Tire height vs. rim width- Mtbr.com

# Thread: Tire height vs. rim width

1. ## Tire height vs. rim width

A recent thread got me thinking again about the influence of rim width on tire height, so I decided to play around with a geometry program to help visualize it. Below is a screenshot of the results. Each circle fragment is of identical length.

What happens is that the tire initially gets taller, then eventually gets shorter again. The overall variation is about 15%, but over the range of interesting rim widths the variation is under 5%. For a typical MTB tire over 2", height peaks around a 40-45mm rim width but it doesn't get significantly shorter even for a 50mm rim (nor for a 30mm rim). Interestingly, the peak corresponds with traditional recommendations with road tires, probably not a coincidence.

We all know that tire width increases with rim width, but it turns out that's not really true for tire height. Since height, not volume or width, is a determining factor in pinch flats, I think this is important. Also, height is a more reliable tool for characterizing tires since it is largely immune to the influence of rim size. No more worrying about the internal width or shape of the rim, the larger tire will always be taller.

2. Very nice. I performed similar calculations once upon a time.

The only problem with measuring and reporting tire height is that it is impossible to measure height without the addition of the breaker and the base layer of tread rubber, which can & will vary depending on tire model, manufacturer, etc. Unless you cut the tire afterwards, and subtract this thickness...

It should be easy to calculate a rough estimate of "cross-sectional casing circumference" using the inflated casing width and the rim width, though. However this does not take into account casing stretch at different inflation pressures, and "casing loss" due to tall rim walls and aggressive bead hooks.

3. Originally Posted by bholwell
The only problem with measuring and reporting tire height is that it is impossible to measure height without the addition of the breaker and the base layer of tread rubber, which can & will vary depending on tire model, manufacturer, etc. Unless you cut the tire afterwards, and subtract this thickness...
Yes that's true. Width measurements share that problem.

Originally Posted by bholwell
It should be easy to calculate a rough estimate of "cross-sectional casing circumference" using the inflated casing width and the rim width, though. However this does not take into account casing stretch at different inflation pressures, and "casing loss" due to tall rim walls and aggressive bead hooks.
Yes, that's something I've been interested in. I've always thought the bead-to-bead width of an unmounted tire is the interesting measurement ignoring the difficulty and the casing stretch. I always measure that first.

I'm also interested in the contributions of rim width to minimum pressure, pinch flat resistance, and grip. If wider rims reduce pinch flats, it's clear to me now that it isn't because of increased volume because height doesn't change. There are other things in play, though. There's a general assumption that wider rims are good, and I'm inclined to agree, but I'd like a better technical understanding of why.

4. Height is easy to measure.....just inflate and roll the tire one rev....measure distance and divide by Pi...

That is the OD of the tire.....

Then subtract what ever dimension you want from the rim...

Easy Peasy...

5. Originally Posted by jeffscott
Height is easy to measure.....
Craig and I are interested in the casing height of the tire, not the OD. Actually, we are interested in the casing volume.

6. Originally Posted by bholwell
Craig and I are interested in the casing height of the tire, not the OD. Actually, we are interested in the casing volume.
Well it is a start and casing height would simply be the roll ouot less the tread thickness also easily measured.

7. Originally Posted by craigsj
Yes that's true. Width measurements share that problem..
But to a lesser degree. Obviously there are no breakers or thick layers of rubber on the sidewalls of most bicycle tires. Only the addition of sidewall reinforcement fabric or sidewall decorations in some models.

Originally Posted by craigsj
Yes, that's something I've been interested in. I've always thought the bead-to-bead width of an unmounted tire is the interesting measurement ignoring the difficulty and the casing stretch. I always measure that first.

I'm also interested in the contributions of rim width to minimum pressure, pinch flat resistance, and grip. If wider rims reduce pinch flats, it's clear to me now that it isn't because of increased volume because height doesn't change. There are other things in play, though. There's a general assumption that wider rims are good, and I'm inclined to agree, but I'd like a better technical understanding of why.
Here at the tech center we have a load deflection machine for testing LT/Passenger tires, ATV tires, and motorcycle tires. Like this one, but from a different manufacturer -
One day I hope to make an adapter for bicycle wheels- I might need to replace the load cells with ones with higher resolution, though. This would give me nice data on the relationship between tire stability and rim width / geometry.

8. Originally Posted by jeffscott
Well it is a start and casing height would simply be the roll ouot less the tread thickness also easily measured.
Also minus the thickness of the base layer of tread rubber and the breaker. These are only measured by cutting / destroying the tire.

9. Originally Posted by bholwell
But to a lesser degree. Obviously there are no breakers or thick layers of rubber on the sidewalls of most bicycle tires. Only the addition of sidewall reinforcement fabric or sidewall decorations in some models.
Yes. I could be convinced a height measurement is harder to do. You'd have to estimate the bead location inside the rim as well. At least the rim width has little effect.

So I've imagined the following formula for casing height:

ch = (cc / pi) * (1 + sin((pi^2 * rw) / ( 2 * cc)) / 2 * pi) where cc is casing circumference and rw is rim width. Just a swag.

I've used a road, cross, and MTB tire on a few rims and get results that agree ignoring tread thickness and difficulty with measurement.

Originally Posted by bholwell
This would give me nice data on the relationship between tire stability and rim width / geometry.
Agree, that would be interesting.

10. nice work... definitely something to chew on.
off-hand, it seems like there'd be more at work than just tire height when considering pinch flat resistance as a function of rim width... not saying i know what the 'more' is. i've got this idea that sidewall buckling might play a role... not sure how much is there or how you'd even go about isolating that factor... just a thought.
i'd love to take a sabatical and go to work for a month with mr. holwell, that's for sure

11. In your original diagram, were you able to estimate what base width has the greatest resulting volume?

If they are different (that is, the base width with greatest volume vs casing width), I wonder which ultimately makes more difference for preventing pinch flats and/or rim damage (or what combination).

12. Originally Posted by kapusta
In your original diagram, were you able to estimate what base width has the greatest resulting volume?

If they are different (that is, the base width with greatest volume vs casing width), I wonder which ultimately makes more difference for preventing pinch flats and/or rim damage (or what combination).
Yes. In the diagram, the circle has a diameter of 4 and represents a rim with zero width. The tire has a carcass width of 4Pi, or 12.57. The greatest height was achieved when the rim width was also 4.

