EDITED TO ADD: in a Bullseye the throat angle can actually be less to restrain the ring, as the method of restraint is via the combination of the two loops, not their actual throats, so ignore this. I think throat ratio can actually be a bit greater than 2:1.
A 2:1 throat on its own will not actually perfectly retain a ring with the type of flanges the Wichard LF rings have. The ring can be forced out, although not easily if only the throat is held. It needs to be less than 2:1, with greater associated system strength losses.
What throat angle is needed to retain the ring with flogging?
Well it depends on the size of the flange relative to the bit the line sits on.
The size the little loop at the end needs to be before the ring comes off is complex to calculate mathematically, as it is not the difference between the diameter of the bit the little loop clenches and the total diameter of the LF ring (the line moves obliquely in the flange as the little loop is being forced off).
By the way, if you are using fingers to do this, it is less, as two fingers can spread the throat. A 2:1 throat on the Wichard LF ring comes off pretty easily doing this.
I have just had a bit of a rough play by using a constrictor knot
on some 6mm dyneema
with a Wichard ring: 25mm inner diam, 35mm outer diam of the central bit, 60mm overall diameter, ie overall diameter).
I looped the dyneema
around the ring, tied a tight constrictor knot
in the dyneema using slightly slippery waxed twine, then forced the ring off by gripping the ring and the base of the throat. The constrictor knot slid down, enabling me to do this.
I put it back on the ring, applied a little load to the legs to tighten the system up, photographed it and took measurements from the photos: