# wheelbuilding "bracing angle"

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**wheelbuilding "bracing angle"**

I'm having some trouble understanding "bracing angle" as I've seen it used in various wheelbuilding discussions. I thought it refered to the angle the spokes make with the plane of the wheel (this is the definition in Brandt's book). So a rear hub with a cassette has a smaller bracing angle on the DS, and the NDS flange can be moved further in to try to equalize the angle and the tension.

However, I've read in a few places that the spoke cross pattern can affect bracing angle (such as here). If the flange spacing stays the same, and the cross pattern changes, how does the bracing angle change? I'm imaging the cross-section view that shows the spoke, flange and rim as a triangle, and the # of spoke crosses doesn't seem to have any effect here... what am I missing?

However, I've read in a few places that the spoke cross pattern can affect bracing angle (such as here). If the flange spacing stays the same, and the cross pattern changes, how does the bracing angle change? I'm imaging the cross-section view that shows the spoke, flange and rim as a triangle, and the # of spoke crosses doesn't seem to have any effect here... what am I missing?

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if the hub and frame are the same ,

and there are still the same number of cogs on the gear cluster so the same amount of space must be created by differential spoke tensions R/L , then a pattern change is really slight in 'bracing angle', as the hub flanges and the rim center have not moved.

off center drilled rims shift the centerline of the spoke holes within the rim

Now, If you spread the rear triangle wider to accommodate a wider axle , then the gear cluster

as it stays close to the right dropout, also moves to the right

the wheel rim is re-centered between the wider

dropouts , of 140 0r 145 mm frame tandem stuff, the tension is reduced on the right side spokes

as it , the rim, has to move to the left

and increased on the left side .. when spoke tensions are equal then the center line of the rim ,

is also the center line between the hub flanges .

You could say the bracing angle is the angle apex at the rim

spokes on one side, centerline is the other side

the base of that triangle is the difference between the rim center line

and the hub flange that the spoke holes are in.

Experimentally on a Campagnolo High right flange, low left flange, hub

I used different patterns for each side , slightly increasing the spoke length to the left

by, on a 36 hole hub, using a 4 cross pattern, while on the right ,

staying with a 3 cross pattern. increasing the length differential that was already going to be there.

don't have 2 sets of wheels to compare , but the build was 25 years ago

without any truing its been fine. and I still ride the wheels .

Noted Phil Wood made some hubs larger left flange than the right,

plan, for that, was to use the same length spoke, though the tension

on each side has to be different , you have to pull the rim to the right,

to make room for all those cogs, on the right..

and there are still the same number of cogs on the gear cluster so the same amount of space must be created by differential spoke tensions R/L , then a pattern change is really slight in 'bracing angle', as the hub flanges and the rim center have not moved.

off center drilled rims shift the centerline of the spoke holes within the rim

Now, If you spread the rear triangle wider to accommodate a wider axle , then the gear cluster

as it stays close to the right dropout, also moves to the right

the wheel rim is re-centered between the wider

dropouts , of 140 0r 145 mm frame tandem stuff, the tension is reduced on the right side spokes

as it , the rim, has to move to the left

and increased on the left side .. when spoke tensions are equal then the center line of the rim ,

is also the center line between the hub flanges .

You could say the bracing angle is the angle apex at the rim

spokes on one side, centerline is the other side

the base of that triangle is the difference between the rim center line

and the hub flange that the spoke holes are in.

Experimentally on a Campagnolo High right flange, low left flange, hub

I used different patterns for each side , slightly increasing the spoke length to the left

by, on a 36 hole hub, using a 4 cross pattern, while on the right ,

staying with a 3 cross pattern. increasing the length differential that was already going to be there.

don't have 2 sets of wheels to compare , but the build was 25 years ago

without any truing its been fine. and I still ride the wheels .

Noted Phil Wood made some hubs larger left flange than the right,

plan, for that, was to use the same length spoke, though the tension

on each side has to be different , you have to pull the rim to the right,

to make room for all those cogs, on the right..

*Last edited by fietsbob; 11-06-10 at 12:48 PM.*

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You have the definition right in terms of how most folks use the term. It's the angle the spoke meets the rim with respect to the central plane. However it's affected not only by flange separation but by flange diameter, and spoke pattern also.

To understand, draw yourself a quick schematic consisting of an "H" to represent the hub and a dot above it to represent a spoke hole in the rim. It's obvious that broadening the H will increase the bracing angle, likewise making it taller will also. Now here's how cross pattern affects it.

A radial spoke will meet the flange at the uppermost point, giving you the maximum possible bracing angle. A tangent spoke, ie. 4x with 36h will meet the flange at a point on line with the axle, (where the upright meets the cross of your H in the sketch) resulting in a smaller bracing angle. In between cross patterns will yield bracing angles between these extremes. The amount of difference depends on the flange size, and is nearly negligible for very small flanges.

I hope that helped.

To understand, draw yourself a quick schematic consisting of an "H" to represent the hub and a dot above it to represent a spoke hole in the rim. It's obvious that broadening the H will increase the bracing angle, likewise making it taller will also. Now here's how cross pattern affects it.

A radial spoke will meet the flange at the uppermost point, giving you the maximum possible bracing angle. A tangent spoke, ie. 4x with 36h will meet the flange at a point on line with the axle, (where the upright meets the cross of your H in the sketch) resulting in a smaller bracing angle. In between cross patterns will yield bracing angles between these extremes. The amount of difference depends on the flange size, and is nearly negligible for very small flanges.

