I ran a simulation on WinPlot (see attached video) on my computer and was a bit surprised to see that the optimal launch angle of a projectile (with NO air drag) leaving uniform circular motion is dependent on the initial tangential velocity (or at least Winplot thinks it does).

Can someone shed some light on this phenomenon or point me to my error?

As opposed to being launched from ground level from a cannon or something.
The range equation (with no air drag) is ##R=v^2sin(2a)/(2g)##. In that case the maximum range is achieved by using a 45 degree angle of elevation REGARDLESS of the initial velocity.