Tire width on Hooked rim vs Hookless rim
04-25-24, 09:27 PM
#26
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I was discussing it because you brought it up. Specifically, your objection to a point in my first post is where the circular-arc tire approximation entered the thread:
Although it's not a very accurate model, I think it's fun and interesting to talk about, and a good comprehension of it is handy for understanding why tire height and width changes how it does with changing rim width. Although the edge cases that I described are not realistic, they are illustrative because they can be visualized very easily: most people with a high-school education are good enough with geometry to understand that the circle and semicircle have the same height and arc length. Computing the scaling of width and height in the intermediate cases requires significantly more complex math, but most people can intuitively visualize them once they understand the two bounding cases that I showed.
At any rate, I don't think we actually have a lot of disagreement on the original matter that I was addressing (i.e cyclezen's statement being wrong).
Although it's not a very accurate model, I think it's fun and interesting to talk about, and a good comprehension of it is handy for understanding why tire height and width changes how it does with changing rim width. Although the edge cases that I described are not realistic, they are illustrative because they can be visualized very easily: most people with a high-school education are good enough with geometry to understand that the circle and semicircle have the same height and arc length. Computing the scaling of width and height in the intermediate cases requires significantly more complex math, but most people can intuitively visualize them once they understand the two bounding cases that I showed.
At any rate, I don't think we actually have a lot of disagreement on the original matter that I was addressing (i.e cyclezen's statement being wrong).
04-25-24, 10:35 PM
#27
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Previously in the thread, you implied that the point at which a setup is no longer functional is the point at which it is no longer wider than its seating on the rim:
In the case of the red curve, the "rim width" is the circumference of the semicircle. The semicircle's arclength is Pi*r, and the circumference is 2*r, so the ratio of rim width to tire arclength is (2*r)/(Pi*r) = 2/Pi = .637. Or, in other words, it's the example where the rim width is about 64% of the tire arclength.
If the rim width were brought to anything less than this, the tire width would bulge outward relative to its anchor point on the rim, and would thus satisfy your requirement for a non-"impossible" setup.
In other words, as rim widths go from 30% of tire arclength through 64% of tire arclength, we have a very large range of non-"impossible" setups where increasing the rim width results in a decrease of inflated tire height. That's an extremely wide range!
Now, is that a useful practical conclusion? Of course not. We probably both agree that it sounds stupid, and has very little to do with practical setups that road cyclists use. And even if it did, it would have significant inaccuracy.
I'm not using the framing I'm using to mystify anybody. I'm doing it because the stuff you claim is "abundantly clear" is actually pretty deep in the murky weeds where real-world practice (and more-robust theory) introduces complicated considerations.
Last edited by HTupolev; 04-25-24 at 11:59 PM.
04-26-24, 04:16 AM
#28
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You seem to only consider a part of the overall equation and make a simple assumption that’s correct in some cases but not all. Kinda like your saddle design which I researched a bit about recently and doesn’t actually work for a lot of people as you seem to think/market it to. Studies/facts can seem to support a lot of theories if you’re careful about what data you do/don’t collect and include. That doesn’t make them the absolute truth….
04-26-24, 06:47 AM
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You seem to only consider a part of the overall equation and make a simple assumption that’s correct in some cases but not all. Kinda like your saddle design which I researched a bit about recently and doesn’t actually work for a lot of people as you seem to think/market it to. Studies/facts can seem to support a lot of theories if you’re careful about what data you do/don’t collect and include. That doesn’t make them the absolute truth….
The "overall equation" with bike tires just doesn't include tire and rim combinations that are theoretical. Do you understand that if the inner width of the rim was so wide that the sidewall was at an angle the hook bead would fail to function, and the rim would hit the pavement in corners?
You could also propose that bike tires be designed like low profile car tires, with so much rubber and such low pressure that they hold a box shape once mounted, and collapse in the middle if the rim gets too wide. But bike tires aren't made like that, but because bikes are leaned in corners and cars are not, so bike tires are supposed to be round.
And this isn't a theoretical discussion. If a bike owner with minimum tire clearance wants to know if they can get more clearance by going to a wider rim, the answer is "no". Not some theoretical "maybe", but an unequivocal "no". Which is why I pointed this out in the first place - in case people who ride bikes were reading.
04-26-24, 08:29 AM
#30
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Not necessarily. Inflated tire height is not guaranteed to change monotonically with rim width.
If a tire is inflated to a light-bulb-like profile on a narrow rim, a chunk of the tire's "cross-sectional arc length" is used up bending inward toward the hooks, rather than adding height.
When comparing between common practical setups, internal rim width has a pretty modest impact on inflated height. And sometimes, going from a narrow internal to a wider internal can add a bit of height.
If a tire is inflated to a light-bulb-like profile on a narrow rim, a chunk of the tire's "cross-sectional arc length" is used up bending inward toward the hooks, rather than adding height.
When comparing between common practical setups, internal rim width has a pretty modest impact on inflated height. And sometimes, going from a narrow internal to a wider internal can add a bit of height.
all worth discussion... Thanks
The relationship of height/width is tied to many factors - tire profile design as well as tire width, rim width, hook/hookless .
your subsequent example is, however, also well outside of reality. placing the beads anywhere along that base line, within those extremes you show, would give differing results, depending on factors mentioned - so might be taller or lower, wider or narrower.
And rim manufacturers do have 'suggested' tire sizes/ranges for their rims, for good reason.
Maybe worth a thread on it's own ? If the concerns of tire width/rim width combinations, and resulting real world effects, are worth a discussion.
But not today...
I have to bail, off for 5 day travel and not opportune to spend time on BF.
Sadly, I won't have any saddle time either during that period. but maybe...
As Always...
Ride On
Yuri
Quick EDIT: The idea of 'hookless' has it's merits, at first glance. But then on further thought, there are merits to 'hook' rims as well...
also worth discussion... at the moment, I'm staying in 'hooked' camp, and my coming set of CF wheels will be hooked...
Last edited by cyclezen; 04-26-24 at 08:34 AM.
