Lombard

Are your current rims tubeless compatible? If so, they are designed to fit very tight and are more difficult to mount by design. The key to mounting a tire on these kind of rims is to seat the bead into the center channel and work it around starting opposite the valve stem and working the tire toward the valve stem.

FBinNY 

Nice analysis, but most folks don't have access to Autocad, and fortunately don't need it to work a problem like this, just a pencil or some visualization skill. A simple sketch will help.

Start with the premise that the inside of the inflated tire outside the rim is a near perfect circle. (This is true for the same reason bubbles are round)

So you have a circle of X circumference nesting on the rim. If you mark the points where the tire meets the rim, the outside arc has a fixed length. So the total perimeter is that arc plus the rim width. Add to the rim and the new perimeter is increased by the same amount. Fill it with air and you have a new larger circle with a diameter increased by the same amount. The rest is easy.

Note, there's a bit of fudge here because the rim width is a secant on the circle, and shorter of the arc, but that difference is negligible for this purpose

grumpus

The tyre won't retain a circular section, as the circumference is determined by forces applied to the tread band by inflation and its elastic behaviour. It will have a lower profile on a wider rim.

Lombard

Incorrect. The tire will increase in height as well as width when the rim is wider.

Atlas Shrugged

That makes no sense. A tire will be at its smallest diameter when stretched onto the widest rim possible and increase diameter in proportion as rim narrows.

crn3371

Thanks everyone for your input. The AutoCAD results seem to jive with what I’ve discovered in my searches. I stumbled across a rule of thumb which stated “for every 1mm increase in rim width the tire width will increase by 0.4mm” matching what 79pmooney came up with on AutoCAD.

Lombard

As the photo below will show you, you are wrong:

FBinNY 

I hate to be a pain, but you and the post you corrected are both wrong.

Bicycle tires, like any flexible tube will form a near perfect circle when inflated. The basic physics is that shapes under internal fluid pressure will deflect to maximize volume for the perimeter (circumference).

Of course this depends in the structural factors that would resist that tendency, so won't apply near the rim.

In the case of bike tires, with supple bias ply sidewalls, the resisrance is near zero compared to the high inflation pressure.

Note that the circle is at the wall, so different tread and wall thickness will cause the outpear more oval.

Atlas Shrugged

Thanks for the correction, and I agree that it is not a linear response when narrowing the rim dimension. I would love to see the actual numbers. In my own experience, when using a very supple tire and wide rim, the outside diameter went down noticeably. The image provided proves nothing and is based on the theoretical response of a tire when placed on various rim diameters. If an open non-moulded tire like a Challenge or Rene Herse was modelled, the results would be substantially different.

Lombard

Exactly my point.

FBinNY 

Like you, I dislike computer generated images because we never know what assumptions were factored into the calculations. My reference to a circular profile relates to the unsupported section of the tire, based on a typical Omega profile. As rims get disproportionately wide compared to the tire, the constraints near the rim will distort the profile to a greater extent forcing the tire to a more U'shaped profile, but the rules still apply in the free section, which will still form an arc of constant radius.

79pmooney

My tires don't look like that. My Corsas look just like my AutoCAD sketch. I remember seeing that diagram you posted a while ago and thinking those tires didn't look like mine. I'm guessing those are molded tires, not flat tires of thinnish tread laid over high TPI casing.

Lombard

The tires in the diahram are Conti GP4000's which are pretty high TPI.

79pmooney

Do the 4000s have molding down the sides? (I haven't ridden a Conti for decades so I wouldn't know.) If the sidewalls are just thread, then - is that diagram from an actual tire, a 3-D stress-strain model or a pretty picture drawn with CAD?

crn3371

Here’s a good article https://www.bicyclerollingresistance...test#road-bike

Lombard

Not sure about either of your questions. The Corsas are hand made rather than vulcanized. Not sure about the Conti GP's.

As far as AutoCAD, I'm not familiar with it for the same reason most people in the Western world can't speak Asian languages.

