The wheel turns

Brown's Law Of Tire Sizing states: If two tires are marked with sizes that are mathematically equal, but one is expressed as a decimal and the other as a fraction, these two tires will not be interchangeable.

I have to deal with this first hand as my rear tire has worn to the point of replacement. Several years ago, I had my rim break. A spoke pulled a chunk of the rim out. When I replaced the wheels, they didn't seem to be the same size. My brakes didn't bear down on the rims the way they used to because the new rims were more narrow. My existing tires didn't fit right. I had trouble replacing the tires when their time came, I suspect because of the rims that I had gotten. So, now that it was time to replace another tire, I wanted to be sure of what I was in for.

The only information I could find on my original rims was "alloy 36H", which only seems to indicate that they have 36 spoke holes. Not really relevant until I want to replace my current rims, which are Alexrims RP15F rims.

Tech Spec
Pin joint 36 holes, silver/black
Optional CSW
700C, ERD 602.9mm, ETRTO 622X16mm
26"×1.0"

The tires I currently have are Bontrager 700x38C (40-622). Notice that the rims and tires are not described in quite the same way. You'll see that both the numbers 700 and 622 appear, but neither of them actually conform to an actual measurement on the wheel. ERD (Effective rim diameter) apparently refers to the interior diameter of the rim; 202.9mm (which is actually measured correct). But then the external diameter is 636.5. So, given that the tire needs to fit under the lip of the rim, you might think that the ERTO (European Tyre and Rim Technical Organization) number of 622 would refer to the interior diameter of the wheel. However, that actually measures closer to 627mm. One would think that if you're accurately measuring millimeters, you wouldn't be off by half a centimeter.

And then there's that pesky ERTO number of 16mm. Doesn't that refer to the width? 15.7 is close enough to 16 to think they just rounded that number. Except that my tire is labeled 40-622 compared to the wheel's 622-16mm. I suppose that the 40 refers to the width of the inflated wheel, but then why is there that 38C. Why say both 38 AND 40?

In the end, I purchased a Specialized Nimbus 700x38C because it was labeled the same as my current tire. Of course, according to the tire size charts, my tire is too wide for my rims. I should be using nothing larger than a 35mm wide tire when I am actually using a 38 or 40 (depending on which number is true). Sheldon Brown's website says, "if you use a very wide tire on a narrow rim, you risk sidewall or rim failure." Well, I've been riding this combination for a few years without tragedy but eventually I'll want to replace the undersized rims with what should be on the bike so that I can restore my braking performance.