zandoval 

The wheel lacing looks discombobulated, but it would appear this is normal for 4X Lacing.

Interesting Thread... But I am confused.

FBinNY 

There's no reason you should be. 4x and 3x patterns are identical in every way but one --- the number of crosses. If you can build a 3x wheel, you can build 4x or any standard pattern by following the same process.

OTOH if there's a specific point confusing you, ask and folks will explain.

zandoval 

OK... Just looked um up, I get it. The more crosses the stronger the wheel (torsion).

The more crosses the better for strength but the angle of the spokes in the picture seams to touch the heads of the other spokes. It just looks strange to me. Maybe its just the way the hub is designed. I have seen 4x on BMX bikes and they don't touch. I have also seen 4x lacing on a few of the touring bikes that come through my area.

Anyway FB, thanks, I get it now...

FBinNY 

Touching the heads is incidental, and doesn't matter EXCEPT, it can be a bit of an annoyance if replacing a broken spoke in the field.

Whether it happens or not depends on the flange size and number of holes. On this hub, the curvature is such that the next hole doesn't move out of the adjacent spokes line. You may not see this with BMX, either because of more spokes or a smaller flange.

Duragrouch

Regarding reasons for 4X lacing (someone above didn't see value):

- Having the spokes closer to meeting the hub flange tangentially, puts less stress on the hub; The exact opposite is radial spoking, where all the spokes pull outward, and on early hubs not designed for that, you could get cracks between adjacent spoke holes on the hub flange (destroying the hub and possibly causing a mishap while riding). However, there is way less difference in this, between 4X and 3X, versus comparing to radial or 1X.

- Tangential spoking on a large-flange hub, made for longer spokes, so more elastic for the same gauge, and this improved the ride quality of the wheel, and made the spokes more a bit more resilient to breakage from peak overloads. This difference in spoke length as a result of X number, is much less on a small-flange hub. And, small flange hubs, running 3X or 4X, the spoke angle at the rim, is closer to optimum of 90 degrees (given that most rims are not "aimed and drilled" to compensate for error there).

FBinNY 

As someone whose been building and teaching about wheels for half a century, I can honestly and politely say that all that followed is BS. To be clear, none of it was technically wrong. It's just that the real world differences are too small to matter.

First of all, the length difference is a few mm out of near 300, so roughly 0.3%. Similar comparisons can be made with all the rest. Based on experience, the biggest difference is with bracing angle, but to get amy benefit you'd need to build dished rear wheels with radial spokes on the right side, which few ever would consider.

Some of this MIGHT have been meaningful BITD when we were using much lighter spokes with much lighter rims. However wheels today have massive deadloads compared to what we generate when riding, rendering the debate moot, except for an excuse to argue about over beers.

sd5782 

Would not a benefit be the use and convenience of using the same spoke length too?

Duragrouch

Good points. Makes sense, at least with regard to spoke length difference. I just remember the very first wheels I ever built up (maybe 50 years ago, I was assembling salvaged parts into my first good bike), I bought new spokes at the LBS, and they recommended 4X pattern, saying it would "ride nice". I didn't even have a guide, so ended up assembling it with the spokes crossing over the valve hole, but there was still tons of room for the pump head.

I think what I said about flange stress between 3X or 4X and radial spoking, is still valid, even though modern hubs are designed for radial, I still don't like it, it's inherently less robust, and like you said, marginal difference in spoke length for any weight savings.

FBinNY 

Yes, and I touched on that earlier.

BITD, I could use the same spoke for 90% or of my builds. These days, despite keeping well over 20 different spokes on hand, I still end up without one I need. Plus I have a large stock of odd-size leftovers that I'll never use.

Duragrouch

See I wondered about that. Someone above said that any wheel that could be done 3X could be done 4X (or perhaps the reverse?) and I immediately wondered about 32h, but wasn't certain. All my large wheel bikes have factory 3X wheels. (I've only been riding 20" wheels for the past ten years, and most are 28h or 20h 2X, except for one front that is radial, which I will respoke to 2X if comes into regular use.)

FBinNY 

Any is a big word, so needs qualification, as in any wheel 36h or greater.

It's simple geometry. 4x 36h is full tangent. Likewise, 3x28, 2x24, and 1x12. You could do 4x32, but the spokes would leave the hole on a secant, passing inward before going out to the rim. It's possible, but annoying and pointless.

