calculating theoretical spoke tension - how?

[fat cat]

Hello, all. After sporadically lurking the forums for the last year, I've registered to ask questions of my own.

I'm currently planning wheels that I wish to build for my touring bicycle. I've noticed in some threads here people discussing NDS and DS spoke tension balance. At least one person (ligero in this thread) has claimed certain lace patterns and hub dimensions attribute certain percentages of the difference between the two sides' spoke tensions. What I'm wondering: does anyone here know the math that can provide such a figure based on all the known variables involved, or are such claims pure guesswork? I'd like to do calculations of my own, if possible.

[deepsix]

spokecalc on excel

[fat cat]

I hadn't considered spocalc having such a feature. Thank you.

How about spoke tension variance relative to spoke diameter?

[dgaddis]

I hadn't considered spocalc having such a feature. Thank you.

How about spoke tension variance relative to spoke diameter?

Diameter doesn't matter.

It's a statics problem. The spokes on the NDS have to pull egually as hard in the lateral direction as the spokes on the DS, their lateral force equals out and holds the rim in place. It's all geometry: bracing angle and # of spokes is what matters. If you know the tension on one side, and the spoke angle, you can calculate the lateral force due to the tension. The lateral force on the opposite side is the same, but the angle is different, so the tension will be different.

[fat cat]

Upon receiving your answer, Dustin, I went through my history and found the page at which I first came to believe spoke diameter had an effect. I see now I had just misinterpreted what someone else wrote. Thanks for sorting me out.

[dgaddis]

Upon receiving your answer, Dustin, I went through my history and found the page at which I first came to believe spoke diameter had an effect. I see now I had just misinterpreted what someone else wrote. Thanks for sorting me out.

No sweat. Spoke diameter will effect the # the tension meter gives you, but not the tension.

[fat cat]

Is that simply due to how much the tension meter "closes" for each diameter, or is there more to it?

[dgaddis]

Is that simply due to how much the tension meter "closes" for each diameter, or is there more to it?

Has to do with the stiffness of the spoke. A 1.8mm steel spoke will deflect less than a 1.5mm steel spoke at the same tension because it's thicker and stiffer, that's why you have to use the conversion chart to see what X number on the meter actually means for any given spoke.

[fat cat]

Oh, duh. I was imagining a tension meter that provides kilograms force when I read your comment, and that's why I disregarded stiffness variation of the spokes when I asked my question. It's been too long since I've used a tension meter. haha.

[Human Epic Jolt]

plenty of gaps to fall through here.

[Gattonero]

plenty of gaps to fall through here.

Indeed.
Not to count the the time spend for this, would result in several wheelsets build.
Don't want to sound like patronizing, but a correct choice of materials, correct lacing, proper even tensioning is the key for good wheels. All this implies lots of things to put into accounts.

Needs to be more specific about the project and the usage, then I can give an answer

[fat cat]

plenty of gaps to fall through here.

I have no doubt you speak the truth and I appreciate you making me aware, but what you've said does nothing to fill them in.

Indeed.
Not to count the the time spend for this, would result in several wheelsets build.

What do you mean by "this"? I only plan to build one wheel set.

Don't want to sound like patronizing, but a correct choice of materials, correct lacing, proper even tensioning is the key for good wheels. All this implies lots of things to put into accounts.

Even if you were intending to patronize, I would not mind. Anyway, I've certainly come across the notion that choice of materials and the build itself are key to good wheels, and I believe that to be true given all the successful history of bicycle wheels, but I enjoy learning more ideal methods whenever I can and implementing them when I consider them possible, practical, and fun.

Needs to be more specific about the project and the usage, then I can give an answer

I think you might have misunderstood my initial question, because I wasn't asking about designing wheels for a specific purpose, but instead was just wondering about how to calculate spoke tension balance between two sides of a wheel, and such a concept applies to all wheels.

But I imagine it would be useful and edifying for me to expand the conversation to hear opinions on my project. Like I said, I'm planning a wheel set for my touring rig. I only weigh about 145 pounds and I intend to keep my load weight to a minimum to accommodate my low strength, but I want to be able to monster truck over anything. :)

The wheels will be size 700, each with 36 Wheelsmith double-butted spokes and brass nipples. The front plan is a White Industries Daisy laced to a Velocity Dyad with a basically arbitrary 3-cross pattern (I would definitely appreciate any theory and suggestions for front lacing patterns specific to loaded touring). The rear plan is a White Industries MI5 laced to an off-center Velocity Synergy. I chose the rim primarily for tension balance. I was thinking a 4-cross pattern on the non drive side and a 1-cross pattern on the drive side. I started with the 4-cross for torque transfer, put it on the non drive side for tension balance, and chose the 1-cross to both bring the balance closer to 100% and increase lateral stiffness more than higher- and lower-cross counts could.

I am open to criticism. How does my plan sound?

[Gattonero]

So, if I understood, you want to find an universal rule for spoke tension?
Is so, I'm afraid, there's too many things before the job gets completed, that if something really works, it would take ages to figure it out.
In all honestly and with all my sympathy, I'm a mechanic not a scientist or a philosopher :)
To avoid the difference in tension between Lh & Rh is nearly impossible in a standard cassette wheel, I live with it (although not happy!) and work to minimize this.


The Lh radial-Rh crossed, is not my favourite.
There'a afew reasons for this.
First of all, the radial lacing would use less tension (albeit "pulls" more on the rim and hub, as being proper straight force) to achieve the same result.
Then you have the non-laced side that doesn't help keeping things steady, as the spokes are each one alone, they don't work together. The only way to make such lacing patterns work well, is on factory-built wheels, where every detail gets in the compluter and they do lots of testing with special machines, etc. In the real world of a wheelbuilder, this doesn't happen and practice didn't gve me good results with.
Good that you chosen a crossed-lacing on the Lh too, then.
But you may actually want to go for 2x Lh and 3X Rh, on a 36h hub I don't see a 1x working well

[Jacques]

So, if I understood, you want to find an universal rule for spoke tension?
Is so, I'm afraid, there's too many things before the job gets completed, that if something really works, it would take ages to figure it out.

It's really not that complicated. In fact, it was explained quite succinctly in the third reply in this thread.

[Gattonero]

It's really not that complicated. In fact, it was explained quite succinctly in the third reply in this thread.

I see it pretty complicated.

You really need to put into accounts how much the materials "give up"; spoke tension isn't an easy thing to deal with, there IS deformation in the rim and the hub.
Every program that does not include variables of those, won't give a precise figure, therefore is -sorry to say- pure accademic stuff and not much use.

Besides, as far as I can understand, our friend wants to have an idea of "how much" spoke tension a given lacing pattern will provide. But I may be wrong in this! :)

[Jacques]

I see it pretty complicated.

You really need to put into accounts how much the materials "give up"; spoke tension isn't an easy thing to deal with, there IS deformation in the rim and the hub.

Those factors are irrelevant to the OP's query. It's a matter of static forces.

The left and right side spokes exert equal and opposing forces on the rim in the left-right direction (the force vector parallel to the hub axle). Since both are at different angles, the overall tension exerted by each varies accordingly, which is easily calculate by using the cosine function.

[Gattonero]

The spoke tension does change while the wheel gets trued radially and laterally, however this is a value that would not get the numbers change dramatically.
But added to the fact that materials "move", then the story does change.

You note that I am talking about precise answers from those formulas, if they aren't, I don't really see the point of doing it (scratches head)

But going back to this, the drawing you posted does not consider that the spoke is not in an vertical angle, but is also crossed with other spokes. The crossing does make the spoke to not be at 90º with the hub, and the point where two spokes cross would interfere with the formula? Now I am just guessing, in my job I never thought about this :)

[Ligero]

The wheels will be size 700, each with 36 Wheelsmith double-butted spokes and brass nipples. The front plan is a White Industries Daisy laced to a Velocity Dyad with a basically arbitrary 3-cross pattern (I would definitely appreciate any theory and suggestions for front lacing patterns specific to loaded touring). The rear plan is a White Industries MI5 laced to an off-center Velocity Synergy. I chose the rim primarily for tension balance. I was thinking a 4-cross pattern on the non drive side and a 1-cross pattern on the drive side. I started with the 4-cross for torque transfer, put it on the non drive side for tension balance, and chose the 1-cross to both bring the balance closer to 100% and increase lateral stiffness more than higher- and lower-cross counts could.

I am open to criticism. How does my plan sound?

For the front using a Daisy hub laced 3x sounds as good is it gets, the plan for the rear not so much. I was one of the early builders that started the radial or 1x drive side and 3x non drive but I would not use it on your specific build. You are starting out with a hub that is spaced at 135mm so from the start you are 2.5mm better than most road wheels. Then factor in that you are using a offset rim you are gaining another 2.5mm. So in theory your effective spoke flange spacing will be 23.15 DS, 33.5 NDS with a tension balance of 83% between the two sides. That is pretty close already and not worth risking a broken drive side flange over to get an additional 5 to 8% from the 1x elbows out drive side lacing.

The holes on the 36h hub you are using are really close together and with the additional stress of the spokes pulling radial on it I would expect the flange to break. If you really want to get those extra couple mm's then lace the drive side 2x with all of the elbows on the outside of the flange. It will not be easy and you will spend a lot of time "forming" the spokes over each other but it will be much less flange stress than the 1x. I have laced a couple of 32h mtb wheels that way and it worked just fine but was not easy to do.

[fat cat]

In all honestly and with all my sympathy, I'm a mechanic not a scientist or a philosopher :)
To avoid the difference in tension between Lh & Rh is nearly impossible in a standard cassette wheel, I live with it (although not happy!) and work to minimize this.

I'd say I'm a philosopher/scientist in the sense that I try only to believe what I perceive in a logical fashion, and I've always found such a philosophical/scientific bent has helped me much in mechanical endeavors. In this case, that translates into having awareness of the geometry involved and accordingly selecting parts and lacing patterns that will help me minimize that tension difference.

Every program that does not include variables of those, won't give a precise figure, therefore is -sorry to say- pure accademic stuff and not much use.

Besides, as far as I can understand, our friend wants to have an idea of "how much" spoke tension a given lacing pattern will provide. But I may be wrong in this! :)

Jacques was correct in saying those variables are irrelevant to my original query. I was indeed wondering about the stuff you call academic, but not a concept for calculating the amount of tension relative to lacing pattern. Instead I was looking for the concept explaining the ratio of how much spoke tension there is on two sides of a wheel given certain hub dimensions, rim dimensions, and lacing patterns maintaining a rim centerd in the hub's OLD and around the hub's center axis.

The variables you listed are relevant to the wheel's outcome, but because they are a product of manufacturing while I'm only a consumer looking to assemble, they are not relevant to my current deliberations.

You note that I am talking about precise answers from those formulas, if they aren't, I don't really see the point of doing it (scratches head)

Are you sure you're not a philosopher? :)

The crossing does make the spoke to not be at 90º with the hub, and the point where two spokes cross would interfere with the formula? Now I am just guessing, in my job I never thought about this :)

Since the geometry assumes a straight line between spoke hole on the hub and spoke hole on the rim, I also wondered at one time if spokes crossing would render the geometry inaccurate to some amount, but my thought has been that because the crossing spokes tug each other toward their "desired" straight line, they might remain near true to the geometry's assumed straight line. Does anybody else have thoughts on this?

You are starting out with a hub that is spaced at 135mm so from the start you are 2.5mm better than most road wheels. Then factor in that you are using a offset rim you are gaining another 2.5mm. So in theory your effective spoke flange spacing will be 23.15 DS, 33.5 NDS with a tension balance of 83% between the two sides. That is pretty close already and not worth risking a broken drive side flange over to get an additional 5 to 8% from the 1x elbows out drive side lacing..

I've assumed that you mean the hub is 2.5 mm better because half of the extra 5 mm of OLD is 2.5 mm, so would I be correct in saying you've determined I gain 2.5 mm from the rim having a 5 mm offset? I ask, because according to Velocity the Synergy has an offset of 4 mm. Also, WI specs the MI5 as 21 DS and 35 NDS. Spokecalc's math provides a balance of 81% with 4x all around, with the 1x increasing it to 87%. I consider 81% close, too, but like I said before, I enjoy pursuing ideals, so I appreciate your grounding input.

The holes on the 36h hub you are using are really close together and with the additional stress of the spokes pulling radial on it I would expect the flange to break.

To ensure clarity, I want to say that by 1-cross I meant each spoke crossing one other spoke, so when you say "pulling radial" here, are you also referring to 1-cross as I've specified?

WI specs the flange diameter as 55 mm, which would put the spoke hole spacing on center at 4.8 mm. What range of hole spacing do you consider acceptable for radial, and what variables influence that range? I've seen mention of the amount of material between the flange's distal edge and the spoke hole's distal edge as one thing people take into consideration, but nothing about specific math.

If you really want to get those extra couple mm's then lace the drive side 2x with all of the elbows on the outside of the flange. It will not be easy and you will spend a lot of time "forming" the spokes over each other but it will be much less flange stress than the 1x. I have laced a couple of 32h mtb wheels that way and it worked just fine but was not easy to do.

I am glad to take time in building things, so I'm interested. Would the spokes going around the outside have heightened stress at the elbow/head? Also, how much higher would you say lateral stiffness is with 2x having all the elbows out compared to 2x having half in?

[Ligero]

I've assumed that you mean the hub is 2.5 mm better because half of the extra 5 mm of OLD is 2.5 mm, so would I be correct in saying you've determined I gain 2.5 mm from the rim having a 5 mm offset? I ask, because according to Velocity the Synergy has an offset of 4 mm. Also, WI specs the MI5 as 21 DS and 35 NDS. Spokecalc's math provides a balance of 81% with 4x all around, with the 1x increasing it to 87%. I consider 81% close, too, but like I said before, I enjoy pursuing ideals, so I appreciate your grounding input.

The numbers I came up with were off the top of my head without looking at the actual specs and I guess my memory is not what it used to be.

To ensure clarity, I want to say that by 1-cross I meant each spoke crossing one other spoke, so when you say "pulling radial" here, are you also referring to 1-cross as I've specified?

1x and radial are so close to being the same thing, especially when you are talking about a 36h wheel. So yes, the 1x spokes would be pulling on the flange 99% the same as radial spokes would be.

WI specs the flange diameter as 55 mm, which would put the spoke hole spacing on center at 4.8 mm. What range of hole spacing do you consider acceptable for radial, and what variables influence that range? I've seen mention of the amount of material between the flange's distal edge and the spoke hole's distal edge as one thing people take into consideration, but nothing about specific math.

Ideally you want about 2 time the spoke hole size above the spoke holes when designing for radial lacing. So you would want about 5mm of material above the spoke holes but that does not take into a account the spoke holes being so close together as they will be on a 36h hub. Most hub manufactures do not allow radial lacing on the front hub above 28h for that reason. DT did not even make a 32h radial hub for quite a few years because they felt the flange had too much potential to break.

I am glad to take time in building things, so I'm interested. Would the spokes going around the outside have heightened stress at the elbow/head? Also, how much higher would you say lateral stiffness is with 2x having all the elbows out compared to 2x having half in?

Yes, the stress will be higher on the spoke heads but by how much I don't know. You would need a really good fea program and computer to figure it out. As far as how much stiffer would hte wheel be, it would be the equivalent of having the flange about 2mm further out from center. That is a significant amount and I would normally say that it would be worth it if you weren't already at +80% tension balance.

I have built a LOT of wheels and the way I look at it is anything over 60 to 65% is gravy. Most wheels when built correctly hold up just fine for many, many years with tension balance of 45 to 55%. It is great to try and optimise things but you are sweating details that will make so little difference that you will not be able to feel the difference.