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How did 15' become such a common back radius? (I know that not everyone uses the same back radius or a radius at all.) If, say, 25' was used it would allow use of one radius for both top and back, a convenience. But what is the extra advantage that 15' brings? Has anyone measured the extra stiffness to determine if it is significant?

How did builders get from essentially flat 70 years ago to 15' today?

If the back is made from a less stable wood like rosewood (or any slab-cut hardwood), the back needs more curvature to ensure longevity.
That is because the back is much more likely to crack if it shrinks enough to become completely flat.
Gibson used identical radii on the tops and backs for much of their history, but the majority of those guitars were mahogany.
Another consideration is sound. The top radius is one reason a vintage Gibson does not sound like a Martin.

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John

I don't think there's anything magical about 15' radius. It just looks "right" on a guitar back. I'd guess Martin started using that radius and set the style for everyone else.

That's interesting. Trevor Gore was discussing back radius and he said he measured a bunch of Martins which had different longitudinal and cross grain radii. Trevor said that the average of the long and cross radiuses of the guitars he measured gave a 3m (10') radius so he has always used that radius.

I think the trick in controlling the backs flexibility and its interaction with the top is not in the radius, but in how you thickness different woods and what you do with the braces for a given radius.
Cheers
Dom

Likely, it's no where near as scientific or as interesting an explanation as you would hope....

My guess is that if you have a body height at the neck block that's about 1" less than the body height at the heel as on a Martin, and you want a more or less smooth looking curve - you will end up with some certain curve that translates out to be in the 10'-20' range........

Old Gibsons used flat rims and had more or less the same thickness neck to heel block... If you look real close - you will discover that every back brace on those has a different curve.... but I bet they are also in the 10'-20' range too because it just looks about right

As others have wisely stated - the curve also gives the back woods room to move around a bit.... and it doesn't push back in when you hold it against your body...

Feel free to experiment all you want...

Thanks