Spoke angle to decimal crosses conversion?

I have been trying to work out how to do this for ...months years? now...and have got no where. keep coming back to it as I am damned if I am going to let it beat me.

Reason I want to know is that often Spoke length calculators use spoke angle..as in :
http://www.sheldonbrown.com/mismatch/
where you put the angle in to work out spoke length.
That formula..without further work is only good for wheels where the rims is central to the hub


The other sort of spoke length calculator, asks to specify the number of crosses, sometimes as a decimal figure. I always find it easy to calculate the spoke angle as found from using the link above, bu no idea how to convert that angle in to a decimal cross number.

I thought I had it today, but no
I had gone through this page
http://www.sheldonbrown.com/rinard/36-24.htm

made up a theory of how to do it...then tried to apply to Chalo's work

http://rideyourbike.com/36hub24rim.shtml

And it failed
but still can't see if there is an easy way to convert spoke angle to decimal crosses..

Is is simply spoke angle divided by angular spacing of the rim holes?

Neil,

This calculator has a CRAPLOAD of extra functions. Maybe it can do what you want:

http://wheelspoking.com/Build.aspx?Mode=Advanced

(warning: I have not personally tested the results of the calculator yet)

No , thanks though..That is a nice visualser, but it only deals with regular cross patterns from what I have briefly seen of it.

Ummmmaybe my initial computations were correct

going with Chalos work here
http://rideyourbike.com/36hub24rim.shtml

his spoke angles seem to be 50 and 60 degrees, and the angle of the rim holes (per side) is 30 degrees (360/24 holes) ..every other spoke..there fore 30 degrees
so that gives

50/30 = 1.666...as he says

and 60 / 30 ///2 cross

and on the drive side...spoke angle works out to 25 degrees..so 26/30= 0.8333

solved

The reason spoke angle doesn't convert neatly to decimal/fractional cross counts is because the relative sizes of hubs and rims are variable. A big hub laced to a small rim has spokes at a very different angle than a small hub laced to a large diameter rim, even if the spoke counts and cross counts are the same.

To put it another way, it sounds like you are concerning yourself with the angle between the tip of the hour hand (representing the hub hole) and the tip of the minute hand (representing the rim hole), when what you need to be aware of is the relative angle between the hands themselves. That "clock face" angle of arc is directly convertible into a cross value. And that angle doesn't change according to the lengths of the clock hands like actual spoke angle does.

Chalo said:

The reason spoke angle doesn't convert neatly to decimal/fractional cross counts is because the relative sizes of hubs and rims are variable. A big hub laced to a small rim has spokes at a very different angle than a small hub laced to a large diameter rim, even if the spoke counts and cross counts are the same.

Click to expand...

Wrong..unless your definition of spoke angle is different to mine.
I am using what is defined in the link i posted earlier
http://www.sheldonbrown.com/mismatch/


Spoke angle is constant regardless of hub and rim diameter..try it in SketchUp..



Spoke angle is independent of hub or rim diameter...it appears to change in relation to the edge of the hub ..and even the angle the spoke crosses the wheel...but relative angle between base of spoke and its rim end remains constant. I have just done a few different drawings in sketchup..from a 2 meter diameter rim with 38 mm hub, to a 500 mm hub with 350 diameter hub...spoke angle remains the same for any particular cross.

From your mates post of the wheel you did for him

http://rideyourbike.com/36hub24rim.shtml

look at the red spoke...same one..same pattern of lacing, but one with big hub, one with small hub compared to the rim.

Both look different angles because of the different hub diameters, but both have the same cross number and same spoke angle

Looks like a case of each of us not reading/understanding each others posts fully. I did not fully get your second paragraph, and you probably did not follow the link I posted to see what I was referring to when I said spoke angle.

I just re read the second paragraph of your post, Chalo ,

Chalo said:

To put it another way, it sounds like you are concerning yourself with the angle between the tip of the hour hand (representing the hub hole) and the tip of the minute hand (representing the rim hole),

Click to expand...

No, I was not doing that, Some how you got that impression from my question.

Chalo said:

when what you need to be aware of is the relative angle between the hands themselves. That "clock face" angle of arc is directly convertible into a cross value. And that angle doesn't change according to the lengths of the clock hands like actual spoke angle does.

Click to expand...

This is the angle I was asking about

Taken From the linked article in my first paragraph of the first post

Mismatched Wheelbuilding by Benjamin Lewis said:

The "spoke angle" is defined as the angle between the hole in the hub flange and the hole in the rim, measured from the axis of the wheel. This angle is shown as T in the diagrams.

Click to expand...