I've measured a number of carcass widths and they all seem to be about 2.4 times their width rating. For example, an Ikon 2.2 is labeled a 57 and measures 137-138mm IIRC. Dividing that by Pi yields and internal rim width of 44mm so that's where the height would peak. A 22mm internal width rim would be less than 5% less tall than that, though. I don't know how much the carcass stretches but that would increase the peak rim width linearly.

13. Originally Posted by shiggy
The problem with the last link is that it shows the profile of the tire when it is not in contact with the ground. I'd like to know the effect when the tire is actually gripping something. How does rim width effect the shape of the contact patch? I'm not sure it does, at least not directly.

14. Originally Posted by craigsj
Yes. In the diagram, the circle has a diameter of 4 and represents a rim with zero width. The tire has a carcass width of 4Pi, or 12.57. The greatest height was achieved when the rim width was also 4.

I've measured a number of carcass widths and they all seem to be about 2.4 times their width rating. For example, an Ikon 2.2 is labeled a 57 and measures 137-138mm IIRC. Dividing that by Pi yields and internal rim width of 44mm so that's where the height would peak. A 22mm internal width rim would be less than 5% less tall than that, though. I don't know how much the carcass stretches but that would increase the peak rim width linearly.
What I want to know is what rim width yields the greatest volume, and which yields the greatest height.

From what you are telling me, the rim width of 4 (2 on each side of the axis) has the greatest height. But which width has the greatest volume?

15. Originally Posted by kapusta
What I want to know is what rim width yields the greatest volume, and which yields the greatest height.

From what you are telling me, the rim width of 4 (2 on each side of the axis) has the greatest height. But which width has the greatest volume?
The widest rim on the drawing has the greatest volume, but to what benefit?

A higher volume tire is both wider and taller. The highest volume rim is wider but shorter. How is that extra width going to help?

16. Originally Posted by meltingfeather
off-hand, it seems like there'd be more at work than just tire height when considering pinch flat resistance as a function of rim width... not saying i know what the 'more' is. i've got this idea that sidewall buckling might play a role... not sure how much is there or how you'd even go about isolating that factor... just a thought.
If you consider a tire rolling on smooth pavement and striking a square edge head on, then it's a pretty simple problem but real life is more complicated. I agree with you, there's probably more to it than just height but don't know what that is. What I am confident of is that wider rims don't improve pinch flat resistance through an increase in volume.

17. Here are a couple graphs to illustrate the point. For this purpose I chose a casing width of 52mm on a 19mm internal width rim (your typical 2.1" tire).

In the first graph, the casing height was maximized at a rim width of 45mm. Casing width is nearly a linear relationship.

Likewise, volume is nearly a linear relationship at these rim widths. However, as Craig stated once you get to extreme widths, the volume will begin to decrease.

18. Originally Posted by craigsj
The widest rim on the drawing has the greatest volume, but to what benefit?

A higher volume tire is both wider and taller. The highest volume rim is wider but shorter. How is that extra width going to help?
That's what I am wondering. Whether, with a given tire, greater volume or greater height is more important for pinch flats and rim strikes (or what the best balance is), Or what the difference is in how each handle a sharp square edged hit, like a root.

19. Originally Posted by meltingfeather
off-hand, it seems like there'd be more at work than just tire height when considering pinch flat resistance as a function of rim width... not saying i know what the 'more' is. i've got this idea that sidewall buckling might play a role... not sure how much is there or how you'd even go about isolating that factor... just a thought.
i'd love to take a sabatical and go to work for a month with mr. holwell, that's for sure
I agree that "sidewall buckling" likely plays a role in pinchflat resistance (the angle of the casing relative to the rim wall). More than anything, though, I think it's more related to the design of the rim, and how it interacts with the tire.

For example, a rim with tall rim walls and a sharp edge at the top will contact the tire's sidewall above the bead chafer (where it's strongest) and the sharp edge will concentrate forces. Conversely, a rim with a low rim wall and very rounded edges will contact the tire only through the chafer (a much beefier part of the tire) and will disperse the pinch flat force.

(If I weren't designing tires, I'd like to design rims & wheels )

20. bhowell, those graphs are helpful. How are you measuring the "Casing Arc Length" at 143.91mm? I've measured mine from the inner bead to inner bead, basically the shortest measurement. I'd like my approach to be the same as yours. I just measured my Ikon at 138mm but if I go to the outer edges it measures 149mm.

21. Originally Posted by kapusta
That's what I am wondering. Whether, with a given tire, greater volume or greater height is more important for pinch flats and rim strikes (or what the best balance is), Or what the difference is in how each handle a sharp square edged hit, like a root.
By increasing the tire volume, you might actually be increasing the likelihood of pinchflats. Air is compressible, and since casing height is not increased much, the tire still has nearly the same distance to travel before contacting the rim, but since there is more air volume (like in a high-volume shock), compressing the air is more linear, i.e. easier to bottom out.

I think the moral of the story is to choose a rim that is wide enough to laterally support your tires- there's probably not much you can do against pinch flats regarding rim selection, except for avoiding those rims with sharp edges. If you're still pinch flatting, either choose a higher volume tire or run more air pressure.

22. Originally Posted by craigsj
bhowell, those graphs are helpful. How are you measuring the "Casing Arc Length" at 143.91mm? I've measured mine from the inner bead to inner bead, basically the shortest measurement. I'd like my approach to be the same as yours. I just measured my Ikon at 138mm but if I go to the outer edges it measures 149mm.
Thanks. I used SolidWorks to generate the data. The arc length was set fixed to 143.91mm. The other dimensions were driven.

23. Originally Posted by bholwell
Thanks. I used SolidWorks to generate the data. The arc length was set fixed to 143.91mm. The other dimensions were driven.
OK, thanks. 144mm seems OK for a 2.1" tire depending on how you define it. I just want to avoid confusion.

