Cycling UK Forum

Here's an interesting analysis of the stresses on a wheel. Interestingly the non-drive side leading spoke has the highest tension range in a 3 cross pattern. And a three cross pattern had the lowest maximum tension range.

It would have been nice if they'd done an analysis of using heavier gauge spokes on the drive side.

interesting, like you say, but a quick read suggests that there are most likely a few issues with it;

- the lateral displacements appear to be generated assuming that they arise mainly due to the torque on the wheel; the fact that the bike isn't upright when you are riding hard (in or out of the saddle) isn't accounted for. There are lateral forces applied directly at the rim, thus real lateral displacements are much larger than the model indicates and so are the tension variations in the spokes.

- the assumption is that when the wheel flexes laterally, the energy required to cause the maximum deflection is completely lost. Leave aside that what they calculate is only a portion of the whole at times, I'd question this assumption; after all any real net lateral force at the rim also deforms the tyre laterally (you can see this happening in many cases). If this flexing resulted in power always being completely lost then real world tests ought to pick this up (independently of variations in simple rolling resistance) when climbing.

- the torsional stiffness of the hubshell can vary enormously and this can affect the stress distribution between the NDS and DS under torque loading, just as much as the spoking pattern. Some hubs (such as the classic campag nuovo record hubs) have really low torsional stiffness and this is likely to give very different results from the one hubshell used in these models.

- the fact that the spoke crossings are braced against one another appears not to be accounted for. This almost certainly means that the tension variations in spokes are not as high as they appear to be under the model conditions.

Some of these things may not be a big deal and others are understandable omissions; after all you can't vary everything in every combination when modelling a complex system like this. But as with many such models, best to take the conclusions with a pinch of salt.

cheers

Wheels. My favourite debate.

Imagine if you will, a fly jammed in between the tread of the tyre on one of your bike wheels. You are riding along at, say, 20 mph. In the course of one revolution of the wheel as you are riding, that fly, starting at the bottom of the wheel will be stationary, then accelerate up to 40 mph at the top of the wheel before coming to a standstill briefly, at the bottom again. It will repeat this process as long as you keep riding, accelerating from 0mph to double your speed then back again to 0mph once for every full rotation. Gotta love simple mechanics.

I thank forever the maths teacher who proved this to me one day in class. It sends more people barmy trying to figure it out than anything else ever.

Nearly forgot. To add to the joy imagine a second unfortunate fly stuck in the tread of the same wheel on exactly the opposite side to the first. At the same microsecond as fly 1 is stationary at the bottom of the wheel, fly 2 is travelling at 40 mph. Enjoy.

bryce wrote:Here's an interesting analysis of the stresses on a wheel.

Not wishing to be a spoilsport, but I don't find it interesting at all. Sorry. I have built a few wheels for my own use and a couple for other people. Providing you do it well, there is nothing interesting about the stresses IMHO.

The interesting part about wheels is HOW they are built and the components involved.

This is my humble opinion.

Shootist wrote:Wheels. My favourite debate.

Imagine if you will, a fly jammed in between the tread of the tyre on one of your bike wheels. You are riding along at, say, 20 mph. In the course of one revolution of the wheel as you are riding, that fly, starting at the bottom of the wheel will be stationary, then accelerate up to 40 mph at the top of the wheel before coming to a standstill briefly, at the bottom again. It will repeat this process as long as you keep riding, accelerating from 0mph to double your speed then back again to 0mph once for every full rotation. Gotta love simple mechanics.

I thank forever the maths teacher who proved this to me one day in class. It sends more people barmy trying to figure it out than anything else ever.

Einstein has something to say about that. It's about as useful as saying at 09:00 we are hurtling towards the sun at 1000mph and 12hrs later we are hurtling away from it at 1000mph all while hurtling round the sun at 67,000mph. To us in our frame of reference there is none of the drama that seems to imply.

Shootist wrote:Wheels. My favourite debate.

Imagine if you will, a fly jammed in between the tread of the tyre on one of your bike wheels. You are riding along at, say, 20 mph. In the course of one revolution of the wheel as you are riding, that fly, starting at the bottom of the wheel will be stationary, then accelerate up to 40 mph at the top of the wheel before coming to a standstill briefly, at the bottom again. It will repeat this process as long as you keep riding, accelerating from 0mph to double your speed then back again to 0mph once for every full rotation. Gotta love simple mechanics.

I thank forever the maths teacher who proved this to me one day in class. It sends more people barmy trying to figure it out than anything else ever.

I've been trying to get my head around this.
I assume you're talking about speed in the direction of travel of the bike ? If the wheel is turning then the fly will always experiencing forces due to the angular velocity, relative to the wheel axle. However, I'm sure there will probably be a point where the angular velocity with the fly moving 'backwards' will cancel out the lateral forward velocity of the bike.
It's an interesting one.

Well I wasn't expecting all this on a Saturday morning! I think I need to go for a little ride and a nice cuppa...

don1 wrote:

Shootist wrote:Wheels. My favourite debate.

