newRPL: Angles revisited

[Claudio L.]

(04-03-2016 08:12 PM)Vtile Wrote:  Interesting subject, I like to read these on MoHPC. Would be nice to know what angle is in an eyes of mathematician percentage, direction, factor, way of divide Italian food ??

I'm no mathematician, but I learnt long time ago than angles in radians are the ratio of the arc length to the radius (works on a pizza if you like italian food...). Based on that definition it's a non-dimensional unit (m/m).
That's why is doesn't play well with a unit system. It's a unit in its own right, but yet it's non-dimensional, so it has to be consistent with raw numbers.
The current unit system in the 50g or newRPL doesn't achieve this property. 1_r + 1 gives you inconsistent unit error, while in reality the operation should proceed.
Angular velocity in r/s times the radius in m should give you linear velocity in m/s, not in m*r/s.
So angles are always a pain to handle properly. Then we add several ways to measure angles (deg, grad), and throw in there different ways to represent the same measurement (decimal degrees, vs dms), and you have a perfect storm.

Really hard to handle correctly, I thought I had a good idea when I started this thread, now I'm not convinced.