How did nominal come to mean "within acceptable tolerances"?

The aeronautical sense of nominal derives from engineering where the nominal value is the specified dimension and the reference point for tolerances.

The Free Dictionary offers the following definition (from McGraw-Hill Dictionary of Scientific & Technical Terms, 6th edition) for tolerance:

(engineering) A permissible deviation from a specified value, expressed in actual values or more often as a percentage of the nominal value.

Surprisingly, the sense of nominal used in the preceding definition of tolerance is missing from both the Free Dictionary (via AHD4) and OED3. But the requisite definition is found in the Oxford Dictionaries Online:

3 (Of a quantity or dimension) stated or expressed but not necessarily corresponding exactly to the real value: 'EU legislation allowed variation around the nominal weight (that printed on each packet)'

This usage in engineering long predates the space program. The following is from Douglas T. Hamilton's Gages, Gaging, and Inspection(1st edition; 1918; p.30):

It is, therefore, common practice to specify the "limit" -- that is the deviation from the true or nominal size which is permissible. The limit is generally stated by giving the amount that the dimension may be larger or smaller than the nominal size. The diameter of the shaft for example may be given as "one inch plus or minus 0.001 inch..."

A measurement corresponding to the nominal value is "according to plan or design." Similarly, when using bilateral tolerances the nominal value is by definition "within acceptable tolerances." The aeronautical usage is derived from engineering.

One possibility overlooked in the other answers is that although nominal eventually came to mean literally "within normal tolerances", the usage could have been introduced in the sense of "nominal deviation from expected value"; i.e. there is deviation (as there must be from any expected value when measuring real things), but it is small enough to be a deviation in name only.

This also nicely fits as explanation for the other questionable meaning that doesn't suit the etymology: "insignificantly small".