700c front wheel 2-cross lacing vs 3-cross & lateral flex

On Tue, 27 Mar 2007 22:30:01 -0700, kwalters <[email hidden]>

Quoted message said:

I have 2 almost identical front wheels, both: MA40,32 hole 15/16
butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
difference is in the spoke lacing: one is 2-cross, the other
is 3-cross. The 3-cross seems to have noticeably more lateral
rigidity than the 2-cross under similar ride conditions. This
is most appparent when riding in a moderate headwind or crosswind.
The 2-cross is more easily buffeted from side to side and I'm
constantly correcting steering. I get a similar response during
high-speed descents on less than smooth pavement. The 2-cross
wheel seems to jump around more.

Is this to be expected and common knowledge, and I'm just late
in picking up on it, or is it just my imagination?

BTW: same bike.

Thanks for any response?

Ken

Dear Ken,

For the lateral rigidity of different spoke lacings on otherwise
identical wheels with no tires, see #9 here:

http://www.sheldonbrown.com/rinard/wheel/index.htm

In short, not yet tested.

But Damon Rinard's tests involved hanging a 25.78 lb weight from a
horizontal wheel.

In over a hundred wheels, deflection ranged from about 1 to 5 mm.

A rear MA40 32-spoke 3-cross 2x1.8 deflected about 2mm. (It's the
first wheel tested.)

The only 2-cross wheels were carbon-fiber 20-spokes and deflected 2 mm
front and 3 mm rear.

It is unlikely that any ordinary crosswind (much less headwind)
provides the 26 pounds of side force needed to deflect a front MA 40
rim 2~3 mm.

So I doubt that lateral rigidity is involved.

Aerodynamics might somehow explain a noticeable physical difference,
but that seems unlikely, too, particularly when a headwind brings out
the feeling that you mention.

For fun, you might weigh the two "almost identical" wheels on an
electronic scale and see how close they are.

Cheers,

Carl Fogel

kwalters said:

I have 2 almost identical front wheels, both: MA40,32 hole 15/16
butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
difference is in the spoke lacing: one is 2-cross, the other
is 3-cross. The 3-cross seems to have noticeably more lateral
rigidity than the 2-cross under similar ride conditions. This
is most appparent when riding in a moderate headwind or crosswind.
The 2-cross is more easily buffeted from side to side and I'm
constantly correcting steering. I get a similar response during
high-speed descents on less than smooth pavement. The 2-cross
wheel seems to jump around more.

Is this to be expected and common knowledge, and I'm just late
in picking up on it, or is it just my imagination?

The latter, IMHO. There should be only microscopic differences
between the two wheels in terms of "rider feedback" from any
difference in lateral rigidity. If anything, I'd expect the 2X to be
more laterally rigid because the shorter spokes would have a bit more
acute bracing angle (but again, since there's very little lateral
force on the front wheel when you're riding, that small difference is
going to vanish into a myriad of other bigger physical inputs).

As for the effect of the wind on the two wheels - I would expect any
difference to be VERY small, and to go the opposite way from your
perception. Normally the amount a wheel is affected by a cross-wind
has to do with how much of a surface it presents to that wind. The
only difference would be that the 3X wheel has longer spokes, so I
would expect it to be influenced (very, very slightly....) more.

I'd suggest doing a true blind test - have someone swap them out (or
not) and go for a short ride (without looking down at the wheel, of
course - they're similar enough that it should be fairly easy to not
cheat). ;-) I'll bet you a dollar to a donut that you won't be able
to tell which one you're riding.

Remember - a placebo can be an effective drug!

Mark Hickey
Habanero Cycles
http://www.habcycles.com
Home of the $795 ti frame

kwalters said:

I have 2 almost identical front wheels, both: MA40,32 hole 15/16
butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
difference is in the spoke lacing: one is 2-cross, the other
is 3-cross. The 3-cross seems to have noticeably more lateral
rigidity than the 2-cross under similar ride conditions. This
is most appparent when riding in a moderate headwind or crosswind.
The 2-cross is more easily buffeted from side to side and I'm
constantly correcting steering. I get a similar response during
high-speed descents on less than smooth pavement. The 2-cross
wheel seems to jump around more.

Is this to be expected and common knowledge, and I'm just late
in picking up on it, or is it just my imagination?

BTW: same bike.

Thanks for any response?

