Wider inner rim width, lower tire height?

[Black Dog]

Originally Posted by muz

Yes, but I still don't see it. White curve is 25mm on 13mm ID rim, and bright red is the same tire on 20mm ID. Bright red is the tallest, and white is in the shortest group. How is it possible that these two lengths are equal?

The length of the lines is exactly the same in reality. The drawing may not be precise but shows the effect. Height changes as a function of the angle of the side walls. As you widen the rim the sidewalks become more vertical and raise the top of the tire.

[pobrien]

I would presume that the tire tread (centre of tire) is inelastic and would expand to one size once inflated to a maximum pressure recommended.

I can see the tire 'getting shorter' with less air pressure.

Perhaps I am missing something...Just a thought.

[PacNW2Ford]

Originally Posted by Black Dog

The length of the lines is exactly the same in reality. The drawing may not be precise but shows the effect. Height changes as a function of the angle of the side walls. As you widen the rim the sidewalks become more vertical and raise the top of the tire.

The additional width between the beads is adding to the circumference of the cross-section, thus the diameter (height) has to increase proportionally. A stiff belt may minimally affect the section, but this would be canceled out by the spreading of the sidewalls as long as the rim is still narrower than the tire width.
This effect is measurable, so I don't understand why theories are being floated. Measure the tires and report back. All of mine are taller on wider rims. I'll bet very few will be shorter.

[Gummee]

Originally Posted by PacNW2Ford

The additional width between the beads is adding to the circumference of the cross-section, thus the diameter (height) has to increase proportionally. A stiff belt may minimally affect the section, but this would be canceled out by the spreading of the sidewalls as long as the rim is still narrower than the tire width.
This effect is measurable, so I don't understand why theories are being floated. Measure the tires and report back. All of mine are taller on wider rims. I'll bet very few will be shorter.

IDK man. If you spread the legs of a triangle out, the 3rd point comes down because the length of the two sides remains the same length.

Why would it be any different on a hemisphere/tire?

I'm no math genius (obviously!) so someone explain this using simple words

M

[weiwentg]

Originally Posted by PacNW2Ford

The additional width between the beads is adding to the circumference of the cross-section, thus the diameter (height) has to increase proportionally...

The second part of your sentence violates the law of conservation of mass. Basically, some of us are saying that when you add to the width of the rims, then given the total length of the tire is unchanged, the tire should have to sit lower, not higher. Something is missing. But your explanation is not it.

And it's not like I have any more narrow rims sitting around, plus I don't have a pair of vernier calipers. So I can't measure this myself.

Originally Posted by yinzerniner

Did you look at the picture clearly? They're showing two different tires on three different inner width rims. The "length," aka measurement of the tire when laid flat, of the GP4000s stay constant no matter what the rim width, but the shape differs on different rims.



As you can see white, light blue and red are 25mm, and the width gets wider as the rim does, but the height actually decreases from the 17mm to 20mm ID rims.

...

You're correct when you compare light blue and red (albeit light blue has the tire at 100 PSI, and red has it at 75 PSI). The red line (wider rim) has the tire bulging out wider and sitting lower (contradicting the post quoted above).

My issue is with the white versus light blue lines. Those are the same tire and same pressure. White is the super old-style, 13.6mm ID rim. Light blue is a 17.8mm ID rim. Light blue is both wider and higher than white. Again, both lines are a 25mm tire. How is this consistent with the law of conservation of mass? Same with grey and light dark blue (bottom and 3rd from bottom lines, both are 23mm tires at 100 PSI).

[dddd]

Originally Posted by pobrien

I would presume that the tire tread (centre of tire) is inelastic and would expand to one size once inflated to a maximum pressure recommended.

I can see the tire 'getting shorter' with less air pressure.

Perhaps I am missing something...Just a thought.

Ahh, you're sort of right, but this applies to car tires with their very different belt under the tread. The car tire has belt fibers running lengthwise around the outer circumference, to control the outer diameter and keep the tread flat. Bike tires have no such belts and no fibers running circumferentially other than in the beads. Bike tires have bias (angled fibers) plies in the casing and in any puncture-resisting belts.

Antique car tires had no such belts, their narrow casing remained round but the tread was formed to a shape that squared off the tire where it met the road.

My old Trek 720 came with Panaracer TT Radial tires that were true to their name, and the handling/steering qualities were horrible. The casing fibers were at 90-degrees to the circumference of the tire.

[yinzerniner]

Originally Posted by weiwentg

The second part of your sentence violates the law of conservation of mass. Basically, some of us are saying that when you add to the width of the rims, then given the total length of the tire is unchanged, the tire should have to sit lower, not higher. Something is missing. But your explanation is not it.

And it's not like I have any more narrow rims sitting around, plus I don't have a pair of vernier calipers. So I can't measure this myself.



You're correct when you compare light blue and red (albeit light blue has the tire at 100 PSI, and red has it at 75 PSI). The red line (wider rim) has the tire bulging out wider and sitting lower (contradicting the post quoted above).

