## Spoke length with paired-hole hubs

### April 11, 2011

I was trying to calculate spoke length for wheel using rims with uniformly spaced spoke holes but using hubs with paired spoke holes. Specifically Novatec A271SB and F372SB. Hub specs and photos can be found in the Novatec 2011 hub catalog.http://i.imgur.com/spGvz.png

There’s some good pictures of the lacing I’d use on DHgate.

I had been using three spoke length calculators: Spocalc.xls, DTSwiss and Edd.

The DTSwiss and Edd calculators allow you to use fractional cross numbers but offer no guidance on how. Spocalc says: “Note:If paired hub spoke holes are 15 degrees apart, then: For 24 paired spokes laced 2x, enter 2.25 cross. For 24 paired spokes laced 1x, enter 1.25 cross. For 20 paired spokes laced 2x, enter 2.29 cross. For 20 paired spokes laced 1x, enter 1.29 cross. For 16 paired spokes laced 1x, enter 1.33 cross.” But I didn’t understand where those numbers came from or what the resulting lacing pattern would look like.

So I wrote a computer program to help me visualize the designs and understand. I learned a few things.

First, the angular offset of a pair of spoke holes on the left flange relative to the nearest pair on the right flange is determined only by spoke count N. It is independent of the angle between a pair of holes on the hub. A pair of holes on one side at 2π/N relative to the nearest pair on the other side.

Second, it turns out that Spocalc assumes, when it recommends fractional values of cross number X, that the two spokes in a pair of adjacent holes (on one side of the hub) do not cross each other. In other words, the two spokes are pulling on the flange material between the pair of spoke holes. This is why spocalc’s X for a paired-spoke-hole hub is larger than for a regular hub.

Let’s try to visualize this.

Start with X=1 for a regular one-cross lacing with uniform hole spacing.

Here we have a 20-spoke wheel with a small ERD and large hub PCD to help make the images clearer. Hub spoke holes on the front side, as we look at it, are black—on the rear they are green. Front leading spokes are orange, front trailing are red, rear leading are cyan and rear trailing are green.

Now get rid of the rear spokes and spoke holes for clarity.

Next, increase X to 1 < X < 1.5. The diagram shows X = 1.3.

It’s still a one-cross lacing but now the hub has paired holes, meaning that each J end of one spoke is closer to the J end of one neighbor than its other. But these “paired” spokes don’t cross.

Increase X again to 1.5 < X < 2 and now you have a two-spoke lacing—the two paired spokes cross each other. The diagram has X = 1.7.

These last two pictures are of the same hub. Spocalc is offering only the first lacing but I don’t see anything wrong with the second.

If you increase again to X = 2 then the pair move apart so that each hole is equally distant to both of its neighbors and you’re back to a regular hub.

The third lesson is how X relates to the angle θ between a pair of spoke holes. θ = 4π/N when X is an integer. θ = 0 when X = 1/2 + an integer, e.g. X = 1.5, which is an impossible hub in practice. In general θ = 8π/N⋅abs(1/2 – frac(X)), which allows me to calculate X given measurements from the hub.

Now put the rear side spokes and spoke holes back in the picture.

And here’s the actual front wheel I’m considering with two-cross lacing, 38 mm hub PCD and 521 mm ERD.

First off, I really appreciate the work you put into this. I’m looking to build a wheelset in the next month or so with the same A271SB/F372SB hubs, and would love to hear any feedback you could give me.

Is there any reason you opted for the ~2.3 cross rather than 1.7? The wheelset at the DH-Gate link has the rear laced 1.7 and the front laced 1.3 .

Were the calculated lengths spot-on? And finally, do you have \theta for these hubs?

Thanks!

I never bought the hubs or made the wheels. In the end I decided to postpose learning to build wheels indefinitely. So I can’t vouch for the .7 and .3 being the right corrections. You’ll need to calculate the exact X numbers after buying the hubs and carefully measuring spoke hole separation.

I chose 2.3x because it seemed less likely to crack the hub flanges. With 1.7x the spoke is pulling the corner of the “tab” away. With 2.3x, each spoke pair puts the metal between the holes in compression. If you see what I mean.

Dear thefsb, This is great! Thank you SO much for answering a question I’ve had about spocalc for years! Damon is a really bright guy, and I’m sure he worked all this out–but failed to give an explanation in the program comments. I’m grateful to understand it completely now.

[…] […]

Hey I found a bit of info on this on Sheldon’s website. I think your info lines up, but your visuals are a bit nicer. Sweet program!

http://sheldonbrown.com/rinard/36-24.htm

I am struggling with calculating these decimal cross numbers too, for ‘odd ‘ spoke patterns and I still do not get it. Wondering if you can help in how to calculate them.

I have a paired hub…24 hole Nexus 8 speed…but fitting to a 36 hole rim. The pairs of holes are 10 degree spacing. Have created a pattern that seems to work, and want to calculate spoke length, but first need the Cross number. Spoke angle measured from nipple to ‘J’ through the axle is 50 degrees..nipple end is 5 rim holes around from radial. Just can’t get how to calculate the cross number.

Do you get my explanation? can you help shed light?

Neil

I am guessing that mine could well be 2.5 crosses..but not sure.

Have used these sites too for info

http://rideyourbike.com/36hub24rim.shtml

http://www.sheldonbrown.com/mismatch/

Neil, that’s a tough question. You’ve got a paired-hole hub *and* a skip hole rim going on at the same time. This article does not provide a tool to calculate X numbers, it just try to help you visualize what they mean when they are not integers. But I think the method I explained can probably be extended to, what comes down to, paird-hole rims.

I wouldn’t recommend you guess 2.5 X is correct. With a normal rim application, 2.5 X is not possible—it would mean two spokes sharing a hole in the hub—it might be with your wheel.

Try to find a friend who knows wheel building well to help you. Or go to a shop with a competent wheel builder, intending to buy the spokes there, and get help choosing them.

Yes, you are correct, there is the appearance of 2 spokes in one hole, due the fact that a spoke hole in one side is in exact alignment with a single hole of opposite pair on other side.

I live on a small island ( pop.80,000 ) called Jersey, and none of the local stores and their wheel builders would have a clue about this… I know, i already asked.

Will keep trawling the net

Thanks

Jersey, huh? Try asking for help on http://weightweenies.starbike.com/forum/viewtopic.php?f=113&t=74564&sid=7b3355c40c2d369a8cda564273cec90d

It’s not an appearance. With a normal rim application, 0.5, 1.5, 2.5 are impossible X numbers. I don’t know about a skip-hole rim application.

As you say this is a skip a whole pattern.

Since I as yet do not know how to calculate the cross number, it may well not be 2.5 cross,

I do know spoke angle is 50 degrees, and the rim end is 5 holes offset from radial, but other than that, at a loss