Re: Best angle vs best rate
For jet aircraft, best angle of climb occurs at maximum specific excess thrust - i.e. at the speed where the difference between drag and thrust is greatest.
Since the thrust output of a jet engine is relatively constant with speed, max excess thrust occurs close to Vmd (where drag is minimum).
Example: B737, best angle speed usually around 210-220 kias.
Best RATE of climb is related to specific excess POWER (I remember it as POWER being a RATE of doing work) - in other words, we are looking for the maximum difference between aircraft power available and power required (drag * velocity).
Since power is Force x velocity, and thrust(force) for a jet doesn't vary (much) with speed, the relationship of Available power versus speed for a jet is now a (straight-ish)diagonal line. So maximum specific excess POWER occurs at a higher speed.
Example: B737 best rate of climb speed occurs nearer to 270-280 kias.
The FMC works these things out accurately because it knows, based on actual ambient conditions, how 'straight-ish' or not the various thrust & power curves actually are.