# Calculating the spoke approach angle.

J

#### Johan Bornman

##### Guest
Maybe the mathematicians here can help me calculate what I call the
spoke approach angle or, the angle at which the spoke enters the rim.

I've had a problem with a wheel where the angle was way past 90
degrees due to a very big hub. The spokes broke at what I imagine was
the first exposed thread inside the nipple. At the time of the build I
could see that there would be a problem because the bend in the spoke
was clearly visible. I tried to improve the spoke line by squeezing
the Vs in the spokes together and that bent something - the nipples
became oval in the plane of the wheel but obviously it didn't do the
job.

Also, I can't visualise how a bend just before the nipple would help.
Under tension that bend just straightens and bends the nipple like
before. Maybe the answer lies here.

I would like some magic formula where I can plug in the number of
crossings, the length and the hub size. Then at least I could
experimentally determine what natural angle the nipple and rim combo
can handle with a comformable swivel action and see whether it exceeds
it or not.

I've come to believe that some rim and hub combinations make a
reliable build impossible. Someone brought me a deep section Reynolds
rim of the type where the nipple is installed upside down so that no
nipple shaft protrodes beyond the spoke hole. This flat seating
arrangement of the nipple means the spoke has to exit at at right
angle or the spoke will have to bend inside the thread. The only way
to do this is to reduce the hub size, which obviously isn't possible.

I'd like a way of calculating whether or not a particular component
combination will work.

JB

On 2007-10-10, Johan Bornman <[email protected]> wrote:
> Maybe the mathematicians here can help me calculate what I call the
> spoke approach angle or, the angle at which the spoke enters the rim.
>
> I've had a problem with a wheel where the angle was way past 90
> degrees due to a very big hub. The spokes broke at what I imagine was
> the first exposed thread inside the nipple. At the time of the build I
> could see that there would be a problem because the bend in the spoke
> was clearly visible. I tried to improve the spoke line by squeezing
> the Vs in the spokes together and that bent something - the nipples
> became oval in the plane of the wheel but obviously it didn't do the
> job.
>
> Also, I can't visualise how a bend just before the nipple would help.
> Under tension that bend just straightens and bends the nipple like
> before. Maybe the answer lies here.
>
> I would like some magic formula where I can plug in the number of
> crossings, the length and the hub size. Then at least I could
> experimentally determine what natural angle the nipple and rim combo
> can handle with a comformable swivel action and see whether it exceeds
> it or not.
>
> I've come to believe that some rim and hub combinations make a
> reliable build impossible. Someone brought me a deep section Reynolds
> rim of the type where the nipple is installed upside down so that no
> nipple shaft protrodes beyond the spoke hole. This flat seating
> arrangement of the nipple means the spoke has to exit at at right
> angle or the spoke will have to bend inside the thread. The only way
> to do this is to reduce the hub size, which obviously isn't possible.

How many crossings are you using? If you use fewer than normal (i.e. try
2x or 1x) that should improve the approach angle.

Johan Bornman wrote:
> Maybe the mathematicians here can help me calculate what I call the
> spoke approach angle or, the angle at which the spoke enters the rim.
>
> I've had a problem with a wheel where the angle was way past 90
> degrees due to a very big hub. The spokes broke at what I imagine was
> the first exposed thread inside the nipple. At the time of the build I
> could see that there would be a problem because the bend in the spoke
> was clearly visible. I tried to improve the spoke line by squeezing
> the Vs in the spokes together and that bent something - the nipples
> became oval in the plane of the wheel but obviously it didn't do the
> job.
>
> Also, I can't visualise how a bend just before the nipple would help.
> Under tension that bend just straightens and bends the nipple like
> before. Maybe the answer lies here.
>
> I would like some magic formula where I can plug in the number of
> crossings, the length and the hub size. Then at least I could
> experimentally determine what natural angle the nipple and rim combo
> can handle with a comformable swivel action and see whether it exceeds
> it or not.
>
> I've come to believe that some rim and hub combinations make a
> reliable build impossible. Someone brought me a deep section Reynolds
> rim of the type where the nipple is installed upside down so that no
> nipple shaft protrodes beyond the spoke hole. This flat seating
> arrangement of the nipple means the spoke has to exit at at right
> angle or the spoke will have to bend inside the thread. The only way
> to do this is to reduce the hub size, which obviously isn't possible.
>
> I'd like a way of calculating whether or not a particular component
> combination will work.

