Much the same that the author does to start with - he is quite clear that it's a simplified model leading to a first approximation solution to the problem. He considers one speed margin above the stall, two bank angles and a single aeroplane only - and he hasn't validated his results with any flight test results.
I think if you asked David Rogers, he'd probably agree on all these points. What he did was a very good first stab at a mathematical solution to the problem and demonstrated that the maths, and the historical evidence are broadly consistent - to whit, turnbacks can be possible.
However, it's a real shame in my opinion that 18 years later, that good start by Dr Rogers hasn't been actively followed up and published. Given time, I'd like to have a go at it myself, and may yet do so.
G