If a Cessna 172 is dropped from the sky, what minimum altitude is needed to safely land?

Question

If an aircraft like a Cessna 172 is dropped from a helicopter, what absolute minimum altitude above the ground will be required to safely land the aircraft?

CONDITIONS:

Weather: Perfect conditions, 0 knot wind.
Ground: 0f ASL.
Gross weight: Max gross weight.
Engine: off.
Speed: 0 knot(standstill drop).
Pitch Attitude: 0 degrees(as in the picture).
The helicopter is just an "abstraction"(there is no downwash exerted on the airplane)

PS: if you can simulate this on XPlane your results will also be welcomed(I don't have it).

Also, if you want to answer from a slightly different scenario like a stall, though not the same as the scenario described above, your answer will also be welcomed.

NOTE: The question is purely about physics / aerodynamics. Not planning on doing this in real life.

Btw, you did not actually specify the pitch attitude of the airplane at the moment of release. (You drew a picture but did not say that it was supposed to exactly constrain the situation under consideration.) The pitch attitude of the airplane might matter a lot. Google "hang glider balloon drop", this is a zero-airspeed situation at least as far as horizontal airspeed goes, and it has been found to be the best practice to drop the glider in a strongly nose-down pitch attitude. — quiet flyer, Feb 03 '24 at 18:17
@quietflyer that video was very useful to see the physics in a real life example. It looks he is at 0 degree attitude though. The recovery was very quick btw, almost instant, really surprised. — Gabe, Feb 03 '24 at 18:48
Glad I could contribute something useful -- keep in mind though that the moment of rotational inertia of a hang glider might be much lower than that of a Ces. 172-- PS you may not have watched the same video that I did, I know some of the training manuals for hang gliding recommend a rather nose-low pitch attitude for balloon drops-- — quiet flyer, Feb 03 '24 at 18:49
Not to be pedantic, but groundspeed is irrelevant. Forward airspeed is what matters. — Michael Hall, Feb 04 '24 at 00:03
Does the dropped-aircraft already have a lifting point that is structural in that location, or is it added just for this test? IE, does the hook change the flight/loading chars of the cessna ? — Criggie, Feb 04 '24 at 09:42
Does this question: Can a free-falling aircraft with no horizontal (or minimal horizontal velocity) start up and fly to safety? answer your question? — ROIMaison, Feb 06 '24 at 08:29

Therac · Answer 1 · 2024-02-04T10:00:41.087

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Minimum altitude is 0 ft: simply release the plane and let it sit pretty on the ground. Call it cheating, but it fits the scenario perfectly.

If you want it high in the air, what probability of landing is required? Aircraft can sometimes land in the strangest of circumstances. So let's say there's at least a 1% chance at any altitude.

If it's being dropped from an actual helicopter, rotor downwash and attitude will affect the outcome. Safe practice for stall recovery normally requires 3,000 ft, recovery itself takes less than 1,000 ft - so that's a safe altitude, but it's done in a plane with some forward airspeed.

If the "helicopter" is an abstraction, and the conditions are better, this depends on just how good the conditions are. At the right speed and attitude on the glideslope, any altitude will work.

With the new input - 0 airspeed, no engine:

A non-aerobatic GA airplane like the 172 is at risk. At zero initial airspeed, the control surfaces have zero authority; the plane might spin or tumble and never resume controlled flight. Or it might fall nose-down, but that's a gamble.

4+ generation fighters and high-end aerobatic aircraft would most likely recover. They have all-moving tails, oversized control surfaces, can take the g-loads involved, and fighters add thrust vectoring and computers.