DaveSSS 

I have 28mm tires on 25mm internal width hookless rims. They measure a bit over 31mm wide. I have the same tire on 19mm internal width rims and they measure 29mm wide. Careful measuring shows the height to be about 2mm greater on the wider rim.

SoSmellyAir

I wonder, since most (new) tires have a thicker tread than its sidewalls (for wear and puncture protection), would that not cause the tread to be slightly less flexible than the sidewalls, such that the circle is flatter or less curved at the top?

79pmooney

I'm using AutoCAD simply as a drafting tool here. I sketched a rim of 14mm inside width and another of 19mm inside. Then I just drew an arc from those inside points on the 14mm rim of the specified tire's width. (So an arc of 25mm width for the "25C" tire.) Asked Acad for the arc length. Now drew an arc of the same length on the 19mm rim. (Trial and error. Draw, ask Acad, adjust, ask again.) Measure the resulting width. Just old fashioned drafting but sparing the velum paper and 1/4" of erasure. (The reason we drew on velum? Not because we were monks and wanted our work to last for centuries. No, we used it because it could take that 1/4" of eraser without blinking. AutoCAD takes this one step further. No paper smudge.)

icemilkcoffee 

Where did this come from? It doesn't look right at all. If you trace that red line representing the 25mm on the widest rim, vs the white line representing the same 25mm tire on the narrowest rim, you'll see that the red line is obviously longer than the white line. And you know the tire carcass doesn't grow when you change to a wider rim.

Atlas Shrugged

I am still curious at what point when a rim gets wider, does the diameter or height start to drop? When taken to an extreme width, the tire will get smaller in diameter. My gravel wheels are 25mm internal width; what would that do? It would be very interesting to have the actual dimensions over a large range of rim widths and a very supple tire. The graphic presented is laughable in its obvious errors.

79pmooney

I just realized that this could be solved mathematically writing an equation the gives tire height (h) for a given chord length and variable rim width (R). Solve for delta h vs delta R. Where delta h goes to zero, there's the rim width. Good college problem. Sadly, my head injury erased that math. Maybe I'll take it on for brain stimulus but I may well fire up Acad and get there faster by trial and error. (Not as exact but doable, not "can I?") (Say we mount a tire on a rim width that the tire comes off vertically and forms a semi-circle. Height = rim width/2, ie tire radius. Now pinch those rim sides together. Tire a full circle now. Height = full diameter but the diameter had been halved and height is the same. I'll place my first bet on the rim giving the maximum height being half way between.

So (pure fantasy, not drawn or anything - say we have an "25C" tire. Find that if we put if on a 32mm inside width rim the sidewalls come off it vertical. Then, if I placed the winning bet, the highest possible this tire can go will be on a 32/2 = 16mm rim. 1st bet 0.5. Any others? (Don't go measuring your tires and come back and tell me my 32mm for the vertical sidewall is wrong. I just pulled that out of a hat.)

Now, once this rim and maximum height is established, we can make a relationship between tire width and required rim to get maximum height. Then any tire can be simply laid out, width measured and height predicted. (But - a molded thread that holds its shape need not apply. This is just for tires that behave like balloons or flexible pressure vessels.)

FBinNY 

Yes, and no. Consider that the air is exerting a purely radial force on the tire, which produces tension in the wall fabric. So, while a thicker tread might be slightly resistant to flexing, it's also molded into a curve, so we're talking about tiny flex changes in the tread vs the high pressure within.

In any case, we always allow for differences between theory and reality, and only factor them if they're material. As a practical matter, the acceptance of a circular profile serves the purpose of allowing me to get a decent estimate of changes to width without needing CAD or an internet search.

It's also not purely about self reliance. I'm from the slide rule generation and still prefer to have an estimate of the answer as a reality check against the results of a "precise" calculation.

Lombard

Hmmmm. You do have a point here.

grumpus

I think most tyres casings wrap the bead then come back to overlap on the tread area, so that's 50% more structure which would result in less stretch at the circumference.