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So , yet another 'will it fit thread' but with a twist.

What is the limiting factor when looking at wheels? I have a 65 coupe, stock front suspension with Shelby/Arning drop. It seems that the ball joint area of the upper control arm will start making contact with either the tire or the inner lip of the wheel if the backspacing is too large. On a car with stock replacement upper arms How much backspacing can it take, before interference? I am sure this will depend on wheel diameter, so for arguments sake, say 17" wheels

I would think this is less of an issue for the rears with only the inner wheel house flange to hit.

Rusty
 

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16s are usually the first to have ball joint interference issues due to the rim size, actually. The diameter is only part of the equation, so assuming 17x7 or 17x8, you’re usually looking at somewhere around 4-4.25” of BS on a 7” wheel and around 4.75” BS on an 8” wheel for the best fit on a ‘65 or ‘66.
 
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jack front wheel off ground. turn steering wheel each way to full lock, see how much clearance between uca and rim and tie rod
 

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jack front wheel off ground. turn steering wheel each way to full lock, see how much clearance between uca and rim and tie rod
Do this with your current wheels. Add the measured clearance to the current wheels' backspace (leaving a little for safety) and that should be the answer for your car. Of course, if you're changing wheel diameter you will need to account for the change.
I've thought about getting a bent wheel from the junk yard ("pick-n-pull" in some areas) off a more modern Mustang in both 16" and 17". You can shim the wheel out to "decrease" back space and measure what works.
 
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