Not your typical spoke length question...

[Mike G]

So hopefully I can convey it clearly...
Is there a standard formula for spoke lengths going from say a 3X to a 4X, and you know what your required length is for the 3X... this is a hypothetical as obviously there wouldn't be any reason to go 4x from a 3X.

What's prompting the question is I have a wheel set that I want to re lace from something that sort of resembles a 2X, notice I said sort of cause it goes against any convention of lacing a wheel that I have run across in my recent plunge into this realm of black magic... anyway I digress. The current spokes are 10 1/4"/260mm, so without being a math major, they probably won't cut it in a 3x.

So I know there are plenty of calculators out there, I guess I'm looking for something a bit easier....
Spoke length "X" work for a 2X, "X +Y" for spoke length for a 3X pattern, "X+Z" for spoke length for a 4X,
Something along those lines for when you already have an initial spoke length in hand.

 

[SILVERKINGPC]

No lo creo...I don't think so.

 

[Mike G]

Apparently not?

 

[SILVERKINGPC]

Well, its tough to answer because of other factors in the spoke length calc. You have the hub flange diameter, the flange spacing, the lacing pattern, the rim size. the # of holes, and the dish. I don't believe there is an easy reference calc. that can answer your question because of the above variants. Not to say that your 4x spokes couldn't be used on a 3-cross pattern wheel with a smaller hub shell and lesser # of holes in the hub/rim. Yes, a bit of voodoo black majic, but thats why I said I don't think so. I just go to the spoke calculator formula online, where I plug in the figures and get a proper spoke length...I bet you could use the calculator to "back into" the answer you are looking for....

 

[RustySprockets]

Yup, too many variables to predict accurately.

 

[Greg M]

Actually, with all the other variables remaining constant I expect there would be a simple mathematical relationship that would go from 2x to 3x, and 3x to 4x. I've no idea what it would be, but I figure running a few different wheels through an online spoke length calculator changing only the pattern would get you the answer.

 

[RustySprockets]

True that...but the only way he can determine the constants is by measuring them. Once he does that, the calculator will provide his answer and said mathematical relationship will no longer matter, except to satisfy our curiosity.

 

[Greg M]

No, the beauty of this method is you could use any, randomly generated set of dimensions. Say for example a 26" wheel, and then a 28" and a 29er, you can use the same hub dimensions, or change them if you want. All you are looking for is how much longer, in percent, that the spoke becomes going from 2x to 3x. If the percentage that the spokes grow longer is the same in all cases, then all you need to do is measure your existing spoke, and calculate the new spoke length.

 

[mikeeebikey]

True it would be a constant for that rim and hub combination.
But.... the geometry is so different from combo to combo, easier to just use a calculator.

 

[RustySprockets]

Well, Greg gave me quite a lot to think about, so I started juggling the numbers. While not an exact correlation, it does appear a reasonable estimate might be drawn using the following ratios:

2X to 3X = 1:1.0044
3X to 4X = 1:1.006
2X to 4X = 1:1.0125

As I said, the math doesn't work out exactly, but you're going to round off to the nearest mm anyway, and these multipliers should place the result "in the ballpark." The values also appear to work regardless of 32 or 36 spoke wheels.

So, applying this ratio to Mike G's situation, a 36-hole wheel laced in 2X with 260mm spokes would require a spoke length of 261.144 to achieve the 3X pattern. Time for some real-world testing, me thinks.

 

[Greg M]

Cool. Thanks Rusty, I hadn't had time to sit down with an online calculator to see how the ratios came out. Good to know I'm not a crazy as most people say.

 

[Bicycle808]

Well, Greg gave me quite a lot to think about, so I started juggling the numbers. While not an exact correlation, it does appear a reasonable estimate might be drawn using the following ratios:

2X to 3X = 1:1.0044
3X to 4X = 1:1.006
2X to 4X = 1:1.0125

As I said, the math doesn't work out exactly, but you're going to round off to the nearest mm anyway, and these multipliers should place the result "in the ballpark." The values also appear to work regardless of 32 or 36 spoke wheels.

So, applying this ratio to Mike G's situation, a 36-hole wheel laced in 2X with 260mm spokes would require a spoke length of 261.144 to achieve the 3X pattern. Time for some real-world testing, me thinks.

I just tested these "Formulas" on edd, and got markedly different results. To get the hypothetical 36h@ 2x with 260mm spokes, I used a shimano cb-e110 hub's specs and a rim with a 556mm ERD, which gave 259.9 and 259.7mm spokes for left and right, respectively. When I left all the other parameters the same (ERD, hub specs, 36h) bt switched to 3x, edd called for 266.6/266.4mm spokes.

There are too many variables wth wheel building for a universal denominator whereby you simply multiply your current spokes by a single number. There'd have to be multiple steps to the formula. I, for one, haven't a clue as to what those steps are, so i use a spoke calculator online. Fill in a few specs, click a button, and get the required spoke length.