Effective Tire Volume Increase with Rim Width Increase

Discuss light weight issues concerning mountain bikes & parts.

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js
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by js

I'm going full nerd mode at this point and trying to figure out the best rim for a wheel build, looking at weight on the rim versus weight on the tires for a given tire volume.

For example, I know from my road wheel building that going from a rim with a 15mm internal width to one with a 17.5mm internal width allowed my tire to increase from 26mm width to 28.4mm width - quite a nice increase given that the rims used in this particular instance weighed the same.

For mountain biking, I'm interested in comparing something like a Stan's Crest rim (380g & 21mm internal width) versus a Pacenti TL28 (450g & 23mm), and I'm curious to know what the effective increase in tire volume is. It seems that for most high-end tires, a 0.2 inch increase in tire size (eg from a 2.0" model to 2.2") usually corresponds to an increase of around 50g.

So, I'm very curious to know if anyone has access to different rims like these (or any other rims where the internal widths are similarly measured and slightly different) so that they could mount the same tire to each and see what the resulting difference in mounted tire width ends up being between the two.

It would seem that if the difference is 0.3" or more, then it's a no brainer to go with the heavier rim. If it's less then that, then it's back to balancing out all of the other attributes of each rim, but at least we'll have a better idea of how to consider the effective system-weight that each rim would offer.

by Weenie


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dwaharvey
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by dwaharvey

If you make a simple model where the rim is width W, the tire's "flattened-out" width is L (ie distance from bead to bead), its inflated/installed width is D, and you assume that the tire takes the shape of a circle who's bottom is cutoff by the rim... then there are two interesting regimes:

Fat rim (where D ~ W.... tire looks like a half circle with rim width roughly the diameter):
* dD / dW ~= 1

Narrow rim (where D >> W):
* Rate of change of width of tire, D, with rim width, W, is:
dD / dW ~= 1 / Pi < 1

With your road bike rim I think you're pretty close to the first regime: the widths of the rims are fairly comparable to the inflated width of the tire, and for every 1mm increase of rim width you therefore get an increase of roughly 1mm of inflated tire width all else being equal.

Unfortunately, with the mountain bike, I think you're really part way between these two regimes, and so adding 1mm in rim width will get you somewhere between 1/Pi ~ 0.3mm and 1mm of increased tire width. Given that 0.2 inches is 5mm, getting 5mm from the tire change costs you 50g, whereas with the rim change for 70g the 2mm of rim width increase will probably only get you something like 1mm in tire width. So there's really no comparison here at all in terms of the two.
Of course, as you said, that's not to say that there aren't other variables that might make the wider rim worthwhile. But weight per tire width is definitely not one of them.
Last edited by dwaharvey on Mon Feb 25, 2013 9:17 pm, edited 1 time in total.

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the_marsbar
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by the_marsbar

I must've missed something in your post, dwaharvey. First off, what's D (did you mean L as you defined in the beginning)?

Second, is dD / dW supposed to be a derivative? What's the reasoning behind this?

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dwaharvey
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by dwaharvey

Yeah sorry, forgot to define D... the inflated width of the tire. I edited the post to define it explicitly.

Yeah the dD/dW is a derivative: the rate of the change of the inflated width with the rim width. The reason to do this is simply because it makes the math easier and we're not interested so much in what the exact width might be, but how much it will change for a given change in the rim width.

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js
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by js

Thanks dwaharvey - I was working the numbers around in my head a bit on today's ride and realized that there would definitely be diminishing returns, but it's very useful to have it expressed as a formula.

I guess the increased stiffness is going to be the big decider now... but that sure is a lot of weight!

bm0p700f
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by bm0p700f

There is the velocity P35 if you realy want wide.

by Weenie


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