When I was a youngster in school my father, a skilled tool-room engineer, a lways used to press me to remember my tables...mathematical ones, stating t hat one never knew when one might need them in future life. Just after WWII his company invited a number of Chinese undergraduate engin eers to come over to spend some time in the workshops in order to get some quality hands-on experience. One of them, Tsun Ching Chang, stopped in our home for a month or so and, as a farewell present gave me two gifts. One wa s a football shirt with dark brown vertical stripes over a yellow backgroun d ..I have never seen a similar one since. The second gift was a well-used copy of "Mechanical World Year Book" for 1946. The football shirt is long g one, but I still have, and use, the Handbook regularly.
In the 70s when I started to import quality frames from France I noted that although dimensions were given for all manner of things, the seat angle wa s never there. At best a measurement of the distance from a vertical line f rom the top-tube through the centre of the bracket back to the centre of th e seat-tube - known as recul, was always used.
I bought various gadgets to try to measure the angles but in the end recall ed my father's advice - the mathematical tables..but on this occasion remeb red my trigonometrical ones - the tangents, sines and cosines..and I also r emembered Ching Changs gift -the Mechanical Year Book 1946. And you know wh at...those tables hadn't changed a bit in all those years! They still give the same values.
So these days to measure a seat angle on a frame I find my old draughtman's wooden T-square, place it on the top-tube of the frame, aligning the strai ght edge with the centre of the bracket..then I take as precise a measureme nt as possible from the top tube alomg to the centre-line of the seat tube/ seat-lug.
After that, using a combination of either the seat tube length or the verti cal measurement and dividing this into the RECUL ie the distance along the top-tube I can obtain a figure that I then interpret using either cotangent angles or cosine ones. Then its just a simple matter of running my finger down the Trig tables and reading off the angles...and My! aren't they preci se.
I had often wondered how some of the Italian manufacturers managed to build a frame with a 74degrees 48 minutes seat angle...Now I know. BUT I have st ill to work out how to measure the head angle by trigonometry.
Norris Lockley (Never knowingly influenced by progress)/(Family Motto - Festina Lente) - Settle Uk