drop-outs so
the freewheel side has higher spoke tension.
In the diagram above, both sides are tangent laced.
↑For a wheel with the non-freewheel side in radial lacing, it looks like this.
"If we radial lace both front and rear wheels for the best
aerodynamics and weight, but the freewheel side gets intense twisting
so let's keep it in sturdy tangent lacing" — that's the thinking.
Many wheel manufacturers do this, with
Easton being a typical example. But there are plenty of others.
As mentioned, radial lacing lowers spoke tension.
Lowering the already-low non-freewheel side tension further
makes the left-right spoke tension difference even worse.
This is the worst assembly method for wheel balance.
My mysterious Cosmic Carbon has radial lacing on the non-freewheel side,
but that was due to the spoke hole layout on the rim—
it had to be laced that way.
When I grab the non-freewheel spokes, they're quite loose.
However, with radial lacing, spokes don't touch each other, so
there's no creaking noise from contact,
and the weakness on the left goes undetected.
Using ヌポーク for radial lacing is mild rebellion.
↑What if we radial lace the freewheel side
and tangent lace the non-freewheel side? Then the freewheel spoke tension
decreases, and relatively the left-right balance improves.
This would be the best assembly balance-wise. But,
radial lacing is
↑weak to twisting like this.
Front wheels only get twisting from rim brakes,
so it's not a big deal, but rear freewheel sides experience
incredible twisting power from pedaling through the freehub body—that's problematic.
I actually built a hand-laced wheel with freewheel side radial lacing.
This is ヌポーク radial, and there's a reason for that.
With反ヌポーク radial, lateral stiffness is hard to secure.
Lateral stiffness calculations are based on where spokes exit the hub flange,
and with反ヌポーク that's extremely narrow.
Plus, radial lacing lowering spoke tension means
it's less able to handle the freewheel's intense twisting.
For hand-laced wheels, this反ヌポーク radial method is
the worst for spoke neck breakage risk.
But if you ヌポーク radial lace,
spokes aren't woven together, so spoke protrusion increases,
and with the derailleur in low gear, pulley cage and spoke contact—
that problem happens often.
There are workarounds, but even with them,
climbing out of the saddle or hard efforts on flats can still cause contact.
This method should be avoided.
With 2-cross lacing too, if weaving spokes:
Both ヌポーク → possible derailleur contact
Both反ヌポーク → low lateral stiffness
So not recommended.
Still, freewheel side radial lacing has major benefits for correcting
spoke tension left-right difference. How can we solve this...?
↑"What if we make the hub and spokes as a matched set,
and use large-diameter aluminum spokes?" That incredibly smart wheel
is "Kysriumキシリウム." キシリウムキター
Looking at the hub flange structure, it seems spokes won't distort
from freehub twisting, and aluminum spokes look super robust.
That Mavic thought this up in 1999 is amazing.
This is speculation, but I think Kysirium's starting point wasn't
"Let's make an aluminum spoke wheel"
but "Let's make a freewheel-side radial laced wheel."
In pursuit of structure unaffected by freehub twisting,
that's how they arrived at aluminum spokes.
～Digression～
↑This is a 7800-series Dura-Ace complete wheel.
Freewheel side is radial laced. Current models like Zipp wheels and
Mavic Kysirium Elite with steel spokes are radial laced,
and with straight spokes' high tension capacity and smart hub design,
they make steel spoke freewheel radial work without issues.
This wheel similarly has steel spokes and freewheel radial.
People complain this era's Dura-Ace wheels are "hard to adjust,"
but that has nothing to do with how the wheel rides, so whatever.
It's my job to fix them anyway.
The hub internals are a carbon copy of Campagnolo's,
and the lacing is a carbon copy of Kysirium, but
the way this wheel's logic is pursued—this is Shimano's best-ever rear wheel, I think.
After this, trying to think for themselves just made worse wheels.
The left flange is positioned as far out as possible. Smart!
WH-9000 brags about "wide flange," but
it's about the same width as this.
They call it "extra-wide flange,"
but back in the WH-7800 era, it was practically extra-wide already.
Then yesterday it trashed its own previous model (WH-7900)—that's wild.
～End digression～
To T-mura, who cooperated with wheel photography:
Don't let go of that wheel. It's a masterpiece.
You can only freewheel-side radial lace complete wheels!
(Like how you can only read manga anthologies in Jump!)
So let me think about lacing methods to correct spoke tension differences
in hand-laced wheels.
The diagram says 0-8 cross on both sides
What I'm about to write is pretty much my conclusion on this topic.
I've still got plenty more material, but I've been writing about ヌポーク and such just to get to this point.
As usual, it's ridiculously long.
Regarding the left-right difference in spoke tension on rear wheels,
last time I wrote about correction methods when viewing the wheel from front-to-back.
The answer was offset rim and high-low flange,
but today it's about viewing the wheel from left to right.
In this diagram I'm drawing ヌポーク radial spokes,
When viewing from the side, the extension line of spokes in a radial lacing
(the red dashed line in the diagram above) passes through the hub center.
I'll call this the "radial line" from now on.