I hope that helped.

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thanks fbinny, that explained it perfectly. The diagram with the H helped me to visualize it--I knew I was missing something basic here.

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is the spoke tension affected at all by the spoke length, or is it simply a factor of the bracing angle? i.e. if you compare the radially spoked wheel in the above example (with the H) to the cross-spoked wheel, the bracing angle is a little greater for the radial pattern, and the spokes are a little shorter. how is spoke tension affected here?

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Spoke tension is the same; whatever you tighten the nipple to. I think you mean "change in tension with load"? The wider the angle, the more directly the rim pulls on the spoke rather than pivoting the spoke. So there's less movement in order to generate an equal tension-increase to balance the load.

Damon Rinard did a great Wheel Stiffness test with results table. Notice the difference in stiffness between two identical radially-lace wheels (#94,95). But one with heads-in versus heads-out orientation and the difference in bracing angle. Also note the difference between radial versus 3x lacing in #92, 93, although dishing probably has a greater effect in this comparison.

Damon Rinard did a great Wheel Stiffness test with results table. Notice the difference in stiffness between two identical radially-lace wheels (#94,95). But one with heads-in versus heads-out orientation and the difference in bracing angle. Also note the difference between radial versus 3x lacing in #92, 93, although dishing probably has a greater effect in this comparison.

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I realized that my question was stupid after I posted...duh. Obviously tension is determined by how tight the nipple is, and on the front wheel to be dished properly the tension has to be the same. But on the rear wheel it seems that the relative tension between the sides is calculated simply with a ratio of the different bracing angles.

When you say, "the wider the angle, the more direcly the rim pulls on the spoke rather than pivoting the spoke," I'm not sure what you mean by "wider." It would see that a smaller bracing angle puts a more direct pull on the spoke where it enters the rim, when the rim is under deflection. Is that you meant by wider or do I have this mixed up?

When you say, "the wider the angle, the more direcly the rim pulls on the spoke rather than pivoting the spoke," I'm not sure what you mean by "wider." It would see that a smaller bracing angle puts a more direct pull on the spoke where it enters the rim, when the rim is under deflection. Is that you meant by wider or do I have this mixed up?

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When you say, "the wider the angle, the more direcly the rim pulls on the spoke rather than pivoting the spoke," I'm not sure what you mean by "wider." It would see that a smaller bracing angle puts a more direct pull on the spoke where it enters the rim, when the rim is under deflection. Is that you meant by wider or do I have this mixed up?

**Danno**was referring to the case of side loads, as opposed to radial loads where the opposite is true.

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1. For

**lateral-stiffness**, imagine a spoke that's vertical with no angle (as if it came from a flange in the middle of the hub). When there's side loads on the rim, the spoke just rocks back and forth and isn't tensioned by much since the movement is 90-degrees to the spoke.

2. For

**torsional-stiffness**, you're looking at the angle between the spoke and the hub-flange. When the spoke exits the flange at 90-degrees, ALL of the flange's rotation goes into stretching the spoke in-line. The angle where the spoke enters the rim doesn't really matter in this direction.

Note that torsional-stiffness and spoke lacing-patterns only deal with torque from pedaling forces or disc-brakes. The amount of torque generated by a human is tiny after it goes through the gearing. In an all-out sprint, you can actually grab the back tyre with your hand and stop the wheel. So there's very little difference in torsional-stiffness of a wheel that makes a difference that's measureable or performance-related between 2x, 3x, 4x. Heck, I've even built radially laced rear-wheels and rode on them for years. Does stress the hub-flange more though as there's less material on the outer-edge of the flange than between the holes.

3.

**Radial-stiffness**just deals with vertical-loading ability of a wheel and that's very high. Lacing-patterns don't affect this much either as it's really just a sum-total of all the spoke-tension and rim-stiffness.

*Last edited by DannoXYZ; 11-06-10 at 03:15 PM.*

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For radial-stiffness, you're looking at the angle between the spoke and the hub-flange. When the spoke exits the flange at 90-degrees, ALL of the flange's rotation goes into stretching the spoke in-line. The angle where the spoke enters the rim doesn't really matter in this direction.

.

**torsional**stiffness here.

**Radial**stiffness is the complement of lateral or axial stiffness, as you described it earlier.

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**12**To understand, draw yourself a quick schematic consisting of an "H" to represent the hub and a dot above it to represent a spoke hole in the rim. It's obvious that broadening the H will increase the bracing angle, likewise making it taller will also. Now here's how cross pattern affects it.

A radial spoke will meet the flange at the uppermost point, giving you the maximum possible bracing angle. A tangent spoke, ie. 4x with 36h will meet the flange at a point on line with the axle, (where the upright meets the cross of your H in the sketch) resulting in a smaller bracing angle. In between cross patterns will yield bracing angles between these extremes. The amount of difference depends on the flange size, and is nearly negligible for very small flanges.

I hope that helped.

Well done.

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dasding, Thanks for bringing this up as this winter I want to rebuild a couple of wheels from scratch, rather than just replace one spoke at a time.

Well worded answers by the responders. It's tough for those of us who only have written material, as good as it may be written, to fully understand a point the author is making.

Brad

Well worded answers by the responders. It's tough for those of us who only have written material, as good as it may be written, to fully understand a point the author is making.

Brad

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