What is "design rim width"?
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From http://www.yokohamatire.com/utperf.asp:
For 50-series tires and higher, the measuring rim width is 70% of the tire's section width rounded off to the nearest 0.5". For example, a P255/50VR16 tire, which has a design section width of 10.04", is measured on a 7" wide wheel.
For tires that have an aspect ratio lower than a 50-series, the measuring rim is 85% of the tire's section design width. Therefore, a 255/40ZR17 tire with the same 10.04" section width would be measured on an 8.5" wide wheel.
In cases where the aspect ratio is less than 50%, the width is also rounded off to the nearest 0.5", according to the numbers in this list on the tirerack.com Web site, listing Yokohama ADVAN Neova AD07 tire specs. The list includes tire sizes & corresponding design rim widths. For example, for the 225/40-17 size, the design rim width is listed as 8" (85% of 225 is 7.52952").
From http://www.dunloptires.com/care/widthRatio.html:
To accurately measure the width of a tire, the tire must be mounted on a rim. Since a tire's section width is larger if the tire is mounted on a wide rim, and smaller if it is mounted on a narrow rim, each tire is measured on a specific rim width.
For example: For tires with aspect ratios from 80 to 50, the measuring rim, also called the design rim, is specified to be 70% of the section width. For tires with an aspect ratio less than 50, the measuring rim is 85% of the section width.