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I've heard that the pendulum rocket fallacy applies to rotorcraft as well. As stated above, I'm curious to know if a helicopter with blades on the bottom of the body would experience any effects from this. (Yes I know it's impractical and landing would be terribly difficult.)

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    $\begingroup$ Given the practical difficulties in such a configuration, it's unlikely you'll find a full-sized built version. But fixed-wing aircraft fly very similarly whether high-wing or low-wing. Maybe there's a drone version out there you could fly upside down. $\endgroup$ – BowlOfRed Jul 31 '17 at 20:15
  • $\begingroup$ @mms That seems right if the helicopter blades counter-rotate to point "up and down" as the craft wobbles. But if they rotate with the craft? Imagine the craft rotates 45 degrees from vertical; the rotor thrust doesn't "pull it vertical", it just pulls it towards 45 degrees. There is no torque towards vertical unless you turn the helicopter blades away from the axis of symmetry of the craft. $\endgroup$ – Yakk Aug 1 '17 at 18:53
  • $\begingroup$ Somehow this question reminds me of a completely unrelated question. $\endgroup$ – Mast Aug 2 '17 at 12:45
  • $\begingroup$ @Mast yes, it makes a huge difference if the rotor actually rotates. $\endgroup$ – Koyovis Aug 2 '17 at 22:53
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Yes that is possible, like the Hiller flying platform demonstrated. It had two counter-rotating propellers inside a shroud and the pilot controlled his craft by shifting his body weight, like on a Segway. There is no law of physics that prohibits a helicopter from flying upside down.

enter image description here

The Hiller flying platform was one of several types built in the 1950s, after it was observed that controlling an underslung rotorcraft by weight shift could be learned by untrained personnel in 20 minutes. The DeLackner Aerocycle was another platform built based on this finding. The idea was later abandoned due to practical issues like kicking up rocks into the rotor blades, and an at the time unexplainable interference between the counter-rotating blades. The Aerocycle had a fixed rotor head, the dynamics of which were poorly understood at the time.

For full scale helicopters, having the rotor underneath the helicopter has the same stabilising effect on flight characteristics. Stability of helicopters (and of fixed wing aircraft) is studied from the perspective of aerodynamics: the effects of wind gusts or control inputs.

In the hover, the speed stability ${\delta M}/{\delta{\dot{x}}}$ plays a significant role: if positive, the hover is unstable. A human can learn how to control an unstable platform if the time period of the oscillation is high enough (conventional helicopter pilot), but it is much easier to fly in an aerodynamically stable aircraft (the underslung platforms intended for general infantry personnel). The speed stability effect in the hover equates to a gust of wind blowing from directly forward, does then the change in moment tend to amplify or counteract the effects of the gust. This can be visualised like so:

enter image description hereImage source

The gust blowing on the helicopter tilts the rotor back, which tilts the thrust vector. A teetering conventional rotor has a positive ${\delta M}/{\delta{\dot{x}}}$: it wants to flip backwards ever stronger, and is therefore aerodynamically unstable in the hover. An underslung teetering rotor has a moment change that stabilises: it tilts the fuselage back, and due to aerodynamic coupling the rotor follows back to neutral. A rotor with hinge offset has a smaller stabilising moment, but a stronger fuselage/rotor coupling.

So to answer your original questions: Yes the helicopter with an underslung rotor would fly, and it would be easier to control than a conventional helicopter. It is just a bit unpractical, that's all.

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    $\begingroup$ The main problem is rather pilot / passenger might accidentally step into a rotor that is below them instead of above them. $\endgroup$ – Adwaenyth Aug 1 '17 at 6:40
  • $\begingroup$ @mins A rotor underneath the helicopter is not really less stable than when on top. I remember reading in Prouty that one of the stability parameters was actually better for rotors underneath the heli, but cannot look it up at the moment. But a fully articulated rotor head lines up the fuselage with the rotor disk like described in this answer , works for an underslung rotor as well. The fuselage stays pointed in the same direction as the disk, and the pilot controls direction of the disk with the cyclic stick. $\endgroup$ – Koyovis Aug 1 '17 at 14:31
  • $\begingroup$ @mins with a hinge offset rotor like that, when the rotor is turning the fuselage cannot tilt away from the disk. The rotor disk supports it, like a teacup on top of a saucer. $\endgroup$ – Koyovis Aug 1 '17 at 14:50
  • $\begingroup$ @mins One other thing I can think of as to why we might not see many of these flying around is the stability concerns. Helicopters with the body of the craft under the 'wing' will have a centre-of-gravity lower that the 'lift-point'. In the case that you cannot generate lift and start plummeting downwards, gravity will keep the body below the wing and keep it stable during auto-rotation. However, I am sure someone could design the under-wing version with that stability in mind. $\endgroup$ – Michael Coxon Aug 2 '17 at 7:03
  • $\begingroup$ @MichaelCoxon and that is exactly the pendulum rocket fallacy that the OP mentions in his question. With a fully articulated rotor head, as long as the rotor rotates the body will follow the plane of the rotor disk, whether the rotor is under or above the body. $\endgroup$ – Koyovis Aug 2 '17 at 8:07
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We spend all our weekends mowing lawn with these guys.

