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A friend of mine told me that several years ago she flew on a two-seats general aviation aircraft. She does not remember the exact model, but she remembers well that the pilot flew upside down for a while and she did not feel anything different from the normal upright position. She also noticed that a water in a bottle was stick to the bottom of the bottle.

I guess it means the pilot managed to provide a net 1 g of acceleration upwards, so the body and any other object experienced the usual head-to-toe force.

But to achieve that acceleration it should flew with 2 g of acceleration (to compensate the gravity first). She said the flight path was pretty straight.

Questions:

  1. is my guess correct?
  2. I'm sorry to cannot provide a specific model, but given the short description of the aircraft, what flight path should he follow to get that acceleration?
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  • $\begingroup$ @mins as far as I understand those answers are about a loop. She said "the path was pretty straight". She also said it was a general aviation aircraft, not a military jet. Hence I assumed the speed cannot be so fast $\endgroup$
    – Mark
    Commented Sep 11, 2023 at 9:56
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    $\begingroup$ You cannot fly in straight line and keep water in the glass. Some acceleration is required, and is provided by the turn. You missed that in the linked question: "For an aircraft at 160 km/h the radius of the turn must be smaller than 200 m. On the other hand for a fighter at 500 km/h, the radius may be as large as 2 km". At 160 km/h, on a circle of 200 m, a full turn is about 30 s (see table). $\endgroup$
    – mins
    Commented Sep 11, 2023 at 10:09
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    $\begingroup$ The term "for a while" would normally infer at least several minutes, but that's highly unlikely, so basically unless she gave a time estimate like 15 seconds or whatever, we have no idea how long it lasted. Also with the distraction of flying inverted, presumably a new experience for her, the plane could easily be making changes in direction without her noticing. Also she didn't necessarily feel 1 g, water requires very little g-force to remain in the bottle, the same with her, she wasn't being pulled out of the seat so it felt normal, she may not have noticed a reduced g load in the seat. $\endgroup$ Commented Sep 11, 2023 at 14:07
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    $\begingroup$ Your friend may be interested in this video featuring the amazing Bob Hoover doing a barrel roll while pouring water into a glass: youtube.com/watch?v=V9pvG_ZSnCc $\endgroup$ Commented Sep 12, 2023 at 21:22

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This sounds like a barrel roll.

This is a corkscrew-like flight path in which the airplane rotates around an axis between its longitudinal and pitch axes by flying along a path which lies on the surface of a horizontal cylinder. Like this (source):

Barrel roll

By not following a straight flight path, the airplane experiences a centrifugal force which counteracts gravity when flying inverted. A barrel roll can be interpreted as a combination of a regular roll an a loop. Like in a loop, the centrifugal force can be used to experience positive acceleration throughout the maneuver.

Since the airplane never experiences negative g loads, a barrel roll can be flown with almost all types of airplanes, even airliners. If you know whether the seating was side-by-side or in a tandem arrangement, we can try to narrow down the range of types.

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  • $\begingroup$ For a generic GA aircraft, how much long (in time) should be the barrel roll in order to provide the 1 g acceleration? $\endgroup$
    – Mark
    Commented Sep 11, 2023 at 10:03
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    $\begingroup$ @Mark: Several seconds, details depend on flight speed. Yes, please ask her! $\endgroup$ Commented Sep 11, 2023 at 10:18
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    $\begingroup$ @MichaelHall The interpretation of a blend between roll and loop is spot on! I will update the answer. $\endgroup$ Commented Sep 12, 2023 at 8:18
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    $\begingroup$ If you use the 45° angle from the 1954 US Navy training film then you would be flying perpendicular to your original heading when fully inverted. A smaller angle would give a smaller change of heading, but I suppose it is still the same kind of maneuver. The conceptual difference between "mostly" in the direction of the axis and exactly in the direction of the axis seems very large to me, however, and I felt I had overcome a fundamental misunderstanding when I realized the reference line and cylinder axis were not parallel. $\endgroup$
    – David K
    Commented Sep 12, 2023 at 17:09
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    $\begingroup$ @Fattie Bob Hoover is widely regarded as perhaps the best stick-and-rudder man there has ever been. $\endgroup$ Commented Sep 21, 2023 at 21:21
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I guess it means the pilot managed to provide a net 1 g of acceleration upwards, so the body and any other object experienced the usual head-to-toe force.

