# 2:1 Two-to-one lacing pattern - Calculating spoke length for a 2:1 spoke lacing pattern -

Calculating the correct spoke length for a rather exotic wheelset with a 2:1 (two-to-one) spoke lacing pattern and straight pull hubs is far from being a straight forward process, yet it can be broken down into comprehendible steps every wheel builder can understand. This article is the second part in series of exotic wheel building and shows how to break down the spoke length calculation for a wheel with a 2:1 spoke lacing pattern.

Looking at a racing bike wheelset, Fulcrum Wind 55 DB, I recently had in my workshop, I found an interesting wheel building challenge, induced by its 24 spokes, laced 2 cross in a two-to-one or 2:1 spoke lacing pattern.

In one of my previous articles, Exotic Wheelbuilding: Understanding paired spoke hole hub design, I dived into studying paired spoke hole hub design and understanding the logic behind how to calculate the correct spoke length for a rather exotic wheel hub design.

Having this 2:1 two-to-one carbon wheelset on my workbench, the problem was somehow similar, except instead of dealing with an exotic hub design, there was a mismatch in a spoke count between drive and non-drive side of the wheel. And to make things a bit more complicated spoke length calculation wise, the wheelset was built using straight pull hubs.

## WHY 2:1 Two-to-one LACING PATTERN?

Although such wheels are not so widely spread, 2:1 spoke lacing pattern has been in the industry for a while now. And so, it is certainly not an everyday situation for a wheel builder to build such a wheelset as a new build.

The Cycle Clinic's article states that 2:1 is a lacing pattern where the spoke tensions are more equal than in a conventional wheel. If you have a wheel built 2:1 then as you go around the rim, you will notice repeating pattern - there will be 1 spoke going to the non-drive then 2 going to the drive side of the wheel. From 24 spokes in total, 16 will be on the drive side and only 8 on the non-drive side.

According to Fulrum Wheels page, as a result there are two spokes which carry out the function of one, slackening and torsion are limited and the transfer of the athlete’s power is much more effective.

Also, thanks to this system, spoke tensions are balanced more evenly between drive and non-drive sides and the fatigue life of the rim, hub and spokes is lengthened.

Besides reduced fatigue rate and extended spoke life, a more even tension across each side of the wheel also reduces the stress imbalance around the spoke holes which should prevent possible rim cracks. Moreover, greater spoke count on the drive side (16 spokes) in combination with a 3 cross lacing pattern will also greatly improve an overall torsional stiffness and power transfer from the hub to the rim.

But building a wheel with a 2:1 lacing pattern cannot be done with conventional components as such builds require a stiff rim and hubs with a specific geometry, where the non-drive flange is pushed further to the outside.

## 2:1 LACING AND SPOKE LENGTH

### Identifying the problem

To identify the problem, we should first visualize it correctly. Take a look at the wheel drawing below where only drive side spokes are shown for a clearer understanding. On the drive side of this wheel, a 2 cross spoke lacing pattern is used.

Even a quick glance suggests different than usual spoke placement. Whereas on conventional builds we are dealing with equal spoke count for each side of the wheel which explains why drive and non-drive side spokes are alternating evenly when you go around the rim, the underlying logic behind 2:1 lacing pattern build is somehow different. As the figure suggests, for every 2 drive side spokes, we have only one non-drive spoke and drive side spokes are somehow paired together.

On the other hand, if we turn the wheel and fill the remaining 8 rim holes by adding the non-drive side spokes you should notice that apart from the low spoke count, spoke placement isn’t so unconventional. Rather than that, the non-drive side spokes, laced in a 1 cross lacing pattern, are equally distanced apart, but more on that in the next section.

Let’s now address this 2:1 lacing pattern spoke length calculation challenge for each side of the wheel separately.

Similar to my previous exotic wheel building experiment, the underlying presumption is that for the correct spoke length, we must adjust lacing pattern value from an integer to a floating number. Read further to see how this can be done.