enter image description here

Courtesy: Helifreak.com

You can find thousands of Youtube videos showing how comfortably they can do that

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    $\begingroup$ They sure have different limitations than the full scale ones but then the question is broadly about how a helicopter will react when the rotors are at the bottom and imho this fits in perfectly for an explanation without taking away anything from the big ones. These helis can sustain inverted flight for as long as they have juice $\endgroup$ – Hanky Panky Aug 1 '17 at 8:04
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    $\begingroup$ Without a wider shot of the background, I'm tempted to say that this is an upside-up helicopter whose photo has been flipped =P. $\endgroup$ – E.P. Aug 1 '17 at 11:55
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    $\begingroup$ Yes it is, for inverted flights rotor blades do change into negative pitch $\endgroup$ – Hanky Panky Aug 1 '17 at 14:31
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    $\begingroup$ If you have any doubts about the physics of a helicopter being able to fly with the rotors under the body, here's a video that that happening. youtu.be/Qrmd_Qdryos?t=228 Yes the stunts are impossible for anything larger than an model, but it demonstrates that the rotors can be beneath the craft with no more stabilization needed than with the rotors above the body of the helicopter $\endgroup$ – JustWannaFly Aug 1 '17 at 15:15
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    $\begingroup$ If your lawnmower is flying, you may be doing it wrong. $\endgroup$ – T.E.D. Aug 1 '17 at 15:21
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One of the first helicopters that really flew (c. 1918) was the 'Petróczy-Kármán-Žurovec', intended to be used by the Austro-Hungarian Army as a tethered observation platform. The observer stood above the contra-rotating rotors...

enter image description here
(Image source)

http://www.aviastar.org/helicopters_eng/petroczy.php

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    $\begingroup$ Not bad, but two comments: "this captive observation helicopter", so the problem of balancing is actually avoided due to the cable(s) which holds the aircraft vertical; and we don't know if the center of gravity is really above the rotor. $\endgroup$ – mins Jul 31 '17 at 18:45
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    $\begingroup$ Also, there is clearly a lot of mass below the rotor counterbalancing the observation platform - i.e. three engines, apparently. $\endgroup$ – alephzero Jul 31 '17 at 21:34
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As far as I understand the aerodynamics and dynamics of a rotor wings and disk, it would actually be more stable, at least at some degree, regarding blow back of the rotor disk. Since the CG of such helicopter would be above the rotor disk. Rotor disk/blade aerodynamics are not that straight forward and you have a lot of other forces involved depending on the phase of the flight. I'll try to elaborate more, when I get to the computer.

After finding my notes, interesting enough, only talks about rotor above CG condition, in hover. It states:

"(...) rotor alone, above the CG, is dynamically unstable in hover!

Hovering dynamic instability problem:

In case of an horizontal velocity disturbance:

  • flapping angle appears;
  • flapping angle appears;
  • rotor and thrust are tilted;
  • horizontal acceleration is installed;
  • horizontal velocity builds up untill rotor flapps in the opposite direction;

The process is repeated in the opposite direction with increasing amplitude!

For large helicopters, the hovering oscillation period is usually long enough for safe reaction of the pilot."

It also talks about de Lackner HZ-1 Aerocycle:

https://en.wikipedia.org/wiki/De_Lackner_HZ-1_Aerocycle

When you are flying forward, there is a blow back force, produced by the advancing blade, creating lift, which then reflects 90° due to gyroscopic precession. This make the rotor disk to blow back, that is why when you fly helicopters you are always pushing the cyclic forward, more and more with velocity (this means, more lift created by the advancing blade, due to the increased relative wind).

This is the only reason I am saying that it would be more stable, because the helicopter would have a tendency, in the nose dive, to blow back the disk, thus decreasing the angle of attack of the advancing blade. In the case of helicopters, this also happens, which in turn they need a horizontal stabilizer in the tail, to counter the nose down attitude.