Ken

Bracing angle of spokes on 2X is higher than 3X so I would expect the 2X wheel to be more laterally stiff..... all other things being equal.
Did you check the play in the hub(s)?

jim beam said:

daveornee said:

kwalters said:

I have 2 almost identical front wheels, both: MA40,32 hole 15/16
butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
difference is in the spoke lacing: one is 2-cross, the other
is 3-cross. The 3-cross seems to have noticeably more lateral
rigidity than the 2-cross under similar ride conditions. This
is most appparent when riding in a moderate headwind or crosswind.
The 2-cross is more easily buffeted from side to side and I'm
constantly correcting steering. I get a similar response during
high-speed descents on less than smooth pavement. The 2-cross
wheel seems to jump around more.

Quoted message said:

Quoted message said:

Bracing angle of spokes on 2X is higher than 3X so I would expect the
2X wheel to be more laterally stiff..... all other things being equal.

and the slightly shorter spokes are less elastic.

Jim, you just lambasted another poster for being a "non-techie" so I
thought it'd be a great idea to let you strut your stuff here and show
us your own technical contributions...

Just how MUCH more "elastic" are those longer spokes going to be, and
how does that actually impact the ride impressions that the OP is
asking about. Percentagewise, just how much will those longer, more
elastic spokes change the rim deflection?

Inquiring minds wanna know...

Mark Hickey
Habanero Cycles
http://www.habcycles.com
Home of the $795 ti frame

Mark Hickey said:

jim beam said:

daveornee said:

kwalters Wrote:
> I have 2 almost identical front wheels, both: MA40,32 hole 15/16
> butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
> difference is in the spoke lacing: one is 2-cross, the other
> is 3-cross. The 3-cross seems to have noticeably more lateral
> rigidity than the 2-cross under similar ride conditions. This
> is most appparent when riding in a moderate headwind or crosswind.
> The 2-cross is more easily buffeted from side to side and I'm
> constantly correcting steering. I get a similar response during
> high-speed descents on less than smooth pavement. The 2-cross
> wheel seems to jump around more.

Quoted message said:

Quoted message said:

Bracing angle of spokes on 2X is higher than 3X so I would expect the
2X wheel to be more laterally stiff..... all other things being equal.

and the slightly shorter spokes are less elastic.

Jim, you just lambasted another poster for being a "non-techie" so I
thought it'd be a great idea to let you strut your stuff here and show
us your own technical contributions...

Just how MUCH more "elastic" are those longer spokes going to be, and
how does that actually impact the ride impressions that the OP is
asking about. Percentagewise, just how much will those longer, more
elastic spokes change the rim deflection?

percentage? simple length ratio. it's trivial, but it exists. about
the same order as the angle change described by dave.

Quoted message said:

Inquiring minds wanna know...

sure you do.

jim beam said:

Mark Hickey said:

jim beam said:

daveornee wrote:
> kwalters Wrote:
>> I have 2 almost identical front wheels, both: MA40,32 hole 15/16
>> butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
>> difference is in the spoke lacing: one is 2-cross, the other
>> is 3-cross. The 3-cross seems to have noticeably more lateral
>> rigidity than the 2-cross under similar ride conditions. This
>> is most appparent when riding in a moderate headwind or crosswind.
>> The 2-cross is more easily buffeted from side to side and I'm
>> constantly correcting steering. I get a similar response during
>> high-speed descents on less than smooth pavement. The 2-cross
>> wheel seems to jump around more.

Quoted message said:

> Bracing angle of spokes on 2X is higher than 3X so I would expect the
> 2X wheel to be more laterally stiff..... all other things being equal.
and the slightly shorter spokes are less elastic.

Jim, you just lambasted another poster for being a "non-techie" so I
thought it'd be a great idea to let you strut your stuff here and show
us your own technical contributions...

Just how MUCH more "elastic" are those longer spokes going to be, and
how does that actually impact the ride impressions that the OP is
asking about. Percentagewise, just how much will those longer, more
elastic spokes change the rim deflection?

percentage? simple length ratio. it's trivial, but it exists. about
the same order as the angle change described by dave.

Separating these effects makes no sense. Lateral stiffnes due to the
spokes, for a given rim and hub, is inversely proportional to the
length of the spokes. For a typical wheel, the percent change from a
radial to an n-cross spoke pattern is about 2.5% for n=2, 5% for n=3.
So if you're wheel is moving about laterally 5mm with a 3X pattern,
going to a radial pattern might reduce this by 0.25mm (about 3 sheets
of paper). Less when you account for rim stiffness.