You could also think of it as a line segment derived from a circle's radius.
The word "radial line" exists in amateur radio circles too,
but that's completely unrelated. It's my own invention.
Next, let me consider the case of 4-cross lacing with ヌポーク and反ヌポーク.
This is what the radial line looks like from the hub hole of ヌポーク.
To make it clearer, I removed反ヌポーク and left only ヌポーク.
The most direct way a spoke coming from the hub pulls the rim
is when the spoke overlaps the radial line (radial lacing).
From there, as tangent lacing increases in cross count and spokes
deviate further from the radial line, spoke tension loss occurs.
Spoke tension (how taut the spoke is)
can be measured by observing deflection the way shown in the diagram above.
Thicker spokes deform less easily (deflect less),
so technically it's not a unique measurement method,
but since there's no other way, we measure it like this.
↑This diagram shows the rim and hub at 90° to each other,
which is weird, but please don't nitpick that.
When you tighten the nipple, spoke tension increases.
(the red arrow in the diagram above)
At the same time, the nipple's neck digs into the rim.
(the blue arrow in the diagram above)
If you keep raising spoke tension indefinitely from here,
one of the four components—rim, nipple, spoke, or hub—will break
and the wheel becomes unusable.
If the hub is weak, the hub flange tears.
I haven't seen this happen during assembly,
but there are real examples of it happening after time has passed following radial lacing.
This is the least likely of the four to occur.
If the spoke is weak, it breaks at the neck where it's bent.
This also rarely happens during assembly, but spoke breakage from fatigue
during wheel use does happen.
When truing a well-used wheel, sometimes the spoke snaps at the neck
with a crack the moment you tighten the nipple.
This is the most likely of the four to occur.
If the nipple is weak, a crack develops all the way around
where the nipple's neck digs into the rim, and the spoke slips out.
This is the second most common failure.
Amateurs often call this "spoke breakage" too.
Since there's damage in the spoke area requiring repair,
it's not wrong, really.
Nipples come in brass and aluminum materials.
It's commonly thought that the lighter aluminum is more prone to this.
It's true that aluminum nipples have their corners rounded more easily
when assembling a wheel,
but I'm not sure the tensile strength is actually weaker than brass.
From my personal experience, aluminum seems stronger once assembled,
but since my theoretical basis for this is weak, I won't state it as fact.
If aluminum were stronger, it would mean (for the user, not the wheel builder)
weight reduction with no risk.
If the rim is weak, it breaks like in the diagram above.
(The text got so long you probably can't see the diagram anymore.)
Sometimes this happens from age and use,
but with rims having low tensile strength at spoke holes,
it can happen during assembly too.
I'd like to say carbon rims are weaker than aluminum at this,
but lately some aluminum rims or better can take the same spoke tension,
so it's hard to generalize.
Rim manufacturers set spoke tension upper limits
specifically to prevent this.
Here I'll express spoke tension asST,
and the force trying to break through the rim by the nipple asRK.
SpokeTension for ST and
RimKui (break through) for RK.
Back to a diagram like the opening: when tensioning spokes
with 100 ST in radial lacing, let's say 100 RK of pull is generated on the rim.
Manufacturers are concerned with RK regarding rim breakage,
but since RK can't be measured (except maybe by specialized testing labs),
normally we measure ST using the method described earlier.
Next, consider achieving 100 RK of pull with 4-cross lacing.
4-cross spokes pull at an angle away from the radial line,
so there's loss in pulling force. To achieve 100 RK despite that,
you'd need to tension beyond 100 ST.
The diagram shows 120 ST, but that's not the exact value.
It's definitely more than 100 ST, just a rough estimate.
If a manufacturer says "don't assemble beyond 100 ST,"
you'd assemble at 100 ST max with 4-cross too,
but the RK would then be maybe 80 RK.
What's important here is that with the same RK, radial lacing
requires lower spoke tension than tangent lacing.
Everything I've written so far has been to make this one point.
RK directly relates to vertical wheel stiffness, but since rim manufacturers
specify the ST limit, when tensioning to the max ST limit,
the highest RK occurs with 0-cross (radial lacing).
"Radial lacing makes vertically stiff wheels" is no myth.
Moving from there through 2→4→6→8-cross tangent lacing,
the RK increase per 1 ST decreases due to loss from deviation off the radial line.
↑The spokes colored blue in this image are 8-cross ヌポーク,
nearly perpendicular to the radial line.
Almost tangent to the circle (hub flange). "Tangent" lacing
means tangent line lacing, literally.
Here's what hub hole counts are possible for 0-8 cross lacing.
I'll use y≦4/x. Yeah, so convenient.
When viewing wheels front-to-back, I usually intend to draw from straight behind,
but this time it's from above.
The perspective is sharp, you know. But
that has nothing to do with Sharp (the company).
If Sharp designed a bicycle wheel,
they'd probably add Plasmacluster technology to it.
Imagine a wheel built on a hub with Plasmacluster generator
rolling by, and blowing エヘン bugs (coughing bugs) from the front.
Thanks to negative ions,
the エヘン bugs became clean.
