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Use standard iron rings in the standard size. Your ring end gap is what it is. You either go the full way and do a proper rebuild with machine work or do a re ring. In the case of the re ring I normally don't associate strong and dependable in the same sentence. Its Its normally done for vehicles you are looking to flip.
I am going to have to disagree with you on the ring choice. Moly rings are more forgiving for cylinders that may not be properly prepped (honed) and are better for amateur builders. The guy in my rebuild book says you can even perform surgery on a engine in the vehicle, and if you have to replace a piston or something like that, you can use moly rings without even honing the cylinder, and they will eventually break in and do fine. Cast rings are ok also, they may not last as long as the Moly rings though.
I would trust what the manufacturers and racing have proven over what that book says. Moly rings need a 280 to 320 finish anything above and below is going to cause issues. Moly rings will also not seat in a glazed cylinder. Soft cast iron rings will gladly seat into a glazed cylinder and it doesn't take much heat or cylinder pressure to make them seat.
I like math, and wanted to try to answer your original question. As the others said, buying 0.010 over rings refers to the bore diameter. It has a relation to the ring gap, of course, but not 1:1.
Due to the very very very tiny angle your ring gap creates in the bore "pie", I assume for my calculations that the chord length (i.e. ring gap) and arc length (the arc this gap makes directly at the cylinder wall) are essentially the same value. The actual difference is something like 0.08%, so pretty negligible haha.
Aaaaaanyways... with a 4.00" cylinder bore (nominal), you want a ring gap of 0.015" (nominal). Since you are measuring a ring gap of 0.025", circumference calculations show that your actual bore is something like 4.003" (again, assuming arc and chord length are essentially equal) in the area of the bore where you took the gap measurement (it is probably tapered as others said, so this diameter won't be the same at all "depths"). This 0.003" increase in bore diameter over stock (the wear of your cylinder) is the reason why your gaps are over the spec limit with standard rings. Therefore, you would want to buy a set of rings that are 0.003" oversized, since this refers to diameter. This also explains why the 0.010" over rings are too big.
This probably doesn't help you, as I'm pretty sure you can't get that specific with ring sizes but maybe it clears up your initial confusion.
That does help. Thank you. I was able to find some file to fit that should work. Although even the manufacturer states that they are 4.005” rings made to be filed to fit in 4.000” bore. They are total seal rings.
Since my calculations were just that: “calculations” - based on nominal values, those 4.005” rings might actually give you a gap within tolerance right out of the box without filing. You can always hope, right? Good luck!
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