TIRES AND RIMS

ISO/ERTRO
traditional tire sizes are not real measurements. ex.: 700C x 25; 27" x 1 1/4"
ISO is an actual measurement
ERTRO is for tires and is defined by ISO starndards: it lists width of inflated tire and diameter with which tire sits on rim
ISO 20-622 = traditional 700C x 25
ISO 20-559 = traditional 26" x 1.75"

ABC
A, B or C indicate width of tire, so,
the larger the tire, the smaller the rim for the same wheel:
700A obsolete = ISO 642mm
700B = ISO 635mm
700C = ISO 622mm

C
when C is after width of rim, it indicates the shape of rim
ex: 622x19C where C= Crochet type
wikipedia: Most bicycle tires are clincher for use with "clincher" rims.  The ISO standard defines designations for bicycle rims. It distinguishes between 1 Straight-side (SS) rims, 2. Crochet-type (C) rims, 3. Hooked-bead (HB) rims. Traditional wired-on rims were straight-sided. Various "hook" (also called "crochet") designs re-emerged in the 1970s to hold the bead of the tire in place, resulting in the modern clincher design. This allows higher (80–150 psi or 6–10 bar) air pressures than older wired-on tires. In these designs, it is the interlocking of the bead with the rim, not the tight fit or resistance to stretching of the bead, that keeps the tire on the rim and contains the air pressure.

20, 26, 27, 27.5, 28 and 29ers

BMX
ISO 406mm
20  inch

MTB
ISO 559 mm
26 inch


ISO 584 mm
27.5 inch
650B

ISO 622 mm + tire approx 59-622 (outside diameter comes to approx 740 mm)
29er


29 inch in front + 26 inch in back
96er


26 inch in front + 29 inch in back
69er

Road
ISO 622 mm
28 inch
700C


Tire fit on rim with for example a tire marked 20-622
622 =
- bead diameter = on tire, diameter at the inside perimeter
- bead-seat diameter = same but on rim, i.e. diameter at point on rim where tire bead sits
     to measure on rim, measure rim diameter and subtract 2x flange height
20 =
- tire ISO section width = width of flattened tire divided by 2.5
- rim width = distance between rim flanges = rim inside width

tire fit for road bikes: tire section width can be 1.4 - 2 x rim's inside width
tire fit for MTB: tire section width can be 1.4 - 3 times rim's inside width

Tire fit
1) measure tire flattened width and rim inside width
2) divide real tire width by 2.5 to obtain nominal tire section width
3) multiply rim width by 1.4 (this gives narrowest tire section width) and by 2 or 3 (this gives widest section width)

a tire that has a 20 section width will fit road rims with width between 10 and 14.
a road rim with width of 20 will require a tire with section width between 28 and 40.

some other usefull references
Sutherland's
wikipedia
sheldon brown tire sizing
Chapter 19 in Barnett