Unusual tyre sizes help needed.

J, JJ, K, JK, B, P and D : Tyre bead profiles / rim contour designations.

No, my keyboard letters weren't stuck down when I typed this. The letter that typically sits between the rim width and diameter figures stamped on the wheel, and indicates the physical shape of the wheel where the tyre bead meets it. In the cross-section on the left you can see the area highlighted in red.



Like so many topics, the answer as to which letter represents which profile is a long and complicated one. Common wisdom has it that the letter represents the shape. ie. "J" means the bead profile is the shape of the letter "J". Not so, although "J" is the most common profile identifier. 4x4 vehicles often have "JJ" wheels. Jaguar vehicles (especially older ones) have "K" profile wheels. Some of the very old VW Beetles had "P" and "B" profile wheels.

Anyway the reason it is an "awkward topic to find definitive data on" is very apparent if you've ever looked at Standards Manual of the European Tyre and Rim Technical Organisation. It is extremely hard to follow! There are pages and pages (64 in total) on wheel contours and bead profiles alone, including dimensions for every type of wheel you can think of (and many you can't) with at least a dozen tabled dimensions for each. Casually looking through the manual is enough to send you to sleep. Looking at it with some concentration is enough to make your brain run out of your ears. To try to boil it all down for you, it seems that they divide up the rim into different sections and have various codes to describe the geometry of each area. For example, the "J" code makes up the "Rim Contour" and specifies rim contour dimensions in a single category of rims called "Code 10 to 26 on 5deg. Drop-Centre Rims". To give you some idea of just how complex / anal this process is, I've recreated one such diagram with Photoshop here to try to put you off the scent.



From the tables present in this manual, the difference in dimensions between "J" and "B" rims is mainly due to the shape of the rim flange. This is the part in the diagram defined by the R radius and B and Pmin parameters. Hence my somewhat simpler description : tyre bead profiles.
Note that in my example, the difference between "J" and "B" rims is small but not negligible. This area of rim-to-tyre interface is very critical. Very small changes in a tyre's bead profile make large differences in mounting pressures and rim slip.
"A" and "D" contour designations come under the category of "Cycles, Motorcycles, and Scooters" but also show up in the "Industrial Vehicles and Lift Trucks" category. Naturally, the contours have completely different geometry for the same designation in two different categories.
The "S", "T", "V" and "W" contour designation codes fall into the "Commercial Vehicles, Flat Base Rims" category. The "E", "F", "G" and "H" codes fall into the "Commercial Vehicles, Semi-Drop Centre Rims" category. Are you beginning to see just how complex this all is?

I think the best thing for you, dear reader, is a general rule-of-thumb, and it is this : if your wheels are stamped 5J15 and you buy 5K15 tyres, rest assured they absolutely won't fit.