Duragrouch

Thank you for that. Even with my geometry superpowers, the above explanation did not occur to me. I can easily visualize this. But it's not obvious if there is an easy way to determine the above numerically, versus doing math on the full geometry. Full tangent spoke (let's say a leading spoke), means the opposing spoke (so the trailing spoke, on the same side), also tangent, is parallel to the first spoke... that means the distance between those spokes at the rim, must be equal or greater than the diameter across spoke holes at the hub. 36h means rim holes are 10 degrees apart... so 20 degrees between those two rim spoke holes... no, I think doesn't matter, but rather the *distance* between those holes, versus the diameter at the hub holes, so the spokes are parallel, or get wider apart at the rim... the rim holes cannot be too close together or that is not the case... I'm seeing the geometry, just can't yet figure if there's an easy numerical relationship, like 36/4=9, but no, that won't work if, for example, the hub is very large diameter in relation to the rim, then 4X won't work on 36h, because like you said, secant (what I'll call "overtangent" ) So I think it's all about, take the diameter of the hub spoke holes, assume tangent, parallel leading/trailing spoke pairs, determine the distance between those at the rim (about half that distance is the space between adjacent rim holes, close, is actually the cosine of a low angle with the rim), and based on that, figure out how many spoke holes you have room for. OK, that distance at the rim is about the hub hole radius. Looking up... typical shimano hub rear 36h shows 45mm, so 22.5mm radius, so... also long as 22.5mm x (hole number) is *smaller* than the actual rim *circumference*, should be good to go. Let's see... My 406 wheels, about 390mm inside diameter, so 390 x pi = 1225mm circumference. 22.5 x 36 = 810, so far so good. (Wheels are actually 28 hole, I have seen 36 hole 406s, but I think they were 3X, I think 4X might have spokes over adjacent (first cross) spoke heads.) Now let's go way down, like 305, so assuming same 8mm depth on each side for a diameter of 305-16=289. 289 x pi = 908 circumference. That 810 number is awful close, given that 22.5 is an underestimate of the actual circumference distance. Let's say 100mm hub hole diameter so 50mm radius, on the 406 rims: 50x36=1800, that's way over the 1225 estimated circumfirence, so no way for 36h 4X pure tangential. So yeah, for ability for tangential spoking, it's about the relationship between the hub spoke hole radius and the distance between rim spoke holes. It's not just about number of crosses versus number of holes. (The above took me at least a half hour to think out, maybe an hour.) But the practical result is exactly what you said. I was just trying to figure it out or prove it numerically. Brain tired.

Bill Kapaun

Max crosses= INT(N/9) where N = number of spokes. (Max might not be "best")
Large flanges can reduce that.

Duragrouch

See, that's what I was looking for! I noticed that N/crosses was always 9 or more if deemed possible. I just couldn't see the significance of 9.

I think large flanges may make things worse. There is more space for spoke heads, but it may become "overtangent", spokes tapering smaller than parallel toward the rim. (Oh, I think now you don't mean "reduce" difficulty, but reduce in possibility.) Yes, relationship between rim diameter and hub hole diameter matters a lot, the closer in size, the more that 4X and 3X become impossible, sometimes even 2X.

Trakhak

As far back as the mid-'70's, I occasionally built and rode rear wheels with odd patterns, for my own amusement, such as a 36-spoke wheel with a cross-radial-radial-cross pattern on the non-drive side and radial on the drive side. Held up and rode fine, of course. Years later, a young guy I'd taught to build wheels miscalculated the spoke lengths for the first set of wheels he built for himself, but built them anyway: radial front, radial both sides in the rear. Held up and rode fine.

Which makes sense. After all, the earliest racing ordinary/penny farthing bikes had all-radial spoking. As I understand it, crossing and lacing spokes came to be a common practice solely to minimize damage from the flapping around of broken spokes, a common occurrence with the weak steel spokes used in those wheels.

One pattern I never had the nerve to try was one that a young engineering student I used to ride with theorized would work fine: a non-radial build with no crosses, with all of the leading spokes on one flange and all of the trailing spokes on the other. Tough on the middle of the hub, if nothing else.

Duragrouch

Danger Will Robinson. From Sheldon Brown and John Allen:

Cross-radial-cross pattern, there's a name for that... crow's foot? EDIT: Verified on Sheldon Brown.

Penny farthings, if radial spoked, may have had spokes that were so long, they elasticly stretched to a semi-tangential position under drive torque, which limits the mechanical advantage, then flex back to radial when stopped, and that works, mechanically. But if spokes much shorter stay mostly radial, when just off center under torque, there's a huge mechanical advantage pulling on the rim.

FBinNY 

There is (was?) a guy in San Diego that built odd wheels for fancy showpiece bikes. He did one of those, and AFAIK it held up fine.