Are you using excessively high or low cross pattern?
Some wheelbuilding software lists the spoke angle with the length for
each cross option. Not the one my staff uses but I have a copy which
does. Write me if you find no other quick solution.

--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

Johan Bornman wrote:
> Also, I can't visualise how a bend just before the nipple would help.
> Under tension that bend just straightens and bends the nipple like
> before.

That is the appropriate solution. The load required to straighten out
the bend is very close to the tensile yield of spoke, so it isn't
going to occur in normal use. Bending the spoke so that the nipple
goes more directly into the rim should also reduce the rim stress and
make cracks less likely. Every rim will differ in the sort of angle it
tolerates, so I don't see much point in formulas. If in doubt, bend it.

Johan Bornman writes:

> Maybe the mathematicians here can help me calculate what I call the
> spoke approach angle or, the angle at which the spoke enters the
> rim.

> I've had a problem with a wheel where the angle was way past 90
> degrees due to a very big hub. The spokes broke at what I imagine
> was the first exposed thread inside the nipple. At the time of the
> build I could see that there would be a problem because the bend in
> the spoke was clearly visible. I tried to improve the spoke line by
> squeezing the Vs in the spokes together and that bent something -
> the nipples became oval in the plane of the wheel but obviously it
> didn't do the job.

> Also, I can't visualise how a bend just before the nipple would
> help. Under tension that bend just straightens and bends the nipple
> like before. Maybe the answer lies here.

> I would like some magic formula where I can plug in the number of
> crossings, the length and the hub size. Then at least I could
> experimentally determine what natural angle the nipple and rim combo
> can handle with a comformable swivel action and see whether it
> exceeds it or not.

> I've come to believe that some rim and hub combinations make a
> reliable build impossible. Someone brought me a deep section
> Reynolds rim of the type where the nipple is installed upside down
> so that no nipple shaft protrodes beyond the spoke hole. This flat
> seating arrangement of the nipple means the spoke has to exit at at
> right angle or the spoke will have to bend inside the thread. The
> only way to do this is to reduce the hub size, which obviously isn't
> possible.

> I'd like a way of calculating whether or not a particular component
> combination will work.

You didn't say what the hole circle diameter of the hub is or the rim
size. With that info, more could be said. From the 90Â° comment it
seems to me that radial would be good enough but barring that
approach, x1 should do.

Jobst Brandt

On Oct 11, 6:07 am, [email protected] wrote:
> You didn't say what the hole circle diameter of the hub is or the rim
> size. With that info, more could be said. From the 90° comment it
> seems to me that radial would be good enough but barring that
> approach, x1 should do.
>

The hole centre diameter is 70mm both sides.
The one rim I had to use was the Reynolds deep section, but I didn't
measure it at the time since I only had to replace a spoke for
someone.

Nevertheless, it was a good 40mm deep, if not more.

What drawbacks can I expect from using 1X ona rear wheel?

JB

On Oct 10, 9:45 pm, A Muzi <[email protected]> wrote:

> Are you using excessively high or low cross pattern?
> Some wheelbuilding software lists the spoke angle with the length for
> each cross option. Not the one my staff uses but I have a copy which
> does. Write me if you find no other quick solution.
>

No Andrew, I'm vascilating between 3X and now 2X.

I use Damon's spocalc.xls and that doesn't seem to have a spoke
approach angle.

If you have another one and it is freeware, I'll appreciate a copy.

