Fishy Spaghetti Explanation

Cecil's Columns/Staff Reports
81

[QUOTE=tim314]
Before you start sucking, the pressure exerted by the air outside your mouth is normal to the surface. Are you telling me that reducing the pressure inside your mouth changes the direction of the pressure vectors pushing from outside your mouth? That doesn’t make sense to me.
[/QUOTE]

Ummm… Yeah, I think that’s exactly what sturmhauke is saying. The difference is that changes in air pressure inside your mouth affect changes in air pressure outside of your mouth only in relativity to each other. If you keep your lips closed and suck air out of your mouth creating a light vaccum the air pressure inside your mouth is lower than outside, and the air pressure outside is higher.

The same can be said with a plastic bottle. If you squeeze a closed bottle, the air inside is higher and the air outside is lower. Poke a hole in the bottle and the high pressure air rushes out to meet the low pressure air and form an equilibrium.

The same with an airplane wing. Rushing air below the wing causes the pressure under the wing to rise and the pressure above the wing to fall creating lift.

The bouncing molecule effect, although essential for a fluid universe, is kind of a red herring in the spaghetti issue.

IANA Italian Chef, but at least that’s how I see it.

  • Nate (who has spent the last 5 years dealing with assorted pneumatic cylanders)
82

[QUOTE=tim314]
Well, if the noodle was like a vertical stick with one end exactly at the plate, I’m not sure you could suck it straight up. But realistically, the noodle is usually going to be longer than the distance to the plate, meaning there’s a little space directly below it where it curves onto the plate. Or, if it’s the exact right length, then the slightest upward movement of your head creates space beneath it (since it’s pressed between your lips).

I think even having a micrometer of air in between the noodle and the plate would be more than enough to exert air pressure. I realize now that’s what was wrong with me previously saying there’s a pressure difference just because you get close to your face. The average spacing between air particles at standard temperature and pressure is on the order of a nanometer, so as long as you’ve got well over a nanometer of space between the spaghetti and the plate there’s plenty of room for air to get in there and push against it.
[/QUOTE]

Are you saying what I think you’re saying - that a piece of limp spaghetti is pushed into your mouth from the very end furthest away from you?

If so, that’s patently absurd.

83

[QUOTE=sturmhauke]
Imagine putting a piece of plastic wrap over your mouth and sucking in. (Don’t try this at home, kids!) The pressure differential causes the plastic to bulge inwards, even though no air is entering your mouth. The pressure vectors on the plastic are not normal to the surface until the system reaches equilibrium and the plastic stops deforming.
[/QUOTE]
That’s true only in an extremely narrow nonstandard sense.

First of all, the “pressure” is always normal to the surface. You’re adding in shear force due to air motion in the “bulge.” That is, perhaps, a pedantic distinction, but it’s useful.

Second of all, in this case, any shear force developed is extremely small, so you’re talking about an overall force on the plastic that’s very-very-very-close to perpendicular; enough so that we can ignore the additional shear without loss of accuracy.

Third, and most important, a force from the air that is non-normal to the surface of the plastic is not necessary to explain what is happening to the plastic. You’re presenting an extremely tiny and extraneous force, but not showing how this force affect the plastic, let alone how it affects the spaghetti.

84

[QUOTE=mwbrooks]
Either one of our arguments will require a large number of molecules. As to direction I think we agree that the spaghetti moves towards the vacuum. You’re saying the only air molecules that matter are those that hit directly opposite the mouth opening, and I’m saying the ones near the mouth impart a shear force.
[/quote]
For the most part, yes. I might quibble a bit with the “directly opposite the mouth opening” part, but that’s close enough that it will work for a thought model.

[QUOTE=mwbrooks]
Let’s try another experiment. Forget the noodle. Build two machines, each with a vacuum pump and a chamber designed to “suck” on, say, a 1" round plastic rod. The machines are bolted to the floor with their orifices facing each other. If you stick a rod partway into just one orifice and turn on the pump on that side, the chamber sucks in the rod. OK. Now turn the pump off, stick the other end of the rod partway into the other orifice, and turn on both pumps.

So both ends of the rod are in an equally hard vacuum, with only “side” surfaces exposed to the air pressure in between.

