Lateral strength of bicycle wheels

[dabac]

Quote: Originally Posted by lukeevans .
...the question is where does it fail? bicycle wheel manufacturers do not have this data in the public, and the few which I contacted last year could not tell me how much lateral force it could take. I was asking bmx wheel manufacturers as I thought that they would be by far the strongest, but they could not tell me where the failure would occur, would it be the hub, the spokes or the rim?


I think you can forget getting an answer out of the manufacturers, beacuse they probably don't know, and probably don't care. In the intended usage, bike wheels don't see much lateral load. And as there's precious little useful riding that can be done while exposing wheels to a lateral load, it's pretty much a dead end to research from their perspective.

And where the failure occur would be down to the specific configuration of the wheel. All the failure modes you list are possible, although some are more common.
Hub flanges do fail occasionally. Usually in association with radial lacing, but with a marginal hub flange or high tensions it can happen even for a tangential lace. Nipples pull through rims every now and then too, particularly on no-eyelet rims. Never seen it on a double eyelet rim though. Nipples fail occasionally as well.

So there's really no telling.
If I had to guess, I'd rate rim taco-ing as the most probable. 2nd most probable, nipples pulling through rim. 3rd, nipples breaking. 4th spokes snapping due to overload. 5th, hub flanges failing. But anything goes. On a light weight hub, the flanges may go early. On a hub using a soft alloy, spokes may shear through.

 

[lukeevans]

Hi Tony,

I have the first addition of The Bicycle Wheel but it does not look at lateral forces, does a later version?

Thanks

Luke

 

[lukeevans]

Hi Alienator,

Thanks for explaining that, I do understand how stiffness is not effected by the spoke tension.

I'm also beginning to understand how difficult this is going to be realising why there is very little data out there for this problem. I was expecting to make a certain number of assumptions - such as the tyre types and pressure, but I did not consider the effects of damping from the spokes.

Going to have to have a serious think on whether I will be able to do this as a project.

Thanks again!

 

[lukeevans]

Hi Dabac,

Thanks for your thoughts and sharing your experience, that gives a useful insight if I do decide to attempt some kind of modelling.

I think your reasoning re the manufacturers is why I have had no response from any!

 

[dabac]

Quote:Originally Posted by lukeevans .Hi Dabac,

Thanks for your thoughts and sharing your experience, that gives a useful insight if I do decide to attempt some kind of modelling.

I think your reasoning re the manufacturers is why I have had no response from any!





Parts of this should be possible to model and guesstimate with reasonable precision. Hub flanges basically see a pull. Calculating if it's possible for a single spoke to pull its way through the material shouldn't be too bad. Calculating if several spokes could make the flange split would be a bit more complicated. The individual spoke is also fairly simple. The force needed before the nipple pulls through the rim, or the nipple flange shearing is also within easy grasp. Unfortunately, just because you can figure out if the parts survive doesn't automatically mean you can figure out if the wheel would survive. Calculating when a wheel would flop over into taco is entirely beyond me at least.

 

[alfeng]

Originally Posted by lukeevans
Hi all,

I know there was a bit of discussion about this regarding a 20" recumbent bicycle wheel a while back, but I am wondering if anybody out there could help me out.

I am a final year student of an integrated masters of engineering program and am going to investigate the lateral behaviour of a bicycle wheel when held in the upright position.

The reason why I think this is important is because I think there will be an increase in human powered load carriers which have either three or four wheels which cannot lean like the conventional bicycle. Last year I attempted to design a human powered log delivery vehicle, but got stuck on the specification of the wheels. I contacted hub manufacturers, spoke manufacturers, and wheel manufacturers who could not give me any quantifiable data and all said that if their components failed they would replace them for free. It was great to hear such confidence in their products but I would like to know a safe limit to use wheels.

I would just like to appeal to the expertise on this forum to see if anybody would like to offer ideas of how to do this. My current plan is to model a wheel in Pro Engineer and run some finite element analysis, then compare the results with hanging weights on the wheel whilst attaching strain gauges to the spokes, much like the tests people have posted on the internet to understand the stiffness of wheels. Im also interested in seeing at which point if fails and understanding where it fails, whether the spokes pull through the rim, the rim deforms, or the spokes pull through the hubs.

I'm also after some advice on some wheel manufacturers who may be interested in giving/selling me some cheap wheels to use for testing.

