To begin with it will be helpeful to consider only the spokes on one side of the wheel, and to assume that the wheel has no dish - that is the spokes are all perpedicular to the axis of the wheel.

Below are some different spoke lacing patterns for one side of a 32 spoke wheel:

The radial pattern is simple. Each of the 16 spokes connects hub hole *n* to rim hole *n*. The same hub and rim hole numbering system will be used in the explanations of the other spoke lacing patterns

In the 1x pattern, spokes laced through hub hole *n*, where *n* is an odd number, are laced to the rim hole 1 place clockwise from rim hole *n*. A spoke laced through hub hole *n*, where *n* is even, will be laced through the rim hole one place anticlockwise from rim hole *n*.

In the 2x pattern, spokes laced through hub hole *n*, where *n* is an odd number, are laced to the rim hole 2 places clockwise from rim hole *n*. A spoke laced through hub hole *n*, where *n* is even, will be laced through the rim hole 2 places anticlockwise from rim hole *n*.

In the 3x pattern, spokes laced through hub hole *n*, where *n* is an odd number, are laced to the rim hole 3 places clockwise from rim hole *n*. A spoke laced through hub hole *n*, where *n* is even, will be laced through the rim hole 3 places anticlockwise from rim hole *n*.

The calculation of the spoke length for the radial laced wheel is easy. It is the hub radius subtracted from the rim radius. To calculate the spoke length for a crossed spoke lacing pattern, a bit of trigonometry can be used. In each case we have a non right angle triangle where lengths *b* and *c* and angle *A* are known, but where length *a* (the spoke length) is unknown. If the angle from the axis of the wheel between two adjacent holes on the hub is *B*, and the spoke pattern is an x-cross pattern then the angle *A* will be *xB*. So for a wheel with *n* spokes, there will be *n*/2 spokes on one side of the wheel and the angle *B* will be

Therefore the angle *A* will be

(*eq. 1*).

The length *a* can be calculated using the cosine law:

(*eq. 2*)

When considering the length of a spoke in a real wheel, which will have have one of the hub flanges offset lateraly by a distance *f* from the centre of the axle, then we have a right angle triangle where one of the short sides is *f* and the other is *a*.

Pythagoras' theorem can now be used to calculate the length of the long side of the triangle (which is the actual spoke length). If *d* is the actual spoke length then we have:

By substituting the RHS of *eq. 2* for in this equation we have

If we substitute the RHS of *eq 1* for *A* in this equation we have:

So the actual spoke length *d* is: