Which hub geometry for the strongest wheel?

Saved by the Aussie, as Colin submitted two good questions. Today we'll address his first:

"Bracing angles.  The Onyx hub has pretty narrow flange spacing.  I'd pretty much assumed that would make a weakish wheel.  But I've heard trustworthy others say that although the spacing is narrow it leads to more equal drive side and non drive side spoke tension and in the real world that gives an absurdly strong wheel.  Flange spacing versus spoke tension variation. Discuss."

First, thank you to Colin for the question. Since it looks like this post a day business will be with us until into the summer, we need the help. Otherwise I'm just going to post lyrics from Paul's Boutique and 3 Feet High and Rising, which would be edifying and wonderful but have nothing to do with bikes.

Back to hubs...

First we need to dissect Colin's question and provide some definitions (which may be mine and not precisely what Colin intended but we'll go with mine)

Flange spacing is the distance between the right and left flanges on a hub. I think everyone knows what flanges are - they are where the spokes connect to the hub. In the chart below, I separate left from right flange spacing. The flange spacing in the absolute, as a sum, is significant, but it's also meaningless without parsing left and right. Right and left flange offsets are from the lateral centerline of the hub to the lateral centerline of the flange. 

Trustworthy others is an internet myth. There are no trustworthy others. Kidding aside, you need to be a critical consumer of information, about hubs, viruses, and everything else. Unlike other so-called "others," we absolutely welcome questioning - you need to be critical of our information just like you need to be with others (just please be courteous, it makes all of this more fun). 

Real world - The place where personal/confirmation/selection biases feel most at home.

Spoke tension variation: every other time I've spoken of spoke tension variation, it has been in context of one spoke's tension relative to its neighbor on that side of the wheel. If you pluck all of the spokes on the right side of the wheel, for example, they should all sound as close to the same note as possible. On a disc wheel, each spoke group (front left, front right, rear left, rear right) will sound different from every other spoke group (the front left and rear right will be fairly similar, as will the front right and rear left). But you want to minimize spoke tension variation within a group. Significant spoke tension variations cause spoke longevity problems (under-tensioned spokes tend to break) and will generally cause an untrue wheel. Better rims allow for more uniform tension, but the wheel builder plays a huge role too.

Tension balance is what Colin meant when he mentioned spoke tension variation. Tension balance is the average tension of spokes on one side versus the average spoke tension on the other side. All else being equal*, the lower the tension imbalance, the better. I worry an awful lot about the lowest tensioned spoke when I build wheels.

Bracing angle is the lateral angle at which the spoke enters the rim (see pic below, the green arrow is right side bracing angle, the red arrow is left side bracing angle). Bracing angle is function of flange spacing and flange diameter, properly referred to as "pitch circle diameter, or PCD" PCD is more accurate than flange spacing since the spoke hole circle's diameter doesn't have a prescribed relationship to flange diameter. Bracing angle is a function of the flange spacing (the wider the flange spacing, the higher the bracing angle) and PCD (the bigger the PCD, the higher the bracing angle).

Bracing angle helps prevents the wheel from flexing laterally (laterally stiff!). Imagine a tall flagpole that you want to keep from swaying too much. If you braced it with something parallel to the direction of the pole (vertically), that something would need to be pretty darn strong to have any effect. But if you tied a piece of dental floss to the top of the pole and anchored that piece of floss so that it was perpendicular to the pole, it would have a huge effect. 

Now I know you're saying "but the floss would only work in one direction, it wouldn't do anything if you pushed against the floss." True, and this is why we don't build wheels using dental floss for spokes. If you used a metal spoke in place of the dental floss, it provide a butt load of support against tension (the pole being pulled away from the spoke) and compression (the pole being pushed toward the spoke). For the purposes of this discussion, we're going to isolate to those two dimensions. 

Ok, we got all that?

Now, I need to address a fallacy here. Many people think that increasing spoke tension increases wheel stiffness. Absolutely false. In fact we tweeted about this like a week ago, totally out of thin air. Once a spoke has any tension at all, it has achieved maximum stiffness. Start mumbling about cross sectional area and Young's modulus and you're all set. But let me repeat this - once a spoke has any tension at all, more tension does nothing to improve stiffness. So what that means is that Colin's so-called "trustworthy others" are not so much.

What a balanced tension ratio does is prevent the "loose side" spokes (non-drive rear and drive-side front disc wheel spokes) from going slack. And to illustrate the benefit there, I will resort to an old illustration. Take a paper clip and straighten it out, then try to break it by stretching it. Not happening. Then bend it back and forth in the middle, and it will break after not that long. That is called cycling fatigue, and when your spokes are too loose they experience this. This is why non-drive side spokes fail so much more often than drive side spokes - you almost never see a broken drive side spoke except when the chain jumps the cassette and mangles the spokes. Spokes don't break from too much tension, they break from not enough tension. Spokes that are too loose go from tension to compression and back again, cycling, as the wheel turns. Balanced tension ratios mitigate this.

Bracing angles, on the other hand, provide lateral stiffness to a wheel. They are the dental floss part of the equation. The higher the bracing angle, the higher the stiffness. But then you have to watch out for tension balance - you can't help one without hurting the other. All hub designs are a compromise. 

I will leave you with the following chart of hubs that we use. We'll refer back to this chart in a future episode, but if I've done a good job today (and you're still awake), this chart will make a whole lot more sense to you now than it would have before you read this post. 

Be well, be distant, and do try to stay sane. 

*all else being equal is an important concept, and is implied throughout