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Old Dec 08, 2008, 09:01 AM
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The Pendulum Rocket Fallacy - Helicopter stability

I often hear people saying things like, 'A low centre of gravity will make it more stable', or 'Helicopters are less stable inverted, because the mass is balanced above the rotor.'
This has always seemed pretty logical to me. However, reading up on Goddard's rockets (revision), I came across the Pendulum Rocket Fallacy. The gist of it is that a rocket does not behave like a pendulum because it's thrust does not point in a constant direction, unlike gravity. The thrust points in whatever direction the rocket points. Therefore, it makes no difference whether the centre of mass (fuel, control systems etc.) is above or below the engine.
http://unreasonablerocket.blogspot.c...onception.html
This got me thinking, and wondering if the same thing doesn't apply to helicopters.
Just like rockets, they produce thrust in a direction that is fixed relative to the machine. Unlike rockets, it is more convenient to have the centre of mass below the source of thrust.
So I guess what I'm asking is;
given a trimmed helicopter initially in a hover with zero velocity, does the location of the vertical centre of gravity make a difference to the stability of the helicopter?
Or, simple version, is it less stable inverted?
Sam
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Old Dec 08, 2008, 10:28 AM
3vw
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Excellent question ... I await the discussion on this one.
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Old Dec 08, 2008, 10:35 AM
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Hmm, I'm going to open my mouth and insert my foot before really thinking about this... but...

In a rocket the thrust is way stronger than gravity, so the pendulum restoring force has little effect compared to any (un)intended "thrust vectoring" or aerodynamic forces from velocity. In a helicopter they are hopefully about equal and I was assume we are talking about hover with low airspead, so I think if you have the CG way below the rotor (as in a coax for example) there might be a noticeable stability effect. It seems pretty hard to tip a coax over... especially in real flight were I tried to mod the axe Ez with 'binary' collective pitch, but can't get it upside down except in one of their silly crash animations where it's sitting on the rotor head.

Consider a fixed wing plane for a minute. Upwards thrust (lift) depends on the bank of the wing, but a CG well below the wing (high wing trainer) will want to adjust that bank angle. Or not - maybe it's the dihedral in the air stream that does it.
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Old Dec 08, 2008, 10:56 AM
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I believe it all comes down the the helis ability to balance on its head. The Blade Disk is the fulcrum as thats where the heli would tilt upon (CG is at Main Shaft). The center of fuse would be the load arm as thats where the mass is centralized with the tank and motor/battery,etc.. The Landing gear would be the moment arm or input. An inverted Heli is like a Class 2 Lever. I would believe that its the same concept of why a high wing trainer is less stable inverted than when compared to a Low wing plane. The place of lift is also the balance point. Gravity is going to have its strongest pull on the center of mass (planes fuse, or helis fuse), thus pulling it down around the fulcrom (rotor disck or wing). I would assume that to make a heli more stable, the center of mass would need to be higher up the fuse and closer to the rotor head. This would in turn make the heli less stable when upright. This is an interesting question and would like to see what any physics people would have to say.
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Old Dec 08, 2008, 10:57 AM
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Low CG only stabilises Helicopters that have non rigid heads like old fullscale models like the huey.
Model helicopter have appr. rigid head if head dampening is hard (which i assume it is in most rc helis).
In this case it is exactly like the rocket.
see pictures added.
greetings,
marvin
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Old Dec 08, 2008, 11:11 AM
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Having the CG well below the rotor head would also simply slow response down due to the greater moment arm.
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Old Dec 08, 2008, 11:48 AM
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Reading the article and the Q&A below and thinking about it some more, it does make sense.

Gravity is going to pull the entire heli down no matter what orientation it's in, in other words, if the heli is on it's side gravity isn't going to pull the bottom down faster than the top. So gravity doesn't help you with stability, it's all aerodynamics.

It goes back to the classic experiment with a feather and a lead ball, in a vacuum they will fall at the same rate. Gravity doesn't care where the COG is, it pulls on all parts of the heli the same.

The stability from a lower COG is aerodynamic resistance from a larger body and simple mechanics, a longer lever makes it easier to move the load.

The pendulum effect is an illusion caused by the operator as force vectors are changed to alter trajectory. For example if you start in a hover with no wind, all the force of the blades is balanced with gravity, you try to move to the side so you divert some of that force to the side, now the heli starts to move both sideways and drop because you took some of the downward force away, so you give it more throttle, this increases all your force vectors so you are now pitching over to the side more, you back off the side force and the helli goes up, so you reduce throttle, now your back to hovering and start over, looks like a pendulum but it's all caused by you altering force vectors.

Also forget about balancing on a fulcrum, a fulcrum is a fixed point, unless you attach part of the heli to the ground you don't have a fulcrum, what you have are force vectors being applied to a load free floating in space. When inverted the only major difference is the aerodynamic forces on the fuselage, and your perception of what is going on. Think about how the air is flowing over the fuselage, it's a huge difference when inverted.

