Page 7 of 7
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 18 Nov 2023, 5:27pm
by Brucey
he only considered deflections in the radial direction. I agree that a wheel with 36 3D hinges would never have worked but what about 36 2D
hinges? I supposed he meant the rim to have the usual lateral stiffness and compressive stiffness but no radial stiffness.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 21 Nov 2023, 9:17pm
by CJ
Brucey wrote: ↑18 Nov 2023, 5:27pm
he only considered deflections in the radial direction. I agree that a wheel with 36 3D hinges would never have worked but what about 36 2D
hinges? I supposed he meant the rim to have the usual lateral stiffness and compressive stiffness but no radial stiffness.
Jobst Brandt, page 20 wrote:I developed a mathematical model to compute the wheel deformations... This model defined the wheel in terms of its shape and size and the elasticity of the spoke and rim material.
And further down the page, when describing deformations under braking load:
The bending stiffness of the rim causes the change in spoke tension to be gradual as the rim passes through the brake caliper.
So clearly, the radial bending stiffness of the rim plays a part in his computation of radial deflections. He does NOT assume the rim sections to be connected by hinges of any sort at each node, but to be built into each other. And any engineering student who made such a stupid assumption should not be allowed to graduate!
As for whether Brandt developed his model to the level where it was able to process the interplay between spoke tension and the torsional and lateral bending stiffnesses of a rim, I think you're probably right, he didn't. His diagrams of how a wheel collapses into what he calls a "potato chip", I call a "Pringle" and is technically called a "saddle" shape, is merely a nice description of what we all know to be the case. (FWIW, a slice of potato adopts this shape for the exact same reason: when cooked, the soft and moist body of the potato shrinks more than its firmer and drier periphery, so you get a situation exactly similar to lot of tensioned spokes inside a circumferentially stiff rim. The core tension is relaxed by the periphery adopting a wavy shape and a 'saddle' is the least wavy shape that'll do that, allowing the greatest core shrinkage with the least amount of bending and twisting of the periphery.) Upon re-reading his text, looking for claims to have done something more sophisticated and finding none, I think Brandt's graphic Fig.17 on p42, most probably deals only with spoke tension, assuming negligible torsional and lateral bending stiffness in the rim. That's fair enough for small deflections, but not the 50mm or so to which he takes it. That figure is quite nonsensical in allowing the slack-side spokes to support a negative tension when the rim is pushed their way. (Negative tension means a compressive force, which anyone knows a thin wire spoke cannot support, it simply bows when pushed with very little force.)
This non-linear behavior of spokes however, makes it extremely difficult to construct a true mathematical model of what's going on here, so I don't blame Brandt for dodging that problem. I did too when I suggested how far sideways the spokes tend to deflect the rim, when loaded radially. The rim won't actually deflect quite that far, almost but not quite, thanks mostly to it's own lateral stiffness. Knowing this is why I wrote "
tends to". I've only mentioned lateral bending here, because for small lateral deflections over a distance spanning just a few spokes, are most easily accommodated by bending rather than twisting. Torsion will takes over once a local distortion spreads to involve the whole rim, but by then I reckon all is lost anyway, so I'm not sure torsional stiffness is such a big deal in stopping a wheel from buckling in the first place. Best defence against that I reckon - after matching the spokes to the dish of course - is a wide rim with thick sides.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 21 Nov 2023, 9:18pm
by CJ
CJ wrote: ↑21 Nov 2023, 9:17pm
Brucey wrote: ↑18 Nov 2023, 5:27pm
he only considered deflections in the radial direction. I agree that a wheel with 36 3D hinges would never have worked but what about 36 2D
hinges? I supposed he meant the rim to have the usual lateral stiffness and compressive stiffness but no radial stiffness.
Jobst Brandt, page 20 wrote:I developed a mathematical model to compute the wheel deformations... This model defined the wheel in terms of its shape and size and the elasticity of the spoke and rim material.
And further down the page, when describing deformations under braking load:
The bending stiffness of the rim causes the change in spoke tension to be gradual as the rim passes through the brake caliper.
So clearly, the radial bending stiffness of the rim plays a part in Brandt's computation of radial deflections. He does NOT assume the rim sections to be connected by hinges of any sort at each node, but to be built into each other. And any engineering student who made such a stupid assumption should not be allowed to graduate!
As for whether Brandt developed his model to the level where it was able to process the interplay between spoke tension and the torsional and lateral bending stiffnesses of a rim, I think you're probably right, he didn't. His diagrams of how a wheel collapses into what he calls a "potato chip", I call a "Pringle" and is technically called a "saddle" shape, is merely a nice description of what we all know to be the case. (FWIW, a slice of potato adopts this shape for the exact same reason: when cooked, the soft and moist body of the potato shrinks more than its firmer and drier periphery, so you get a situation exactly similar to lot of tensioned spokes inside a circumferentially stiff rim. The core tension is relaxed by the periphery adopting a wavy shape and a 'saddle' is the least wavy shape that'll do that, allowing the greatest core shrinkage with the least amount of bending and twisting of the periphery.) Upon re-reading his text, looking for claims to have done something more sophisticated and finding none, I think Brandt's graphic Fig.17 on p42, most probably deals only with spoke tension, assuming negligible torsional and lateral bending stiffness in the rim. That's fair enough for small deflections, but not the 50mm or so to which he takes it. That figure is quite nonsensical in allowing the slack-side spokes to support a negative tension when the rim is pushed their way. (Negative tension means a compressive force, which anyone knows a thin wire spoke cannot support, it simply bows when pushed with very little force.)
