Are there any aeronautical experts out there that can tell us what the ideal bank angle would be??? Something that gives the best rate of turn / rate of descent ratio I suppose.
My gut feeling says 45 degrees bank angle. Don't ask me why.
If you were doing say 210kts and you just tried to do a 180 degree turn back, the radius of turn would be about 1.4 nm. So if say you were 3 nm up wind, you'd end up about 45 degrees off the runway centre line.
So to track back the the upwind end of the runway you would have to turn 225 degrees and then try and judge a 45 degree turn right at the last moment to track down the centreline. A total heading change of 270 degrees.
If you did a 80/260 turn you'd have to turn a total of 340 degrees. You'd be on the centreline for sure but I just wonder if the extra heading change might be the difference between making it back or not. Depends on how much altitude you've got to play with of course.
Great topic.
Oops.

That radius of turn assumes 25 degrees bank angle. At 45 degrees bank angle the radius is 0.63nm. Therefore at say 3nm upwind that would put you 23 degrees off the centreline. The total change in heading would be 226 degrees (180+23+23).
I think too that it would have to be a situation where you had a sudden double engine failure after climbing away on two engines. If it was the case where you had an engine failure early on in the piece say, soon after v1 and then you had a second failure after climbing at around 2.4 to 3 percent climb gradient, you wouldn't have a hope of turning back would you? Climb angle of 3 percent plus a glide angle of at least 5 percent, means that unless you find that nice open field in front of you, there's an exellent chance you'll scratch the paint.