--
Joe Riel

Joe Riel said:

jim beam said:

Mark Hickey said:

jim beam <[email hidden]> wrote:

> daveornee wrote:
>> kwalters Wrote:
>>> I have 2 almost identical front wheels, both: MA40,32 hole 15/16
>>> butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
>>> difference is in the spoke lacing: one is 2-cross, the other
>>> is 3-cross. The 3-cross seems to have noticeably more lateral
>>> rigidity than the 2-cross under similar ride conditions. This
>>> is most appparent when riding in a moderate headwind or crosswind.
>>> The 2-cross is more easily buffeted from side to side and I'm
>>> constantly correcting steering. I get a similar response during
>>> high-speed descents on less than smooth pavement. The 2-cross
>>> wheel seems to jump around more.
>> Bracing angle of spokes on 2X is higher than 3X so I would expect the
>> 2X wheel to be more laterally stiff..... all other things being equal.
> and the slightly shorter spokes are less elastic.
Jim, you just lambasted another poster for being a "non-techie" so I
thought it'd be a great idea to let you strut your stuff here and show
us your own technical contributions...

Just how MUCH more "elastic" are those longer spokes going to be, and
how does that actually impact the ride impressions that the OP is
asking about. Percentagewise, just how much will those longer, more
elastic spokes change the rim deflection?

percentage? simple length ratio. it's trivial, but it exists. about
the same order as the angle change described by dave.

Separating these effects makes no sense. Lateral stiffnes due to the
spokes, for a given rim and hub, is inversely proportional to the
length of the spokes. For a typical wheel, the percent change from a
radial to an n-cross spoke pattern is about 2.5% for n=2, 5% for n=3.
So if you're wheel is moving about laterally 5mm with a 3X pattern,
going to a radial pattern might reduce this by 0.25mm (about 3 sheets
of paper). Less when you account for rim stiffness.

let's assume rim stiffness is a constant. lateral stiffness is
therefore a function of the bracing angle and the spoke stiffness. the
greater the angle, the stiffer. the shorter the spoke, the stiffer.
you're correct that they're inter-related [lacing will affect bracing
angle /and/ length] but they are separate elements.

jim beam said:

Joe Riel wrote:

[...]

Quoted message said:

Quoted message said:

Separating these effects makes no sense. Lateral stiffnes due to the
spokes, for a given rim and hub, is inversely proportional to the
length of the spokes. For a typical wheel, the percent change from a
radial to an n-cross spoke pattern is about 2.5% for n=2, 5% for n=3.
So if you're wheel is moving about laterally 5mm with a 3X pattern,
going to a radial pattern might reduce this by 0.25mm (about 3 sheets
of paper). Less when you account for rim stiffness.

let's assume rim stiffness is a constant. lateral stiffness is
therefore a function of the bracing angle and the spoke stiffness. the
greater the angle, the stiffer. the shorter the spoke, the stiffer.
you're correct that they're inter-related [lacing will affect bracing
angle /and/ length] but they are separate elements.

I saw a wheel on an MTB the other day with mostly normal 3X wheels
except the outbound spokes on the disk side of the front wheel were
interleaved twice, which put quite a bend in them at the second
crossing. I wonder what the point of that was.

jim beam said:

Joe Riel said:

jim beam said:

Mark Hickey wrote:
> jim beam <[email hidden]> wrote:
>> daveornee wrote:
>>> kwalters Wrote:
>>>> I have 2 almost identical front wheels, both: MA40,32 hole 15/16
>>>> butted spokes, D-A 8spd hubs, 700*25 Conti U2K tires. The
>>>> difference is in the spoke lacing: one is 2-cross, the other
>>>> is 3-cross. The 3-cross seems to have noticeably more lateral
>>>> rigidity than the 2-cross under similar ride conditions. This
>>>> is most appparent when riding in a moderate headwind or crosswind.
>>>> The 2-cross is more easily buffeted from side to side and I'm
>>>> constantly correcting steering. I get a similar response during
>>>> high-speed descents on less than smooth pavement. The 2-cross
>>>> wheel seems to jump around more.
>>> Bracing angle of spokes on 2X is higher than 3X so I would expect the
>>> 2X wheel to be more laterally stiff..... all other things being equal.
>> and the slightly shorter spokes are less elastic.
> Jim, you just lambasted another poster for being a "non-techie" so I
> thought it'd be a great idea to let you strut your stuff here and show
> us your own technical contributions...
>
> Just how MUCH more "elastic" are those longer spokes going to be, and
> how does that actually impact the ride impressions that the OP is
> asking about. Percentagewise, just how much will those longer, more
> elastic spokes change the rim deflection?

