Triplet lacing (1:2) and correct spoke lenght ........?

[LouisN]

I'm looking at finding the right spoke lenght for a triplet lacing rear wheel (3 X DS / 1 X NDS ).

The different table calculations I have (3 of them) give me up to 10-12 mm in spoke lenght differences !!!!

Any wheelbuilder did a triplet lately and used a precise measuring table for it ?

Thanks ,

Louis

[Mackers]

Use 3.35x and treat the DS as a 32 spoke wheel if your calculator will accept it.

If not, treat the DS as a 48 spoke 5x wheel.

[WMW]

I've built several wheels with mine, and it has always worked. It was derived from the geometry, which shouldn't be that hard for anyone who passed the subject in HS. If in doubt, I think it would be a good idea to start at the basics...

Where are you getting the other two?

[kavitator]

i think it works if you take DS as 28 spokes - http://www.wheelpro.co.uk/spokecalc/

for 24 spokes 2:1 (16 ds (3x); 8 nds (0x))

[LouisN]

I've built several wheels with mine, and it has always worked. It was derived from the geometry, which shouldn't be that hard for anyone who passed the subject in HS. If in doubt, I think it would be a good idea to start at the basics...

Where are you getting the other two?

I built my wheel yesterday. Using YOUR table. Bang on !!!

Thanks !! IOU a coffee ...

The 5 X 48 spoke method gives me too long by 8 mm.

Louis

[ergott]

It's not just 48X5. I'll post it here for clarity.

Using 48 spokes cross 5 in the calculator:

resulting right side spoke length - ((3.14*right flange diameter)*0.0104).

It's the only formula I've used and I know it works. The formula was given to me by Jeremy at Alchemy Bicycle Works. It's easiest to simply put the formula in a cell of a spreadsheet and linkback to the corresponding cells.

-parenthetical edit.

[dwaharvey]

Ergott, just want to clarify... are you saying that you calculate the 48x5 spoke lengths in the standard way, but then subtract 3.14 * right_flange_diameter * 0.0104 = 0.032656 * right_flange_diameter? (If so I think this could be more clear, and regardless you are missing a parethesis!) Either way, that seems funny given LouisN's statement, because a typical hub might have a 55mm flange diameter, which would give a correction of only ~2mm, whereas LouisN said the 48x5 was off by 8mm...

[LouisN]

I copied your gold Tune hub / AC 420 rim wheel for the crossing pattern Ergott (the opposite pattern of Troy's) !!!

Yeah, small world. Maybe I didn't calculate right, I just threw the numbers in the spreadsheet like a usual spocalc calculation (I didn't bother looking at the formulas either... ).

It turned out fine for the build, despite I had to work with a mix of used parts (38 mm Boyd carbon rim, Sapim CX-Rays (DS) and DT Swiss Champ (NDS).
We'll see for durability and "effectiveness" now, as the hub is a pretty narrow one, and carries power data......

@ dwaharvey: I used some 270 mm and 275 mm spokes for DS because I didn't really know where exactly I was going between the different tables. They both fit, but the 275 mm are at the end of the threads, and I don't know if I went more than 105 kgf DS I think I would have to change all the 275 mm spokes...
The 270 mm are about perfect. I got 278 mm from the 5 X 48 spreadsheet, so I figure 276 mm would be still a little long...

Louis

[ergott]

snipped

I fixed the parenthesis, thanks.

[LouisN]

1I've built several wheels with mine, and it has always worked. It was derived from the geometry, which shouldn't be that hard for anyone who passed the subject in HS. If in doubt, I think it would be a good idea to start at the basics...

2Where are you getting the other two?

1) I know, you're right. My geometry is far, far away...left it somewhere in the mid 80's. And I don't master these terms very well in english either....

2) From some WW members...

Louis

[dwaharvey]

I fixed the parenthesis, thanks.

Not trying to be picky, just was confused if a different error had been made since the associativity of the expression meant the parenthesis weren't needed and the two numbers could be multiplied together rather than kept separate.

[ergott]

Not, picky. It's a mistake that's worth clarifying.

[dwaharvey]

I got curious about this, and since I haven't seen the spoke length calculation presented explicitly anywhere, I thought I'd do it myself. Hopefully someone here finds it useful or interesting!

For a normal build (equal # of spokes on each side), using the following notation:
E = ERD of rim
D = Diameter of flange
X = flange offset
N = Number of spokes
i = Number of crosses

Define:
Theta = 2 * Pi * i / (N / 2) = 4 * Pi * i / N = angle measured at the hub between a line passing through a hub spoke hole and wheel center and the line passing through rim spoke hole and wheel center for the same spoke

... then, aside from a correction of about 0.8mm from spoke stretch (~0.6mm) and extra spoke hole room (~0.2mm), the length of the spoke comes out to be:

Length = 0.5 * sqrt [ X^2 + E^2 + D^2 - 2 * E * D * cos( theta ) ]

[Note this matches with the results of United Bicycle Institute online calculator]

When one laces a triplet wheel with 24 spokes (16 DS, and 8 NDS), the angle theta turns out to be:

Theta_triplet = 2 * Pi * (19/4) / 24 = 4 * Pi * 4.75 / 48... ie the same angle as for a 48 spoke wheel laced with 4.75 crosses, or a 32 spoke wheel laced with 3.17 crosses

If one's calculator forces an integer for the number of crosses, and one made the calculation for a 5x wheel with 48 spokes, it would lead to a length that is slightly too long, because the angle theta would be off by Pi / 48 radians. If one imagines just the key spoke laced, then it'd be like rotating the hub by an extra quarter of the 24 hole spoke separation of the rim. Since the DS spokes are pretty much perpendicular to a radial line through the spoke hole, the effect of this is to change the length by roughly the angle of rotation multiplied by the radius of the hub flange, ie

Approx_length_error = Pi * (D / 2) / 48 = Pi * D / 96 = Pi * D * 0.010416666

... which is the formula Jeremy came up with and Ergott presented. Moral of the story: you can trust Jeremy

[WMW]

Theta_triplet = 2 * Pi * (19/4) / 24 = 4 * Pi * 4.75 / 48... ie the same angle as for a 48 spoke wheel laced with 4.75 crosses, or a 32 spoke wheel laced with 3.17 crosses

I calculate the angle for the DS spokes in a conventional build. If we are doing a 24h rim and 32h hub, this is always 67.5 deg. Then calculate the offset from this due to the rim having fewer holes, which is always 3.75 deg in this case. Then there are two different ways you can go... 67.5 +3.75 or 67.5 -3.75. You can lace it more tangential or less, depending on the components. At least that is what I have in the spreadsheet... but I haven't done a triplet build in a long time... and I don't know if I ever laced a wheel with the lesser angle.

[virenque]

What about a 21 spoke rear? Is it possible to calculate that?