### Non-drive side of a 2:1 wheel

When you comprehend the logic, the non-drive side calculation becomes very intuitive. With our wheel having 24 spokes, with equally spaced holes in the rim, there should be 15 degrees between every spoke looking from the center of the hub:

α = 360 / 24

Like mentioned before, every non-drive side spoke is equally spaced apart from the nearest non-drive spoke in both directions, which is also explained by:

α = 360 / 8

Since two drive side spokes are always in-between, looking from the center of the hub, there is exactly 45 degrees between each non-drive side spoke. Or in simple terms, 15 degrees to the nearest drive side spoke, another 15 degrees to the second drive side spoke and final 15 degrees to the next non-drive spoke. Or 3 x 15 degrees in total, 45 degrees.

But how can you translate this logic into a spoke calculator such as spokeCalc?

Since this spacing is equal for each non-drive side spoke, it doesn’t affect the standard spoke length calculation in any way. Meaning you just have to use the same exact spoke count for each side of the wheel. Why? Imagine a more intuitive build where you have 16 spokes in total, 8 being non-drive and 8 drive side. Divide the full circle by 16 and you will get 360/16, which translates to 22.5 degrees between every hole in the rim (spoke). But now in-between two non-drive side spokes, there is only one drive spoke and so the angle between them is 2 x 22.5 degrees or 45 degrees, see? Exactly the same as before, but now spokes are alternating in the more conventional pattern - one drive side, then one non-drive side spoke and so on. With this kind of thinking, we have just tricked a spoke calculator to think our situation is rather a normal build.

So, to get the correct spoke length for our 8 non-drive side spokes on 2:1 lacing pattern, use 16 spokes as a total spoke count (8 for each side) and select a correct lacing pattern. Once you get the spoke calculation for each side, use only non-drive side spoke length and proceed to the next section to determine the calculation for a drive side spoke length.

Note: our wheelset has non-drive side spokes laced in 1 cross pattern. But what about radial pattern, which is also common? It is even simpler as drive side spoke count and lacing pattern doesn’t affect non-drive side spoke length in any way.

### 2:1 lacing and the drive side spoke length

The drive side of the wheel is where it actually gets tricky, because as we mentioned before, the drive side spokes are somehow paired together. The figure below indicates just that.

Since drive side spokes are not positioned in every other rim hole, we have an alternating angle in-between - 30 degrees and 15 degrees respectively.

What is going on actually? Basically, the two drive side spokes that cross at the outermost cross are spaced apart more than they would be on a convention wheel. That is why these drive side spoke pairs look so obvious. But what is this angle difference?

Let’s think of it in terms of a more conventional wheel with 16 spokes on each side. Such wheel should have exactly 360/32 or 11.25 degrees between every rim hole. Moreover, same side spokes on such a wheel should be positioned 22.5 degrees apart. If we return to our case, this is not the case as they are 30 degrees apart. And so the difference, 7.5 degrees, is the total angle difference for two nearest same side spokes, meaning every spoke is positioned 7.5/2, or 3.75 degrees from where it should be on a conventional wheel. The figure below is a visualization of what was just explained.

But still we aren’t exactly closer to our calculation. Or are we?

Now it is time to include our underlying theory about lacing pattern correction factor. In that way our drive side lacing pattern will actually not be an integer, but a fracture number. So, our wheel is actually not built using a 2 cross lacing pattern indeed.

If we continue to move the highlighted drive side spoke on the figure below even more to the outside, the two paired spokes will inevitably be positioned in the same exact rim hole. This is an impossible situation, yet, in that exact point, it is +0.5 cross. And somewhere between these two points lies our spoke.

So, to get our lacing pattern correction coefficient, we should divide our angle difference with the rim hole spacing angle of a conventional wheel and multiply it by a 0.5 cross.

(3.75 / 11.25) * 0.5 = 0.166

This is our partial lacing pattern, but since the geometry of a normal straight pull hub like ours dictates paired spoke holes in the hub, we actually started with 2.5 cross lacing pattern. Our final lacing pattern for this specific racing bike wheelset would be 2.66 for the drive side and 1.5 for a non-drive side.

Note: 0.5 cross correction is always added in the process of calculating the spoke length for straight pull hubs if spokes do not run directly from the hub to the rim (radial pattern).

## Final thoughts

Not all builds are conventional and knowing the logic how a spoke calculator and its algorithm works can help a wheel builder get the correct spoke length even for more exotic wheel builds. Wheels with 2:1 spoke lacing pattern, such as this Fulcrum 55 DB, certainly offer such a challenge if you are positioned in a situation when a spoke length calculation from scratch is needed.

Enjoy wheel building!