Quoted message said:

Quoted message said:

Quoted message said:

percentage? simple length ratio. it's trivial, but it exists. about
the same order as the angle change described by dave.

Separating these effects makes no sense. Lateral stiffnes due to the
spokes, for a given rim and hub, is inversely proportional to the
length of the spokes. For a typical wheel, the percent change from a
radial to an n-cross spoke pattern is about 2.5% for n=2, 5% for n=3.
So if you're wheel is moving about laterally 5mm with a 3X pattern,
going to a radial pattern might reduce this by 0.25mm (about 3 sheets
of paper). Less when you account for rim stiffness.

let's assume rim stiffness is a constant. lateral stiffness is
therefore a function of the bracing angle and the spoke stiffness. the
greater the angle, the stiffer. the shorter the spoke, the stiffer.
you're correct that they're inter-related [lacing will affect bracing
angle /and/ length] but they are separate elements.

No one doubts that there is a theoretical difference in spoke
stiffness between two otherwise identical spokes of different lengths.
But you intimate that spoke stiffness is one of the causes of the
difference the OP is sensing between the two wheels. To do that, you
must have some idea of just how much more the 3X spokes "give" than
the 2X spokes, and it must be in the "rider-discernable range". C'mon
- give all us lowly non-techie types a dose of beam wisdom and tell us
just HOW much more....

Mark Hickey
Habanero Cycles
http://www.habcycles.com
Home of the $795 ti frame

jim beam said:

let's assume rim stiffness is a constant. lateral stiffness is
therefore a function of the bracing angle and the spoke stiffness.
the greater the angle, the stiffer. the shorter the spoke, the
stiffer. you're correct that they're inter-related [lacing will affect
bracing angle /and/ length] but they are separate elements.

As we agree, for a given rim, the bracing angle and the spoke length
are not independent. However, if we take the change in stiffness due
a change in spoke length and divide by the change in stiffness due to
a change in bracing angle, then subsitute the actual changes for a
given hub, we find that the ratio is approximately -2*L/Wh, where L is
the spoke length and Wh the hub width. So, we conclude that virtually
all the change in lateral stiffness is due to the change in spoke
length and not the change in bracing angle.

--
Joe Riel

Joe Riel said:

jim beam said:

let's assume rim stiffness is a constant. lateral stiffness is
therefore a function of the bracing angle and the spoke stiffness.
the greater the angle, the stiffer. the shorter the spoke, the
stiffer. you're correct that they're inter-related [lacing will affect
bracing angle /and/ length] but they are separate elements.

As we agree, for a given rim, the bracing angle and the spoke length
are not independent. However, if we take the change in stiffness due
a change in spoke length and divide by the change in stiffness due to
a change in bracing angle, then subsitute the actual changes for a
given hub, we find that the ratio is approximately -2*L/Wh, where L is
the spoke length and Wh the hub width. So, we conclude that virtually
all the change in lateral stiffness is due to the change in spoke
length and not the change in bracing angle.

good!

despite the fact that i introduced the spoke length factor to this
debate, not bracing angle, i still find bracing angle to be an
interesting component. for instance, in damon rinard's lateral
stiffness experiments, otherwise identical wheels with radial heads-in
vs. radial heads-out lacing do show a measurable difference.

Ben C said:

jim beam said:

Joe Riel wrote:

[...]

Quoted message said:

Quoted message said:

Separating these effects makes no sense. Lateral stiffnes due to the
spokes, for a given rim and hub, is inversely proportional to the
length of the spokes. For a typical wheel, the percent change from a
radial to an n-cross spoke pattern is about 2.5% for n=2, 5% for n=3.
So if you're wheel is moving about laterally 5mm with a 3X pattern,
going to a radial pattern might reduce this by 0.25mm (about 3 sheets
of paper). Less when you account for rim stiffness.

let's assume rim stiffness is a constant. lateral stiffness is
therefore a function of the bracing angle and the spoke stiffness. the
greater the angle, the stiffer. the shorter the spoke, the stiffer.
you're correct that they're inter-related [lacing will affect bracing
angle /and/ length] but they are separate elements.