Now, is there any strain on the rod? As I see it, if my arguments are correct, yes. If yours are correct, no.
[/QUOTE]
Yes; good idea. That’s quite a nice little thought experiment.

OK, first of all, some pedantry: I would say there’s no stress along the length of the rod. There’s still stress (and strain) radially and circumferentially due to the air pressure still around the center of the rod, and there’s other material stuff going on, but your basic idea is correct: I would say that a strain gage measuring longitudinal strain will show a difference when the machines are turned on.

OK, then let’s run with this thought experiment. Let me propose a parallel one, that you might actually be able to do at your desk: Take a cylinder, say, an unsharpened pencil. Hold it lengthwise between your palms. Now squeeze together, trying to compress the pencil. Would you think there should be strain in the pencil? Now relax. Does that additional strain go away?

Now, instead of your hands, imagine a magic device that increases air pressure on the ends of the pencil, but only on the ends. Will the increase in air pressure increase strain in the pencil? If you turn off the device, will the additional strain go away? If you run the device in reverse and decrease the air pressure at the ends of the pencil, what do you think happens?

[QUOTE=mwbrooks]
I’m curious about what happens if you put one machine on rollers. I think it will get sucked towards the other, but is the rod pulling it, or is it being pushed by the air on its other side? How does the presence of the rod engender a force without transmitting it?
[/QUOTE]
The machine is not physically attached to the rod, and so cannot transfer longitudinal force to the rod (or not much, at any rate). That means that all the forces on the machine do not sum to zero, because the total air pressure is unbalanced. Ergo, a force pushing the machine along the rod.

85

[QUOTE=nd_n8]
Ummm… Yeah, I think that’s exactly what sturmhauke is saying. The difference is that changes in air pressure inside your mouth affect changes in air pressure outside of your mouth only in relativity to each other. If you keep your lips closed and suck air out of your mouth creating a light vaccum the air pressure inside your mouth is lower than outside, and the air pressure outside is higher.
[/QUOTE]
In what way does changing differential air pressure alter pressure vectors so they are not normal to the surface any longer? That’s what Tim’s objecting to.

Well, yes and no. Tim can answer for himself, of course, but I think he was trying to work through the issue by applying a special case. In this instance, the “issue” is a little tangential, being “what happens with air pressure on a molecular level between two extremely flat, dry surfaces?” I think I can safely say this isn’t really applicable to the spaghetti problem.

In a general case, the spaghetti is pushed into your mouth because an unbalanced force exists. You can think of that unbalanced force as being created by the air pressure applied to whatever section of the spaghetti is perpendicularly opposite the hole between your lips. That section could be the end furthest away from you, if that’s the way you suck your spaghetti. That conclusion is kind of non-intuitive, which is why this is a Cecil question in the first place.

I’m not sure if you have a problem with this as an explanation, or only Tim’s use of it, but I’d be happy to explain further if you like.

86

[QUOTE=zut]
Air pressure acts perpendicular to the surface everywhere;
[/QUOTE]

Then there can be no such thing as wind.

-FrL-

87

First of all, viscous drag does not equal pressure.

Second of all, “wind” (air velocity, I assume you mean) is not caused by drag; drag is caused by the velocity. “Wind” can perfectly well exist in an inviscid environment.

Third of all, you’re quoting my statement out of context, and, apparently, not reading the rest of the thread.

Fourth of all, meaningless soundbytes don’t add much to the general conversation, as John W. Kennedy has already ably demonstrated.

Care to try again, with a little extra explanation?

88

[QUOTE=zut]
In what way does changing differential air pressure alter pressure vectors so they are not normal to the surface any longer? That’s what Tim’s objecting to
[/QUOTE]

The pressure vectors are normal to the surface, they are disproportional to each other and this imbalance affects the medium seperating the two until an equalibrium is reached (the spaghetti gets sucked in, the plastic wrap bulges and the empty bottle hisses). It’s just that without the elasticity of the medium and the fluidity of the atmosphere none of this would happen. Debating the importance of elasticity and or fluidity detracts from the basic idea of a transfer of energy that occurs when the two parts of the system act toward equilibrium.
Thus a school of red herring and no sour cream sauce.