24. Originally Posted by bholwell
By increasing the tire volume, you might actually be increasing the likelihood of pinchflats. Air is compressible, and since casing height is not increased much, the tire still has nearly the same distance to travel before contacting the rim, but since there is more air volume (like in a high-volume shock), compressing the air is more linear, i.e. easier to bottom out.
This is a great point, and something I thought a lot about in the context of 29ers vs. 26" bikes 8 or so years ago, when I was baffled by the fact that I could run lower pressure in a tire with significantly more volume. In that case, the other factors outweigh the increased elasticity of the tire deflection, but I think it could be more at play here. I was thinking about that this morning in the case of craig's suggestion that height plays a more significant role than volume or width.

25. Originally Posted by bholwell
By increasing the tire volume, you might actually be increasing the likelihood of pinchflats. Air is compressible, and since casing height is not increased much, the tire still has nearly the same distance to travel before contacting the rim, but since there is more air volume (like in a high-volume shock), compressing the air is more linear, i.e. easier to bottom out.
I think that the percentage of the total total tire volume that is displaced is so small, that the actual pressure is going to change very little in a typical compression of the tire resulting in a pinch flat or rim strike. But even if it does change a relevant amount, I think it would change pretty much the same in tires of different volumes (of identical heights), because in the case of a larger volume tire, more volume needs to be displaced in order to hit the rim.

So it is like having a higher volume shock (more linear), but being able to push the piston in farther without bottoming.

I think the moral of the story is to choose a rim that is wide enough to laterally support your tires- there's probably not much you can do against pinch flats regarding rim selection, except for avoiding those rims with sharp edges. If you're still pinch flatting, either choose a higher volume tire or run more air pressure.
This is true. I understand that this thread is largely theoretical, and hair splitting.

26. I wonder if the point of diminishing returns for tire height as you increase rim width is a more-or-less fixed ratio of rim width:casing width.

27. Originally Posted by kapusta
This is true. I understand that this thread is largely theoretical, and hair splitting.
I've read here a few times that wider rims increase tire diameter and reduce pinch flats so I think the information serves a purpose. Yes, the differences are small...exactly!

I'm just trying to show that this "benefit" is really an illusion. Not trying to say wider rims aren't good, just separating fact from fiction.

28. Originally Posted by meltingfeather
I wonder if the point of diminishing returns for tire height as you increase rim width is a more-or-less fixed ratio of rim width:casing width.
I believe it is, and I believe the peak occurs at an inner rim width of b2b casing width divided by Pi (provided you determine that width correctly).

P.S. Handy rule of thumb would be 80% of rated tire width.

29. Originally Posted by bholwell
By increasing the tire volume, you might actually be increasing the likelihood of pinchflats. Air is compressible, and since casing height is not increased much, the tire still has nearly the same distance to travel before contacting the rim, but since there is more air volume (like in a high-volume shock), compressing the air is more linear, i.e. easier to bottom out.

I think the moral of the story is to choose a rim that is wide enough to laterally support your tires- there's probably not much you can do against pinch flats regarding rim selection, except for avoiding those rims with sharp edges. If you're still pinch flatting, either choose a higher volume tire or run more air pressure.
IME a narrowish tire on a wide rim is more prone to pinch flats than on a narrowish rim, for whatever reasons.

30. This thread is very interesting. Thanks for all the information.

Originally Posted by craigsj
I've read here a few times that wider rims increase tire diameter and reduce pinch flats so I think the information serves a purpose. Yes, the differences are small...exactly!

I'm just trying to show that this "benefit" is really an illusion. Not trying to say wider rims aren't good, just separating fact from fiction.
I always thought that wider rims diminished the chances of pinch flat by preventing the tire from folding over itself and therefore pinching the tube... As bholwell said, "sidewall buclking" certainly plays a role... I'm not convinced it is an illusion.

31. Originally Posted by PissedOffCil
As bholwell said, "sidewall buclking" certainly plays a role... I'm not convinced it is an illusion.
Yes, I agree. I was referring to the rim making the tire taller. I believe other factors could exist.

32. Originally Posted by craigsj
I believe it is, and I believe the peak occurs at an inner rim width of b2b casing width divided by Pi (provided you determine that width correctly).

P.S. Handy rule of thumb would be 80% of rated tire width.
ha... that was kind of a dull thought, wasn't it?
that was covered (more-or-less) in the OP... I was just looking at bholwell's figure and thinking sort of abstractly.
bholwell... next time you mess around in that file, put some dang units on your x-axis!
kidding (sorta)... also nice work.

33. Originally Posted by meltingfeather
bholwell... next time you mess around in that file, put some dang units on your x-axis!
Whoops! Fixed, now.

Why don't you go ahead and take that sabbatical? I've got lots of projects you can help me on, and then I wouldn't be so rushed on extracurricular activities like this.

34. I derived some equations for tire width and volume and used the tire height formula I post earlier to graph the details for a tire 157mm wide bead-to-bead using rims from 0-100mm wide. 157mm is conveniently 50mm * Pi so a 50mm produces the tallest tire. It would be rated somewhere between 60-65mm I'd imagine, but remember these dimensions don't include any tire thickness which would add to width and height. Volume is internal volume ignoring rim volume. Here are the results.

Tech Tuesday

36. Originally Posted by PissedOffCil

Tech Tuesday
I thought pslide's quote was apt / accurate:

Originally Posted by pslide

I wonder if RC contacted any actual tire engineers when he wrote this? Because certainly they would talk about things like bead seating, bead compression, bead shape vs. rim shape, etc.

Can't argue with his conclusions though. Wider is better, but there is a lot more to the story when you get into the actual engineering involved.

37. Originally Posted by bholwell
I thought pslide's quote was apt / accurate:
Yeah... it's pretty hard to take anything Richard Cunningham writes seriously.

(I recognize and own the irony of this comment in the context of the Bike Magazine fork testing discussion, btw... my apologies for that)

38. Originally Posted by bholwell
I thought pslide's quote was apt / accurate:
I don't think it's meant to be mathematical science, rather a vulgarisation people can easily understand. Basically the principles involved are right but they let out some elements to keep it simple... nothing wrong with that

39. Originally Posted by PissedOffCil
I don't think it's meant to be mathematical science, rather a vulgarisation people can easily understand.
I get that. But some of the things stated are just plain incorrect. The article made me

The initial calculation assume that the tire cross section is circular, but is that really true for bike tires? Car tires, for example, have radial(?) belts that make them keep a square cross section.

