Which way to turn to return to runway for downwind landing-- into crosswind or with crosswind?

Question

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:

1. 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?

2. 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?

3. 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?

4. 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?

5. 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.

Answer 1

If your objective is to make a 180 and land on the runway you took off from, always turn into wind. Less of a reverse turn to line up will be required the stronger the crosswind is, and I can't see any case where a downwind turn would make that any better since you will always end up farther off the center line than if you turn upwind, unless the crosswind component is zero.

When you fly gliders and have to be ready for rope breaks on tow, part of your mental self briefing is to note the crosswind direction and pre-plan your turn-back direction so it is into wind. In gliders, the problem is usually not making it back; it's not overshooting after the turn back so if you are too low to complete a full circuit you must be turning into wind or you will find yourself low and abeam the mid point of the runway, the worst place to be.

Answer 2

Your questions are fair and there is a unique optimal response (or family of responses) to each question. It will be quite lengthy to detail all the variations, but I can at least answer some of them.

Goal state

First, we have to define what we wish to accomplish. Is the goal to be over the approach end of the runway at a reasonable height or to be down and stopped by the departure end? I would posit that a successful landing is not defined by how early the plane stops, but instead by (1) can it cross the arrival threshold while still in the air and (2) how much speed it carries over the departure end.

The conclusion is that the runway brackets our landing. Landing both too early and too late lead to 0% survival rates.

Initial conditions

Factors all of which need to be taken into account:

• headwind component
  • The stronger the headwind, the less distance the plane travels from its starting point but also the stronger the tailwind on the downwind landing
• crosswind component
  • The stronger the crosswind, the less(more) distance a turn upwind(downwind) carries the plane away from the airport
• min sink airspeed
  • This establishes a maximum floor for time aloft
• stall airspeed
  • In order to minimize the ground distance traveled in a 180 degree turn, the plane should be flying the most slowly possible, definitely below v_x.
• best L/D airspeed
  • This is a useful indicator for determining the altitude required for a successful turnaround
• climbout angle
  • This is mostly relevant to gliders, since their effective v_x on aerotow or winch launch is far higher than their v_y.
• runway length
  • The longer the runway, the closer the runway end is when the engine fails.
• landing distance
  • The plane needs to be able to stop on the runway.
• Any local lift or sink.
  • There's a lot more +-500fpm lift/sink around than many people realize.

Topical analysis

For any given airplane, the answer completely lies in the airplane's polars. Although this is something that typically only glider pilots are trained in, which is reasonable, because engine failure is a glider pilot's de facto state. However, it means that a detailed analysis is outside the scope of this answer, since it requires background to understand how to adjust polars for headwind/tailwind and lift/sink.

Answering your questions

Let's start off by examining a 0-wind situation. In this case, the optimal maneuver is going to look something like a chandelle. The goal is to immediately exchange as much airspeed as possible for altitude and have the lowest speed possible during the 180 degree turn. Once the plane is turned around, min sink (aka v_x) or best L/D (aka v_y) might be appropriate, depending on if the problem is the runway approach end being too far or the runway departure end being too close.

(Note that this is very different from what is taught for PPL-SEL, which is first to establish min sink. That's okay, unless you're an experienced glider pilot you're probably best off not trying to optimize the solution. A stall-spin is going to finish off far worse than a landing straight ahead.)

For the purposes of your question, I'm going to assume that the winds are not more than 15% of the plane's v_y. That's a round number I pulled out of my hat because I feel the airspeed polar starts to really suffer afterwards.

1. 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?

The optimal turn is the one which puts you the closest, in time, to the runway centerline. In other words, if you started the maneuver sufficiently far upwind that a 180 degree downwind maneuver left you 5 seconds from the runway centerline whereas the equivalent upwind maneuver left you 10 seconds from it, then you should turn downwind.

This could practically happen if, for noise abatement, you turned early and were already upwind when the engine failed.

2. 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?