edited Feb 04 '24 at 10:00

answered Feb 03 '24 at 06:48

Therac

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It takes 3000ft to recover from a (power off) stall in a Cessna 172? – 300D7309EF17 Feb 03 '24 at 07:15
@tedder42 To do so safely. But I'm not sure what it takes and if it's been done from power off and zero airspeed condition. – Therac Feb 03 '24 at 07:19
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Stalls are often done at 3000 feet, but yikes, a power off stall recovery, even without reapplying power, doesn’t take more than a couple hundred feet. – 300D7309EF17 Feb 03 '24 at 07:33
@tedder42 But that happens when you're already in controlled flight, and lost some airspeed. Your controls work. A plane dropped from a helicopter isn't going to be stable or controllable to begin with. – Therac Feb 03 '24 at 07:45
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Not disputing that. But your original statement of “Stall recovery normally requires at least 3,000 ft.” was wildly inaccurate. – 300D7309EF17 Feb 03 '24 at 07:47
@tedder42 True. I missed the "safely" qualifier. As for the actual answer for recovery from 0 airspeed, I think the only way to figure it out is to try it in a simulator, probably X-plane. Unless someone's got a skycrane, a spare 172, and a pilot with a death wish. – Therac Feb 03 '24 at 08:16
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Or, edit the drawing so it drops with the nose pointing down... – Ralph J Feb 03 '24 at 08:29
@Therac does something like a Extra 300 (with engine off) would be able to recover? – Gabe Feb 03 '24 at 17:47
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@Gabe No idea. You'd have to test it in a simulator. X-Plane actually has an Extra 330 module. I recommend that one because it relies almost entirely on physics-based simulation, which is more accurate in abnormal cases like this one. – Therac Feb 03 '24 at 17:54
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A C172 dropped from standstill is more than likely recoverable. Worst case is it enters a spin, which is recoverable if C172 is within weight&balance. More likely it just goes 45+ degrees nose down almost immediately (due to tailplane generating a force), and picks up airspeed in a non-spin spiral until controls regain authority. – Roman Feb 03 '24 at 18:05
"The aircraft might spin or tumble and never resume controlled flight." Agree it might spin or tumble (though I think a spiral is dramatically more likely for reasons I've laid out in my answer), but why would this prevent it from resuming controlled flight? Whether it goes nose down or nose up it will regain control authority as it speeds up, and a 172 should be recoverable from any attitude so long as it has sufficient altitude and can avoid breaking up. You'd definitely want a pilot comfortable with aerobatics at the controls, though! – Chris Feb 03 '24 at 19:48
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@Chris IDK. I just know I wouldn't risk it. A lot of good pilots have bought the farm in spins and spirals. There's a lot of uncontrolled flight modes that can happen from zero airspeed. The control surfaces don't work when the main surface is stalled, and they can break off if the wind's too strong. I believe some pilots, sometimes, will recover, but far from all. Aerobatics or jet fighters are very different, their large all-moving surfaces work even when airflow over the wing is completely detached. – Therac Feb 03 '24 at 19:54
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@Therac Certainly I would never suggest anyone try this maneuver in real life. But in principle it is probably safer than other stunts that are actually done in real life (which I also would never suggest anyone do in real life lol). Actually the second one is pretty similar- taking off from a helipad at very little forward speed is not so different from being dropped from a helicopter! – Chris Feb 03 '24 at 20:07
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@Chris That's a Red Bull Carbon Cub, though! Twice the power/weight, 60 ft takeoff distance, full aerobatic build. Guess I should try it in a simulator to see how it goes, just have to set it up properly. My guess is, the heavy engine in front will save the plane most of the times, but not every time. – Therac Feb 03 '24 at 20:31
@Therac Yes, doing some back-of-the-envelope calculations it looks like its actually closer to its flying speed when it goes over the edge than I first imagined. So it's certainly not a 1:1 comparison. – Chris Feb 03 '24 at 22:41
Are we going to have a flood of questions about all the ways one might hang a c172 and whether it can recover? Like "hung from prop" and "from wingtip" and "from rudder" and "from one undercarriage wheel" ... etc ? – Criggie Feb 04 '24 at 09:45
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"So let's say there's at least a 1% chance at any altitude." - not really. If the altitude is not enough for it to start flying, but enough to be utterly destroyed, there is zero chance. Drop it from 100 feet, and unless you prepared something below it, it will 100% be destroyed. – vsz Feb 05 '24 at 07:54

Chris · Answer 2 · 2024-02-04T08:49:50.677

Not much in principle. In freefall, the 172 would reach its stall speed in a little over a hundred feet. You'd need to make sure to get the nose down as soon as possible. Then you need to gain a little more speed and pull out of the dive. Probably less than 1000 feet in total to recover to controlled flight as long as you can get the nose down relatively quickly. Then you still need however much altitude is required to find a safe landing spot. To do this remotely safely, you'd want a very healthy margin.

The plane would most likely enter a spiral at first. Both the wings and tailplane are behind the center of gravity, so unlike in normal flight they both produce a nose-down moment when they have air coming from below, and at 90 degrees angle of attack they are producing a lot of upward force along the vertical axis for a given vertical speed- significantly more than they would produce in horizontal flight at the same speed!

So the nose should drop pretty quickly even without pilot input. With the engine off, the airframe is completely symmetrical and there is no yawing or rolling moment. Eventually one wing will drop by chance and the plane will enter a spiral. But as the nose drops, the airspeed increases and the pilot regains control authority. Then they only need to recover from the ensuing dive.

"at 90 degrees angle of attack they are producing a lot of upward force along the vertical axis for a given vertical speed- significantly more than they would produce in horizontal flight at the same speed!". It's comparable. Airfoils right before stall have a lift coefficient of ~1.5 and a flat plate drag (a good approximation for the falling plane) is ~1.3. It's counter-intuitive that an airfoil with a modest downward deflection of air can produce as much lift force as a flat plate produces drag! — Kevin Kostlan, Feb 04 '24 at 04:22

If a Cessna 172 is dropped from the sky, what minimum altitude is needed to safely land?

2 Answers2