41. Originally Posted by beanbag

The initial calculation assume that the tire cross section is circular, but is that really true for bike tires? Car tires, for example, have radial(?) belts that make them keep a square cross section.
bhowell is probably better to answer that question but I'll take a shot.

The internal pressure of a tire will force the casing to be round absent anything that prevents it from doing so. Bicycle casings may have a distribution of materials that could distort the roundness but those materials will be quite flexible compared to the construction of car tires in your example. The more interesting question is, then, in what way could tire construction invalidate the basic conclusions above? How could a bicycle tire be made that has a fundamentally different, and beneficial, reaction to rim width?

What I tried to show in the analysis is that tire height doesn't vary as much as some people think and therefore minimum tire pressures may also not vary so much assuming that pinch flats are the limitation (which I realize is not always the case). Widths do vary a fair amount but it's not clear why anyone cares about that at all. The tire still has the same tread, that doesn't change, it's contact shape with the ground will be the same and the unloaded curvature of the tire, as little as it changes, won't affect that. It's commonly accepted that wider rims are better and it's often said that's it's because of the increased volume. I think the volume increase isn't the reason at all.

42. Originally Posted by beanbag

The initial calculation assume that the tire cross section is circular, but is that really true for bike tires? Car tires, for example, have radial(?) belts that make them keep a square cross section.
A tire's carcass is completely circular in cross section. There is nothing like a belt to alter the profile in any way. Some tires have breakers, but this affects the profile very little, if at all.

Even motorcycle tires, which have a much more substantial construction, are pretty circular in cross section.

With bicycle tires, the tread depth is usually varied to alter the tire's profile.

43. Originally Posted by craigsj
bhowell is probably better to answer that question but I'll take a shot.

The internal pressure of a tire will force the casing to be round absent anything that prevents it from doing so. Bicycle casings may have a distribution of materials that could distort the roundness but those materials will be quite flexible compared to the construction of car tires in your example. The more interesting question is, then, in what way could tire construction invalidate the basic conclusions above? How could a bicycle tire be made that has a fundamentally different, and beneficial, reaction to rim width?

What I tried to show in the analysis is that tire height doesn't vary as much as some people think and therefore minimum tire pressures may also not vary so much assuming that pinch flats are the limitation (which I realize is not always the case). Widths do vary a fair amount but it's not clear why anyone cares about that at all. The tire still has the same tread, that doesn't change, it's contact shape with the ground will be the same and the unloaded curvature of the tire, as little as it changes, won't affect that. It's commonly accepted that wider rims are better and it's often said that's it's because of the increased volume. I think the volume increase isn't the reason at all.
Pretty spot on.

An increase in volume should theoretically improve the comfort of the tire. But the real benefit (imo) is that when the distance between the two beads is increased, the lateral stability of the tire is improved, allowing less tire 'roll' when cornering hard. I think this improves up to a point, and then the improvement in lateral stiffness starts to level out. Going too wide, however, will slow the steering response and will expose the sidewalls to trail damage more.

I think your next project should be measuring lateral deflection for a given tire at a given load, using several different rims of varying widths.

44. removed - I "luv" the random thread a post goes to when quotes are not used.

45. A wider rim changes a tire's profile, but height at the center of the tire does not change.

The original drawings posted are true for a single line or end view of a square sheet, but not true for a belted tire. The tire height doesn't change with rim width, because the tire circumference remains constant. ...well the circumference does stretch a couple millimeters as it ages from tire pressure.

46. Originally Posted by derby
A wider rim changes a tire's profile, but height at the center of the tire does not change.

The original drawings posted are true for a single line or end view of a square sheet, but not true for a belted tire. The tire height doesn't change with rim width, because the tire circumference remains constant. ...well the circumference does stretch a couple millimeters as it ages from tire pressure.
Hmmm, good point.

47. "...but not true for a belted tire."

Not true for a belted tire where the belt cannot stretch. Such a tire would have a flat tread even when unloaded. How many bicycle tires look like that?

Bicycle tire circumference does not remain constant and that is trivially verifiable. Try measuring it, derby.

48. Originally Posted by derby
The original drawings posted are true for a single line or end view of a square sheet, but not true for a belted tire. The tire height doesn't change with rim width, because the tire circumference remains constant. ...well the circumference does stretch a couple millimeters as it ages from tire pressure.
You are seeming to suggest that a bicycle tire is belted like an automotive tire... that's not the case and the height of bicycle tires definitely changes with rim width.

49. Originally Posted by meltingfeather
You are seeming to suggest that a bicycle tire is belted like an automotive tire... that's not the case and the height of bicycle tires definitely changes with rim width.
The center strip of the tire is a certain length. Once inflated, the diameter (height) of the tire is that length / pi. Yes, tire pressure could stretch that length slightly, but that is a separate issue from rim width.

If two identical tires at identical pressure on rims of different width were to have different diameters (height), that would mean that some force is stretching the tire material along the center strip more in the taller one. I can't think of anything that would explain that, which is why I agree with what Derby is saying.

I think that the problem with the diagrams above is that they assume the cross section of the tire retains a perfect arc shape as you change the rim width. this would be true for a straight tube, but not for one in a ring like a tire.

50. If bike tires were belted circumferentially, then rim width would not affect the outside diameter. However, most tires (ok, the ones I have) have two belts 90 degrees to each other and 45 degrees to the equator. With this belting pattern, an individual patch of tire is "area conserving", but can stretch in one direction and shrink in another (e.g. an X that gets taller / skinnier, or shorter / fatter), or it can shear. So I think the overall outside diameter, and thus wheel height, can change.

Also, my slide rule is longer than yours.

51. Originally Posted by kapusta
The center strip of the tire is a certain length. Once inflated, the diameter (height) of the tire is that length / pi. Yes, tire pressure could stretch that length slightly, but that is a separate issue from rim width.

If two identical tires at identical pressure on rims of different width were to have different diameters (height), that would mean that some force is stretching the tire material along the center strip more in the taller one. I can't think of anything that would explain that, which is why I agree with what Derby is saying.

I think that the problem with the diagrams above is that they assume the cross section of the tire retains a perfect arc shape as you change the rim width. this would be true for a straight tube, but not for one in a ring like a tire.
(Edited, based on measurements, facts. See measured evidence: Tire height vs. rim width - Page 3)

This is long..... Maybe I should simply stand by my claim that by changing rim width, the tire's profile is changed, but the tire height does not change.... However, due to tire construction, not by geometry, there could be minimal height difference from structural casing tension changes, but in practice the height does not change when the rim width is changed.