Unlikely. Turning first one way and then the other is effectively an s-turn, which is what you'd want to do to burn altitude. If you are too close to the runway and do indeed need to burn some altitude then it would be better to glide a little farther away before making the 180 degree turn.

3. 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?

This would be by maneuver of choice, for the reasons stated above.

4. 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?

Yes and no. If the pilot is perfect, and is already controlling the convergence to the touchdown point before even beginning the turn, then they are identical. For us mere mortals, it will be very hard to gauge being too high vs too low at that point, and so the critical facet would be to get to where the runway is in sight and made before burning altitude.

5. 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?

If the plane is already substantially upwind, you'd want to know how long your 180 degree turn will take, and use that to figure out if a downwind turn will leave you closer to the runway. I'd say it's somewhere in the several hundred feet range, for a small GA plane with stall speed ~60kts.

Using the formula from What is the relation between airspeed and rate of turn?, a 60kt airspeed yields (1120*tand(30)/60 = 10.8deg/s. So ~17seconds for the full 180 degree turn. At 10kts (~1000fpm) crosswind, which is already quite substantial, the downwind drift during the turn is 17/60*10000 = ~280ft. So either turn initiated parallel to, but 280' upwind from, the runway would yield identical placement to a turn started on the runway centerline with calm conditions.

And still, I would choose the upwind turn since once I'm parallel to the runway the crosswind would help me glide back inline with the runway whereas downwind I'd have to fight it.

Answer 3

Instead of confusing yourself with crosswind and relative velocity, imagine a parallel runway you want to land on. The answer is then obvious. You always turn in the direction the runway is located

In the case it is close by, it just makes the required teardrop slightly smaller, say from turning 210° to only 190° before turning back to line up.

In case it is a bit further away, the runway is exactly in front of you after completing an approximate 180° turn (a little bit less because you need a bit of crab angle). Perfect!

In case it is really far away you will need to extend your lateral distance, either by turning 90° initially and only after a while turn to final, or by turning less than 180° and approaching the runway at an angle.

In all cases the best solution is to turn in the direction of the runway. You would never do a 270° turn in the opposite direction followed by a 90° turn to final if altitude is critical.

Going back to our crosswind example, note that a parallel runway is very much the same as a stationary runway that has moved relative to the airmass after a certain amount of time. So, always turn into the crosswind!

The only material difference is that you may want to end up in a crabbed configuration on short final to compensate for the crosswind. For a small crosswind component this is only a small factor and is probably solved with a boot of rudder. For a large crosswind you are already pointing in the right direction to approach the runway so there's no problem.

In any case, remember that your best option is probably to land straight ahead.

Answer 4

You would want to turn into wind for two reasons:

1. The wind will push you away from the runway centerline, if you turn away from the wind then you will get pushed farther off the centerline then if you turned towards the wind. Turning to the wind means you will be in a better position to make the runway once the turn is completed, then you can let the wind push you back on the centerline on your approach. If you turn away then you have to fight the wind to get back to the runway, and you have less chance of making it
2. 1/2mv²: that formula is for kinetic energy. If you have misjudged and you don't have enough altitude to make the turn back to the runway after all you will have to make an off-field landing and this formula becomes very important for your survival, as it tells you how much energy your airplane has if it impacts something, and the less energy your airplane has on impact the more chance you have of not dying. Let's imagine hypothetical 10 knot crosswind, and you are going into some trees as there's no field to land in. As the legend Bob Hoover advised you fly your airplane as far into the crash as possible and have it down to the slowest speed you can before impact, say just over stall speed. A Cessna 172 stalls around 43 knots, so I'll say your airspeed is 45 knots. If you turn into wind then your ground speed - which is how fast you will hit something - will be 35 knots, if you turn away from wind your ground speed will be 55 knots. To compare the relative kinetic energy we can throw away the 1/2m from the equation and just use the v² part. 35² is 1225, 55² is 3025, which is almost 2.5 times higher, i.e. your airplane has 2.5 times more kinetic energy if you turn away from wind