I don't know if I am making any sense, it is really hard to explain all the dynamics involved, but there are some good books regarding the matter of helicopter aerodynamics.

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  • $\begingroup$ Why would having the CG above the disk make a difference to stability? $\endgroup$ – Carl Kevinson Aug 1 '17 at 12:58
  • $\begingroup$ @CarlKevinson as I said above, as soon as I get the opportunity I'll elaborate more on the subject. I remember a few years ago, a professor from helicopter dynamics, talking about this. It is not a simple answer, it involves a lot more than just the Center of Mass and Center of Pressure. It also involves forces that are acting upon the rotor disk, depending on the phase of flight. I will try to look for my books on this subject and elaborate more later. $\endgroup$ – Focha Aug 1 '17 at 13:34
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    $\begingroup$ @mins well... stick to a phase of flight. Stability changes depending on the phase of flight. If you want to study a rotor disk, you have to study it depending if it is hovering, ascending or descending powered, horizontal flight or autorotative flight. I am no expert in helicopter dynamics. I am a helicopter pilot with and aeronautical engineer degree, but no specialization in aerodynamics. What I can do, is try to answer accordingly with the material I have. As soon as I get a more complete answer, I will reply to you. But basically, it depends on the phase of flight. $\endgroup$ – Focha Aug 1 '17 at 14:26
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A way to simplify the presentation of a helicopter with the rotor assembly on the bottom is to consider the lift created by the rotors as buoyancy and therefore create a direct comparison to a ship/boat. The described helicopter would demonstrate negative static stability (regardless of your discipline). As the center of lift moves away from the center of gravity (think of an extreme: a 30' vertical pole with a horizontal force at the top), no force exists naturally to return the system to equilibrium. The lift created by the rotors is now through a line perpendicular to the plane of the rotors. When the rotors are above the center of gravity, the vertical force of gravity drives the center of gravity below the center of lift (or center of buoyancy in the ship example). hope this helps.

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  • $\begingroup$ A ship does not flip over though, does it. My updated answer contains an explanation of what happens in a helicopter in the hover. $\endgroup$ – Koyovis Aug 4 '17 at 6:58
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Reverse blade pitch and it should push instead of pull you up. No landing gear would be my problem. I'm a helo mechanic not engineer just to be clear.

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  • $\begingroup$ To much collective up would cause the blades to strike the aircraft if they worked like normal. An inverted helo flies down so reverse the pitch not rotation $\endgroup$ – Derek Aug 4 '17 at 4:41
  • $\begingroup$ Blades rise into a more conical shape when gaining altitude if you stay with a normal configuration you hit the aircraft. And still no landing gear $\endgroup$ – Derek Aug 4 '17 at 7:37
  • $\begingroup$ You didn't say inverted you said under the aircraft $\endgroup$ – Derek Aug 4 '17 at 7:48
  • $\begingroup$ @Derek Ues there would be all kimds of practical problems with placimg the rotor underneath.. You could assemble all your points into an answer to this question $\endgroup$ – Koyovis Aug 5 '17 at 19:10
  • $\begingroup$ I never said that flying with the main rotor beneath the aircraft wasn't possible but show me how to land. $\endgroup$ – Derek Aug 6 '17 at 8:25
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the issue that isnt being adressed by these "engineers" is stability. lower rotor/tall mass mass aircraft are heavily affected by small movements of the mass above the rotor, taller rotor/lower level mass aircraft dont have this issue due to the fact that changes in mass position do not affect the vector of the thrust to mass position in the same manner as it does when the payload is above the rotor. this was proven by the navy and the airforce with their "lifting platforms" that utilized thrust from below the pilots. the other issue is the fact that these craft used liquid fueled internal combustion engines which also caused mass changes due to fuel use, which destabilized mass distribution. Electric model choppers and drones dont use liquid fuelwhich shifts as the craft shifts from upright to upside down. In short there are multiple laws of physics that work against low rotor position air craft.

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  • $\begingroup$ Electric Model helicopters are a recent entry, Nitro Helis have been here for decades and can do the same $\endgroup$ – Hanky Panky Aug 2 '17 at 5:29
  • $\begingroup$ youtube.com/watch?v=Qrmd_Qdryos&feature=youtu.be&t=228 $\endgroup$ – Hanky Panky Aug 2 '17 at 9:27
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    $\begingroup$ you could try being a little less condescending when speaking of people you don't know. $\endgroup$ – Federico Aug 4 '17 at 6:54
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    $\begingroup$ Yawn. Aways a bore to meet a repository of all wisdom. $\endgroup$ – Koyovis Aug 4 '17 at 7:08

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