Yesterday I did some experiments to determine how
much altitude I would need to turn around and land
on the runway where I had just taken off.

Conventional wisdom says if the engine quits after takeoff,
land straight ahead if below XXXX feet. I wanted to know
what that value of XXXX is.

Well away from the ground, I flew past a visible marker
(a cloud wisp surrounded by good visibility) and started a
climb at 80, 100, or 120 kias. After climbing 500 feet, I
closed the mixture, paused 0.5 sec to say "oh sh*t",
lowered the nose to 100 kias attitude, then paused 2 more seconds
to simulate decision time.
From that position, I dropped the nose into a 45 deg banked
turn towards the runway maintaining 100 kias.
After 225 deg of turn, I reversed the bank to simulate a teardrop
return. A gentle rollout put me on the simulated runway centerline.

so... how much altitude did that burn?

From 80 kias, about 700 feet. The rollin is a little slow as
there is a need to build a little speed for the turn. A nose-high
turn here would be very close to stall.

From 100 kias, about 500 feet, but I would probably overshoot
the landing. It was fairly straightforward to fly a coordinated
turn with two green lights on the AoA. i.e. safe maneuvering
at moderately high angle of attack.

From 120 kias, it took about 500 feet, but to avoid overshoot, I would
have to fly straight for a few more seconds before reversing.

Those were all in a clean configuration. The overshoot could be
managed by dropping the gear and lowering the flaps. But in real
life, I might use the few seconds available trying for a restart
rather than gear or flaps.

At my home field, RHV, the straight ahead options from runways 31
are pretty scary. Houses, schools, and busy roads with powerlines.
With power out below 500 feet, I'll pick the best spot I can.
With power out above 500 feet, I'm going to start a turn and land
with the wings level on the airfield.  If on the low side, I just
level the wings and flare. If a bit higher, I align with a runway
or taxiway. RHV has parallel runways, so the initial turn should
be towards the other runway, or upwind in the rare case of a strong
crosswind.

These decisions are mine and I believe they fit my piloting skills
and my aircraft. The aircraft is a Lancair 235/320 with a fixed 64x78
prop. With a bigger or C/S prop, the required altitudes will be higher.


BTW, I've made many returns to the airfield in a glider from 200-500'.
A standard training practice in sailplanes is for the student pilot
to call out "200 feet" when climbing on tow. If the student doesn't
call it out, the instructor pulls the tow release at some point in the
tow.... at which point the student calls out "oh sh*t".

My lowest tow release, in a Schweitzer 1-26, was about 120 feet.
The towplane hit a dust devil just off the runway and climbed
about 45 deg above me. As I hit the dust devil a second later,
I climbed past the tow plane and kept climbing with full forward stick.
When the towplane starts to disappear below the nose, tow release is
mandatory. Otherwise the glider can lift the towplane's tail and force
the tug to fly into the ground. So, I released, still in strong lift.
I climbed in the lift to about 300 feet, then dove out the other side
and teardropped back to the field for a vigorous landing.

I'd highly recommend sailplane flying as good training for
Lancair pilots. Even without the radical dust devil flight.