Rear wheel differential spoking....AS IF!

For discussions about bikes and equipment.
User avatar
531colin
Posts: 12274
Joined: 4 Dec 2009, 6:56pm
Location: North Yorkshire

Rear wheel differential spoking....AS IF!

Postby 531colin » 20 Nov 2012, 4:13pm

One of my pet hates is the large difference in tension between left and right side spokes in a conventionally-dished rear wheel.
This thread http://forum.ctc.org.uk/viewtopic.php?f=5&t=67423&start=45 got me thinking about different spoke crossings left and right sides, as this appears to offer a way of reducing the difference in the tensions.
I had a large flange hub going spare, its a lousy day and I need a wheel, so I built one......
Driveside 2 cross.....

Image

other side 4 cross......

Image

This is a 135mm OLN hub, and a conventional wheel, ie dished for 8,9,&10 speed.
The tensions run 120kgf driveside, and 80kgf non-driveside if you build it 3 cross both sides, as near as I can measure.

So I built it 2 cross driveside, and 4 cross non-driveside, and guess what.....the tensions run 120/80kgf, as close as I can measure. :roll:

bikepacker
Posts: 1935
Joined: 5 Jan 2007, 7:08pm
Location: Worcestershire
Contact:

Re: Rear wheel differential spoking....AS IF!

Postby bikepacker » 20 Nov 2012, 4:25pm

I have had many debates about wheel building and follow most of the threads on this forum. About 8 years ago I decided like yourself to experiment with different widths spokes and or different spoke lacing on opposite sides. I came to a final conclusion that it was a pointless exercise as there was little or no difference. Since then I have just built wheels with DB race spokes of equal width on both sides (obviously lengths vary) and never had a failure of any kind. This is cycling about 10,000 miles a year and sometimes carrying very heavy loads especially when cycle camping with my wife.
There is your way. There is my way. But there is no "the way".

Brucey
Posts: 32295
Joined: 4 Jan 2012, 6:25pm

Re: Rear wheel differential spoking....AS IF!

Postby Brucey » 20 Nov 2012, 4:57pm

Colin,
if I'm right in my thinking the best you might have expected to manage there could have been similar to a hi-lo rear hub, which is something I've never bothered with on the basis that it won't do very much good. Still, proof of the pudding.....

I guess there will be a marginal improvement in the stability of the wheel under radial loading (since the spokes with less tension are now longer, they may stretch a little more?) but that is about it.

IIRC the difference might be along the same lines as (say) ~0.5mm change in dish (or less) could achieve. Where appropriate, I've always sought to mitigate the effects of dished rear wheels by robbing a little back here and there; even one or two mm seems worthwhile to me.

