I have Bontrager TLR wheels, which I can't really find specific information about online, but appear to be a cheaper version of the Bontrager Race TLR, which is the cheapest road wheel you can actually buy from Trek. (My assumption is the wheels I have are a part they throw onto lower end bikes to keep costs down).

I am developing a curiosity for wheel building so I wanted ask, if the spokes cross anywhere, even directly next to the hub with little or no visible light in the triangle that is formed, that counts as a cross, right? So in the case of my 24 spoke rear wheel where it crosses immediately after that, it would be a 2 cross wheel? Is it typical for a 24 spoke 2 cross wheel to have one of the crosses so close to the hub?

I have found lots of information online about 32 hole wheels, but in the interest of education, can anyone point me to a source for getting more details about 24 hole wheels like the ones I have?

You can build a 24 to be 0, 1, or 2 cross. At 3 cross, the exit angle from the hub flange is below tangent (360/12 = 30 deg per hole, 3 holes = 90 deg) and the first cross will interfere with the adjacent spoke head.

Play around here Spoke length calculator for wheel building

Yes, the cross immediately at the hub counts. There's always one that close or closer because you have the two spokes in adjacent holes going past each other.

In fact, with more crosses, that first cross may be hidden by the flange, and easily missed.

And yet, I've been encountering 24 spoke OE wheels laced 3 cross. They are lower end A Class wheels, which I think are from the same company as Alex rims.
Dunno why they do it, but they do.

Maybe an overstock of a certain spoke length?
Spoke overlap is only an issue if/when a spoke has to be replaced.
Which may never happen.

If you need to visualise it then... 24, 0 cross, 1 cross, 2 cross and 3 cross. 2 cross the triangle is, as you surmise, hidden by the flange. 3 cross, as Darth Lefty suggests, fouls the adjacent spoke head.

..

build 36 hole, 4 cross, and 48 hole 5 cross *, my bike friday tikit built their rear wheel 24 spoke rim 36 spoke hub.

large flange, IGH, it's 2 cross . but a 349 (16") rim not 622/(700c)

* my road bike has a Campg Hi-Low 36 spoke rear hub... in the 70s, I built is 4X to the NDS low flange, 3X to the DS High flange ..
its still good.




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Thank you! The visualizations are very helpful. What program do you use to do this?

I'm tempted to think someone read that "3-cross is strongest" online or in a book, and never stopped to think about what the real goal was.

I wrote my own. It is not yet complete and comes with Quirks. It uses Free Pascal and Lazarus. Compiles and works under Linux. Lazarus is supposedly cross platform but it will probably fall over under Windows. Let me know if you want to try it.

Tangent spoke patterns like 4 cross in a 36 hole hub are the very least likely to have the spoke shear forces, pull,
and tear out the metal between the hole in the hub flange and the edge.

Thanks for the offer, and I would love to, but I think I need to learn more about wheels in general for it to mean anything to me.

Good choice. I often do my head in trying to think about how they work given the spokes are under tension and, as a result, rely on the rim and perhaps other spokes to transmit forces elsewhere. I guess someone did a 'what if?' and it worked.

https://en.wikipedia.org/wiki/Wire_wheel

YMMV. However if you are prepared to Ride over Heads you might wish to go 5 cross and gain even more metal before you start hitting same side spokes... 3, 4, 5.

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5 cross on 48 spoke medium flange Phil rear worked fine.

Excellent. You have more experience of medium flanging a Phil than myself. I am a bit lost as to how this might relate to a 4 cross 36 hole situation. However good to know it worked out for you.

With fewer spokes the holes are further apart so the spoke angle at the hub will be smaller and in turn the crosses closer to the hub flange.

in both 4x 36 and 5x 48
the 1st cross is passing the spoke in the opposite side of the hub flange and going to the rim hole on the opposite side,

so the forces between them is compression rather than shear,

which is true , at its maximum with a radially spoked wheel.