JB

On Oct 11, 12:41 am, Ron Ruff <[email protected]> wrote:

> That is the appropriate solution. The load required to straighten out
> the bend is very close to the tensile yield of spoke, so it isn't
> going to occur in normal use. Bending the spoke so that the nipple
> goes more directly into the rim should also reduce the rim stress and
> make cracks less likely. Every rim will differ in the sort of angle it
> tolerates, so I don't see much point in formulas. If in doubt, bend it.

I find that most of the bend disappears during stress relieving and I
still end up with either an oval nipple or a spoke that clearly
doesn't enter the nipple square-on.

JB

On Oct 11, 6:07 am, [email protected] wrote:
> Johan Bornman writes:
> > You didn't say what the hole circle diameter of the hub is or the rim

> size. With that info, more could be said. From the 90° comment it
> seems to me that radial would be good enough but barring that
> approach, x1 should do.

I omitted the size of one of the rims I experienced this problem on.
It is a shallow box section rim, 15 or so mm deep with ERD of 608mm.
As I said, the spoke hole dia on the hub is 70mm both sides, quite
large by modern hub standards. What's more, with power training the
fad, I'm getting lots of request to build with these PowerTap hubs on
all sorts of bleeding edge rims and I don't want comebacks if I can
help it.

JB

Johan Bornman writes:

>> You didn't say what the hole circle diameter of the hub is or the
>> rim size. With that info, more could be said. From the 90Â°
>> comment it seems to me that radial would be good enough but barring
>> that approach, x1 should do.

> I omitted the size of one of the rims I experienced this problem on.
> It is a shallow box section rim, 15 or so mm deep with ERD of 608mm.
> As I said, the spoke hole dia on the hub is 70mm both sides, quite
> large by modern hub standards. What's more, with power training the
> fad, I'm getting lots of request to build with these PowerTap hubs
> on all sorts of bleeding edge rims and I don't want comebacks if I
> can help it.

Then I don't understand where you measured 90Â° between spoke and spoke
nipple. A 70mm hole circle on a hub flange is common as are 700c
rims, a combination that is often spoked x3 and x4 with no problem. I
thought you had some unusually large diameter hubs, however, flange
hole circles are generally kept between 40 and 50mm to not cause a
large angle at the spoke nipple. Large flange hubs were common in the
days of frequent spoke failures so track riders could replace a spoke
without removing the sprocket.

Jobst Brandt

[email protected] writes:

> Large flange hubs were common in the days of frequent spoke failures
> so track riders could replace a spoke without removing the sprocket.

That seems surprising since a track rider, unlike a road rider,

--
Joe Riel

Joe Riel writes:

>> Large flange hubs were common in the days of frequent spoke
>> failures so track riders could replace a spoke without removing the
>> sprocket.

> That seems surprising since a track rider, unlike a road rider,
> sprocket.

That's true but how else do you explain that the old large flange hubs
went away with the advent of better spokes and means by which spoke
failure can be prevented practically.

Old caster brake sprockets even had a spoke slot so that spokes could
be replaced with no removal of the sprocket.

It was the large flange hubs that enabled me to replace spokes on the
road when I had no FW removing tool. Disassembling the FW with hammer
and punch worked but it would not have been enough to expose the
flange of a low flange road hub. Even a 22t sprocket on the road
obscured flange holes on Campagnolo large flange hubs.

Jobst Brandt

[email protected] wrote:
>>> Large flange hubs were common in the days of frequent spoke
>>> failures so track riders could replace a spoke without removing the
>>> sprocket.

> Joe Riel writes:
>> That seems surprising since a track rider, unlike a road rider,
>> sprocket.

[email protected] wrote:
> That's true but how else do you explain that the old large flange hubs
> went away with the advent of better spokes and means by which spoke
> failure can be prevented practically.
> Old coaster brake sprockets even had a spoke slot so that spokes could
> be replaced with no removal of the sprocket.
> It was the large flange hubs that enabled me to replace spokes on the
> road when I had no FW removing tool. Disassembling the FW with hammer
> and punch worked but it would not have been enough to expose the
> flange of a low flange road hub. Even a 22t sprocket on the road
> obscured flange holes on Campagnolo large flange hubs.