My issue is with the white versus light blue lines. Those are the same tire and same pressure. White is the super old-style, 13.6mm ID rim. Light blue is a 17.8mm ID rim. Light blue is both wider and higher than white. Again, both lines are a 25mm tire. How is this consistent with the law of conservation of mass? Same with grey and light dark blue (bottom and 3rd from bottom lines, both are 23mm tires at 100 PSI).

This has NOTHING to do with conservation of mass. It has to do with the total circumference of a circular object, the arc length and circular coverage of that arc.

Let me see if I can take 5 mins away from work and illustrate this out to ALL YOU CONFUSED FOLKS in CAD.

Total length of tire when laid flat aka arc length is say, 100 just to keep it even. On a 20 inner diameter rim, the 100 arc length covers roughly 296deg of the 360deg total circle ie 82.2%. Thus, the total circumference of that circle is (360/296)*100=121.6. On a 25 inner diameter rim, the 100 arc covers only 286deg of the total circle ie 79.4%. Thus, the total circumference of that circle is (360/286)*100=125.9.

Since we all know (I hope) that increased circumference equals increased diameter of height and width, then it proves given the above numbers that the width and height increases as the inner diameter does. But as mentioned before the height increase is only up to a certain point. And in real world examples of tires and rims the tire compound, shape, rim shape, rim compound, bead design, etc. will all have small effects on how much the increase in height is and at what point the height doesn't increase with inner rim diameter increase.

I've attached an aptly named pdf showing the work, since those of us with understanding of basic geometry know how important it is. Black is for the 20 ID, Red for the 25 ID.
Tire-and-Rim-Widths-for-Idiots.jpg

[weiwentg]

Originally Posted by yinzerniner

...

Total length of tire when laid flat aka arc length is say, 100 just to keep it even. On a 20 inner diameter rim, the 100 arc length covers roughly 296deg of the 360deg total circle ie 82.2%. Thus, the total circumference of that circle is (360/296)*100=121.6. On a 25 inner diameter rim, the 100 arc covers only 286deg of the total circle ie 79.4%. Thus, the total circumference of that circle is (360/286)*100=125.9.

Since we all know ... that increased circumference equals increased diameter of height and width, then it proves given the above numbers that the width and height increases as the inner diameter does. But as mentioned before the height increase is only up to a certain point. And in real world examples of tires and rims the tire compound, shape, rim shape, rim compound, bead design, etc. will all have small effects on how much the increase in height is and at what point the height doesn't increase with inner rim diameter increase.

I've attached an aptly named pdf showing the work ... Black is for the 20 ID, Red for the 25 ID.
Attachment 1697965158

If you learn to avoid being condescending and not shout unnecessarily, you will go far in life.

You raise a good point, and that's an excellent illustration, although I think I'd remove the narrow lines (I think you are comparing the thick lines). It is true I'd neglected to consider the length added to the circumference. Or,

That said, while you do show that going from 20 to 25mm ID produces slightly bigger height and bigger width, thanks to the added rim, does that still apply if we go from 13.6mm to 17.8mm? Because that's the one that's really tripping me up. Does the added rim width result in that much more width and height, as in Hed's diagram? That's adding less than 5mm to the width.

Also, you appear to be assuming the tire stays circular. I think this will have to do as an approximation, but the tires clearly don't stay circular. Not sure how much a difference that makes.

[yinzerniner]

Originally Posted by weiwentg

If you learn to avoid being condescending and not shout unnecessarily, you will go far in life.

It's only perceived as shouting by people who clearly lack the capacity for listening/reading comprehension and critical thinking. All others will see it as strong emphasis.

Originally Posted by weiwentg

You raise a good point, and that's an excellent illustration, although I think I'd remove the narrow lines (I think you are comparing the thick lines). It is true I'd neglected to consider the length added to the circumference.

Narrow lines are the "showing the work" portion of my response. They are the verified dimensions of each component of the diagram. The thicker lines are the simple graphical representations of the components ie tires and rims. If I had another 30 hours of free time I'd be able to photorealistically model everything in 3ds Max or Maya with material finishes, lens effects, lighting shadows, etc.

Originally Posted by weiwentg

That said, while you do show that going from 20 to 25mm ID produces slightly bigger height and bigger width, thanks to the added rim, does that still apply if we go from 13.6mm to 17.8mm? Because that's the one that's really tripping me up. Does the added rim width result in that much more width and height, as in Hed's diagram? That's adding less than 5mm to the width.

Yes, it does. Over and over again, it's proven. If you need to see it with your own eyes then get a set of 13.6 and 17.8 ID rims and measure the same tire on both.

Originally Posted by weiwentg

Also, you appear to be assuming the tire stays circular. I think this will have to do as an approximation, but the tires clearly don't stay circular. Not sure how much a difference that makes.

Again, reading comprehension is your friend.

Originally Posted by yinzerniner

And in real world examples of tires and rims the tire compound, shape, rim shape, rim compound, bead design, etc. will all have small effects on how much the increase in height is and at what point the height doesn't increase with inner rim diameter increase.