Yes, without changing a rim width, a the tire circumference can stretch or shrink very slightly with higher or lower air pressure tension with the “bias-ply”, 45 degree to bead, crossing thread directional cloth in mountain tire casings.

I guess the question then becomes would a wider rim (up to a width the beads can't reach) reduce the spread of the thread spacing near the circumference and allow the tire to grow higher with the same air pressure?

The casing on either side of the tread center which is the line of circumference, is also limiting growth in height of this near tread center area.

I think the sidewall closer to the bead is relaxed in structural thread tension with a wider rim. So more structural thread tension is transferred towards the tread area. The area near the corner knobs then supports more of the resistance to the same air pressure, stretches and stands up the corner knobs taller.

1. Does the added tension taken by the corner knob area of the casing then relax thread tension along the tread center area of the casing? Would the center tread then shrink shorter in height? (Edit added: the answer is yes, see measured evidence: Tire height vs. rim width - Page 3)

2. Or the taller corner knob area of casing maintain center tread height? (Edit: Maybe, the measured difference is minimal, less than 0.0005 % smaller circumference with a wider rim).

Then the same air pressure could stretch the relaxed casing threads in the center tread area, and raise the center height as much as the edge knob height is raised. (Edit added: No, wrong, this does not happen using the same tire pressure with a wider rim. The fact is that a good quality mountain bike tire does not increase in height or circumference when going to a wider rim)

I suspect the more stretched edge knob cloth area profile angle does not raise in height much, and the center of the tread could not be raised in height further than the edge casing is raised. And visually we always see the tread become more square, the edge knobs are raised more than the center knobs.

Generally we lower tire pressures when going to a wider rim to maintain consistent tire suspension bump feel. And the lower pressure would negate any minimal tread center height stretch gained by relaxed center tread structural resistance to the air pressure.

Edit added: Measuring the same tire and rim with pressure dropped from 30psi to 20psi, may have shortened the rollout circumference, by 0.5mm, less than 0.00025%. In conclusion lower or higher practical use air pressures do not significantly stretch a good quality mountain bike tire.

52. Originally Posted by derby
Maybe I should simply stand by my claim that by changing rim width, the tire's profile is changed, but the tire height does not change....
By definition, if you change the profile of the tire, then the length of various (virtual) circumferential bands along that profile must change length / diameter also. So what makes the top / outermost band special?

53. Originally Posted by derby
This is long..... Maybe I should simply stand by my claim that by changing rim width, the tire's profile is changed, but the tire height does not change.... However, due to tire construction, not by geometry, there could be minimal height difference from structural casing tension changes, but in practice the height does not change when the rim width is changed.
And this would be incorrect. Not just in theory, but in practice.

54. Originally Posted by kapusta
The center strip of the tire is a certain length. Once inflated, the diameter (height) of the tire is that length / pi. Yes, tire pressure could stretch that length slightly, but that is a separate issue from rim width.

If two identical tires at identical pressure on rims of different width were to have different diameters (height), that would mean that some force is stretching the tire material along the center strip more in the taller one. I can't think of anything that would explain that, which is why I agree with what Derby is saying.

I think that the problem with the diagrams above is that they assume the cross section of the tire retains a perfect arc shape as you change the rim width. this would be true for a straight tube, but not for one in a ring like a tire.
Center strip? Do you mean breaker? A breaker is not a belt. It is not intended to alter the profile of the tire. It's purpose is to increase the puncture resistance of the tire in the tread area, not alter the profile of the tire. When I worked at Maxxis / CST we commonly added or removed breakers from tires, and it had no effect on the tire's profile.

FWIW, I now design and develop ATV and UTV tires for Carlisle / ITP. These are bias and radial, belted and non-belted tires. Even in belted radial ATV tires there is a change in O.D. with a change in rim width. Granted, these are 2 ply high angle nylon belts (not steel), but belts nonetheless.

55. Originally Posted by bholwell
And this would be incorrect. Not just in theory, but in practice.
I see derby's point being dismissed without really addressing it. Even if the tire can stretch enough to allow it to get taller (I'll take your word that it does) surely that resistance to stretching will result in a profile different that what those diagrams indicate.

I'm thinking I need to see some actual evidence that the diagrams used in this thread work out in reality to believe it. Because at this point I am doubtful.

56. Originally Posted by kapusta
I see derby's point being dismissed without really addressing it. Even if the tire can stretch enough to allow it to get taller (I'll take your word that it does) surely that resistance to stretching will result in a profile different that what those diagrams indicate.

I'm thinking I need to see some actual evidence that the diagrams used in this thread work out in reality to believe it. Because at this point I am doubtful.
Ok. Nylon fabric is elastic in the direction of the threads, and has almost no strength in the direction perpendicular to the threads. This is why two plies are needed at opposing angles (all mountain bike tires are of bias construction).

Yes the hoop tension at the outermost circumference of the tire will increase as the tire O.D. attempts to increase, and will restrict it to some degree. In my first graph, the section height changes, what, 1mm when going from a 17mm rim to a 27mm rim? Or less than a 3mm change MAX? I would venture to guess that in practice, the section height would change 80-90% of the theoretical.

57. ## Tire height vs. rim width

Originally Posted by kapusta
I see derby's point being dismissed without really addressing it. Even if the tire can stretch enough to allow it to get taller (I'll take your word that it does) surely that resistance to stretching will result in a profile different that what those diagrams indicate.

I'm thinking I need to see some actual evidence that the diagrams used in this thread work out in reality to believe it. Because at this point I am doubtful.
He just proclaimed that tire height doesn't change and followed that with a 500-word post that I can't really make any sense of. He also states as fact things that are demonstrably untrue, so it's hard to take him seriously.
If you need to see some evidence and you don't believe a tire development engineer telling you then bust out some measuring equipment.

