Well, I did some math (my mom always said it would come in handy someday) and I came up with some equations that seem to work...at least they did for my CA. (If you see any errors in my logic or calculations please let me know.)
I have all this in an Excel spreadsheet. If anyone wants it, PM me with your email address and I'll send it to you.
I used the measurements from the chains for my CA (tire size: 11.2-24) in the examples below. And I rounded Pi to 3.14159
Measurements Needed:
Chain Width (CW)
Tire Width (TW)
Tire Radius (TR); this can also be calculated if you have the Tire Circumference (TC)
My measurements
CW: 17" (Chain length was posted as 114")
TW: 11.2"
TC: 132" (As best as I was able to measure it by myself)
If radius needs to be calculated from circumference
(For reference circumference of a circle is 2*Pi*radius)
Formula
TC=2*Pi*TR
Example
132=2*Pi*TR
66=3.14159*TR
21.01=TR
Chain Width Adjustment (CWA)
Formula
CWA=(CW-TW)/2
Example
CWA=(17-11.2)/2
CWA=5.80/2
CWA=2.90
Radius of chains on tire (CR)
Formula
CR=TR-CWA
Example
CR=21.01-2.90
CR=18.11
Minimum chain length (MCL)
Formula
MCL=2*Pi*CR
Example
MCL=2*Pi*18.11
MCL=36.22*Pi
MCL=36.22*3.14159
MCL=113.78
So to make this as a single equation
Formula
MCL=2*Pi*(TR-((CW-TW)/2))
Example
MCL=2*3.14159*(21.01-((17-11.2)/2))
These equations will only tell you if the chains are long enough to go around the tire. Some common sense still has to be used. You need to determine if the width of the chains is appropriate for your sized tire. For example, you’re not going to put a 10” wide set of chains on a 16” wide set of tires.
Also, the measurements are for the chain, not including the clasp.
Hope this helps,
Greg
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