Cheers

Luke

FWIW. To a lay person like myself, a laterally stiffer wheel is a stronger wheel ... laterally, or otherwise.

A false premise?

I think not.

But, supposing it is a false premise ...

 

[alfeng]

Oops!

I don't know what happened to the rest of the preceding post!

I'll have to reconstruct it.

 

[alfeng]

Originally Posted by alienator


As I wrote before, tension has to be enough that the spoke does not go slack. It's not rhetoric. It's physics and engineering. The only stiffness a spoke can add to the lateral stiffness of a wheel is its own stiffness. You won't believe this because for some reason you, like a few others, refuse to accept the physics and engineering principles because you apparently harbor some belief that some as yet undiscovered physics applies to bicycles. Yet somehow you and your ilk cannot justify your "beliefs", i.e. you have zero proof of anything.

In the off chance that you actually have some intellectual curiosity about why a wheel's lateral wheel stiffness is not a function of spoke tension, here's the equation for the stiffness of a straight gauge spoke:





"k" is the stiffness, i.e. spring constant; "E" is Young's Modulus; "A0" is the cross-sectional area of the untensioned spoke; and "L0" is the unstretched length of the spoke. Okay, here's a quiz: where's the spoke tension in that equation? (Hint: it's not there)

Here's the equation for a double butted spoke:





"keq" is the overall stiffness of the spoke; "k1" is the stiffness of the end sections of the spoke; and "k2" is the stiffness of the middle section.

If you still crave knowledge, here's the equation of a spoke with "n" different diameters:





If you can't figure out how equation 2 came from equation 3, well, I'm sorry because that means algebra isn't your strong suit.

Now I know you're about to reflexively say, "But Alfeng said..." or "....in the real world"..... Well, Klabs, physics and engineering principles (the product of physics) apply in the real world. The reason that the spoke has to be tensioned enough that it doesn't go slack is that if the spoke goes slack, spoke stiffness is contributing nothing to wheel stiffness at that point. If for example a spoke tension of 50KgF keeps a spoke from going slack, then cranking tension up to 130KgF is not going to make a laterally stiffer wheel. There might be other benefits, but that increase won't increase lateral wheel stiffness.

As for what the minimum spoke tension needed is for every hub, spoke, and rim combination out there, I suggest you either buy everyone and try all the combinations or your created solid models of all the different pieces and then build solid models of every combination possible and test them with FEA at every bike/rider system weight possible, from the lightest possible rider to the heaviest possible rider. Also be sure to test them at every speed possible and every road condition possible. Since no one in history has done that, make sure to leave a lot of room in your schedule over the next year or two or three or four.

Gosh ...

Look at that long rant ...

YOU even took the time to include ME in it!

I guess that for those of us who live in the Real World that for someone living in YOUR situational world the actual number of dimensions doesn't matter ...

So it is that you keep trying to analyse the possible effects of lateral forces by ignoring them and then cutting-and-pasting this-or-that while bloviating about Hooke's Law ...

Well, no offense ... I think the following MAXIM sums it up:

alienator apparently doesn't know the difference between Hooke's Law and Captain Hook.

alienator apparently doesn't know the difference between Hooke's Law and Captain Hook because as he arbitrarily uses the former, it is as much a fantasy as the latter.

​

 

[alienator]

It's not a rant, dipshit. It's the physics of what's going on, idiot.

 

[alfeng]

Originally Posted by alienator

It's not a rant, dipshit. It's the physics of what's going on, idiot.

Wow!!!


Is THAT your idea of a cogent argument?!?

I think that it's definitely worth repeating that ...

alienator apparently doesn't know the difference between Hooke's Law and Captain Hook.​

 

[Eichers]

Originally Posted by alfeng
FWIW. To a lay person like myself, a laterally stiffer wheel is a stronger wheel ... laterally, or otherwise ...

Hi alfeng, yes usually, but especially if shallow depth, single shell, rims (19/20mm) are used ...

Lateral stiffness is essentially determined by Spoke Bracing Angle (6 degrees of BA is generally sufficient), Rim width/design/strength, and sufficient Spoke tension so that the spoke does not go slack (which also depends on rim width/strength).

Radial stiffness is essentially determined by Rim design/shape/depth/strength and Spoke tension (to create a sprung rim/wheel).

