Calculating 'EXTERNAL' thread minor diameter range ASME B1.1-2003

[bm2018]

HI,

I am trying to compute the limits of specification for the minor diameter on an external unified thread.
I understand that the minor diameter is of least concern regarding the manufacture of a screw thread.
However, I am interested in calculating it, otherwise.

The Machinery's Handbook offers table 3 under it's Unified Threads section where it provides sizes for each series of thread.
Lets use 1/2-13 UNC 2A for an example. For this series, table 3 provides a column headed UNR Minor Dia Max (Ref).
Practically, I assume this is simply a value that is for reference, indicating the maximum the minor diameter can be
and still produce a thread that mates with it's internal counterpart.

Regardless, when I attempt to solve for this value via the design profile, I am unsuccessful. ASME B1.1-2003 in section 5.8.1 says this for 'minor diameter tolerance'

(2) UN Classes 1A, 2A, and 3A. To intersection of
flat root with flanks of threads (see Figs. 2 and 3), equals
pitch diameter tolerance for class of thread specified,
plus 0.21650635P (see Table 5).

Lets attempt to solve this with a 1/2-13 UNC 2A thread using the design profile:

1/2-13 UNC 2A:

Basic: .500

pitch: .0769​

Allowance: 0.0015 Major: 0.4985-0.4876​

UNR Minor Dia max: .4069​

Fundamental height of triangle (H) for MMC of this series (.4985 dia) is...
H = 0.86602540P
H = .0665

And we see form the design profile that .625H gives us our minimum thread depth...
D = .625H
D = .0417

Solving for a diameter value...

d = .0417 * 2
d = .0831

Now, subtracting this depth from the maximum allowed diameter...

.4985 - .0831 = .4153. <--- Not the same as .4069?

Lets use what the actuals standard says in section 5.8.1....

equals pitch diameter tolerance for class of thread specified, plus 0.21650635P

Therefore, the tolerance of the minor diameter equals...
.005 + .0167 = .0217

Now how do I apply this to an actual SIZE ?


Thanks