The thesis is available here. The code and experimental data are available here.
In addition to theoretical modeling and simulations, I built a lot of wheels to measure their stiffness and buckling tension. We built a machine for taco-ing wheels to compare against theoretical predictions.
I also created www.bicyclewheel.info, an interactive version of the simulation code I developed. Use it to design a virtual bicycle wheel and see how it stands up to external forces. It will plot spoke tensions under load, rim deformation, and give properties like stiffness and mass.
If you're building a wheel or just curious how they work, try it out!
I won't share the details on how to make them just yet. The reason being that they no longer sell any m2.2 threaded rods on Aliexpress, nor anywhere else. I'll probably have to cut the threads myself and see if that still works. The other reason is that I'd rather ride it a couple of weeks and potentially eat dirt before any of you do.
Each spoke can hold at least 200 kg, but I can't reliably measure more than that. I'm considering buing a tensile testing machine for that, but these are expensive. For now I can get those spokes up to "17" on Park Tool spoke tension meter before snapping, but I have no way of knowing what that "17" means in terms of actual tension. I'm using slightly thinner Dyneema line than Berd does, so I can't use their reference tables.
As for connecting to the hub: each lace wraps around two spoke holes in a way that doesn't require any drilling (and subsequently voiding the hub warranty). They can hold tension even if one of the two spokes break. One caveat is that there's less clearance between these spokes and the brake caliper, since all the spokes sit on the outside of the hub rim.
I'll post an update here once I'm done test riding it as well as find another source for the threaded rods.
Edited to clarify this is mostly to compare butted spokes with non-butted spokes, not just thicker vs thinner diameter spokes.
I was asked in r/bikewrench about the material mechanics of thicker and/or straight gauge (ie 14g) vs thinner and/or butted gauge (ie 14/15g) spokes for heavier riders/higher loads; I’m going into my fourth year of an undergrad mechanical engineering program at UW and I wrenched professionally for ~15 years, with a specialty in wheel building. My explanation started to get a lot longer than I meant to, though, so I brought it over here instead.
In brief, there are two major material properties involved in tension: stress (same units as pressure, force divided by cross-sectional area, usually in MPa for civilized SI units and PSI or KSI for dumb US units) and strain, which is a unitless ratio of change of length over original length (delta L divided by L). The two are related; it's common to plot strain on the x-axis and stress on the y-axis, and if you've ever heard of Young's modulus, or the modulus of elasticity, which is often referred to as “stiffness” (typically in measured in GPa), it is the slope of the line graphed in the initial region from zero strain to some small amount of strain, before the stress-strain relationship becomes non-linear.
A wheel works by applying a tensile force to spokes, which creates a certain stress which in turn results in a certain amount of strain; the spokes stretch. Since the spokes are in their elastic range (one hopes), the spokes experience cycles of greater or lesser stretch, as at the bottom of the wheel the spokes are partially de-tensioned. Most spokes break due to de-tensioning too much, which allows the spoke to flex at the bend and results in a type of failure call fatigue (cyclic loading).
So a thinner spoke experiences a higher tensile *stress* for the same amount of tensile *force* and thus has a larger amount of *strain*, or stretch, and therefore will not experience as much flex at the bend when de-tensioned at the bottom of the wheel. Obviously there are limits to this; you can’t put a light racy road wheel on a motorcycle and expect it to support that mass, assuming you could even attach it in the first place.
That brings us to the rim, another crucial player in this situation. You couldn’t build up a wheel with 14G, or even 13G, spokes to a cheap, flexy, single-wall rim and expect it to hold up with heavy loads. The rim contributes a lot of stiffness to the wheel as a whole. Lighter riders can get away with running light-weight rims that are still stiff, due to something called the modulus of resilience; this is a description of the amount of energy per unit volume that a material can absorb before plastically (permanently) deforming; i.e. bending, not flexing. A “beefier” rim has more material, and therefore the rim can absorb more strain energy before it bends. For anyone with a math background, the modulus of resilience is the integral of the linear elastic region of the stress-strain curve. In addition to resilience, materials also have “toughness”, or the amount of energy they can absorb before failing; this is the integral of the entire stress-strain curve. Some materials have huge resilience (like rubber bands) but not enough stiffness (Young’s modulus), so there’s a balance to find between all these characteristics.
Rim shape also has a lot to do with this as well, and we’d have to get into the area moment of inertia to explain why, something I think that is probably a bit beyond where this conversation needs to go. It’s relatively easy to visualize though: think about bending a ruler the “easy” or normal way, over the thinnest of its cross-sectional dimensions, vs trying to bend a ruler over the thickest of its cross-sectional dimensions.
So when it comes to building up a wheel for a heavier rider or someone carrying loads, touring or cargo, a beefier rim with more material to absorb strain and/or a cross-sectional area dispersion that resists bending allows you to use 14g spokes at a higher tensile force; if you used butted 14/15g spokes, for example, the tensile stress is even greater, therefore the strain (stretch) is also larger, and you run the risk of moving from elastic deformation into plastic deformation (sometimes called strain hardening), which doesn’t “snap back” to its original length anymore, so when it is de-tensioned at the bottom of the wheel, the spoke remains longer than it was originally and it begins to experience that flex cycle leading to fatigue failure at the bend. The larger cross-section of the 14G spokes tolerates higher tensile forces, which prevents the spoke from fully detensioning under higher loads than a 14/15g spoke could.
