How the Bicycle Wheel Carries its Load: Held Up by Downward Pull (1980)(johnforester.com)
johnforester.com
How the Bicycle Wheel Carries its Load: Held Up by Downward Pull (1980)
http://johnforester.com/Articles/BicycleEng/Wheel.htm
5 comments
Did you find any interesting dependency on the geometrical characteristics of the rim? When I was in grad school doing my masters, I wound up spending a few weeks playing with wheels using my FEA stuff. I found that the torsional and lateral stability of the rim are very important when you start going to road racing wheels with fewer spokes. (Especially as you raise the tension to get better durability)
Also, how did you do the FEA models? Did you wind up meshing all the parts, or did you use higher order beam elements for the spokes and rim bits?
Also, how did you do the FEA models? Did you wind up meshing all the parts, or did you use higher order beam elements for the spokes and rim bits?
Since the algorithm needs to evaluate hundreds of thousands of wheels, it's not a full-blown FEA model, as that would have taken far too long. It's written in a real-time physics library called Bullet, and the rim can at most be modeled as a few, infinitely stiff segments.
I'd bet with a good model generation, the FEA on this is completely tractable in realtime now. It's only ~2(spokes)*6 dof, and that was doable in a second or so on a sparc in matlab 20 years ago. But to do that, you'd need to be doing beam elements for the spokes and rim segments, not meshing them with smaller solid elements. (And unless you're in non-linear land in material or geometry, a 2 node beam element with 6 dof /node is going to be an exact solution for the spokes, and a good approximate solution for the rim as long as the chord/arc error isn't large. ) And I've found some of the code, and holy crap it's still on the web. http://www.ce.washington.edu/~soroos/matlab/501/1../wheel2.h... (I'm sure I'm going to hate the 19yr ago me when I dig into that and try to figure out what the hell I was doing based on the comments, because I only remember the outlines of the math at this point. But... I could put this in numpy... I need this like I need another project to suck up my time... And I'm not sure what the me of 2034 is going to think of my code now. But that's another story.)
The real trick with wheels from experience as a wheel builder is that all the really interesting behavior is in the non-linear region. And you're butting right up against that when you lace the wheels tightly. Calculating that limit is tricky.
(Briefly, Ultimate load limit is ~ the sum of the tension in the spokes in the loaded zone of the wheel, roughly 4 or so with the rims/spokes I was looking at at the time. The tension limit is just under what will potato chip buckle the rim. So there's a complex interaction between spoke stiffness, rim lateral stiffness, and rim radial stiffness that affects performance at the load limit. Helpfully, fatigue durability is also better with higher tension in the spokes, since the fatigue performance goes to hell when you get stress reversals.)
FWIW, My masters was investigating back calculating material parameters from a dynamic pavement test based on time histories of surface loading and displacement at known locations. I basically figured out that the error measure that we were using was pretty smooth as the stiffness of the subsurface layers varied and that it was possible to home in on a stiffness profile pretty consistently if there was at least a plausible guess of what was under there. It took a long time then though, overnight runs were common, and we didn't have clusters then. (also, uphill both ways, through the snow) I bet I could do it in near realtime now on my ipad, but that's a masters thesis for someone else.
The real trick with wheels from experience as a wheel builder is that all the really interesting behavior is in the non-linear region. And you're butting right up against that when you lace the wheels tightly. Calculating that limit is tricky.
(Briefly, Ultimate load limit is ~ the sum of the tension in the spokes in the loaded zone of the wheel, roughly 4 or so with the rims/spokes I was looking at at the time. The tension limit is just under what will potato chip buckle the rim. So there's a complex interaction between spoke stiffness, rim lateral stiffness, and rim radial stiffness that affects performance at the load limit. Helpfully, fatigue durability is also better with higher tension in the spokes, since the fatigue performance goes to hell when you get stress reversals.)
FWIW, My masters was investigating back calculating material parameters from a dynamic pavement test based on time histories of surface loading and displacement at known locations. I basically figured out that the error measure that we were using was pretty smooth as the stiffness of the subsurface layers varied and that it was possible to home in on a stiffness profile pretty consistently if there was at least a plausible guess of what was under there. It took a long time then though, overnight runs were common, and we didn't have clusters then. (also, uphill both ways, through the snow) I bet I could do it in near realtime now on my ipad, but that's a masters thesis for someone else.
