Heavier section for 29er wheels?

[dgillette]

Greetings, engineers on bikes and cyclists doing engineering.

My neighbor, a rather large strong guy who is hard on bikes, recently got a 29er and almost immediately tacoed the front wheel. In theory at least, the bending moments could be larger in a 29" wheel than in a 26" wheel, but it did not appear to us that his wheel or the other 29" wheels we saw had a higher section modulus than the 26" wheels. Is this a common issue, and are the mfrs using stouter sections in response?

Thanks,
DRG

 

[tnkayaker]

With the mtb industry moving toward 29ers I'd think that the rim mfgr would be optimizing the x-sections of 29er's for the higher moments that can be applied. Stan's website says their 29er rim has been optimized using FEA.

http://www.notubes.com/rim_builder.php/cPath/680

 

[drawoh]

dgillette,

When I bought my new road bike a few years ago, I put skinny racing tires on it. Then I put new, skinny racing tires on it. Then I put more new, skinny, racing tires on it. The store finally pointed out that I am too big to ride on small tires. I am using 28mm tires at the moment, and they work fine.

Tnkayaker's comment about optimizing with FEA makes me nervous. FEA is nowhere near infallible. Minimum weight design involves all sorts of compromises with cost and strength.

We big guys need to put weight reduction into perspective. I figure my bicycle and I weigh around 240lb. If I spend another thousand dollars, my bike and I can weigh 235lb!

Are you sure it is not just a faulty wheel?

JHG

 

[dgillette]

Thanks, tnkayaker and drawoh. Nice avatar or whatever you call that blinking bug-eyed monster space alien thing.

Well, I don't know about the faulty wheel - I'll ask Stu if he saw any evidence thereof. He is heavier than you are, drawoh, weighing over 240 with no help from the bike (he's not fat, but he's 6'4" tall and not skinny), and he rides on trails I have a hard time walking on. If anybody is going to bust things, it's him.

The web page tnkayaker linked to shows the same section for both wheel sizes. Also, the lower "sidewalls" would tend to reduce the moment of inertia relative to a wheel that is otherwise the same. The arch shape might be a real advantage in reducing weight, if the force is resisted primarily by the arch in compression and not a conventional shape in bending. A 2-d FEA analysis might support that, but it would probably take a 3-d analysis to get the whole picture including bending.

Speaking of which, where is the maximum bending moment in the wheel? If the rider's weight is transferred to the wheel by the spokes on top in tension, it would be like a hoop loaded by almost-point loads top and bottom, which would make the maximum bending moment occur at the mid height, although where they are horizontal, the spokes would also be in tension, reducing the bending moment. Off hand, it would seem that shifts the location of maximum bending down below the mid height. Does anybody do ever these analyses?

(I've never ridden a 29er. I'm not a mountain biker, primarily just a bike commuter who sometimes goes for a ride in the country. Besides, I probably couldn't find a 29er that would fit my short legs. Some tall guys love them for the better fit. I was in a bike shop when a guy about 6'6" came back from a test ride whoopin' with delight and just about falling over himself trying to get his credit card out as fast as possible.)

DRG

 

[drawoh]

dgillette,

The loads on the rim are nicely distributed around the top, and there is a point load at the bottom.

On my bike, I had to replace all the spokes on my rear wheel. I never did figure why my spokes kept breaking. They have stopped breaking now. Perhaps bad stringing of the wheel causes problems.

Your friend can reduce damage to his rims by losing weight, riding more gently, and using fatter tires. I do not know how much of this is acceptable to him.

How well does his suspension work? If his suspension, perhaps optimised for a 150lb rider, bottomed out, his rims would sustain the entire impact load of his weight.

I am not a mountain biker and I do not know what hardware is available. Look at his shocks and springs. Get stiffer springs and/or longer shocks.

You can do the math on this. Your buddy is three feet in the air.

Potential Energy = 240lb x 3ft = 720ft.lb.

The bike decelerates to a halt in 0.2ft.

Strain Energy = 720ft.lb

Impact Force = 720ft.lb / 0.2ft = 3600lb force on the rim, and on the pedals -- hopefully not on the bike seat.

Play with the numbers.

JHG

 

[dgillette]

I suspect the deceleration distance is A LOT more than 0.2 feet, considering the travel in the suspension, the 'give' in the tires, and especially the 'give' in his legs, as long as he doesn't have his knees locked. As much $ as he puts into his bikes, I would bet the bike is set up for someone his size, to the extent that can be done. It didn't come from Walmart. Still, could probably get pretty large forces, and he's broken components on other bikes.

He already had some pretty hefty tires. He might be persuaded to lose a LITTLE bit of weight, but he isn't going to tame down his riding. That's the end to which the rest is the means.

Anyway, I should peruse the wheel mfrs' sites to see if they address this. I started here, because I probably would get a straighter answer, without any commercial interest.

One more idea: With a 29" wheel, the spokes are closer to vertical than they are with a 26" wheel, for a given spacing between the hub flanges. Therefore, for a given spoke tension, the lateral component of the tensile force is smaller with the larger wheel, providing less lateral support for the wheel. Maybe they need really stout spokes and really high tension in the spokes.

Regards,
DRG

 

[drawoh]

dgillette,

My impact force is out by a factor of 2!

The energy is based on the average force exerted from zero to maximum. The maximum force is therefore double the average. The contact force I calculated should be 7200lb.

