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.

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Presented by Arc en Ceil Racing Team, NBX/Narragansett Beer p/b Apex Technology
Ninigret Park, Charlestown, RI Saturday, April 02, 2011 12:45pm

This was my first race at Ninigret and my first masters crit. They have a race track on a disused airfield on the south coast of Rhode Island. Folk down there crash a lot. The fire brigade were hosing a dramatically igneous car on Rt 4, the paramedics were stretching someone from another car on 95 near Cranston, the cops were sorting out a crumpled pair of cars a little north of Providence. And that was just the ride home. The Ninigret race track, otoh, is safe. No cars, curbs, railings, drains or potholes. In a pinch you can safely ride off the track and on the grass.

Clearly most contestants race that track a lot and the racing style is interesting. Frequent very short-lived attacks. Just as frequent, the speed drops to a crawl. Nobody cooperates with anyone, it seemed. As though there’s a repeating 15-way match sprint going on at the front. Intriguing and good fun. Keep your eyes on the front to save energy. Skills were generally very good so I felt safe despite a lot of hard, close racing. And it was very windy which made it particularly interesting.

I’m no sprinter and never will be so opportunism is my only hope in a race like this. On (maybe) the 3rd bell lap I got near the front. The attack went in the usual place, after the 2nd last turn, and I found a good wheel. Three guys got well clear and then I found myself in 4th with the gap ahead of me. I started slowing thinking the sprinters would finish the job and then we regroup. The guy behind me said something to me, either encouraging or exasperated at my slowing, I’m not sure which, and I responded with my best shot. Meanwhile, three sprinters ahead were side-by-side looking at each other deciding who would lead it out, and I sailed past. That felt nice.

Later, pretty much the same thing happened again, I got past a small group of stalling sprinters. But I couldn’t believe the situation and decided something was wrong. It must be a straight prime and there’s a break down the road and I’m sprinting for nothing and everyone will think I’m foolish. So I sat up. I was passed close to the line by one of the Fuji chaps, whom I asked, to confirm, is there anyone ahead of us? He said yes, those two (pointing). I said, so that was for nothing? He said, no, we were racing for the field sprint. Fooey!

At that point I was miffed and directed my anger at the two ahead so I led for nearly a lap to bring them in. They weren’t going to confuse me again. Actually, it was so windy that I couldn’t hear the prime announcements, only the bell.

That tired me out a bit. But there were still a few laps to the finish. It looked like the race would stay together. What to do? The way it was working meant I didn’t want to attack, because I knew I’d get no help and with that wind would need it. So I wanted to go with a late attack. But nothing stuck and in the drag race to the finish I sat up when I saw I couldn’t make top 10.

Won some Fuji handlebar tape on that prime.