Spoke tension is further determined by the type of spoke and spoke pattern being used off each flange.

So, there are quite a few variables but if the variables are reduced or minimised then it becomes less complicated. All part of the fun

thanks KL

 

[Eichers]

Hi lukeevans, I forgot to say that if the spoke Bracing Angle (BA) is about 6 degrees off each flange then spoke tension of between 90kgf to 100kgf is generally sufficient. As mentioned, the spoke tension will depend on rim strength and the spokes used for the build.

thanks KL

 

[alfeng]

Originally Posted by Eichers
Hi alfeng, yes usually, but especially if shallow depth, single shell, rims (19/20mm) are used ...

Lateral stiffness is essentially determined by Spoke Bracing Angle (6 degrees of BA is generally sufficient), Rim width/design/strength, and sufficient Spoke tension so that the spoke does not go slack (which also depends on rim width/strength).

Radial stiffness is essentially determined by Rim design/shape/depth/strength and Spoke tension (to create a sprung rim/wheel).

Spoke tension is further determined by the type of spoke and spoke pattern being used off each flange.

So, there are quite a few variables but if the variables are reduced or minimised then it becomes less complicated. All part of the fun

thanks KL

Thanks ...

Your earlier observations were worth being repeated.

 

[alienator]

Lateral stiffness is essentially determined by Spoke Bracing Angle (6 degrees of BA is generally sufficient), Rim width/design/strength, and sufficient Spoke tension so that the spoke does not go slack (which also depends on rim width/strength).

Yup. It's as I stated earlier.

Radial stiffness is essentially determined by Rim design/shape/depth/strength and Spoke tension (to create a sprung rim/wheel).

This isn't exactly true. Radial stiffness is only dependent on spoke tension in that spoke tension has to be enough that spokes don't go slack. With respect to spoke tension and the static cases (like the magnitude of rim deflection at a given force or the force needed to produce a given rim deflection) the radial case is exactly like the lateral case. The dynamics of the lateral and radial cases (i.e. things like radial or lateral rim position vs. time; radial or lateral rim velocity vs. time; and radial or lateral rim acceleration vs. time) do depend on spoke tension because those cases are dependent on Fspoke(t). The only stiffness a spoke contributes to the system is the spoke's own stiffness which is determined by its material, cross-sectional diameter, and butting (because of differing cross-sectional areas in a butted spoke)

 

[Eichers]

Originally Posted by alfeng Thanks ... Your earlier observations were worth being repeated.

Thanks alfeng, appreciated :=)

Some interesting points are...

• If the BA is more than 6 degrees of both flanges than the lateral stiffness is increased but the radial stiffness is reduced.
• If the BA is less than 6 degrees of both flanges than the lateral stiffness is reduced but the radial stiffness is increased.
• If the BA is less than 6 degrees of one flange then the BA of other flange needs to be more than 6 degrees to ensure lateral stiffness is maintained. For example, a good approach is to maintain a total BA of about 11 to 13 degrees. Unfortunately this does course issues with left/right tension ratios which needs to be managed by Rim depth/OCR drilling, spoke types, and spoke lacing patterns.
• Reducing the variables by assuming that a spoke/flange BA of 6 degrees is optimal, simplifies the maths :=)

Of course if 3 hub flanges are used where the outer 2 flanges control lateral stiffness and the inner flange controls radial stiffness and Torque Drive then even further optimisation can be obtained :=)

thanks KL

 

[alfeng]

Originally Posted by alienator


Yup. It's as I stated earlier.
This isn't exactly true. Radial stiffness is only dependent on spoke tension in that spoke tension has to be enough that spokes don't go slack. With respect to spoke tension and the static cases (like the magnitude of rim deflection at a given force or the force needed to produce a given rim deflection) the radial case is exactly like the lateral case. The dynamics of the lateral and radial cases (i.e. things like radial or lateral rim position vs. time; radial or lateral rim velocity vs. time; and radial or lateral rim acceleration vs. time) do depend on spoke tension because those cases are dependent on Fspoke(t).

The only stiffness a spoke contributes to the system is the spoke's own stiffness which is determined by its material, cross-sectional diameter, and butting (because of differing cross-sectional areas in a butted spoke)

NICE!!!