Impact Force = 720ft.lb / 0.2ft x 2 = 7200lb.

The spokes' force is approximately radial on any large wheel with lots of spokes.

You can make all sorts of assumptions, and plug them into the calculation. I still wonder if his suspension is bottoming out.

JHG

 

[dgillette]

OK, energy = 1/2 k x^2 for an elastic spring and load = kx, although the suspension springs may be "precompressed" so they pick up load faster (load>>0 as soon as the displacement starts).

Stu's a strong guy, but I don't believe his legs can handle 7200 lb. That part of the system would definitely be nonlinear. ;-)

I think top-shelf bikes have about 6" travel on the front fork, so it very well might bottom out with that sort of impact.

DRG

 

[tnkayaker]

Bottoming out the suspension would more likely cause the rim to flat-spot not taco. To taco a wheel the force would have to be applied normal to the rim x-section and not radially.

 

[drawoh]

tnkayaker,

A flat spot is one possible failure when you apply an excessive radial load. Another possible failure is for the rim to buckle under the load. This is a common compression mode failure.

Is it even possible for a bicycle to apply side loads to its wheels? The only failure mode that would directly cause tacoing would be an enraged hiker stomping on the rims. This sounds unlikely, given the description of the OP's friend.

JHG

 

[dgillette]

No enraged hiker was involved, just gravity, F=MA, and that kind of stuff.

I'd never thought about it before, but the tension in the spokes must play a role in preventing out-of-plane bending and buckling. For a given flange spacing and spoke tension, the lateral component of the spoke tension would be smaller for a larger wheel diameter (because of the different angle of the spoke from vertical). However, the angle would not change all that much going from 26" to 29" diameter. Dished rear wheels might be more vulnerable, but they may not get the same kind of forces as a front wheel.

When cornering hard on pavement, the lateral force imposes a shear force on the tire, which must impose a bending moment (however small) on the wheel, which would increase the tension in spokes on one side and decrease it on the other side. (Sew-ups have been known to slip off.) A mountain biker hitting irregular surfaces in irregular directions or catching a wheel in a crack in the rock probably does much worse. If a spoke went into compression and buckled, that might be it. Just speculating, based on no actual structural analysis.

Thanks gents (assuming you are gents).

When in China a few years ago, I was eating wonderful spicy barbecued squid and pork on metal skewers at a hole-in-the-wall restaurant. At the blunt end of each skewer, there was a 90-degree bend and a "mushroom" at the end of the wire. Took a few minutes before it dawned on me what they were originally made for.

 

[lawayosh]

Tension of the spokes has to be right and depends on the type of wheel, rim, hub, size of rider, riding surface, etc. Commercially built wheels are built to the lowest common denominator, acceptance level, price point and are usually not tensioned to very high levels. Custom wheels are hand assembled and trued, but that is no guarantee of suitability or durability in a specific application.

Conventional spoked wheels can be surprisingly strong with properly selected components and professional assembly, which is not that easy to find. They can also potato chip readily if the spoke tension is insufficient or out of balance. In some cases, rear wheels have been warped by a rider attempting a sudden burst of speed, no impact involved.

Riding style and/or competence can play a significant role in longevity of spoked wheels. The smoother and more fluid the rider is the longer their wheels will last. Riders that tend to throw the bike from side-to-side are much tougher on wheels.

If a sew-up rolls off not due to an accident, then the glue and/or the glue job was probably not very good.

 

[dgillette]

The light is slowly going on: Every function of the wheel is controlled by spoke tension. Spokes don't get enough respect.

For practical purposes, they have tensile capacity only. The hub hangs from the spokes in the upper half of the wheel. The near-horizontal spokes keep the rim circular. If the spokes in the bottom half of the wheel are loose enough that they go into compression, you probably have a problem because there is no lateral restraint for the lower portion of the rim.

Lateral movement of the rim is prevented by the component of the spoke tension in the horizontal direction (T sin alpha, where alpha is the angle between spoke and vertical). If the spokes on one side ever go into compression and buckle, you probably have a taco or a potato chip, and now I'm getting hungry.

Driving force is applied to the rim by the fact that the spokes are not directly radial from the axle, which is why we lace wheels with spokes crossing two or three others.

I'm sure this is all obvious to anyone who's ever built a wheel, but I never actually thought it through before.

5:45, and time to ride home.

 

[lawayosh]

Tension of each spoke has to maintain roundness of the rim regardless where they are in relation to the direction of loading. The portion of the rim being compressed can reduce spoke tension. However, if the wheel is to have a chance of staying round and true, all spokes have to have been tensioned to pre-compress the rim sufficiently in excess of the (anticipated) imposed load. Otherwise, it will deflect as you have stated and problems begin. The rule is, tight, but not too tight.

Even tensioning of spokes is one of the goals of a good wheel build. Some builders use tension measuring devises, others (old school) twang or squeeze adjacent spokes as they tighten and just go by feel. I am an old geezer, therefore, a squeezer.

Correct tension for a given wheel will depend on the components selected. There are also a few tricks of the trade that can make a difference in how well the wheel goes together, its durability and how soon and the degree to which it has to be touched up after it is first ridden. A really good wheel will not need much re-truing, if any.

There are some rear wheels that are radial on the off side and cross one, two or three on the drive side. Not usually recommended for large riders, especially off-road.

 

[dgillette]

What's the advantage of the one-side-radial spoke arrangement? Shorter spokes -> lighter weight?