cheers
-------------------------------------------------------------------------------
~~~~~~~~~~~~~~~~~~~~~~Brucey~~~~~~~~~~~~~~~~~~~~~~~~

stewartpratt
Posts: 2566
Joined: 27 Dec 2007, 5:12pm

Re: Rear wheel differential spoking....AS IF!

Postby stewartpratt » 20 Nov 2012, 4:59pm

531colin wrote:The tensions run 120kgf driveside, and 80kgf non-driveside if you build it 3 cross both sides, as near as I can measure.
So I built it 2 cross driveside, and 4 cross non-driveside, and guess what.....the tensions run 120/80kgf, as close as I can measure.


Well, of course. It's simple trigonometry :)

The lateral forces on the rim - ie the force pulling it left from the NDS and that pulling it right from the DS - have to balance (otherwise the rim will accelerate to one side or the other).

The rim's position relative to the flanges doesn't change with different spokings, and the number of spokes on each side is still the same.

So you have, laterally, the exact same triangles. The angle of the NDS spokes in a plane perpendicular to the rim is identical regardless of lacing, and so is that of the DS.

The only ways to even up the tensions in the spokes are either to adjust the geometry (eg make the DS flange diameter huge or pull the NDS flange inboard) or to have fewer spokes on the wider-flange side, hence 2:1 lacing patterns.

(FWIW I always build 3x DS and radial heads-out NDS for rim brakes and 3x both sides for disc brakes.)

User avatar
531colin
Posts: 12274
Joined: 4 Dec 2009, 6:56pm
Location: North Yorkshire

Re: Rear wheel differential spoking....AS IF!

Postby 531colin » 20 Nov 2012, 5:26pm

stewartpratt wrote:............So you have, laterally, the exact same triangles. The angle of the NDS spokes in a plane perpendicular to the rim is identical regardless of lacing, and so is that of the DS.................


Well, no not exactly "exactly the same".
I assumed the reason for the different crossing pattern was that the driveside spokes emerge from as near as possible the top of the flange, and the NDS from actually below the axle, in 4x 36 hole, which should just slightly alter the "pulling angle" on the rim....?
(To take it to the absurd degree, if the driveside flange came up nearly to the rim, you could get a 45deg angle on some very short spokes!)

stewartpratt
Posts: 2566
Joined: 27 Dec 2007, 5:12pm

Re: Rear wheel differential spoking....AS IF!

Postby stewartpratt » 20 Nov 2012, 5:46pm

531colin wrote:Well, no not exactly "exactly the same".


Yes, true enough so. But I don't *think* (without having flopped out a calculator for it) that it's a significant difference.

Obviously when I say "exactly" I mean "roughly" ;)

axel_knutt
Posts: 1456
Joined: 11 Jan 2007, 12:20pm

Re: Rear wheel differential spoking....AS IF!

Postby axel_knutt » 20 Nov 2012, 5:47pm

The length (L) of the spokes is comprised of three orthogonal dimensions, one radial (R), one tangential due to the cross pattern (X), and the lateral one (W) due to the width from the centre to the flange.
For the drive side:

Ld^2= Rd^2+Xd^2+Wd^2

Similarly for the non-drive side:

Ln^2= Rn^2+Xn^2+Wn^2

But since the tension acts along the axis of the spoke the three orthogonal components of the tension are proportional to the dimensions above:

Td^2= (KdLd)^2= (KdRd)^2+(KdXd)^2+(KdWd)^2

and

Tn^2= (KnLn)^2= (KnRn)^2+(KnXn)^2+(KnWn)^2

but for the rim to be in equilibrium the lateral force to one side has to equal the lateral force to the other, so:

KdWd= KnWn

therefore

Wn/Wd= Kd/Kn

so

Td/Tn= KdLd/(KnLn)

Td/Tn= (Wn/Wd)(Ld/Ln)

So you can now see that the only factors affecting the tension ratio are the ratio of the spoke lengths, and the inverse ratio of the width of the flanges from the centre line of the wheel.
With the same pattern both sides, the spoke lengths will match to within 0.5%, so the expression reduces to:

Td/Tn= Wn/Wd

Changing the spoking pattern from side to side will affect the tension ratio in as far as it affects the length of the spokes, but again, since the difference is only small compared with the difference in the flange spacing, the benefit is pretty negligible considering the loss of torsional stiffness with radial spokes.

Taking my wheel as an example, the tension ratio is 1.75:1 calculated from flange spacing only, or 1.742:1 calculated accurately from spoke lengths as well, and 1.67:1 if I were to use radial spoking on the drive side.
“I'm not upset that you lied to me, I'm upset that from now on I can't believe you.”
― Friedrich Nietzsche

User avatar
531colin
Posts: 12274
Joined: 4 Dec 2009, 6:56pm
Location: North Yorkshire

Re: Rear wheel differential spoking....AS IF!

Postby 531colin » 20 Nov 2012, 5:59pm

Axel.....taking a firm grasp of the only bit of your post that I actually understood, my spoke lengths were 276 and 298.

User avatar
531colin
Posts: 12274
Joined: 4 Dec 2009, 6:56pm
Location: North Yorkshire

Re: Rear wheel differential spoking....AS IF!

Postby 531colin » 20 Nov 2012, 6:01pm

stewartpratt wrote:............. I don't *think* (without having flopped out a calculator for it) that it's a significant difference.........


My experience tends to bear that out! :wink:

Brucey
Posts: 32295
Joined: 4 Jan 2012, 6:25pm

Re: Rear wheel differential spoking....AS IF!

Postby Brucey » 20 Nov 2012, 6:11pm

axel_knutt wrote: ...With the same pattern both sides, the spoke lengths will match to within 0.5%, so the expression reduces to:

Td/Tn= Wn/Wd

Changing the spoking pattern from side to side will affect the tension ratio in as far as it affects the length of the spokes, but again, since the difference is only small compared with the difference in the flange spacing, the benefit is pretty negligible considering the loss of torsional stiffness with radial spokes.


The spoke lengths will only match to 0.5% if the wheel dish is small (and the spoking pattern is the same). x2 spoking retains a substantial torsional stiffness whilst requiring a spoke only fractionally longer than radial which is why Colin chose it no doubt. The x2/x4 spoking should have given a spoke length difference of a few %. Not enough to make up for the wheel dish, but -in theory anyway- slightly better than a poke in the eye with a sharp stick, even if it isn't as good as reducing the dish even a small amount.

cheers
-------------------------------------------------------------------------------
~~~~~~~~~~~~~~~~~~~~~~Brucey~~~~~~~~~~~~~~~~~~~~~~~~

