The bank angle that gives the least altitude loss for a
180 degree turn (or, for that matter, a turn through any other angle) is
45 degrees, neither more nor less (this can be proven mathematically). A steeper turn will shorten the time
taken to make the turn but will increase the sink rate even faster,
resulting in a greater altitude loss; a shallower turn will reduce the
sink rate but increase the time required to make the turn, again
resulting in a greater altitude loss in the turn. To put some numbers on
it, if it would take 200 feet to make the turn at 45 degrees, it would
take 244 feet to make it at 30 degrees - or at 60 degrees.
not the only consideration. The airspeed required to make the turn at 60
degrees is substantially higher, about 32% higher than at 30 degrees,
and the calculation above ignores the altitude loss required to
accelerate to the proper airspeed. In a lighter, slower aircraft this
will not be much, but the altitude loss involved will go as the square
of the airspeeds involved, so in a heavier, faster airplane it may be
substantial, while in an LSA or glider it may be very little. This gives the
advantage to erring on the side of a shallower bank, rather than a
But, there's more. The shallower bank will involve a
wider turning circle, so that at the end of the turn the aircraft will
have been moved to the side. Obviously, being laterally displaced from
the runway centerline will complicate the return. The lateral distance
will be 43% greater at 30 degrees than at 45 degrees - but at 60 degrees
it will be only 16% smaller than at 45 degrees. Thus, if altitude
allows, the advantage is with the steeper turn - but a steeper turn
doesn't gain much once you go beyond 45 degrees.
The radius of
turn will also be proportional to the square of the required speed,
which means that the faster the airplane, the more rapidly the turn
radius becomes a big problem. That would argue for erring on the side of
a steeper bank in a faster airplane - but the altitude loss in getting
to the required airspeed also gets bigger, fast.
high-performance aircraft the climb angle may be quite a bit steeper
than the glide angle. The recent video on the AOPA site showing the
"impossible turn" is a case in point. When this happens, making the turn
back with the minimum possible altitude loss may leave you with a new
"impossible" problem - it may be impossible to get the aircraft down before
you have overflown the entire runway behind you.
My takeaways are
1. Based on my own simulated attempts, in a glider or an
LSA or other
aircraft capable of flying slowly, the "impossible turn" is quite
feasible. I can't guarantee it, but based entirely on my simulated
attempts, if you are far enough down a several-thousand-foot runway in
an LSA to prevent landing straight ahead, there's a good chance you can
turn back - but once the turn is assured you may need to work hard to get down before you run out of runway behind you.
Also based on my own simulated attempts, in a higher-performance
aircraft you need to be quite a bit higher before thinking about turning
back. A little more speed makes a really big difference to how much
altitude you'll need.
3. If you have a good flight simulator, with
an aircraft model similar
in performance to the aircraft you actually fly, you can try the
"impossible turn" on the simulator. It's pretty illuminating.
4. You can try the impossible turn at altitude, to figure out the
best technique and minimum altitude loss. If you have a faster aircraft you'll probably find you first need to push the nose down aggressively and wait while you get up to the right speed for the turn. This is worth remembering: in an emergency it's hard enough to push the nose over; it's going to be downright counterintuitive to continue to dive away from the runway.
5. At altitude, you'll
learn even more if you carry a logging GPS with you when you practice, so that you can address the lateral displacement problem. If
the GPS has a display that shows your track as a trail, you can practice
getting re-aligned with the "runway" and later, from the track log, you
can determine how far down the runway you would have touched down.
I tend to think that the "impossible turn" is something we get warned away from too much, and that it may often be preferable to trying to land ahead - but it's a complicated maneuver that must be executed under stress. I wouldn't want to try it for the first time in an emergency.