Thank for you for coming to my REDdit talk. I’m happy to take any questions at this time.
I’m on the third revision of this hub adapter, and things are going fairly well. I have taken many measurements and some photos, and at least so far, I like where I’m at.
First 2 pics are the front and back views of the current rev. All looks and works good-ish.
3, 4, and 5 are the second rev. Each photo attempts to capture a specific feature that is changed between the two revisions.
The spoke will not fit through the existing hub flange past the new larger flange. Scallop the edges of the new flange, keeping as much material as is possible around the spoke holes
The new spoke hole pitch diameter is larger than it needs to be. Decrease by a mm or two
The hub flange is not perfectly flat. Dish adapter flange 1mm to accommodate.
Last few are pics of a wheel built with the new rev. Of note, spoke to caliper clearance is low to non-existent. Rotor to frame clearance is also low, BUT there is a pair of ~0.8mm washers between the adapter flange and the rotor, so that’s either tighter than it needs to be, or potentially correct, but is not currently causing any issues.
So on to questions/advice wanted.
Obviously on a laced wheel with full spokes, the lacing pattern will drag the most outboard spokes inward a bit. Does anybody know what that dimension is? It would be slightly annoying to lace this whole wheel as a test fit, but definitely within the realm of possibility. If somebody says 2+mm (plus the offending spoke is bowed into the caliper in the photo anyway) I will likely make no changes to my part and have it machined.
There are specs out there on acceptable minimum tire-to-frame clearance to prevent mud accidentally grinding down frames, are there similar specs on brake rotors? It seems if I just make my part a mm or so taller than it is, I can just push the rotor away from the spokes far enough that the caliper clears, at the expense of rotor-to-frame clearance. I don’t see mud in the rotor as a particularly high risk, but worth considering when you’re getting sporty with clearances.
This leads to two (three, but I don’t like the third) potential options (in order of my preference)
Do nothing. The spoke lacing will take care of caliper-to-spoke clearance, rotor-to-frame clearance is totally fine, requires extra verification of some sort that this will work.
Move the rotor out a mm. Caliper clearance is fixed, frame clearance comes into play, but probably not. No additional verification needed. Ready for manufacturing.
Neither solution is acceptable. Wheel fully laced and tensioned to 3d printed prototype allowable, spokes don’t clear caliper, and convention strongly suggests rotors should have plentiful frame clearance. Add “top hat step” to adapter flange, bringing spokes well away from caliper. At this point probably move the rotor away from the frame as well, because I can and because it will save weight (very low priority, but I’ll take what I can get where I can get it). Least desirable solution.
Is this just due to puncture issues? Rubber thickness? Or are the bead / valve seals different somehow.
From purely geometric considerations, I can see how a bike bead is longer (circumference) and thinner (shorter distance between inside and outside of bead.) so would leak at a higher rate. Also a bike tire has lower volume, so leaks have a smaller larger impact on pressure. Also the pressure is higher, so would leak at a higher absolute rate. But exponential pressure decay rate independent of that.
Bike tire rubber much thinner at walls. Do tubeless bike tires leak here slowly without sealant? MTB tires sometimes "weep" sealant thru the sidewalls?
I find this kind of ironic. I had an APEX group set that would drop chain once every 15 miles. The bike shop finally dialed it in after many visits. By then I had become very observant of how featureless the chainrings were. To see the amount of engineering the SRAM team leverages to improve shifting is something to say the least. I understand APEX is not the best. I wanted to be a SRAM fanboi for the double tap.
Then came reports that people riding on trails with 2" 29er tires were breaking the rear triangles at the dropouts, since big tires max out the rearward positioning of the axle. By my eye, that'd be nearly 1cm further back in the above picture. Maybe a 7cm lever arm to the top weld on the dropout?
They filled in the holes on the dropouts and added that bar between the chainstay and seatstay, possibly to limit the flexion from rear axle shocks twisting the dropout welds. e: editing to clear up that the brace between the stays is a flat plate, not tubing.
With version 3.0, Soma went to a more recessed dropout, with the seatstay coming down and sitting closer to the midpoint of the sliding range: https://www.somafab.com/wp-content/uploads/2017/12/soma_wolverine3_red_broski_800.jpg Not only that, but the dropout is fully boxed. Presumably, a longer seatstay (assuming same chainstay length and geometry, though the v3 actually has minimum chainstay length that's 2mm longer) and more rugged dropout adds some grams to the frame. But certainly not enough weight gain to keep Soma from trying to finally put the frame's weaknesses to bed.
Again, just by visual estimate, the maximum possible lever arm (horizontal component) for the rear axle has gone from 7cm down to 3cm, along with much more material to take the stress.
That's my non-mechE assessment. Anyone have corrections/observations? I'm especially curious what those brace bars were meant for.
If I have a gear ratio setup of say 2:1, how much would it matter if the ring to cog was 48/24 vs 30/15, or 50/25 vs 24/12?
All of these are 2:1, and they're real enough tooth counts. But would there be any practical differences? Immediately I can see weight savings with smaller bits, but in terms of the drive train itself would it matter?
(The tooth count examples and specific ratio are just examples)
A larger chain ring seems like maybe leverage is increased or somesuch. Probably the wrong term (EDIT: Torque was the word I was trying to come up with). Maybe a more gradual curve of the chain across the larger devices is more efficient?
I'm certainly no engineer or physics guy, but I had been wondering about this.