Later,
Marty
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Old Dec 08, 2008, 01:05 PM
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I think it is important to note that gravity acts on all parts of the heli identically. This means that all parts of the helicopter would accelerate downwards in the adsence of any force from the rotor or from air resistance. But obviously the supporting force from the rotor acts on the rotor only, not the fuselage. This is where the differences between helicopters and rockets come in - in a rocket, the engine's nozzle and therefore the direction of the thrust is fixed compared to the rocket. But in a helicopter, if there is any flex in the rotor system, eg. from blades, dampers, the fuselage isn't going to be fixed in orientation with regard to the rotor disc, it's going to have some freedom to move. We've all seen this, you power up the heli on the ground and give the cyclic a stir, the disc is going to tilt compared to the helicopter. I think this makes a difference; the helicopter is to some extent hanging from the rotor rather than rigidly fixed to it. Obviously this relates to what Marvin says about the amount of rigidity in the head.
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Old Dec 08, 2008, 01:29 PM
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Hmm.... a load slung under a parachute will definitely pendulum. What if we look at the rotors as a drag source on the falling rather than a lift source on the flying?
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Old Dec 08, 2008, 01:38 PM
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Quote:
Originally Posted by chench
I think it is important to note that gravity acts on all parts of the heli identically. This means that all parts of the helicopter would accelerate downwards in the adsence of any force from the rotor or from air resistance. But obviously the supporting force from the rotor acts on the rotor only, not the fuselage. This is where the differences between helicopters and rockets come in - in a rocket, the engine's nozzle and therefore the direction of the thrust is fixed compared to the rocket. But in a helicopter, if there is any flex in the rotor system, eg. from blades, dampers, the fuselage isn't going to be fixed in orientation with regard to the rotor disc, it's going to have some freedom to move. We've all seen this, you power up the heli on the ground and give the cyclic a stir, the disc is going to tilt compared to the helicopter. I think this makes a difference; the helicopter is to some extent hanging from the rotor rather than rigidly fixed to it. Obviously this relates to what Marvin says about the amount of rigidity in the head.
Rockets have gimbals on the engines to adjust the direction of the thrust, same as altering the tilt of the rotor blades in a heli. They really are the same.
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Old Dec 08, 2008, 01:50 PM
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Quote:
Originally Posted by cstratton
Hmm.... a load slung under a parachute will definitely pendulum. What if we look at the rotors as a drag source on the falling rather than a lift source on the flying?
Nope, gravity is still pulling on the parachute as hard as the load, it's all aerodynamic drag causing what looks like a pendulum. Look closer and you'll see the chute and load move opposite each other, caused by an imbalance in the amount of resistance on one end vs. the other. You could compare it to a torsion pendulum (like in a mechanical watch), has nothing to do with gravity other than gravity is making it move downward through the air causing the air to apply different forces to different parts of the object.
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Old Dec 08, 2008, 01:51 PM
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Originally Posted by mrschultz02
it's all areodynamic drag causeing what looks like a pendulum.
Yes, that's my point. Could this effect also apply in a helicopter system, where the rotor could be seen as having a secondary role of drag opposing movement, especially vertical movement?
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Old Dec 08, 2008, 01:55 PM
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For those of you who are really interested, check out this thread: http://www.rcgroups.com/forums/showt...hlight=edmonds

They're talking about a VTOL, but it's just about the same idea.

The answer is that there is no stability gained or lost by CG on helis. It'll only mess with the agility (i think)
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Old Dec 08, 2008, 01:57 PM
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True on the gimbals, but I doubt that they are able to move under outside influences like a non-rigid or dampened rotor is to a degree. In addition, the helicopter is controlled by altering the distribution of the thrust on the rotor disk, not the direction of the thrust per se. The tilting of the disk is a by product of the uneven distribution.
In the case of the parachute, it is stable as it falls because the centre of the aerodynamic drag from the chute is above the centre of gravity. However, in the case of our hovering heli, it's not descending or moving through the air at all, so air resistance does not play a part.
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Old Dec 08, 2008, 02:08 PM
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Originally Posted by chench
However, in the case of our hovering heli, it's not descending or moving through the air at all, so air resistance does not play a part.
But if it's not moving then you can take your hands off the sticks.

If it's response to pertubation - starting to move or at least tilt over - is a reaction force that tends to oppose that tendency, then we'd call it stable.

So the question in my mind is, if the heli does start moving horizontally, and by implication descending slightly due to the component of lift now going to horizontal acceleration, will it now experience a force as a result of that movement which opposes the movement?

Or we could just ask the practical question of those who've done the experiment: if a coax heli is modified to fly upside down, will it still hover hands off?
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