This is the angle I was referring to and calling spoke angle, and trying to convert to decimal cross figure. I have been trying to figure this for a year or more now and have asked about it before on other threads and also have asked both your self via PM and JRH via e-mail, and no one knowing how to do the conversion I decided to post this thread.


I wanted to know how to convert that spoke angle to decimal cross figure, but it seems mo one here knew how to do if. Even John Holmes said he did not know and the way he would do it wss to start building and work spoke length by trial and error

Okay, cool. You and I are talking about the same geometric value.

For "crosses" to make sense in any intuitive way, either the hub or the rim should have regularly spaced holes. But in truth, you only have to decide on a base drilling for the purposes of calculation. So even if you were doing a wheel with irregular hole spacing on both hub and rim, you could decide arbitrarily that you were going to use 36 spoke as the setting for the calculator.

If you use the 36 spoke setting of a calculator, then the value of one "cross" is the same as the angular interval between each of the 18 holes in the flange of a 36 hole hub, or between each of the corresponding holes in the rim. Thus 20 degrees of offset between hub hole and rim hole equals one cross of a 36 spoke wheel.

As a demonstration of the idea, consider that holes in 32 hole hub flanges fall 22.5 degrees apart, as opposed to 20 degrees apart on a 36 hole hub. So one cross in a 32 spoke wheel equals 1.125 cross in a 36 spoke wheel. Try it out. Set the calculator for 36 spokes and then calculate for 3.375 cross. Then set it for 32 spokes and calculate for 3 cross without changing any other values. The spoke length will be the same.

If you set the calculator to 720 spokes, then each flange in the hypothetical wheel would contain 360 spokes one degree apart. Then if you entered your "spoke angle" (hole offset) in degrees instead of the cross count, you'd get the right spoke length. So to extend the above example of a 32 spoke, 3 cross wheel being calculable as a 36 spoke, 3.375 cross wheel, you could enter it as a 720 spoke, 67.5 cross wheel and yield the same spoke length.

Not digested any of that yet..will play with it graphically in Sketch Up to get it..
Only just started playing with it..no 3d modelling, just 2d..but here is model made by some one else of a Nexus hub I was trying to build..they got the spoking slightly wrong..Two left, two to the right..but otherwise impressive work to my eye.

Yep, I get it now.

I am writing this post to clarify it for myself when I come back to this again in the future and need to re learn this.


You have to calculate spoke angle as per Mismatched and as Chalo described above, angle between 'small hand and big hand' of any SINGLE Spoke
So draw it out, and get the spoke angle, from hub hole to spoke tip = spoke angle.

Divide that by the angular spacing of the holes in the rim FOR THAT SIDE Spokes..so a 36 hole rim...holes are spaced 10 degrees..therefore spokes for either side are every other spoke hole in the rim, so 20 degree..


Decimal Cross figure = Spoke Angle / Twice the rim hole angle

Edit:

I sorted it...I got my division upside down ...was using 1.33 cross instead of 0.75

Use 0.75 in the online calculators and it comes up with exactly the same figure i get doing it long hand 74.7mm


Hi Chalo.

Hope you are monitoring this thread, or i'll have to PM you. Been tinkering with this for a day or two..and I am now at a stage of dreaming about bloody spokes and not getting a proper nights sleep!

Thought I had got the hang of all this..till I started trying to get a spoke length for a unknown hub motor..and well i gota still be missing someting .

Had this hub on 20 inch, 28 hole rim, swapping rim for a smaller diameter rim, also 28 hole

Original lacing :
Paired holes, on hole on one side exactly in line with hole on opposite flange.

View attachment 3

Have done manual calculation using
http://www.sheldonbrown.com/mismatch/ and get 74.7
also
http://www.ebikes.ca/SpokeCalc.shtml and http://leonard.io/edd/ gives 91.3

also get figures of 70.2, 72.1 from other calculations..

I have worked out a decimal crosses figure, but wont post that now. I want to see what figure you come up wit,,,if you have the time and inclination of course.



here are the numbers and pics

the Hub and rim ARE BOTH 28 hole., but the hub is paired holes, with pairs being spaced as if 28 holes in EACH Flange..so 360/28= 12.857 deg...see pic...Two holes used...two holes not drilled.
Opposite flange is offset by one hole, with one hole on each flange lining up with other side flange.

ERD 292mm
Spoke hole circle diameter to centre of spoke hole 164mm
Spoke hole diameter 2.9mm
Flanges are 4mm thick, central to hub
Hub centre to flange centre 19mm.

It is laced to give the appearance of single cross..though for calcs it won't be I am sure, because of the paired hub holes