I cannot say but after listening to sidepull/centerpull, high flange/low
flange etc for many years, I think fashion is at much the reason as any.

Sometimes actual albeit small, advantages, such as quick spoke change on
a track bike, are less compelling than the current 'look'.

Back to the OP; Perhaps it's an electric motor hub or some such? They
run in the 250mm range or bigger.
--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

[email protected] wrote:
> Joe Riel writes:
>
>>> Large flange hubs were common in the days of frequent spoke
>>> failures so track riders could replace a spoke without removing the
>>> sprocket.

> .... how else do you explain that the old large flange hubs
> went away with the advent of better spokes and means by which spoke
> failure can be prevented practically.

Why should these events be connected? Looks and manufacturing cost have
always been more important than reliabilty
--
/Marten

info(apestaartje)m-gineering(punt)nl

In article <[email protected]>,
[email protected] wrote:

> Joe Riel writes:
>
> >> Large flange hubs were common in the days of frequent spoke
> >> failures so track riders could replace a spoke without removing
> >> the sprocket.

>
> > That seems surprising since a track rider, unlike a road rider,
> > sprocket.

>
> That's true but how else do you explain that the old large flange
> hubs went away with the advent of better spokes and means by which
> spoke failure can be prevented practically.

I recall being told (30+ years ago) that large flange spokes resulted in
stiffer wheels and decreased spoke windup for faster sprints. I think
that this was eventually discredited enough than the fashion changed.

> Old caster brake sprockets even had a spoke slot so that spokes could
> be replaced with no removal of the sprocket.
>
> It was the large flange hubs that enabled me to replace spokes on the
> road when I had no FW removing tool. Disassembling the FW with
> hammer and punch worked but it would not have been enough to expose
> the flange of a low flange road hub. Even a 22t sprocket on the road
> obscured flange holes on Campagnolo large flange hubs.

Herse and Singer used to rivet gigantic flanges onto hubs to address
this. Maxi-CAR put "keyhole" slots in the drive-side flange to allow
the head of the spoke to be inserted into the flange. Dunno if either
of those were good solutions, though.

On Oct 10, 7:34 am, Johan Bornman <[email protected]> wrote:
> Maybe the mathematicians here can help me calculate what I call the
> spoke approach angle or, the angle at which the spoke enters the rim.
>

Consider the triangle formed by the points:
A. center of the hub flange (inside the axle)
B. spoke hole
C. base of the spoke nipple

Side AB has length f, the flange radius.
Side BC has length l, the spoke length.
Side AC has length r, the rim effective radius.
(Actually it's a little longer than r because the
hub flange is displaced out from the centerline of
the wheel, but this is a small effect, ~1mm,
which you can calculate.)

The approach angle X that you seek is the angle
between sides BC and AC, opposite the side that
has length f. By the law of cosines,

f^2 = l^2 + r^2 - 2*r*l * cos(X),
so cos(X) = (l^2 + r^2 -f^2) / (2*r*l)

Plug your wheel dimensions including f and r (r=ERD/2)
into a spoke calculator, get the spoke length l,
and use this formula to get an approximate angle X.

I neglected the stretch of the spoke, which many
calculators do use, e.g.
http://www.appliedthought.com/danny/Spoke/SpokeCalculator.html
so you can compensate for that if you want to
be picky. However, this formula isn't exact.
Because f is often small compared to r and l,
cos(X) will often be close to 1, and the formula
will be fairly rough for small spoke approach angles.
Fortunately, nobody worries about small angles.
You're worried about big hubs with larger f,
and larger angles, and there the formula should
be reasonable.

Ben

[email protected] wrote:
>

Snip snip snip

> so you can compensate for that if you want to
> be picky. However, this formula isn't exact.
> Because f is often small compared to r and l,
> cos(X) will often be close to 1, and the formula
> will be fairly rough for small spoke approach angles.
> Fortunately, nobody worries about small angles.
> You're worried about big hubs with larger f,
> and larger angles, and there the formula should
> be reasonable.
>
> Ben

Thanks Ben, this is what I wanted.

JB

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