Hahn, you were talking about 42 vs 48 mm diameter tyres then went on to use that diameter as a radius in your maths. Your ratio of tyre cross sectional areas still works but the actual areas are four times larger than reality. Just mentioning it in case someone uses this as a guide.
I agree wholeheartedly that it’s the tyre volume that’s most important to the ride experience, not just width, as the volume of air acts as a spring. You used four significant digits but I’d like to suggest two enhancements to the calculation, and even they will only bring it closer to justifying two places.
First, allow for the thickness of the tyre and tube. Don’t worry about tubeless - the volume of the sealant approximates a good quality light tube. In a spreadsheet I have, I use a radius that is 1.75mm less than half the tyre diameter. You can get some properly measured tread and sidewall thicknesses from that
bicyclerollingresistance.com website tests. My number is sort of for supple tyres with tread around 40% of the cross sectional circumference, sidewall for another 40 and the the inner rim gap for the rest. You could choose a different number but it would be fairly close. The importance of this refinement is that is shows why there is such a bid difference between narrow tyres and the wider supple tyres. 23mm tyres only have about 600ml of air, and RTPs have over 5litres each - over 8 times as much!
Second, allow for the extra diameter around the rim lengthening the toroid (donut shape) of air by increasing the tyre height. Assuming the tyre is round in cross section, a 6mm increase in tyre height will give a 6mm increase in diameter of the centerline of the larger diameter of the toroid (the central line of least cooked dough around the doughnut) and thus pretty close to an extra 1% volume for the 559, 584 and 622 wheels we mostly use.
So rather than your 30.6% difference in volume, I’d put it at around 35%.
Nick, no idea where you got 4mm - Franklyn was talking about 4cm. And if that 4cm was accurately measured then to get back to the OP’s actual question, the SBH on Franklyn’s bike is almost exactly the extra 12mm times pi that we’d expect in extra circumference for a 6mm wider tyre that is also only 6mm higher - nice confirmation that the tyre is round in cross section.
Andrew L
I On Tuesday, January 24, 2017 at 3:59:36 AM UTC+11, Hahn Rossman wrote:
> Nick and everybody else-
> It's theoretically 6mm, but don't get me started about nominal size versus stated. The Switchback Hills tend to be true to size or bigger and many of the BSP are between 40.5-42.
> But more importantly the real difference is in tire volume. The difference in cross sectional area is:
>
> The area of a circle is r2 where r is the radius and hence the percentage increase in the area is
> ( 482 - 422)/( 422) 100 = (7238.23- 5541.77)/5541.77 100 = 30.61
> Hence there is a 30.61% increase in the area going from a circle of radius 42MM to a circle of radius 48MM.
> That's the reason bigger tires are so much more comfortable and why you can notive the difference between 23 and 25 etc. Glad you like the tires and are having fun on that bike Zak made!
> Hahn Rossman
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> On Fri, Jan 20, 2017 at 8:11 PM, Nick Favicchio <
nickfa...@gmail.com> wrote:
> Don't notice it. Some of that 4mm diffence is lost in additional squish.
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> And it's just 4mm :).
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> Just switched from EL 42s to standard 48s and I'm super in love with the 48s. Really don't notice the weight but singletrack is crazy fun on the custom now and the paved stuff is just as fast and nicer on the hands and bum.
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> All of the win!!!
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>
https://flic.kr/p/QV9XxN
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