I notice you found the regular lacings. Did you explore more fancy designs such as Crow's feet?
I tried with an unbiased representation, and then it found all kinds of stuff, mostly bad patterns. The ones in the video are the non-dominated solutions found, and no crow foot there. It did find it, or something similar, on many of the runs. But it was dominated by other solutions. Of course, this may be an artifact of my simulation.
What about the POWerwheel lacing pattern? Remove some of those retarding spokes for extreme power gains! It may have dominated the other solutions so hard your computer tossed it out as an outlier and was too ashamed to report the error.
Riders of the POWerwheel lacing pattern go so fast it's usually impossible to discern the lacing pattern from the wreckage they leave behind. To compound the problem most POWerwheel accidents are covered up as "space" attacking us with "meteors".
http://sheldonbrown.com/power-wheel.html
Riders of the POWerwheel lacing pattern go so fast it's usually impossible to discern the lacing pattern from the wreckage they leave behind. To compound the problem most POWerwheel accidents are covered up as "space" attacking us with "meteors".
http://sheldonbrown.com/power-wheel.html
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I tried running a POWerwheel-laced wheel for a while, but the problem was that the wheel eventually shot off ahead of the rest of the bike. When i got a new one, i stuck to the conventional pattern.
That wheel is probably still going, out there, somewhere.
That wheel is probably still going, out there, somewhere.
FWIW, if you're interested in this subject, the best reference is Jobst Brandt's "The Bicycle Wheel". It's been out for 30 years or so, but it's still the best reference.
Past that, you might want to look at Timeshenko and Geere's "Theory of Elastic Stability", but you'd need a good university library for that one.
Past that, you might want to look at Timeshenko and Geere's "Theory of Elastic Stability", but you'd need a good university library for that one.
I'm a qualified wheel builder. It's not that difficult, just takes up to a couple of hours per wheel. Of course, they are mostly laced by machine nowadays.
Building your own is good fun, plus you can do specials with fancy lacing or unusual hubs (such as hub based dynamos)
Building your own is good fun, plus you can do specials with fancy lacing or unusual hubs (such as hub based dynamos)
It's not that difficult, just takes up to a couple of hours per wheel
Once you know how to do it properly that is. The key to that is mentioned in the article: applying tension while building the wheel. Lots of it, in my (borrowed) experience.
The first couple of wheels I built was before I had internet access and I just copied the lacing pattern from an existing wheel, then tightened and trued the wheel. It were the worst wheels I ever had and impossible to keep true (though I was riding trials back then which does require more from wheels).
Then one day I found http://sheldonbrown.com/wheelbuild.html and would basically put all sorts of tension on wheels while building them. Lean on them, hammer the spokes, pull them together, smash the wheel against the wall and so on. This, together whith experience gained from many iterations, yields wheels which do not make the slightest sound when ridden for the first time and stay true even under heavy circumstances (I ride street/dirt on a 24" bmx now). As another comment mentions: wheelbuilding is definitely some sort of an art.
Once you know how to do it properly that is. The key to that is mentioned in the article: applying tension while building the wheel. Lots of it, in my (borrowed) experience.
The first couple of wheels I built was before I had internet access and I just copied the lacing pattern from an existing wheel, then tightened and trued the wheel. It were the worst wheels I ever had and impossible to keep true (though I was riding trials back then which does require more from wheels).
Then one day I found http://sheldonbrown.com/wheelbuild.html and would basically put all sorts of tension on wheels while building them. Lean on them, hammer the spokes, pull them together, smash the wheel against the wall and so on. This, together whith experience gained from many iterations, yields wheels which do not make the slightest sound when ridden for the first time and stay true even under heavy circumstances (I ride street/dirt on a 24" bmx now). As another comment mentions: wheelbuilding is definitely some sort of an art.
Counter-position:
I've built lots of wheels, and raced on them (off road -- Canada Cup, NORBA, World Cup) and I have built wheels loading them up w/ stress (standing on them) based on conversations w/ other people, trading stories, etc., but after reading Jobst Brandts "The Bicycle Wheel" I chalk up those practices more to "voodoo" than science. Mind that the spoke will twist when you're tightening the nipple. Tighten evenly. Tighten in small increments. Tighten tight. Then relieve the twist in the spokes.
