How do you gauge your speed

Hi ABenn,
Good effort with the trigonometry. A generalised solution with parameterised OA and boat speed as a fraction of true wind speed. Hats off. My maths is caked in rust. My erstwhile ability to solve a 4th order differential equation has been slowly dissolved in 2 decades of the cheapest beer available at the time :)

When I did the calculations first, at OA = 45deg, it comes out that at f=1, TA = 90deg ie on a beam reach, which sounds plausible.

Yes - intuitively what you would expect once you think about it

With OA=30deg, you can see from the chart that the speed can increase to >1, ie faster than the wind speed, before you reach TA=90deg

I think once the OA = 45 case is understood that it becomes clear that f will always exceed 1 at TA=90 for any OA < 45 ?

Any suggestions as to how to vary the model to make it more realistic ?
there will actually be a limit to how fast you can go but how do I work that out ?

I was really just talking about the pure maths problem you seem to have just solved. I may be wrong but I would think trying to model the ability to achieve the speed that relates to any given sailing angle would be dependent on boat configuration?