But to achieve that (1G) acceleration it should flew with 2 g of acceleration (to compensate the gravity first). She said the flight path was pretty straight.

No, you are mistaken here, unless I am misunderstanding your meaning, which is possible. (These concepts are kind of "squirrely" -- the net acceleration on the aircraft is indeed 2 G if the aircraft is inverted and the occupants are experiencing the same sensations that they'd feel in normal upright flight, but there's no "compensation" going on. Read on for more.)

The net acceleration in "usual" life is actually 0 G.

For example, standing on the ground, the ground is pushing up on our feet with a 1 G upward force, and gravity is pulling down on our body with a 1 G downward force.

Flying straight-and-level, the aircraft wings are generating a 1 G upward force, which is transferred through the aircraft structure, and ultimately through the seats, to our body, while gravity is pulling down on our body with a 1 G downward force.

In what we call "0 G" flight or "weightlessness", the aircraft wings are unloaded (i.e. the angle-of-attack is reduced) so that they generate 0 G of force. Gravity still pulls down on us with 1 G of downward force, so the net force is 1 G downward.

To experience the sensations of normal upright flight while inverted, the aircraft must generate 1 G of force in the "upwards" direction in the aircraft's own reference frame. This means the aircraft must generate 1 G of earthward force, i.e. toward the ground. Meanwhile, gravity is also pulling down with 1 G of earthward force. The net force is 2 G, acting in the earthward direction. So the lift force generated by the aircraft is not compensating for gravity, rather it is adding to the effect of gravity, in terms of the net acceleration experienced by the aircraft.

You can see why this would not be sustainable for long-- the flight path is going to be curving earthward very rapidly. Even if the segment starts with the aircraft's nose pointed well skyward, it will soon be pointed steeply downward.

However, it's been pointed out in a comment that even a slight mild positive G-loading generated by the aircraft will produce sensations that might be hard to distinguish from the normal full positive G-loading of 1 G, especially for an inexperienced passenger. Still, even if the aircraft was producing a positive G-loading that was just barely above zero, the net acceleration on the aircraft will still be slightly more than 1 G earthwards, so even in this case the maneuver is only sustainable for a relative brief interval. It's pretty clear that your informant is simply not reliable-- either she is not remembering her perceptions clearly, or she was too overwhelmed by the newness and strangeness of the experience to clearly perceive what was really going on. (Especially this part: "She said the flight path was pretty straight.")

"Reading between the lines" of this answer, I hope you can see that the only force we actually feel in flight is due to the real aerodynamic and thrust force generated by the aircraft. We don't "feel" the force or acceleration component that is due to the pull of gravity, because gravity acts "from within" and exerts an equal pull (per unit mass) on every particle of our body, creating no stresses or strains, and thus no sensations.

Disclaimer: this answer is written from a Newtonian perspective, treating gravity as an actual force.

Disclaimer: this answer has treated G-loading as a measure of force as well as acceleration. Strictly speaking, G-loading is not actually a measure of force, but a measure of force per unit mass, which is the same thing as acceleration.

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  • $\begingroup$ Very interesting answer. Thanks for taking the time to write it. $\endgroup$
    – Mark
    Commented Sep 12, 2023 at 17:04
  • $\begingroup$ the net acceleration on the aircraft is indeed 2 G in "weightless" flight - Should be 1 G downward for "weightless", airplane accelerating downward around the freefalling occupants. Or 2 G downward for "feels normal" inverted flight (occupants feel 1G "downward" in the reference frame of the inverted aircraft). This is what the rest of your answer explained, so I assume that early sentence is a typo or editing error. $\endgroup$ Commented Sep 13, 2023 at 9:27
  • $\begingroup$ @PeterCordes -- yes, I slipped a cog somewhere, edited, thanks $\endgroup$ Commented Sep 13, 2023 at 20:05
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Peter Kämpf has the right idea here. It sounds very much like the pilot is doing positive G or so-called “Gentlemen’s aerobatics”. Aileron rolls, barrel rolls, and even some variants of inside loops are all positive G maneuvers.

In regards to your comments, yes, an aircraft inverted, and experiencing a positive G loading would have to be experiencing an acceleration towards the Earth greater than 9.81 m/sec^2 in order for the air frame and pilot to experience this. This kind of flight regime and loading is possible for a limited period of time while inverted. In sustained, level, inverted flight or in an outside maneuver, the pilot would experience a negative G loading. Slow rolls and outside loops are some examples of negative G aerobatic maneuvers.

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