58. Originally Posted by meltingfeather
He just proclaimed that tire height doesn't change and followed that with a 500-word post that I can't really make any sense of.
If you need to see some evidence and you don't believe a tire development engineer telling you then bust out some measuring equipment.
You missed my point. Luckily, the tire developer you refer to did not

59. ## Tire height vs. rim width

Originally Posted by kapusta
You missed my point. Luckily, the tire developer you refer to did not
I didn't think I missed it, but I'm always glad when Bryan jumps in anyway.
derby essentially proclaimed that tire casings do not stretch. He said "in practice" as if he has some working knowledge of the fact that they do not, which he can't, since they do. A few minutes and a measuring tape will demonstrate it.

60. Originally Posted by bholwell
Ok. Nylon fabric is elastic in the direction of the threads, and has almost no strength in the direction perpendicular to the threads. This is why two plies are needed at opposing angles (all mountain bike tires are of bias construction).

Yes the hoop tension at the outermost circumference of the tire will increase as the tire O.D. attempts to increase, and will restrict it to some degree. In my first graph, the section height changes, what, 1mm when going from a 17mm rim to a 27mm rim? Or less than a 3mm change MAX? I would venture to guess that in practice, the section height would change 80-90% of the theoretical.
I realize we are splitting hairs, since we are talking about very small height differences for typical rims and tires. I figured this discussion was more more one of concept rather than practical application.

But back to the topic, a 1mm increase in tire height is a roughly 6.3mm increase in the outermost circumference. Is that amount of stretching achieved (or 80-90% of that) at mtb tire pressures?

61. Originally Posted by kapusta
But back to the topic, a 1mm increase in tire height is a roughly 6.3mm increase in the outermost circumference. Is that amount of stretching achieved (or 80-90% of that) at mtb tire pressures?

Yes, easily.

Circumference of a 26x2.0 mtb tire = approx 2074.71mm

Add 2mm to diameter = circumference of 2080.99mm

So that's an increase in circumference of 6.28mm (like you said), or an increase of 0.3 percent.

Keep in mind that the threads of the casing fabric do not run parallel to the direction of travel, but are at an angle. Inflation pressure easily spreads the threads apart (so if the tire was an unbelted radial, there would be little to no resistance to OD growth), but since the tire is a bias construction the threads pantograph a bit with inflation.

62. Originally Posted by bholwell
Yes, easily.

Circumference of a 26x2.0 mtb tire = approx 2074.71mm

Add 2mm to diameter = circumference of 2080.99mm

So that's an increase in circumference of 6.28mm (like you said), or an increase of 0.3 percent.

Keep in mind that the threads of the casing fabric do not run parallel to the direction of travel, but are at an angle. Inflation pressure easily spreads the threads apart (so if the tire was an unbelted radial, there would be little to no resistance to OD growth), but since the tire is a bias construction the threads pantograph a bit with inflation.
Right. Thanks!

63. ## measured: no difference, if anything shorter with a wider rim

Measured three times with each rim, the same new unused tire on the same brand rims, Velocity 28mm Blunt and 35mm P35, inflated carefully to 30 psi with the same pump. Measured carefully at 1" mark on tape for accuracy, square to the corner edge of the closest outer knob with valve aligned plumb with axle.

In fact the wider rim rolled out the same tire with same air pressure on a 7mm wider rim almost 1/16th inch shorter, so I'll round to 1mm shorter rollout. Virtually the same circumference, certainly not larger.

I don't have a narrower rim to measure with a greater difference.

I don't think it matters except bigger wheels would show more difference if there is any.... the rim and tire were 584 size bead-seat, VeeRubber Trail Taker 2.4, 88 1/8 inch rollout with 28mm wide rim, 88 1/16 inch rollout with 35mm wide rim.

BTW, the trail Taker is still very round in profile on a 35mm rim, looks like it would require a 60mm wide rim to square the edge knobs up slightly.

I'll go edit my 500 word essay and correct it to explain why wider rims in fact slightly shorten a tire circumference and height!

64. ## Tire height vs. rim width

Originally Posted by derby
Measured three times with each rim, the same new unused tire on the same brand rims, Velocity 28mm Blunt and 35mm P35, inflated carefully to 30 psi with the same pump. Measured carefully at 1" mark on tape for accuracy, square to the corner edge of the closest outer knob with valve aligned plumb with axle.

In fact the wider rim rolled out the same tire with same air pressure on a 7mm wider rim almost 1/16th inch shorter, so I'll round to 1mm shorter rollout. Virtually the same circumference, certainly not larger.

I don't have a narrower rim to measure with a greater difference.

I don't think it matters except bigger wheels would show more difference if there is any.... the rim and tire were 584 size bead-seat, VeeRubber Trail Taker 2.4, 88 1/8 inch rollout with 28mm wide rim, 88 1/16 inch rollout with 35mm wide rim.

BTW, the trail Taker is still very round in profile on a 35mm rim, looks like it would require a 60mm wide rim to square the edge knobs up slightly.

I'll go edit my 500 word essay and correct it to explain why wider rims in fact slightly shorten a tire circumference and height!

How many times did you measure the rollout?

I usually do two revolutions, three times and average. Normal to have a 10mm range in the double rollout distances.

65. Originally Posted by shiggy
How many times did you measure the rollout?

I usually do two revolutions, three times and average. Normal to have a 10mm range in the double rollout distances.
5 times the first time, there was a 1/8 inch, about 3-4mm, difference from the first to the next 4 virtually identical rollouts after I got the alignment with the tape squared consistently. The second set of runs of the same tire with the wider rim, same high traction rug surface, 3 rollouts all measured within less than 1/32 inch, virtually identical, well within a margin of error.

I was concerned with the first 4mm variance in a single revolution from all the others being within 1mm, I threw out that first measurement due to error in my technique.

I may do another test with two wheel revolutions for each measured rollout. I thought of that during the second rim test. But the measurements were consistent and virtually identical after correcting my alignment method.

The small reduction in circumference measured with the wider rim, could be better verified with doing two revolution rollouts many times and averaging. Right now I've proved to myself that good quality mountain tires don't stretch longer in circumference or height when going to a larger rim.

BTW, after the tests at 30 psi in the same tire with both rims, I lowered pressure to 20 psi more appropriate while on the wider rim, but the tire still measure nearly the same in circumference, possibly 1mm shorter at most, insignificant, IMO. However, I imagine race car bias-ply tires, much fatter higher volume smaller rim and light weight, would stretch and shrink far more significantly from air pressure variation, and those tires are designed to do so for tuning.

