The scenario-- you are taking off with a significant headwind component but also a significant crosswind component. You experience a power loss (or perhaps a tow rope break in a glider). You judge that you are high enough to make a downwind landing on the same runway that you took off from, but not by a huge margin.
Assume that there is ample runway length downwind of you, but the runway is narrow enough that you must land on or near the centerline. Your goal is to minimize your time in the air, and therefore your altitude lost, before you are positioned for landing, on the runway centerline and travelling downwind.
Assume you are on the extended centerline of the runway at the point of engine failure or rope break. (Granted, there are valid reasons why it's sometimes good airmanship not to stay on the extended centerline during climbout.)
Which direction to turn initially? Into the crosswind or away from the crosswind? And is the answer always the same?
Please read on to better understand some of the nuances at play here--
If the crosswind component is strong enough, it is clearly best to make your initial turn into the crosswind, and to continue that turn until you are back near the runway centerline, when you'll need to make a slight reversal to align your ground track with the runway.
Intuitively it seems that if the crosswind component is lighter, there might be a case where it is beneficial to initially turn away from the crosswind component rather than into the crosswind component, to help get some lateral separation from the runway to give room to complete the turn. Is this correct, or is this a misconception?
In more detail:
Is it ever optimal to turn away from the crosswind component and then maintain that direction of turn through the bulk of the maneuver, except for any corrections needed at the end to line up on the runway centerline?
Is it ever optimal to do an initial turn away from the crosswind component and then reverse into a turn in the opposite direction for the bulk of the maneuver?
Or is it always best to simply turn into the crosswind component and hold that turn until the maneuver is complete, except for any corrections needed at the end to line up on the runway centerline?
In the case where the crosswind component is rather light, or zero, are methods #2 and #3 essentially just two different ways to accomplish the same thing, with little difference in the outcome?
If the answer to 1) or 2) is "yes", is there a simple rule of thumb, in terms of the strength of the crosswind component, to know when either of those approaches would be optimal?
This is not meant to be a question about how the aircraft "feels" the wind in flight, i.e. about a possible risk of stalling when turning away from the wind or into the wind. In horizontal flight, turning doesn't affect the wind the aircraft "feels". When we are descending, the wind gradient can add or subtract energy from the aircraft depending on which direction we are flying, but for the purposes of this question, assume that the wind gradient is trivial above a wingspan or so above the ground and will have no significant effect on the outcome of the maneuver.
Once more for emphasis-- the constraints of the question are that we are trying to minimize altitude loss, not to minimize how far downwind along the runway we touch down. If we ended up with altitude to spare after getting back to the runway, obviously we'd dump it as quickly as possible by sideslipping. We could imagine a different scenario where we are just barely maintaining altitude with a poorly-performing engine and want to position the aircraft for a downwind landing near the upwind threshold of the runway as quickly as possible, which may well have a different optimal solution, but that's not the question that's being asked here.