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If your rocket starts to tilt over, a high centre of mass means more air will be pushing the back half of the rocket than the front half. That means the airflow will end up pushing the back end of your rocket down and getting the nose to point into the wind again. It’ll keep you pointing in the direction you’re flying.
Short point made long; it gives you stability while flying out of the atmosphere by making the entire back half of the rocket act like one giant stabilising fin.
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As for how high, depends on a few things.
How much is your centre of mass changing as you.
How wide is the bottom of your rocket?*
*(How much more drag will it generate relative to the top?)
How much torque you have to turn your rocket with.*
*(If your rocket doesn't have much in the way of control you'll want to make the rocket LESS stable or you might find yourself unable to turn at all on the way up.)
Other thing or two I probably forgot goes here.
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Hope this helps! :)
Figures.
I don't find it to be nearly as strict as CoL-CoM balance, though. But it will be stabler going up.
Remember that in a free standing object not anchored to anything, the center of mass of the object is the fulcrum point it will rotate around when a rotation is applied to it.
When the center of mass is not very far from where the fins are, then the angular force the fins provide by dragging in the wind isn't very strong because the lever arm from the fins to the fulcrum is short. Meanwhile the opposite becomes true of the draggy bits up at the top - because they are farther from the fulcrum when the CoM is lower, their influence is higher. Thus with a lower CoM you are making the drag of the top parts cause more torque than the drag of the bottom parts do, so it flips to put the "more draggy" top part at the tail end of the headwind.
Incidentally, this is also why the "pendulum rocket fallacy" is fallacious. It doesn't act like a pendulum any more than a thrown yo-yo does.
Okay, makes sense now.
The reason it's a fallacy is because rockets can be modeled as one stiff piece. There is no fulcrum point between where the force of thrust applies to the rocket and where the center of mass is on which the rocket can swing. There's plenty of good engineering reasons not to make a rocket be bendy. But if you *could*, then it would make a difference to put the thrust at the top.
Stiffness is why it's a fallacy (no hinge on which to pendulate), not because it's in freefall. From the frame of reference of the rocket, hovering on a rocket thrust with TWR=1.0 is the same thing as resting on a table. That's not freefall.
Remember: every reference frame is correct. From inside the (windowless) rocket, as soon as you lose contact with the ground, the only acceleration you feel is due to your own engine. When you shut it off, you can't tell whether you're falling through the atmosphere, orbiting a planet, or drifting in deep space. So let's remove the atmosphere and ground to simplify the situation; picture this flexible-link rocket in orbit. The mass is off to the right when the engine starts firing. It's off-axis, so the rocket begins to spin to the right. The engine gets tugged around, but it's happy to rotate since it's not actively stabilized, and it continues to accelerate the spin. Centrifugal force will eventually drag the mass around, but at that point any concept of "stability" has gone out the airlock.
And that bent shape will end up excacerbating the error, as it moves the center of mass even further off line, and also increases the drag on the top as it exposes more of the surface diagonally to the headwind.
When talking about why rockets flipover in the game, and how to design them to avoid this, drag cannot be ignored. Drag is the *primary* cause of the flipover. The only reason it's impossible to design a rocket with pull-thrust that works better than push-thrusting is that stiffening the rocket to avoid the bending caused by push-thrusting is a far easier engineering task than trying to design a pull-thrust configuration that doesn't end up also moving the drag higher up the craft because of all the engine bits sticking out the sides at the top. All the advantage of putting the point of thrust higher up is countered by the fact that the bulky volume at the top (instead of having the rocket taper to a point) produces more drag than the fins do, which sort of removes the advantage that otherwise would be there. Also, staging is easier if you can drop off the larger first stage engines from the bottom instead of from the top.
It's not a fallacy to treat a rocket IN ATMOSPHERE as a pendulum, as long as you remember that the center of mass doesn't correspond to the pendulum's bob. It corresponds to the pendulum's fulcrum. The effective center of drag is what makes the pendulum's bob in the analogy.
Imagine you are balancing a midieval morningstar on your fingertip to impress your friends (the spiky ball is on top/handle end on your finger). You can do this because the center of mass of the weapon is towards the spiky end. It only takes small movements to keep it balanced.
Now Imagine trying the same trick with it upside down. The center of mass is much closer to your finger. If you want to keep that thing balanced, you're going to have to move your hand AND take a step every so often. It is much much harder and less forgiving.
If you imagine your fingers are the thrusters, and the morningstar is a rocket, you see the principle.
But who cares? You own a morningstar!
Bit of necro here bub.
This thread last saw action back in 2015.
Good explanation though lol.