After some internet trawling on the likely standard that Herbert have used for this pulley taper, it seems that Fulmen was half right. From some time ago it would seem that industry has generally agreed that the standard for “non-stick” tapers should be 3.5″/foot. This is close to a ratio of 0.3 but not quite.
When it comes to the angle subtended by this specific gradient, there is lots of variation in articles on the net. I ‘think’ this could the result of different ways of measurement leading to people to use Tan instead of Sine and vice versa.
My gauging ball method determined and angle of 16deg 42 mins on my pulley. The 3.5″/ft spec gives a subtended angle of 16deg 36min. This looks surprisingly close but may be more from luck than anything else. However, this raises another question in my mind which time-served designers and machinists may be able to answer. What would be a typical angular tolerance for manufacturing the taper used to couple two parts in a machine?
Gerry