I saw a wheel on an MTB the other day with mostly normal 3X wheels
except the outbound spokes on the disk side of the front wheel were
interleaved twice, which put quite a bend in them at the second
crossing. I wonder what the point of that was.

you got me.

jim beam said:

Joe Riel said:

jim beam said:

let's assume rim stiffness is a constant. lateral stiffness is
therefore a function of the bracing angle and the spoke stiffness.
the greater the angle, the stiffer. the shorter the spoke, the
stiffer. you're correct that they're inter-related [lacing will affect
bracing angle /and/ length] but they are separate elements.

As we agree, for a given rim, the bracing angle and the spoke length
are not independent. However, if we take the change in stiffness due
a change in spoke length and divide by the change in stiffness due to
a change in bracing angle, then subsitute the actual changes for a
given hub, we find that the ratio is approximately -2*L/Wh, where L is
the spoke length and Wh the hub width. So, we conclude that virtually
all the change in lateral stiffness is due to the change in spoke
length and not the change in bracing angle.

good!

despite the fact that i introduced the spoke length factor to this
debate, not bracing angle, i still find bracing angle to be an
interesting component. for instance, in damon rinard's lateral
stiffness experiments, otherwise identical wheels with radial heads-in
vs. radial heads-out lacing do show a measurable difference.

When I stated that length and angle are independent, I did consider
the case of head-in vs heads-out: that is the one opportunity on a
given hub to slightly separate the two effects. That Damon Rinard
measured a difference makes me question whether I might have made a
computational error (it won't be a unique occurrence). Off hand,
I think not---the change in bracing angle as the spoke is repositioned
around the hub (i.e. spoke pattern changes) is small compared to the
change between orientation (in/out). I'll compute the effect due
to orientation.

--
Joe Riel

Joe Riel said:

When I stated that length and angle are independent, I did consider
the case of head-in vs heads-out: that is the one opportunity on a
given hub to slightly separate the two effects. That Damon Rinard
measured a difference makes me question whether I might have made a
computational error (it won't be a unique occurrence). Off hand,
I think not---the change in bracing angle as the spoke is repositioned
around the hub (i.e. spoke pattern changes) is small compared to the
change between orientation (in/out). I'll compute the effect due
to orientation.

A few simple calculations indicate that the effect of orientation
(head-in vs head-out) on lateral stiffness is large. The fractional
change in lateral stiffness is

dK/K = (Ds + Wf)/(Wh/2)

where
K lateral stiffness
Ds spoke diameter
Wf flange width
Wh hub width

For the front wheel on my road bike (which isn't radially spoked, so
the computation is meaningless) I compute

dK/K ~ 0.2/1.4 ~ 14%,

that is, the lateral stiffness of a radially spoked wheel with that
hub/spokes should be 14% greater with the heads-in compared to with
the heads-out.

--
Joe Riel

Joe Riel said:

Joe Riel said:

When I stated that length and angle are independent, I did consider
the case of head-in vs heads-out: that is the one opportunity on a
given hub to slightly separate the two effects. That Damon Rinard
measured a difference makes me question whether I might have made a
computational error (it won't be a unique occurrence). Off hand,
I think not---the change in bracing angle as the spoke is repositioned
around the hub (i.e. spoke pattern changes) is small compared to the
change between orientation (in/out). I'll compute the effect due
to orientation.

A few simple calculations indicate that the effect of orientation
(head-in vs head-out) on lateral stiffness is large. The fractional
change in lateral stiffness is

dK/K = (Ds + Wf)/(Wh/2)

where
K lateral stiffness
Ds spoke diameter
Wf flange width
Wh hub width

For the front wheel on my road bike (which isn't radially spoked, so
the computation is meaningless) I compute

dK/K ~ 0.2/1.4 ~ 14%,

that is, the lateral stiffness of a radially spoked wheel with that
hub/spokes should be 14% greater with the heads-in compared to with
the heads-out.

I see that Damon Rinard measured the difference to be 13.4%, which is
a nice confirmation of the theoretical computation. I expected a
larger difference because I didn't consider the rim's contribution to
the lateral stiffness.

--
Joe Riel