66. Originally Posted by derby
... Right now I've proved to myself that good quality mountain tires don't stretch longer in circumference or height when going to a larger rim.
...
I'm glad that you've proved your own preconceived notions, but that doesn't make them any less incorrect.

A crude rollout measurement is likely not accurate enough to measure the subtle increase in tire circumference.

67. ## My little experiment

To back up my claims, and to satisfy my curiosity, I performed the following experiment:

I mounted a used, 29x2.2 Ikon eXC onto a road rim (13.04mm internal width) and inflated the tire to 40 psi. After 72 hours, I used a calibrated Pi tape to measured the circumference. I then deflated to 25 psi and measured the circumference. Two more measurements were taken at each inflation pressure, and the results were averaged.

I then made a SolidWorks sketch of a tire profile on the narrow road rim, and adjusted the casing arc length so that the diameter matched what was measured. I then adjusted the internal rim width to generate diameter data. This data is plotted in the graph below.

I then mounted the tire onto a Flow rim (22.85mm internal width) and inflated to 40 psi. After 48 hours, diameter measurements were again taken and averaged using a calibrated Pi tape. These measurements can also be seen in the graph below.

At 25 psi, the measured diameter grew to 82.78% of the theoretical growth.

At 40 psi, the measured diameter grew to 68.74% of the theoretical growth.

This difference makes sense, because at higher pressures the casing has less ability to expand at the outer circumference as the rim grows in width. I would expect to also see a smaller percentage of growth with 60 tpi or 27 tpi casings, a heavier UST construction, etc.

Bottom line, even though the growth in O.D. is minor, a bicycle tire will still grow taller when mounted on a wider rim.

68. Originally Posted by derby
5 times the first time, there was a 1/18 inch, about 3-4mm.
Maybe part of your problem is that you can't accurately convert between inches and mm.

Your claim of measurement accuracy of < 1/32" for a rollout test is silly.

69. ## Tire height vs. rim width

Originally Posted by bholwell
To back up my claims, and to satisfy my curiosity, I performed the following experiment:

I mounted a used, 29x2.2 Ikon eXC onto a road rim (13.04mm internal width) and inflated the tire to 40 psi. After 72 hours, I used a calibrated Pi tape to measured the circumference. I then deflated to 25 psi and measured the circumference. Two more measurements were taken at each inflation pressure, and the results were averaged.

I then made a SolidWorks sketch of a tire profile on the narrow road rim, and adjusted the casing arc length so that the diameter matched what was measured. I then adjusted the internal rim width to generate diameter data. This data is plotted in the graph below.

I then mounted the tire onto a Flow rim (22.85mm internal width) and inflated to 40 psi. After 48 hours, diameter measurements were again taken and averaged using a calibrated Pi tape. These measurements can also be seen in the graph below.

At 25 psi, the measured diameter grew to 82.78% of the theoretical growth.

At 40 psi, the measured diameter grew to 68.74% of the theoretical growth.

This difference makes sense, because at higher pressures the casing has less ability to expand at the outer circumference as the rim grows in width. I would expect to also see a smaller percentage of growth with 60 tpi or 27 tpi casings, a heavier UST construction, etc.

Bottom line, even though the growth in O.D. is minor, a bicycle tire will still grow taller when mounted on a wider rim.

What about the differences in the above rims' sidewall height? The interior depth of Notubes rims is less than ISO rims.

70. Originally Posted by shiggy
What about the differences in the above rims' sidewall height? The interior depth of Notubes rims is less than ISO rims.
Very good question. Yes, the bead hook height of the NoTubes rims are lower than a typical rim.

I asked Mike B. (lead engineer at NoTubes) about this a couple years ago. His response was that the bead hook height is only lower because the bead seat diameter of the rim is raised. The actual overall diameter of the rim is the same as a typical rim. Measure them yourself if you have a ZTR rim- you'll see that it's true.

The overall diameter of the rim was my critical dimension in my SolidWorks sketch, since this is where the casing bends and takes on its rounded shape. So my 'casing arc length' that was constrained was the arc distance from bead hook to bead hook.

If you like, I can go back and measure the O.D. of both rims.

71. ## Tire height vs. rim width

Originally Posted by bholwell
Very good question. Yes, the bead hook height of the NoTubes rims are lower than a typical rim.

I asked Mike B. (lead engineer at NoTubes) about this a couple years ago. His response was that the bead hook height is only lower because the bead seat diameter of the rim is raised. The actual overall diameter of the rim is the same as a typical rim. Measure them yourself if you have a ZTR rim- you'll see that it's true.

The overall diameter of the rim was my critical dimension in my SolidWorks sketch, since this is where the casing bends and takes on its rounded shape. So my 'casing arc length' that was constrained was the arc distance from bead hook to bead hook.

If you like, I can go back and measure the O.D. of both rims.
Notubes talks about the shorter rim sidewall giving the tire greater volume.

I have measured the interior depth to the bead seat of Notubes Crest rims and they are ~2mm shallower than UST and standard ISO rims

72. Originally Posted by shiggy
I have measured the interior depth to the bead seat of Notubes Crest rims and they are ~2mm shallower than UST and standard ISO rims
1.8mm is what I have measured.

Originally Posted by shiggy
Notubes talks about the shorter rim sidewall giving the tire greater volume.
This might be true, but only if the tire's beads are stretched beyond what they normally would be on a UST rim.

Going from a UST rim profile, if NoTubes rims just lowered their bead hook height, then yes, the tire would gain volume. (This would also drastically increase the likelihood of blow-offs.) But what they've done instead is left the bead hook location the same, and they've raised the bead seat shelf. So the only way the tire can gain volume is if the bead seat shelf is forcing the beads up and away from center.

Aramid beads are elastic, and this is not outside the realm of possibility. In fact, if my rim was a Flow EX instead, I wouldn't have used it to perform the experiment. The Flow EX has an even larger bead seat shelf diameter. But the beads of the tire in my experiment (used Ikon, regular clincher) seated on the Flows at less than 15 psi, meaning at 25 and 40 psi there is not much, if any, bead elongation occurring.

73. ## Tire height vs. rim width

Originally Posted by bholwell
1.8mm is what I have measured.

This might be true, but only if the tire's beads are stretched beyond what they normally would be on a UST rim.