Imagine if you will, a fly jammed in between the tread of the tyre on one of your bike wheels. You are riding along at, say, 20 mph. In the course of one revolution of the wheel as you are riding, that fly, starting at the bottom of the wheel will be stationary, then accelerate up to 40 mph at the top of the wheel before coming to a standstill briefly, at the bottom again. It will repeat this process as long as you keep riding, accelerating from 0mph to double your speed then back again to 0mph once for every full rotation. Gotta love simple mechanics.

I thank forever the maths teacher who proved this to me one day in class. It sends more people barmy trying to figure it out than anything else ever.

I've been trying to get my head around this.
I assume you're talking about speed in the direction of travel of the bike ? If the wheel is turning then the fly will always experiencing forces due to the angular velocity, relative to the wheel axle. However, I'm sure there will probably be a point where the angular velocity with the fly moving 'backwards' will cancel out the lateral forward velocity of the bike.
It's an interesting one.

Do you remember the old Spirograph 'toy' from years ago? Just think if you took one of the cogs with your pen in it's circumference and 'wheeled' it along a straight track - when your pen comes to the bottom of it's travel it momentarily stops.

Shootist wrote:Wheels. My favourite debate.

Imagine if you will, a fly jammed in between the tread of the tyre on one of your bike wheels. You are riding along at, say, 20 mph. In the course of one revolution of the wheel as you are riding, that fly, starting at the bottom of the wheel will be stationary, then accelerate up to 40 mph at the top of the wheel before coming to a standstill briefly, at the bottom again. It will repeat this process as long as you keep riding, accelerating from 0mph to double your speed then back again to 0mph once for every full rotation. Gotta love simple mechanics.

I thank forever the maths teacher who proved this to me one day in class. It sends more people barmy trying to figure it out than anything else ever.

In practice you won't be riding at a constant 20mph except downhill, but at speeds alternating about 20mph. Resistance will slow you down and each pedal push will speed you up. The steeper the gradient and the slower the cadence the more will be the fluctuation. One reason to reduce rotating mass.

.

I've just built my first set of wheels so was interested in understanding what goes into the design choices. All I know from personal experience is aluminium nipples don't work for my use, knowing enough to pick up faults without needing to hit the road is nice. The new wheel set was overly conservative, but more than good enough given the hub will die first. The tensional difference due to dishing is inelegant.

In that analysis, the gains by moving to a radial non-drive side lacing could be gained by increasing the tension of a 3x lacing to match the radial wheels maximum spoke tension which probably wouldn't change the tension range. Removing the drop in non-drive side tension is the reason for a radial lacing but it increases both the maximum tension and the maximum tension range. Tightening the spokes a bit may provide the benefit of radial non-drive side lacing without the costs.

As Brucey said above, torsional stiffness in hubshell varies, which would make applying lessons from one hub, rim, and riding style to another questionable.

gaz wrote:AFAICT an instant in time, as described in Zeno's arrow paradox, is being applied to the fly when it's at the bottom of the wheel to make it seemingly motionless, made all the worse when your math's teacher has chosen not to apply the same rules to the second fly at the top.

It's only apparently motionless because of the chosen inertial frame of reference. If you choose a more appropriate one of the bike instead of the road, the fly is simply going round and round in a circle and the only acceleration it feels is the radial centrifugal acceleration away from the hub.

Hi Guys & Girls, Very interesting stuff, way above my head & level of maths! But may I throw into the mix the different loads & needs exerted on spokes when used in Tricycle Wheels? R.S.V.P. TTFN MM

Shootist wrote:Wheels. My favourite debate.

Imagine if you will, a fly jammed in between the tread of the tyre on one of your bike wheels. You are riding along at, say, 20 mph. In the course of one revolution of the wheel as you are riding, that fly, starting at the bottom of the wheel will be stationary, then accelerate up to 40 mph at the top of the wheel before coming to a standstill briefly, at the bottom again. It will repeat this process as long as you keep riding, accelerating from 0mph to double your speed then back again to 0mph once for every full rotation. Gotta love simple mechanics.

I thank forever the maths teacher who proved this to me one day in class. It sends more people barmy trying to figure it out than anything else ever.

I seem to vaguely recall this was concerned with loci, where the motion of a point on the circumference of a moving (circular) wheel relative to the ground was a series of half sinoids or something resembling that.

gaz wrote:

Shootist wrote:I thank forever the maths teacher who proved this to me one day in class. It sends more people barmy trying to figure it out than anything else ever.

AFAICT an instant in time, as described in Zeno's arrow paradox, is being applied to the fly when it's at the bottom of the wheel to make it seemingly motionless, made all the worse when your math's teacher has chosen not to apply the same rules to the second fly at the top.

Had to look that one up!

However if you consider an elongated "wheel" such as the track of a track laying vehicle, a point on the lower part of the track will be stationary on the ground for a period of time until the rear roller reaches it. It will then be on the top part of the track and be driven to the front of the vehicle. Relative to the ground it will be travelling faster than the vehicle otherwise it won't reach the front!