Bicycle Mechanics - Is wheel strength inversely proportional to diameter?

I was wondering about this. I just picked up a small-wheeled tandem (a Bike Friday), which uses 20" wheels. The tandem obviously was built to handle more weight than a standard road bike. I noticed that the wheels are 36H, which got me wondering: would these wheels be capable of handling a higher load than regular road wheels with the same number of spokes? Assuming two wheels (700C and 20") both made with 36 spokes of the same gauge, would the 20" wheel be capable of handling a higher total load than the road wheel? I'm asking because I'd like to use the tandem for some loaded touring, and the combined weight of captain + stoker + equipment could top 350 lbs.

the spokes will twist and stretch less and the spoke bracing angle will be larger.

The reason wheels go out of true and round is, mainly, because the wheel is momentarily loaded up so much that the spokes on the impacted side will lose all tension and the nipple unwinds.

Smaller wheels allow less deflection of the rim and because the spokes are shorter, they twist less when being brought up to tension.
The heads of the spokes also contact more of the hub flange, because the bracing angle is greater. More surface contact of the heads will reduce the amount of stress on the J-bends, leading to longer life.

Also, the spokes are spaced closer on the rim, leading to less unsupported areas on the rim.

At least, that's my understanding of wheels.


it's similar in principle to a simple beam bridge and it's support columns.
taller bridges will sway more unless more or sturdier columns are used.
bridges will less columns need a stronger deck so it won't buckle when loaded.

with *all* other things being equal, smaller diameter wheels are stronger than larger diameter wheels.

-rob

The spokes on our Bike Friday wheel with 36 spokes are about the same spacing on the rim as on our 700c tandem wheel with 48 spokes. You should be fine as long as the wheels are properly built (both materials and labor).

A 20 inch wheel with 36 spokes will have about the same strength as a 48 spoke 700c wheel... if the wheels are well built they should have no trouble carrying 350 pounds.

"All else being equal" can mean numerous things. Smaller-diameter rims are typically rolled from the same extrusions as larger rims, so proportionally, the smaller-diameter rims will be stronger because the wall-thickness of the rim remains the same.

Bracing-angle of the spokes are better (wider triangle) if the same hub flange-width are used.

Easy way to combine all the variables together is to just measure the distance between spoke-holes on the rim. This allows you to compare 36-hole 700c wheels versus 24-hole 20" wheels, etc. If the spoke-hole spacing is about the same, the wheels will be roughly the same strength. For ultimate in strength, you can go with 48h 20" BMX wheels. Those suckers can pretty much survive anything.

"All else being equal" means pretty much just the one thing, but it is hard to determine whether or not all of the "else" is indeed "equal".

Still, the simple fact is, if you take ALL the variables in a wheelbuild, and *only* change the rim diameter, the smaller wheel will, *INVARIABLY*, be stronger. the extrusion-similarity factor DannoXYZ mentions only bolsters this assertion, although for reasons other than the typical one.

Discussions of this sort quickly devolve into highly theoretical discussions, far removed from practical discourse on the construction of a strong wheelset. Hence, my hyper-concise, super-simplified and 100000000% accurate original response: with *all* other things being equal, smaller diameter wheels are stronger than larger diameter wheels.

-rob

Yes, as some have said, a smaller wheel is stronger, but as 65er said, a 700c wheel is adequately strong for nearly all applications, provided it's built well and built to the specific application.

You could have a 700c rim with (use the same 32 spokes for both wheels) DT Comp spokes built with a high flange hub and a deep aero dish wheel would be stronger then with a low flange hub with a box rim due to the shorter spoke length.

The difference between small flange hubs and so-called large flange hubs is not significant to affect strength. The notion that it makes a difference is folklore and has been debunked with measurement.

the only thing that high flange does is make the wheel stiffer laterally, because the triangle is a bit shorter. But not by much.

If you really wanted to experiment with how wheel size affects wheel strength, go out and buy CR-18 in 20", 26", 29" and use schwalabe marathon in 1.75", use the same spoke thickness, nipples and the same hub in all wheels. Bring them all up to about 100kg/f and do a battery of tests on them.

Testing for strength requires breaking the object and measuring the force required to break it.

