if you draw your ellipse such that the vertices, or the P to Q distance is 120% of the NTN. (86.5" for a 72" bow), the curve will give a bend that is slightly stiffer in the handle.

this can be a flat very flat ellipse, say one that resembles the bend half way to brace or more. I draw many ellipses on my backboard to compare with occasionally as I tiller out. but getting the right bend at about brace height makes the rest of the job go much easier.

The 120% makes a very nice shape, but you will have to ignore the last 6" or so on each tip. let them be straight and not bend around so much as the ellipse.

Yes, nice... but that's the problem with ellipses... just how much ellipse? Personally I'd prefer it a bit less flat (e.g more circular).

It would be nice to get some sort of consensus on what is considered optimal.

Of course the other problem is how far round the ellipse do you expect the bow to follow... obviously not right round to the horizontal line PQ, but the shorter the portion of the ellipse that is chosen, the closer it becomes arc of a circle.

Like I said very hard to define what we actually mean by "elliptical"

I've drawn a circle matched reasonably to the ellipse, up to the point where they intersect... it shows how subtle the difference is over a realistic arc.

Del