I never built one, the cclosest being rear wheel for a sprinter who swore he could feel wheel windup and wanted some magic.

So, I built a pattern of two spokes left, then one right, repeated on both flanges. He was thrilled and swore it was the first adequately stiff wheel he ever had. I always chalked it up to placebo effect, but was smart enough to keep that to myself.

Anyway, despite the protestations of John Allen and other experts, plenty of us built radial rears, which defied them by holding up fine. The front wheel on ny track bike is radial (to prove a point) on an extremely light vintage (in 1969) hub by a maker with my initials. Still fine.
‐‐‐-----
For anyone with the patience here's one of my favorite wheel stories from BITD.

Within our small circle of serious builders was Marty Mogalin. To set the stage, Marty was one of those Damon Runyon characters who inhabited Greenwich Village back then. A bigger than life Irishman, that could have been in the movies. Part overgrown leprechaun, part conman, all pure Irish charm. Marty could pick someone's pocket, leave, come back 10 minutes making a show of trying to find the owner of a wallet, and be all "no you dont have to" as he accepted the reward.

OK, someone commissioned him to build a pair of wheels, insisting on providing the spokes (something we all hated). Never one to turn down a buck Marty takes the job anyway. I come into the story as Marty is hanging out waiting for his client.

So, the wheels had "half twist" spoking. Meaning they twist a half turn at the cross and continue to thd rim. Ie. a pulling spoke would become a pushing spoke at the rim.

Me, "what gives?"
Marty winking, "I hate #$&%$s who insist on giving me the parts, and anyway they were way too long".

I understood immediately, Marty needed the cash and didn't want to wait. I watch him deliver them with a couple of tons of Blarney, his client left happy.

I saw them still in use over a year later.

The moral --- it's all BS to an extent, and ANY pattern is workable if executed well. That said, the plain vanilla cross spoked wheel is unbeaten for proven reliability.

Duragrouch

Well, I believe ya, and you sound quite experienced, most especially with wheelbuilding. I'd be curious how much the stress changed in the spokes under hard acceleration, versus a cross wheel. I'm thinking there has to be a big change, which equals increased fatigue, but maybe that increase is small compared to the static wheel tension.

FBinNY 

There's a slightly sad element. As I said the hub was a vintage collectible, but I'm not a collector.

Back then I taught wheelbuilding courses. Naturally there would be questions about radial spokes, so I'd use that wheel to make a point. To demonstrate how strong radial bracing is, I put the wheel on the floor, stood my 175#s on it and used it like a teeter-totter.The last time I did that, I got a bit cocky, and did a small jump. Ended up bending one flange. 55 years later, I'm still riding it on the track bike, but no more demos.

Duragrouch

Oh, radial spoking is plenty strong, staticly. My usual statement about it is, the crossed spoke that has lateral pressure on the bottom spoke, helps maintain the tension on the bottom spoke, so less likely to unload and loosen the nipple over time, and the variation in the tension is less, improving fatigue life. (I had thought long ago, why not lace the spokes so them pressing against each other is eliminated (on the same side and flange, inside stays inside, outside stays outside), but now know, that force against each other is intentional.) But without a torque at the hub, on a radial spoked wheel, the "top" spokes in tension at any given time, are not stressed more than with crossed spokes.

Radial spoking makes for an easier and faster wheel build. The high production makers would sell their mother for a nickel. If they could get away with radial for drive side, and for discs, they'd do it. Most especially for small wheels, as radial would reduce the spoke angle at the rim.

Trakhak

I don't think I ever built a crow's-foot-patterned patterned wheel per se - those don't have paired radial spokes such as mine did. Did a Star of David pattern once (some guy pointed out that that's what it looked like). Here are a few other examples of unusual spoke patterns.

The quote from Sheldon Brown and John Allen didn't reproduce when I quoted your post, but: their objections to the use of radial spoking pertain to the likely longevity of the wheel, not to whether such a wheel could be ridden safely. John Allen's "guitar string" report suggests to me that the rear wheel in question not only used radial spoking but also had very few spokes (and possibly was undertensioned). The guy I knew who built his wheelset that was radial throughout used those wheels for at least a couple of months that I know of. May have rebuilt them after that, as I recommended. Those wheels had 36 spokes.

Think about it. People have built plenty of rear wheels with not just 4-cross and 3-cross patterns, but also 2-cross and 1-cross. Going from 1-cross to 0-cross does not equal magically entering the Twilight Zone (a.k.a. entering the Scary Door, for Futurama fans). From an engineering standpoint, given adequate components and an adequate spoke count, 0-cross rear wheels are not significantly different structurally from wheels with crossed-spoke patterns.

