Thanks for your help anyway.
It made me manage to find this... http://www.wikiengineer.com/Transportation/SpiralCurves
From what I can tell, I need to look for 'θs' (which is the total angle my arrow would have to rotate), and divide it by 'ls'(this is the length of the red line, which I believe I can adjust ). That way I get the rate at which my angle should change.
But finding the right formula is proving difficult.
Or maybe I'm just doing it all wrong?