mig
Posts: 1890
Joined: 19 Oct 2011, 9:39pm

Re: Rear wheel differential spoking....AS IF!

Postby mig » 20 Nov 2012, 8:30pm

if it could be pulled sufficiently tightly could the spokes be replaced by a length / lengths of pliable wire and a wheel remain usable in the long term?

User avatar
531colin
Posts: 12274
Joined: 4 Dec 2009, 6:56pm
Location: North Yorkshire

Re: Rear wheel differential spoking....AS IF!

Postby 531colin » 20 Nov 2012, 9:45pm

mig wrote:if it could be pulled sufficiently tightly could the spokes be replaced by a length / lengths of pliable wire and a wheel remain usable in the long term?


I'm not entirely sure what you're asking.....but do these answer it?
http://www.peterwhitecycles.com/fiberfix.asp
http://www.emergency-spoke.co.uk/
....Similar thing used to be available with a bowden cable flexy part.

User avatar
[XAP]Bob
Posts: 16758
Joined: 26 Sep 2008, 4:12pm

Re: Rear wheel differential spoking....AS IF!

Postby [XAP]Bob » 20 Nov 2012, 10:11pm

Yes - a spoke does not ever go into compression. Whilst in tension there is no difference between a rod and a string.
A shortcut has to be a challenge, otherwise it would just be the way. No situation is so dire that panic cannot make it worse.
There are two kinds of people in this world: those can extrapolate from incomplete data.

mig
Posts: 1890
Joined: 19 Oct 2011, 9:39pm

Re: Rear wheel differential spoking....AS IF!

Postby mig » 21 Nov 2012, 9:06am

just wondering how a wheel completely spoked by pliable wire would hold up. although good enough in tension how would it perform against any lateral loading?

BigG
Posts: 982
Joined: 7 Jun 2010, 4:29pm
Location: Devon

Re: Rear wheel differential spoking....AS IF!

Postby BigG » 21 Nov 2012, 9:24am

mig wrote:just wondering how a wheel completely spoked by pliable wire would hold up. although good enough in tension how would it perform against any lateral loading?

All wires are "pliable". The difference is in the degree of pliability. A braided wire, which is what I assume you refer to, has a much higher coefficient of elasticity, i.e. it stretches more easily. The restraint against the wheel moving laterally would therefore be much weaker making such wires impractical as spokes. Once the rim has moved far enough for one set of spokes to be vertical, the system breaks down and the wheel goes lozenge- shaped. Their resistance to radial deformation under a normal vertical load would be similar. That is the rim would move more moving the hub away from the wheel centre making rim braking and tyre clearances problematic. However, for the same spoke tensions, all spokes would remain in tension as on a normal wheel.