RetiredBA/BY. The Turnback is effectively just a case of energy management. Any aeroplane, just after take-off (any given speed and height, ie energy state) transitions from a point where there is simply not enough energy to do anything other than land/crash ahead, through to the stage where you can force land back at the point of departure - even on the same as opposed to reciprocal runway. Now even Sully could possibly have got his Airbus back to LGA if he'd turned pronto (and I'm not knocking his decision making process or the possible outcome if he'd ended up parking his aircraft in a built-up area.) Arguably, if you happen to turn back towards the departure airfield from say 5000ft upwind, that's a PFL rather than a Turnback. Red 3 at Valley = PFL; not a turn back in this sense.
Take the JP/Tucano/Hawk/(and probably Tutor). They will have a minimum speed/height stipulated where one can commence a Turnback. JP was 160Kts or 600ft, Tucano 130kts and 500ft, Hawk was above 250kts. So if one had an engine failure just above these defined parameters, it meant the pilot could commence a Turnback. So if we assume you are going for the reciprocal of the runway, you have to manoeuvre the aircraft in a tear-drop. Invariably a strong crosswind would help, but the exact procedure differed for type. In the Tucano we would invariably turn with the crosswind (ie downwind to maximise displacement from the Rwy CL), before reversing the turn now the long way round onto the reciprocal Rwy (sounds complex – worked a treat!) Other types probably prefer the turn to be into the crosswind to approximately hold your position near the Rwy CL. No matter how you fly it, you are potentially very near the edge of the performance envelope. You invariably require a modest rate-of turn and a low radius, so low IAS but with enough stall-margin to maintain the turn without stalling. Again Tucano, we would instantly take Mid-flap; little drag penalty, increased stall margin and the stall warning system was activated.
The point of the Turnback was to fly a manoeuvre where you could continually assess your parameters. If all went well, you land on the reciprocal Rwy. If it didn't, you either changed the plan, or more likely level the wings, convert speed for height, and ejected. Of course if you're going to eject, you need to be within seat parameters (IAS, RoD and AoB). As has been proved, any mishandling with turning and reducing IAS invariably results in a very narrow window between looking 'okay' to fatal consequences. And perhaps none of this factors in where the now-pilotless aircraft will arrive once you’ve abandoned it.
If practiced and flown accurately, a Turnback will inevitable provide a window where a successful outcome following an EFATO is achieved. Unfortunately, the recent accidents have occurred where either the aircraft was mishandled (perhaps only marginally) followed by a fractionally late decision to eject. If the way ahead is simply to ban the Turnback as too dangerous, then so be it. But I know as a student on the JP where we were explicitly told to eject after an EFATO, many students would consider starting a turn to see how it goes. I’m sure some students on the Tucano had a similar mind-set.