This non-linear behavior of spokes however, makes it extremely difficult to construct a true mathematical model of what's going on here, so I don't blame Brandt for dodging that problem. I did too when I suggested how far sideways the spokes tend to deflect the rim, when loaded radially. The rim won't actually deflect quite that far, almost but not quite, thanks mostly to it's own lateral stiffness. Knowing this is why I wrote "
tends to". I've only mentioned lateral bending here, because for small lateral deflections over a distance spanning just a few spokes, are most easily accommodated by bending rather than twisting. Torsion will takes over once a local distortion spreads to involve the whole rim, but by then I reckon all is lost anyway, so I'm not sure torsional stiffness is such a big deal in stopping a wheel from buckling in the first place. Best defence against that I reckon - after matching the spokes to the dish of course - is a wide rim with thick sides.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 21 Nov 2023, 9:21pm
by CJ
Brucey wrote: ↑18 Nov 2023, 5:27pm
he only considered deflections in the radial direction. I agree that a wheel with 36 3D hinges would never have worked but what about 36 2D
hinges? I supposed he meant the rim to have the usual lateral stiffness and compressive stiffness but no radial stiffness.
However:
Jobst Brandt, page 20 wrote:I developed a mathematical model to compute the wheel deformations... This model defined the wheel in terms of its shape and size and the elasticity of the spoke and rim material.
And further down the page, when describing deformations under braking load:
The bending stiffness of the rim causes the change in spoke tension to be gradual as the rim passes through the brake caliper.
So clearly, the radial bending stiffness of the rim plays a part in Brandt's computation of radial deflections. He does NOT assume the rim sections to be connected by hinges of any sort at each node, but to be built into each other. And any engineering student who made such a stupid assumption should not be allowed to graduate!
As for whether Brandt developed his model to the level where it was able to process the interplay between spoke tension and the torsional and lateral bending stiffnesses of a rim, I think you're probably right, he didn't. His diagrams of how a wheel collapses into what he calls a "potato chip", I call a "Pringle" and is technically called a "saddle" shape, is merely a nice description of what we all know to be the case. (FWIW, a slice of potato adopts this shape for the exact same reason: when cooked, the soft and moist body of the potato shrinks more than its firmer and drier periphery, so you get a situation exactly similar to lot of tensioned spokes inside a circumferentially stiff rim. The core tension is relaxed by the periphery adopting a wavy shape and a 'saddle' is the least wavy shape that'll do that, allowing the greatest core shrinkage with the least amount of bending and twisting of the periphery.) Upon re-reading his text, looking for claims to have done something more sophisticated and finding none, I think Brandt's graphic Fig.17 on p42, most probably deals only with spoke tension, assuming negligible torsional and lateral bending stiffness in the rim. That's fair enough for small deflections, but not the 50mm or so to which he takes it. That figure is quite nonsensical in allowing the slack-side spokes to support a negative tension when the rim is pushed their way. (Negative tension means a compressive force, which anyone knows a thin wire spoke cannot support, it simply bows when pushed with very little force.)
This non-linear behavior of spokes however, makes it extremely difficult to construct a true mathematical model of what's going on here, so I don't blame Brandt for dodging that problem. I did too when I suggested how far sideways the spokes tend to deflect the rim, when loaded radially. The rim won't actually deflect quite that far, almost but not quite, thanks mostly to it's own lateral stiffness. Knowing this is why I wrote "
tends to". I've only mentioned lateral bending here, because for small lateral deflections over a distance spanning just a few spokes, are most easily accommodated by bending rather than twisting. Torsion will takes over once a local distortion spreads to involve the whole rim, but by then I reckon all is lost anyway, so I'm not sure torsional stiffness is such a big deal in stopping a wheel from buckling in the first place. Best defence against that I reckon - after matching the spokes to the dish of course - is a wide rim with thick sides.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 22 Nov 2023, 2:49pm
by Brucey
CJ wrote:.... He does NOT assume the rim sections to be connected by hinges of any sort at each node, but to be built into each other.....
I still think he could have meant 2D hinges. I don't think you can know for sure from what he wrote; as I mentioned previously it doesn't really matter,inasmuch as the contribution of any rim to the overall radial wheel stiffness would have been slight at that time.