Testing for strength requires breaking the object and measuring the force required to break it.That may be dangerous with wheels as it'll take quite a lot of force to break one.

thanks, all! AEO, your explanation of various factors makes perfect sense. so, i should be good to go. for what it's worth, the rims are made by sun and are 20x1.5, but i don't know the model. the hubs are bike-friday branded, so i don't know who makes them. the spokes are DT swiss, 14ga. the tires are 20x1.75 schwalbe marathons.

The difference between small flange hubs and so-called large flange hubs is not significant to affect strength. The notion that it makes a difference is folklore and has been debunked with measurement.

Really? I find it interesting, if what your saying is true, then why do track racers still use high flange hubs?

Oh, wait then there's Jobst Brandt (you know who he is right?) his book "The Bicycle Wheel" (the 2nd edition) states the following: "Tandem bicycles are an exception. With 36 spokes or less, tandem wheels require large-flange hubs to withstand the torque of two riders. And to support the additional weight, durable tandem wheels require at least 48 spokes, which can only be accomodated by larger flanges."

And more torsional stiffness and more lateral stiffness are results of using larger diameter hub flanges (with Flange width spacing held constant). If you need or want them, then larger diameter hub flanges are useful.
Again look what most track and single speed riders are using.

I think it's weird that high flange hubs have come back on most hubs made for disk brakes, hmmm.

But my post was combining that with a deep dish aero wheel to shorten the spokes length.

Really? I find it interesting, if what your saying is true, then why do track racers still use high flange hubs? It's for lateral-stiffness not necessarily strength. The high-flange hub gives you a wider bracing angle for the spokes. Also gives you larger radius to combat torque from disk-brakes.

The issue of semantics here is what does the OP mean by "strength"? Is it stiffness or rigidity? Vertically or laterally? Or does he mean durability? All these are different properties that can be custom-tailored for any particular wheel configuration.

Here's a good wheel study: Damon Rinard - Wheel stiffness test (http://www.sheldonbrown.com/rinard/wheel/index.htm) and the results data (http://www.sheldonbrown.com/rinard/wheel/data.htm).

To describe further Danno's distinction:

Strength is defined as the force required to break something

Stiffness is defined as the force required to deflect something a given distance

They are quite different!

But if any of you have ever seen the kind of lateral forces a track racer puts on wheels, it's huge, that's why they use high flange hubs because they believe their stronger, I would think that after years of track use they would, or should know. And your web site said very little about high and low flange hubs, their study focused on low.

And Danno, you quoted everything I said, except you didn't use all of my quote in your post. Reread my post.

But if any of you have ever seen the kind of lateral forces a track racer puts on wheels, it's huge, that's why they use high flange hubs because they believe their stronger, I would think that after years of track use they would, or should know. And your web site said very little about high and low flange hubs, their study focused on low.

And Danno, you quoted everything I said, except you didn't use all of my quote in your post. Reread my post.

Tradition overcomes engineering facts.

If there is an advantage of high flange hubs to track racers, it's in stiffness, not strength. I doubt track racers break their wheels with torque.

But if any of you have ever seen the kind of lateral forces a track racer puts on wheels, it's huge, that's why they use high flange hubs because they believe their stronger, I would think that after years of track use they would, or should know. And your web site said very little about high and low flange hubs, their study focused on low.

And Danno, you quoted everything I said, except you didn't use all of my quote in your post. Reread my post.I did read your post and agree with everything you said about stiffness and high-flange hubs. I have them on my track bike and along with wide box-section rims, they are definitely stiffer than low-flange hubs with aero rims. Those have their place as well as super-lightweight wheels which aren't super-stiff nor super-aero. Yes, I bring 6 wheels to the track and use the appropriate one for any particular race.

However, we may be talking something different than what the OP was asking about I think. He appears to be talking about "ultimate strength" which is a materials property that may not really apply to wheels. It may perhaps be quantified and measured several ways. He'll have to tell us which:


1. amount of vertical loading where the bottom spokes lose all tension?
2. amount of lateral loading where spokes on one side loses all tension?
3. amount of vertical or lateral impact force that causes a permanent run-out of X millimeters?
4. amount of vertical or lateral load where a wheel collapses?

He's very vague about what he means by "strength" and "load". I won't even go into stress and strain... yet...

Tradition overcomes engineering facts.
+1

Happens disturbingly often in bicycling.