The "pings" and noises you hear from a wheel are the twisted spokes snapping back into a position they really want to be in. They're twisted because the builder didn't relieve that twist as a finishing touch on the build.
I have a 26" Mavic 517 laced to a Paul Components WORD hub with Wheelsmith Competition 14/15g spokes that I raced from ~1995 - 2005, and I still have it. True as the day I built it, and not adjusted after the build.
Edit: add spoke specs.
I've built lots of wheels, and raced on them (off road -- Canada Cup, NORBA, World Cup) and I have built wheels loading them up w/ stress (standing on them) based on conversations w/ other people, trading stories, etc., but after reading Jobst Brandts "The Bicycle Wheel" I chalk up those practices more to "voodoo" than science. Mind that the spoke will twist when you're tightening the nipple. Tighten evenly. Tighten in small increments. Tighten tight. Then relieve the twist in the spokes.
The "pings" and noises you hear from a wheel are the twisted spokes snapping back into a position they really want to be in. They're twisted because the builder didn't relieve that twist as a finishing touch on the build.
I have a 26" Mavic 517 laced to a Paul Components WORD hub with Wheelsmith Competition 14/15g spokes that I raced from ~1995 - 2005, and I still have it. True as the day I built it, and not adjusted after the build.
Edit: add spoke specs.
Hmm, fair point actually. To be honest in all wheels I built after reading Sheldon's article I applied everything ('loading' the wheel, proper tension, relieving twist - I now notice I did't even properly describe that in my original comment) at once. And then assumed rather blindly all of the techniques mattered. After all, I did finally have nice wheels. But now I realize, due to lack of evidence it might just as well be those wheels are all ok due to just one or two of those factors while others are in fact voodoo or don't do much at all. Thanks for bringing attention to that. And I'll definitely get a copy of that book.
to be clear -- leaning on the wheel and forcing the "pings" to happen by stressing has the effect of putting the spokes where they want to be, but I think mostly people don't know why, so it's basically cargo-cult building. The alternative is realize what's going on (ahh! Torsional stress!), fix it (take your spoke wrench, back off spokes a fraction of a turn) and get them setup, knowing exactly what's going on, and not resorting to cargo-cult methods.
I don't do any of those things.
I just progressively and evenly tighten up the nipples and then true the wheel on the stand.
I just progressively and evenly tighten up the nipples and then true the wheel on the stand.
I wonder if some of those rituals have been rendered obsolete by improvements to the quality of components and materials.
I've been building my own wheels, since I started messing around with internal-gear hubs before they became fashionable. Today I follow the method as you describe -- aim for consistent high tension first, and then true it up. The gradual improvement of my technique seems to manifest itself, not so much in the truth of the wheels, but in greatly reduced spoke breakage.
I've been building my own wheels, since I started messing around with internal-gear hubs before they became fashionable. Today I follow the method as you describe -- aim for consistent high tension first, and then true it up. The gradual improvement of my technique seems to manifest itself, not so much in the truth of the wheels, but in greatly reduced spoke breakage.
Right. This is similar to how bolted connections work. Bolted connections must be tight enough that, when loaded with a force pulling the bolted connection apart, the bolted surfaces still have pressure pushing them together. Wikipedia has a good explanation of this.
Yes, and bearings too. For a bearing that will work under heavy load, the balls have to be "pre loaded," meaning that they are actually deformed just a bit, so they don't lose contact with the bearing races.
All of these things are examples of structures held together by springs.
All of these things are examples of structures held together by springs.
I wish that article had a few more diagrams to explain the concept.
Nice read though.
Nice read though.
Just recently I made a crude simulation to compare Radial and cross lacing for wheels. http://gfycat.com/ThreadbareEdibleCormorant.
I did it in response to this reddit post. https://www.reddit.com/r/bicycling/comments/3cxk4v/just_made...
I did it in response to this reddit post. https://www.reddit.com/r/bicycling/comments/3cxk4v/just_made...
And damn, "truing" a wheel to make the wheel round, not wobble and have equal forces on the spokes is an art. Even done iteratively with small changes one often end up making some part of the wheel worse when fixing one part.
[1]: http://master.matsemann.com/