Regarding the importance [or otherwise] of torsional stiffness,.I suspect that this could be practically demonstrated by building a 'wheel' with a special 'H' section rim.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 22 Nov 2023, 7:54pm
by CJ
Brucey wrote: ↑22 Nov 2023, 2:49pm
CJ wrote:.... He does NOT assume the rim sections to be connected by hinges of any sort at each node, but to be built into each other.....
I still think he could have meant 2D hinges. I don't think you can know for sure from what he wrote.
I can tell from the sum total of his writing that Jobst Brandt was neither an idiot nor a charlatan. As he was also a well-qualified engineer (graduate of Stanford no less) I can be VERY sure that he did not mean 2D hinges.
Regarding the importance [or otherwise] of torsional stiffness,.I suspect that this could be practically demonstrated by building a 'wheel' with a special 'H' section rim
No need. Solid section rolled alloy rims of the 1960s (before hollow extrusions became cheap enough) such as the Weinmann 256 had very little torsional stiffness. But they were also wide and thick-sided, so had pretty good lateral stiffness. And the proof of the pudding is that they did not go out of true or start to buckle too easily. Their radial stiffness was also rather low however, and they were rather prone to form a 'flat spot' when one hit a pothole.
I once mended such a flat spot on our tandem's rear wheel, which fortunately ocurred adjacent to a truck repair yard, whence it was easy to borrow some pieces of timber and a big hammer. So I detached four spokes from the rim in the flat spot and supported the wheel across two timbers, one either end of the flat spot, laid another thinner piece of wood upon the spokeface of the rim in the centre of that spot and swung the hammer at it through the gap in the spokes. After a few wallops the flat spot was no longer flat, but near enough the same roundness as the rest of the wheel. So I re-attached the spokes, the tyre, the tube and the wheel to the tandem and we were on our way again within half an hour.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 26 Nov 2023, 4:34pm
by 531colin
Brandt, writing in around 1980 made some calculations involving loading a wheel with 50Kg at the axle, the wheel has an un-specified rim.
CJ calculates the differential spoke tension (in a dished wheel, with the same gauge spokes both sides) will flex the same un-specified rim 3.6mm sideways, if the wheel is loaded (impacted?) 500Kg at the axle. CJ also asserts that having thicker spokes on the driveside will substantially improve the wheels long term stability.
I weigh about 70Kg, and I have built hundreds of pairs of wheels. I know that new wheels will "go off" when the customer rides them unless you work them a bit to settle the spokes. If you only build for local people, you can tell them to bring their wheels back when they "go off", but that doesn't work if you are posting wheels out all over the country. I used to stand the wheel on the axle end on the floor and press down on the rim with both hands diametrically opposite on the rim, pressing with a fair amount of my weight; all round the rim, turn it over and do the other side. I was obviously exerting a lot less force than 500Kg because thats seven times my body weight, but I repeatedly flexed the rims sideways a lot further than 3.6mm..... this procedure is to settle the spokes, so I could true the wheel and re-balance the tension; I repeated the process until the wheel no longer "went off" and i got a reasonable balance between trueness and evenness of tension. EDIT; 07 05 2025; this isn't stress relieving, which is done earlier in the build.
Using thicker spokes on the driveside where the tension is higher in order to more closely balance the "stored stretch" in the spokes is a neat theory, however I haven't seen any actual evidence from real life to support CJ's repeated assertion that having thicker spokes on the driveside of a dished wheel will make a substantial difference to the long term stability or durability of the wheel.
There are now 2 more threads, one on a very similar topic to this thread, ie. wheels going out of true, and one about an e bike wheel built with 13gauge spokes which have gone slack, possibly because 13g spokes don’t stretch very much at normal tensions.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 27 Nov 2023, 3:52pm
by Brucey
CJ wrote:.....Jobst Brandt was neither an idiot nor a charlatan. As he was also a well-qualified engineer (graduate of Stanford no less) I can be VERY sure that he did not mean 2D hinges..........
No need..........Their radial stiffness was also rather low however..........
I wish Brandt had been a bit more explicit about exactly what he did do; I have many times simplified a problem in order to make it more tractable via modelling and I can't help thinking that he [bereft of computing power as he was] might have done likewise.
Re. 'no need'; I think there is every need; my idea would be to match the radial and lateral stiffness of a modern trim, whilst having a very low torsional stiffness courtesy of the 'H' section. As you pointed out all the many wheels which have been built with rims of low torsional stiffness also had rims of low radial stiffness and it is not easy to assess their relative importance.
Re: Rough-stuff touring wheels - frequency of re-truing
Posted: 27 Nov 2023, 5:33pm
by pwa
Reading Colin's account of how he made new wheels in such a way that they didn't need tweaking after a bit of use, I was reminded of the days when I would buy new wheels from a wheel builder in Cardiff, who would always tell me to bring them back for truing after I had put a few miles in. But the wheels I later had from Spa (posted to me) did stay true during the first weeks of use, and have only needed a modest amount of tweaking during their lifetime. I suppose that must be down to manipulation such as Colin describes.