Let's look at this mathematically, since I think the results will surprise you.
If you look at post #60 - In that scenario (based off the OP but with extra specifics), if I'm over the numbers at 500 feet with a tailwind, I have three options: Attempt a downwind landing straight in from current position, attempt a 360 to a downwind landing, or attempt to turn around and land upwind, ideally via a teardrop maneuver. A full pattern, of course, is foolish.
Intuitively, I think I would go for option 3. Groundspeed would be pretty quick at first, and we could start the turn prior to being abeam the threshold to ensure we could make the runway.
If I'm over the numbers at 500 feet with a tailwind and attempt the straight-in downwind landing, my touchdown would be 5,738 feet down the runway, which is to say I would touch down 2,738 feet past the runway if there were no obstacles. In reality, I'd still be 195 feet in the air when passing over the obstacles past the opposite end of the runway, and I'm dead. So, the straight-in downwind landing from 500 AGL at the numbers is definitely a no-go unless you have over 7,000 feet of runway available.
Second scenario, 360 to a downwind landing. We have 40 seconds until we meet terra firma, so we need our turn rate to be triple standard rate, which will require a bank angle of 26.33º, but that's going to increase drag and hasten our meeting with terra firma, so we'll need to pull it around a bit quicker, probably a 30-35º bank angle to make it back around by touchdown. This is a viable option. Keep in mind that a constant bank angle will result in us not landing at the threshold, but about 1,687 feet down the runway, so we're going to go off the end of the runway (again, see post 60). A perfect turn about a point will have us flying at a much higher bank angle at the beginning and end of the turn, increasing the chances of a stall and making the landing very difficult. But, this is a viable option and survivable.
Finally, for the third scenario, assuming the wind is right down the runway, we could offset to either side while flying downwind and make a 180 to land upwind. Let's say we spend half the 40 seconds flying and half turning, so our turn will be very similar to the turn required for the 360 above. 20 seconds of flying downwind will take us 2869 feet from the starting point. We'll want to offset by the diameter of the turn (or twice the radius) so that we're over the runway at the end of the turn. Going with a 30º bank, our turn radius will be 553 feet so we'll want to offset by 1106 feet. Since we're flying the hypoteneuse of the triangle, that means we'll need to turn 22.6 degrees off runway heading to get our offset, and it'll place us abeam a point 2,647 feet down the runway. The wind will push us an additional 843 feet down the runway during the turn, thus we would come up 490 feet short. However, an increased angle of bank early in the turn is safer here as we don't need the higher bank near the ground due to facing into the wind as we approach the ground. So, we could decrease the offset slightly and crank it around a bit on the high side and have an easier approach. In any case, this scenario is survivable as well.
Now, let's throw a crosswind into the mix. Let's say that 25 knots is now 45 degrees off runway heading. First scenario is still fatal. For the second scenario, our 360 maneuver is made more difficult - If we start the turn away from the crosswind to keep the highest bank angles further above the ground, we're going to have a headwind as we come around to the base-to-final portion and we might not make it. We certainly will have eliminated any additional options should we come up short. If we instead begin the turn into the crosswind, we'll need to have our highest bank angle as we're completing the turn near the ground, which is even more risky as we may well hit a wingtip and cartwheel, which is likely to result in serious injuries at least.
But, the "teardrop" is actually helped by the crosswind. Instead of making a turn to offset, we can fly the runway heading. If we fly that heading for 20 seconds again, the wind will blow us 597 feet to the downwind side before the turn, and if we do the same 20-second turn we'd be a total of 1194 feet to the side, except our turn radius will take us 1106 feet back toward the runway, so the 20 seconds straight + 20 second turn puts us 88 feet downwind of centerline. So, the better option is to just fly runway heading for more like 15 seconds, and then make our turn and we'll have a 5-second "final" into the wind. We also blow downwind a shorter distance, meaning we make the threshold without issue.
Let's say we do 15 seconds runway heading followed by a 20-second turn and a 5-second "final". After 15 seconds, we're 447 feet off centerline and 1,966 feet down the runway. At the end of the turn, we'll be 2,562 feet down the runway and 63 feet upwind of centerline. Of course, we've also turned around, so there's 2,562 feet of runway in front of us. Our 5-second final has us touching down 357 feet later, so we stop rolling with 1,950 feet of runway remaining in front of us. The crosswind also pushes us back toward the centerline, in fact we'll need to crab or slip a little bit on our short final to keep from being blown back across the centerline.
So, in this case, I know which one I'm doing! Of course, not all situations are equal, and we obviously don't have time to do these calculations in the air, so to both
@jspilot and
@PaulS, thank you for the opportunity to think this through thoroughly on the ground! We should be able to tell using normal pilot skills whether the downwind landing would put us past the end of the runway for the straight-in downwind landing, but the other options are not so intuitive.
I feel the urge to create a spreadsheet to make these scenarios easier to calculate so I can play around with them a bit...