Not that the bugs matter (then why mention them?),
but let me look at a wheel without tires from above.
Assume the valve hole is at the top.
I'll use the magic knife from ヌポーク Part 1 (→here) to
slice through this wheel. Carefully avoiding rim spoke holes,
I'll cut the hub straight in half.
The direction forward is obviously from the sprocket side shown,
and both sides are radial laced for clarity (laugh).
This time I'll just open it without flattening it.
Like a clam opened to maximum.
Viewing that from the brake zone side of the rim cut, not the cut face itself,
gives you the diagram above.
As I said before, rear wheels have drop-outs so
the freewheel side has higher spoke tension.
In the diagram above, both sides are tangent laced.
↑For a wheel with the non-freewheel side in radial lacing, it looks like this.
"If we radial lace both front and rear wheels for the best
aerodynamics and weight, but the freewheel side gets intense twisting
so let's keep it in sturdy tangent lacing" — that's the thinking.
Many wheel manufacturers do this, with
Easton being a typical example. But there are plenty of others.
As mentioned, radial lacing lowers spoke tension.
Lowering the already-low non-freewheel side tension further
makes the left-right spoke tension difference even worse.
This is the worst assembly method for wheel balance.
My mysterious Cosmic Carbon has radial lacing on the non-freewheel side,
but that was due to the spoke hole layout on the rim—
it had to be laced that way.
When I grab the non-freewheel spokes, they're quite loose.
However, with radial lacing, spokes don't touch each other, so
there's no creaking noise from contact,
and the weakness on the left goes undetected.
Using ヌポーク for radial lacing is mild rebellion.
↑What if we radial lace the freewheel side
and tangent lace the non-freewheel side? Then the freewheel spoke tension
decreases, and relatively the left-right balance improves.
This would be the best assembly balance-wise. But,
radial lacing is
↑weak to twisting like this.
Front wheels only get twisting from rim brakes,
so it's not a big deal, but rear freewheel sides experience
incredible twisting power from pedaling through the freehub body—that's problematic.
I actually built a hand-laced wheel with freewheel side radial lacing.
This is ヌポーク radial, and there's a reason for that.
With反ヌポーク radial, lateral stiffness is hard to secure.
Lateral stiffness calculations are based on where spokes exit the hub flange,
and with反ヌポーク that's extremely narrow.
Plus, radial lacing lowering spoke tension means
it's less able to handle the freewheel's intense twisting.
For hand-laced wheels, this反ヌポーク radial method is
the worst for spoke neck breakage risk.
But if you ヌポーク radial lace,
spokes aren't woven together, so spoke protrusion increases,
and with the derailleur in low gear, pulley cage and spoke contact—
that problem happens often.
There are workarounds, but even with them,
climbing out of the saddle or hard efforts on flats can still cause contact.
This method should be avoided.
With 2-cross lacing too, if weaving spokes:
Both ヌポーク → possible derailleur contact
Both反ヌポーク → low lateral stiffness
So not recommended.
Still, freewheel side radial lacing has major benefits for correcting
spoke tension left-right difference. How can we solve this...?
↑"What if we make the hub and spokes as a matched set,
and use large-diameter aluminum spokes?" That incredibly smart wheel
is "Kysriumキシリウム." キシリウムキター
Looking at the hub flange structure, it seems spokes won't distort
from freehub twisting, and aluminum spokes look super robust.
That Mavic thought this up in 1999 is amazing.
This is speculation, but I think Kysirium's starting point wasn't
"Let's make an aluminum spoke wheel"
but "Let's make a freewheel-side radial laced wheel."
In pursuit of structure unaffected by freehub twisting,
that's how they arrived at aluminum spokes.
～Digression～
↑This is a 7800-series Dura-Ace complete wheel.
Freewheel side is radial laced. Current models like Zipp wheels and
Mavic Kysirium Elite with steel spokes are radial laced,
and with straight spokes' high tension capacity and smart hub design,
they make steel spoke freewheel radial work without issues.
This wheel similarly has steel spokes and freewheel radial.
People complain this era's Dura-Ace wheels are "hard to adjust,"
but that has nothing to do with how the wheel rides, so whatever.
It's my job to fix them anyway.
The hub internals are a carbon copy of Campagnolo's,
and the lacing is a carbon copy of Kysirium, but
the way this wheel's logic is pursued—this is Shimano's best-ever rear wheel, I think.
After this, trying to think for themselves just made worse wheels.
The left flange is positioned as far out as possible. Smart!
WH-9000 brags about "wide flange," but
it's about the same width as this.
They call it "extra-wide flange,"
but back in the WH-7800 era, it was practically extra-wide already.
Then yesterday it trashed its own previous model (WH-7900)—that's wild.
～End digression～
To T-mura, who cooperated with wheel photography:
Don't let go of that wheel. It's a masterpiece.
You can only freewheel-side radial lace complete wheels!
(Like how you can only read manga anthologies in Jump!)
So let me think about lacing methods to correct spoke tension differences
in hand-laced wheels.
The diagram says 0-8 cross on both sides
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