Whitworth bolt's head size

[Paul N-M]

This is just what I was hoping for.
Like Paul N-M I wonder where else on the interweb such informed opinions would be offered.
I believe that the diameter across the points, the length of the flats and the distance across the flats (AF) are all simply related to each other and aren't related linearly to the shank diameter in Whitworth bolts. Like Cliff Ringrose I have read that the diameter across the points is twice the shank diameter, but I am pretty sure that this isn't true.
I have tested the formulae offered and, within the limits of my calculator skills, I think Colin Morgan's 1.5 x Shank diameter + 0.16" gives good results.
I have seen it suggested that the head diameters were specified because there was hex-bar available in an approximately suitable size, so that the head dimensions are basically due to chance. Colin's formula would suggest that this isn't the case.

A detailed and amusing description of various systems of fasteners from an American perspective is on the "Progress is fine but it has gone on too long" web site.

Joseph Whitworth produced the specifications for the Whitworth thread in 1841, but I can't see where he worked out head sizes for bolts.
By the start of last century a finer thread was needed for steel (rather than cast iron) fasteners and so BSF was introduced. With a head size one size smaller than Whitworth. In the 1920s Auto-whit, Whitworth with smaller head-size, steel bolts began to be used in some cars. In the early years of WWII it was decided to reduce the head size of all Whitworth bolts to that of the BSF bolts of the same shank diameter in order to save metal - the bolts could be produced from smaller hex-bar. The new Whitworth bolts were called BSW. The same spanner will fit both BSF and BSW bolts of the same shank diameter and are often marked just BS.

This would explain why old inherited W spanners mixed in with later BSW & BSF dont fit!!!!!! I had to go through the BS tray and take them all out. Though they still get used for some fittings.