(Truncated quote from a quick search for "motorcycle radial spoking": "So a friend of mine has 100 spoke radial lacing for his wheels and has never had an issue with feeling like they . . . ")

About the penny farthings and the idea that the spokes wound up significantly when pedaling force was applied - again, I think you're underestimating the contribution to wheel strength the use of upwards of 72 spokes makes. And fair enough - it's difficult to grasp that such a wheel becomes what is effectively a rigid structure.

Some of the older posters here will undoubtedly remember going to bike trade shows in the early '80's and visiting the Hi-E Engineering booth, where Harlan Meyer's latest wild designs would be on display to marvel at. One year he had a pair of all-aluminum wheels with, depending on how you want to count them, either 32 or 64 aluminum spokes.

Mr. Meyer had apparently been determined to use aluminum spokes (to reduce the wheel weight to a theoretical minimum) along with his featherweight aluminum hubs and rims (the lightest version, with aluminum reinforcement plates riveted in place at each spoke hole in the rim).

To get around the obvious problem, i.e., that aluminum spokes would inevitably break at the elbow before the spokes got anywhere near full tension when the wheel was being built, he simply produced double-length spokes, threaded at both ends, with a kind of Ashtabula-crank-like S-bend in the middle. So 32 spokes that functioned as 64 spokes.

Finally, if you still doubt that early penny farthings used radial spoking: here's a picture of a guy who was likely a champion racer on a high-wheeler with radially spoked wheels:

Trakhak

Quick notes:

Campagnolo has offered wheels with a bunch of different spoke patterns over the years, including rear wheels with radial drive side/2-cross non-drive side. They and many other high-end companies have sold radially spoked front wheels. So not a budget move.

As I mentioned in an earlier post, the practice of crossing and lacing was invented for one reason: to keep broken spokes in high-wheelers from dangerously flailing outward. Plenty of low-end bike wheels, from kid's bike wheels to wheels for heavy-duty factory-use bikes, are built without lacing. And as far as I know, no motorcycle wheels are built with lacing. It's possible that lacing adds a tiny bit of structural integrity to bike wheels, but if so, it's merely a happy accident.

And I'm skeptical about the significance of the effect, just as I reserve judgment on the claim that the wood used to build a solid-body electric guitar makes a material difference to the guitar's tone. (That's a never-to-be-resolved topic that rages on guitar forums.)


(Edit: the forces involved in wheels are far from obvious - see the head-spinning calculations that Jobst Brandt provided in his book The Bicycle Wheel, published back in the 1970s - so I imagine that discussion of this topic tangent will continue here for a while. Have fun!)

By the way, if anyone is interested: I did a search, and apparently "spiral" spoking patterns (clockwise on one side, counterclockwise on the other) are pretty common in the "ratrod" bike community and are used on both rear and front wheels.

Duragrouch

(above) Zero-cross, does not necessarily mean zero-angle. Many bikes with very large diameter hub motors use 0X by necessity, but the spokes are not radial, but are angled. Same with motorcycle hubs, where hubs and rims are much closer in size, that typical bike hubs versus rims. It is not the cross per se that allows transmission of torque from the hub to the wheel, but the spoke angle other than pure radial.

Trakhak

So they're pulling spokes on one side and trailing spokes on the other? Interesting. I was only aware of that spiral spoking being used for show-off wheel builds.

Still, there are zero-cross, zero-angle rear wheels out there, presumably used in applications where the strength of the build might have been inadequate for bikes with motors and/or disc brakes.

Dan Burkhart 

I build large flange hubs often enough. Large flange hub motors often have the spoke holes paired so they can be laced into small rims zero cross yet still have torsional bracing.
One of my recent projects was a severe duty wheel for a 5 passenger bike that kept destroying rear wheels.
I finally built a 36 hole wheel with the Nexus hub and 12 gauge spokes. Holding up so far but the client wanted a spare wheel and wanted it way overbuilt. So I started with a 48 hole Velocity Cliffhanger rim, (26”) and we had adapter flanges made to adapt the 36 hole hub to 48.
The client is a professor at one of the country’s premier engineering schools, so he had the flanges made by the faculty machine shop.
This resulted in 120mm spoke hole circle which definitely limits the number of crosses.
With an ordinary size hub, 5 cross is doable for 48 hole, but in this case, even 2 cross was crowding it a bit. The photo shows it over tangent with 2 cross but the spokes enter the nipples without bending so it worked out.
Oh yeah, in keeping with the overbuilt theme, the spokes are 13g.