Wheel Building - Double Snowflake

for the first snowflake pattern I took the length for a normal 3 times crossing and added 10mm. it worked out very fine! spoke diameter is 2mm... fot 1,8mm spokes I would take 8mm instead.

It seems like it could be quite complicated as the length of spoke taken up by the twists depends on the angle between the spokes on either side of the twists, which depends on the length of the twists...

But i was thinking about this in the shower the other day, and had the idea that modeling the twists as if the spokes were fine thread winding around cylinders lying along the axis of the twists might work. On that assumption it's not too hard to modify the spoke length formula:

r = effective radius of rim = half ERD
f = hub flange offset
h = effective radius of hub = half distance between opposite spoke holes
d = diameter of hub spoke holes
s = number of spokes (total, both sides of wheel)
a = angle between spokes = 360/s in degrees, or 2pi/s in radians
w = width (thickness) of spokes at twists
ti = number of half twists on the middle cross
to = number of half twists on the outer cross

length = sqrt[ f^2

                + (r - h Cos(6a) + pi/2 w (ti Cos(3a) + to Cos(a)))^2
                + (h Sin(6a) + pi/2 w (ti Sin(3a) + to Sin(a)))^2 ]
             - d/2

Doing the sums for a Velocity deep V rim (r=291) on a miche large flange front hub (f=33.3, h=30, d=2.4), 36 (a=10 degrees) butted (w=1.8) spokes i get:

ti / to / Length
0 / 0 / 278 - i.e. a plain 3x wheel. agrees with http://lenni.info/edd/
0 / 1 / 280.8 - normal snowflake: adds 2.8mm per half twist
0 / 2 / 283.6
0 / 3 / 286.4
0 / 4 / 289.2
1 / 0 / 280.6 - 3 cross snowflake with twists on the middle cross
2 / 0 / 283.1 - adds 2.6mm per half twist for these
3 / 0 / 285.7
4 / 0 / 288.3
1 / 1 / 283.4 - the double snowflake, roughly a mix of both.
2 / 1 / 285.9
1 / 2 / 286.2
2 / 2 / 288.7

Making twists at the middle cross where the spokes meet at a larger angle adds less length. The 1 / 0 calculation should also work for Sam's 3 lead, 3 trail, 3 cross snowflake.

Using 2mm thick spokes increases the numbers to 3.1mm per outer twist, 2.8mm per inner twist.

I'd be interested if people who have actually built snowflake wheels could share their numbers.

i got to 2nd para...