Gordon --
Now I'm curious. I don't recall ever seeing a standard or specification for the Unified threadform with radii at both the Major and Minor Diameters, whether internal or external.
The basic Unified threadform has flats (which, despite the name "flat", are really supposed to be helical sectors of cylinders) at both the Major and Minor Diameters, and there are two well-known variant forms of the Unified that require a radius in place of the Minor Diameter flat of the external (only) thread. The Unified R variant has a standard Minor Diameter, and a 0.14434 x Pitch radius in lieu of the 1/4 x Pitch flat; the Unified J variant has an enlarged Minor Diameter, with a 0.15011 to 0.18042 x Pitch radius that, has -- at its points of tangency to the thread flanks -- a chordal length of 5/16 x Pitch.
The Unified R external thread readily engages a standard (flatted at both Major and Minor Diameters) Unified internal thread, meaning that there is no need for a Unified R internal thread specification. On the other hand, the Unified J male thread doesn't necessarily engage a standard Unified internal thread, and there is a specification for a Unified J internal thread. The Unified J internal thread has a 1/8 x Pitch flat at its Major Diameter paired with a 5/16 x Pitch flat at its Minor Diameter.
There is an interesting subtlety associated with the Unified J threadform. The Single Depth of the screwthread is different for the external and internal threads. The external thread's Minor Diameter radius obviously needs to clear the internal thread's flat, so the external thread is "deeper" or "taller" than the internal thread. Quantitatively, the basic Single Depth of the external Unified J threadform is Cosine 30 degree x 2/3 x Pitch , and the basic Single Depth of the external Unified J threadform is Cosine 30 degree x 9/16 x Pitch.
This leads to an interesting bit of trivia that comes into play when needing to cut-tap an internal screwthread of the Sellers, Unified, and Unified J threadforms. Assuming that the Major Diameter and Pitch match, the SAME Sellers (aka U S Standard or American National) tap is used -- and explains why most "inch-sizes" taps in the US are still marked NC or NF rather than UNC or UNF.
If the internal thread is to be a Sellers threadform, the absolute minimum diameter of the hole to be tapped is Major Diameter - 2 x Cosine 30 degree x 3/4 x Pitch.
If the internal thread is to be a standard Unified threadform, the absolute minimum diameter of the hole to be tapped is Major Diameter - 2 x Cosine 30 Degree x 5/8 x Pitch.
If the internal thread is to be a Unified J threadform, the absolute minimum diameter of the hole to be tapped is Major Diameter - 2 x Cosine 30 Degree x 9/16 x Pitch.
By "absolute minimum diameter" in the above paragraphs, I mean "one hundred percent depth of thread, any smaller and the screw probably won't fit, provided you don't plug the hole with a broken tap first"; here in Practical Land the holes need to be a bit larger. And that leads to another interesting bit of trivia: The old US NBS Standard H28 set the maximum permissible depth-of-thread of internal threads for US Government service at 83 percent, and the basic Single Depth of a Unified threadform of a given Pitch is 83 percent of the Single Depth of a Sellers threadform of the same Pitch. In practice, that means a maximum-permissible Sellers internal thread will, if just barely, accept a maximum-permissible Unified external thread of the same Major Diameter and Pitch.
John