I think it's weird that high flange hubs have come back on most hubs made for disk brakes,

Well, flange diameter has to run outside rotor mount diameter to make the hub easy to lace.


...Oh, wait then there's Jobst Brandt ...
...who has his own pet peeves, specific experiences and axes to grind just like everybody else. Having had a book published didn't make him infallible. (much of it is good though). He used to post on a forum connected to cyclingforums.com, and he didn't always come out on top.


... With 36 spokes or less, tandem wheels require large-flange hubs to withstand the torque of two riders. And to support the additional weight, durable tandem wheels require at least 48 spokes, which can only be accomodated by larger flanges.
Quite casual use of the word"require" there. His opinion, his recommendation - not an unquestionable law of nature. 36H tandems won't categorically self-destruct a handful of miles down the road.
And when you go to 48H you're pretty much forced to use larger flanges to keep a reasonable amount of material between the spoke holes. My guess is that this is the design driver, not the bracing angles.

...they use high flange hubs because they believe their stronger....

That might be closer to the truth than you think.

DannoXYZ, you make me wish I had studied mechanical engineering in college.

dabac and davidad (and everyone else), it really is disturbing how mistaken folklore pervades in cycling. I can't say if it's worse in cycling than in other fields, but it seems that way. On the other hand, audiophiles spew a lot of crap.

Jobst is not infallible, but I learned a lot from him. I read his book in 1983 while being mentored by a master mechanic. My boss gave me a copy of Jobst's book while (re)teaching me to build wheels. Then a few years later, I met Jobst on the net, and he was uncharacteristically kind to me.

dabac and davidad (and everyone else), it really is disturbing how mistaken folklore pervades in cycling. I can't say if it's worse in cycling than in other fields, but it seems that way.

Depends on what other fields you'd compare it to. Since virtually no one really needs to ride a bike these days, the drive to truly find out the net benefit of this change vs that change is pretty much zero. Anything that is marketed as an improvement is likely to be perceived as an improvement. And with the gentle hump of the performance curve in a mature technology as cycling it turns into a self-fulfilling prophecy.

There are a few entertaining examples in the area of performance shooting that are every bit as bad as cycle lore.


...On the other hand, audiophiles spew a lot of crap.

Indeed. I'll never forget the time I read a test on cables used between set ups of stand-alone CD-players and separate D/A converters. Despite the fact that a bit counter couldn't see any difference they still knew that the more expensive cabling sounded better when hooked up to a full system than the cheaper ones....


..Jobst is not infallible, but I learned a lot from him. . Agreed, there's plenty of good stuff in the book too - along with the pet peeves and biased experiences.


.Then a few years later, I met Jobst on the net, and he was uncharacteristically kind to me. You struck it lucky then. I miss that forum where Jobst, Carl Fogel and jim beam were slugging it out...

Well , for freestyle BMX tricks there are 48 hole 406 rims manufactured ,

to build a wheel strong enough that will stand up to being jumped on sideways .

That might be closer to the truth than you think. Maybe so. But when use to hang with some track racers they tried both style of hubs and the small (low) flange hubs would cause the wheels to flex to much, so much they would sometimes collapse, but would rub the stays. This was according to them, I was never in that league and I could never get the wheels to flex that much. But I do know that I could get 28 spoke rear wheel to flex under hard load and it would rub both sides of the brake calipers and had to use 36 spoke wheels. This was back in the mid 70's to mid 80's when I use to race. Now the only way I can get the wheel to rub the calipers is when I remove a wheel to fix a flat!

one other spot where tradition trumps engineering is the vertical stiffness of wheels and their comfort factor.

The claim is that low profile box section rims offer a plusher ride than high profile deep section rims.
If a rim flexed enough to cause a noticeable difference in comfort under regular riding conditions, it would cause some serious problems to the spokes. Both deep section and box section rims, when built up properly, will offer the same level of comfort over bumps. The biggest difference in comfort comes from the tire width and inflation pressure.

Maybe so. But when use to hang with some track racers they tried both style of hubs and the small (low) flange hubs would cause the wheels to flex to much...

Not saying there can't be a difference, only that usually it's real hard to separate what's what.
Even if a guy would have two wheels where the only difference was the flange height, he'd still know that he'd switched the wheels out.
I've read translations from a German bicycle mag where they've used disguised bikes, and the results weren't good from the perspective of some fairly established bike opinions.