Going from a UST rim profile, if NoTubes rims just lowered their bead hook height, then yes, the tire would gain volume. (This would also drastically increase the likelihood of blow-offs.) But what they've done instead is left the bead hook location the same, and they've raised the bead seat shelf. So the only way the tire can gain volume is if the bead seat shelf is forcing the beads up and away from center.

Aramid beads are elastic, and this is not outside the realm of possibility. In fact, if my rim was a Flow EX instead, I wouldn't have used it to perform the experiment. The Flow EX has an even larger bead seat shelf diameter. But the beads of the tire in my experiment (used Ikon, regular clincher) seated on the Flows at less than 15 psi, meaning at 25 and 40 psi there is not much, if any, bead elongation occurring.
That would make the Notubes BSD 3.6mm larger than ISO BSD. I am not comfortable in stressing the tire bead in this manner.

74. Originally Posted by meltingfeather
Maybe part of your problem is that you can't accurately convert between inches and mm.

Your claim of measurement accuracy of < 1/32" for a rollout test is silly.
Thanks for finding the typo! Edited the post, corrected to 1/8 inch = 3.175mm.

75. Perhaps 650b behaves differently?

The irony is that the original purpose of the thread was to show that height is relatively insensitive to rim width which ran contrary to common lore. The claim has been that wider rims support lower pressures and that is, at its most generous, an oversimplification. Tire pressures can't be lowered when rim strikes are a threat. For some people rim strikes are never a threat and those people are, no doubt, connoisseurs of tire performance here.

Feel free to deny this despite common sense, readily observable fact, and the experience of an actual tire designer. Funny that it is commonly accepted that tires need to be given days to stretch before measuring their final size yet stretching is rejected here for not suiting the argument. MTBR is place where objective truth is simply not valued. It's more important to win than to learn.

If a bicycle tire stretches when new, which I think everyone accepts as true, then you have to wonder how its construction allows that while preventing growth in overall circumference.

It's comforting to know that drag racing slicks don't change diameter because they are belted.

76. Originally Posted by shiggy
That would make the Notubes BSD 3.6mm larger than ISO BSD. I am not comfortable in stressing the tire bead in this manner.
Whether it's mechanical stress from the rim, or stress from the inflation pressure of the tire, the beads must be strong enough to withstand all situations plus a factor of safety. Responsible tire manufacturers know this and utilize QC checks like hydrostatic burst testing to ensure the construction of the tire is adequately strong. For example, at Maxxis the spec is that the tire must withstand twice the max inflation pressure before it bursts. And many times, the tire's carcass would fail before the beads. And now, Bontrager has released tubeless ready ROAD tires that utilize aramid beads. Have you seen these? But I don't fault you for not trusting the NoTubes rim design; there are certain tires I would not use tubeless on Stan's rims. Even Schwalbe's first tubeless ready tires' beads were of inadequate strength.

That's why I'm all for standardization. The UST standard isn't flawless, but it at least gives tire manufacturers a target to aim at. But you must realize that for a tubeless setup to perform adequately (without burps), there MUST be an interference fit between the beads and the rim. And of course this will induce additional mechanical stress on the beads. No getting around it.

77. ## Tire height vs. rim width

Originally Posted by bholwell
Whether it's mechanical stress from the rim, or stress from the inflation pressure of the tire, the beads must be strong enough to withstand all situations plus a factor of safety. Responsible tire manufacturers know this and utilize QC checks like hydrostatic burst testing to ensure the construction of the tire is adequately strong. For example, at Maxxis the spec is that the tire must withstand twice the max inflation pressure before it bursts. And many times, the tire's carcass would fail before the beads. And now, Bontrager has released tubeless ready ROAD tires that utilize aramid beads. Have you seen these? But I don't fault you for not trusting the NoTubes rim design; there are certain tires I would not use tubeless on Stan's rims. Even Schwalbe's first tubeless ready tires' beads were of inadequate strength.

That's why I'm all for standardization. The UST standard isn't flawless, but it at least gives tire manufacturers a target to aim at. But you must realize that for a tubeless setup to perform adequately (without burps), there MUST be an interference fit between the beads and the rim. And of course this will induce additional mechanical stress on the beads. No getting around it.
I would rather not have the stress of mechanically (over) stretching the tire beads before adding the normal stress of inflation pressures. That the conversion "tubeless" setups are limited to much lower pressures than UST and tubed systems tells me that a pushing hard at the safety margins.

78. Originally Posted by derby
I don't think it matters except bigger wheels would show more difference if there is any.... the rim and tire were 584 size bead-seat, VeeRubber Trail Taker 2.4, 88 1/8 inch rollout with 28mm wide rim, 88 1/16 inch rollout with 35mm wide rim.
Digging up an old thread here, but I hope to have some more numbers for a Vee Trail Taker 2.4 soon.

Originally Posted by derby
BTW, the trail Taker is still very round in profile on a 35mm rim, looks like it would require a 60mm wide rim to square the edge knobs up slightly.
I'll be mounting a 650b 2.4 TT on a WTB Scraper i45 rim. Curious to see if this rim is wide enough to finally to get the TT's side knobs to have a profile similar to something like an HR2.

I'm reading 2.4 TT's on Blunt 35's measures to 27.75" tall. Curious to see what it comes out to on a super wide i45 rim.

79. Originally Posted by bholwell
By increasing the tire volume, you might actually be increasing the likelihood of pinchflats. Air is compressible, and since casing height is not increased much, the tire still has nearly the same distance to travel before contacting the rim, but since there is more air volume (like in a high-volume shock), compressing the air is more linear, i.e. easier to bottom out.

I think the moral of the story is to choose a rim that is wide enough to laterally support your tires- there's probably not much you can do against pinch flats regarding rim selection, except for avoiding those rims with sharp edges. If you're still pinch flatting, either choose a higher volume tire or run more air pressure.
sorry for quoting a ~6 year old post but given the huge developments in the last two years (wider rims and even wider tires) this is a hot topic that should be further discussed

Following this logic one should choose a rim wide enough but not too wide as a too wide rim would let the tire grow in air volume without making him equally higher

I upgraded to 2.6" tires with 30mm rim rear / 35mm rim front for various reasons (rim stability, tire shape, different psi) and this is another reason to run a slightly narrower rim in the rear

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