Are YOU now suggesting that a straight 14g spoke will result in a laterally stiffer wheel than a comparably laced wheel would be if it were laced with double-butted 14-15-14 spokes of comparable material?!?

 

[maydog]

Originally Posted by alfeng

NICE!!!

Are YOU now suggesting that a straight 14g spoke will result in a laterally stiffer wheel than a comparably laced wheel would be if it were laced with double-butted 14-15-14 spokes of comparable material?!?

That sounds about right to be. With a constant cross section, straight spokes are stiffer than a comparable butted spoke.

Here is some quick research:
read the Spoke Stiffness vs Rim Stiffness section - http://www.slowtwitch.com/Tech/Debunking_Wheel_Stiffness_3449.html


http://www.rouesartisanales.com/article-23159755.html

 

[alienator]

I never said that butted spokes were stiffer than straight gauge spokes wherein the butted ends of the spoke are the same gauge as the straight gauge spoke but the middle section is smaller. I never said that. I did say that butted spokes will tend to be more durable and can certainly build a wheel stiff enough to do the job for most people. Learn to read, alfeng.

 

[alfeng]

Originally Posted by alienator

I never said that butted spokes were stiffer than straight gauge spokes wherein the butted ends of the spoke are the same gauge as the straight gauge spoke but the middle section is smaller. I never said that. I did say that butted spokes will tend to be more durable and can certainly build a wheel stiff enough to do the job for most people. Learn to read, alfeng.

Geez ...

Talk about not being able to read!!!

I didn't say that you said that "butted spokes were stiffer than straight gauge spokes .... "

I think that with regards to lacing a bicycle wheel (which you have apparently never done), it is safe to say that you are talking out of your hat ...

BTW. HOW, oh how, can a double-butted spokes be more durable if you were-and-are correct about Hooke's Law which indicates the same level of elasticity (according to your prior statements ... no, you did not use the word "elasticity" ... I presume that you are not now going to redefine Hooke's Law to suit your situational world AND will be using the accepted understanding of Hooke's Law ... or, did you want to backtrack on that, now?)?!?

What you know regarding wheel building can be summed up with the formerly stated maxim WHICH WILL ALWAYS BE WORTH REPEATING regardless of the situation since your little world is forever situational ...

alienator apparently doesn't know the difference between Hooke's Law and Captain Hook.

As needed, any other concept which you are discussing with your typical certitude can be substituted for the phrase "Hooke's Law" in the above sentence ... for example,

alienator apparently doesn't know the difference between "dwell" and Captain Hook.

et cetera!!!

Because, now we see that "stiff enough to do the job for most people" replaces your earlier statements that it didn't matter and/or that a wheel laced with straight 14 gauge wasn't stiffer.

Learn to read your own posts.

Don't forget to show your posts to your wife and daughter.

 

[alienator]

A butted spoke has an effective spring constant that is a function of the different diameters of the spokes. As I've shown before in this thread, the effective spring constant for a straight gauge spoke is a function of the young's modulus for the spoke material, the cross sectional area of the spoke, and the length of the spoke. In equation form it's this:

Notice the dependence on area and consider a double butted spoke. Such a spoke will the one spring constant for one end, one spring constant for the middle, and one spring constant for the other end. The spring constants for the ends are equal. To get the effective spring constant you use the following equation:

Finding the effective spring constant for springs in a series (which is what a butted spoke is) is like finding the overall resistance for resistors in parallel. I did the algebra on that equation to produce the above equation. If you don't believe the result, here's the form of that calculation. Feel free to do the algebra yourself:

So how does a butted spoke make for a more durable spoke? It moves the majority of the strain to the middle section, reducing the strain on the ends, specifically on the spoke head elbows where there are stress risers. You'll note, again, that I never said that a wheel with 14g spokes wasn't stiffer for a particular lacing pattern. I've always said that double spokes can build wheels that are stiff enough for most people. You'll also note that I've always said that wheel stiffness is a function of spoke diameter and material, rim cross section, lacing pattern, and things like bracing angle and flange height. It should be noted that the factors that influence lateral stiffness of a wheel are also the factors that influence the radial stiffness of a wheel. Now, alfeng, why don't demonstrate an understanding of Hooke's Law by seeing how what I wrote above is correct. Why would I be showing my posts to my wife and daughter? Do you show your posts to your family? Is that something we're supposed to be doing?