89

[QUOTE=zut]
For the most part, yes. I might quibble a bit with the “directly opposite the mouth opening” part, but that’s close enough that it will work for a thought model.
[/QUOTE]

I’m not sure it’s valid to call this a quibble. If the molecules in question aren’t directly opposite the mouth opening, they must be along the sides, so then what do we disagree about?

Am I misunderstanding your statements? Am I misconstruing your expression of a mathematical truth (the force equals the difference in pressures times the cross-section of the noodle) for an explanation of how it all works? Are you actually in agreement that it’s impossible to push on a rope, but merely dissatisfied with the undefinability of the “boundary area” where I claim the force occurs? Would it help if I agree that the sum of the shear force that I propose absolutely must be the same as the difference in pressure times the cross-section? Just wondering.

[QUOTE=zut]
I would say that a strain gage measuring longitudinal strain will show a difference when the machines are turned on.
[/QUOTE]

So then where is the strain coming from? How is force being transmitted to the rods? If not from the molecules outside the chambers, which can *only *act in shear, if at all, where?

Do you propose that the vacuum in the chambers is pulling on the rod? That sounds a lot like (I wish I could whisper this, to prevent the inevitable howls from the peanut gallery) vacuum pressure. (No! No! Don’t scream at me, I don’t believe it either! At least, I don’t dare propose it seriously in public.)

[QUOTE=zut]
OK, then let’s run with this thought experiment. Let me propose a parallel one, that you might actually be able to do at your desk: Take a cylinder, say, an unsharpened pencil. Hold it lengthwise between your palms. Now squeeze together, trying to compress the pencil. Would you think there should be strain in the pencil? Now relax. Does that additional strain go away?
[/QUOTE]

Yes, and yes.

[QUOTE=zut]
Now, instead of your hands, imagine a magic device that increases air pressure on the ends of the pencil, but only on the ends. Will the increase in air pressure increase strain in the pencil? If you turn off the device, will the additional strain go away? If you run the device in reverse and decrease the air pressure at the ends of the pencil, what do you think happens?
[/QUOTE]

Setting aside the hope that we could resolve this without resorting to magic, I imagine there is a strain exerted on the pencil by the higher pressure air outside the magic vacuums. Since there’s no perpendicular surface for that pressure to work upon, I can only imagine it exerts a shear force on the pencil’s surface at or near the boundary where the pencil enters the magic vacuum.

Hey, if we return to the same position three times, do the rules of chess apply? Do we have to give up and call it a draw?

[QUOTE=zut]
The machine is not physically attached to the rod, and so cannot transfer longitudinal force to the rod (or not much, at any rate). That means that all the forces on the machine do not sum to zero, because the total air pressure is unbalanced. Ergo, a force pushing the machine along the rod.
[/QUOTE]

I don’t get it. There’s a force pushing the machine along the rod towards the other machine, but how does this force even know the other machine exists if the force isn’t being transmitted by the rod?

90

[QUOTE=mwbrooks]
I’m not sure it’s valid to call this a quibble. If the molecules in question aren’t directly opposite the mouth opening, they must be along the sides, so then what do we disagree about?
[/quote]
I probably should have worded that differently. Saying that the only air molecules that matter are those that hit directly opposite the mouth opening leads, circularly, back to the objection that you can’t push on a rope and so forth and so on, and I didn’t want to have to re-explain that if it wasn’t necessary.

[QUOTE=mwbrooks]
So then where is the strain coming from? How is force being transmitted to the rods? If not from the molecules outside the chambers, which can *only *act in shear, if at all, where?
[/quote]
I said that a strain gage measuring longitudinal strain will show a difference when the machines are turned on. If you eliminate the pressure on the ends of the rod, the compressive strain decreases. That’s the difference.

[QUOTE=mwbrooks]
Setting aside the hope that we could resolve this without resorting to magic, I imagine there is a strain exerted on the pencil by the higher pressure air outside the magic vacuums. Since there’s no perpendicular surface for that pressure to work upon, I can only imagine it exerts a shear force on the pencil’s surface at or near the boundary where the pencil enters the magic vacuum.
[/quote]
You’re being inconsistant. Why does one form of application and removal of force (pressure from your hands) give different results than another form of application and removal of force (pressure from the air)?

[QUOTE=mwbrooks]
I don’t get it. There’s a force pushing the machine along the rod towards the other machine, but how does this force even know the other machine exists if the force isn’t being transmitted by the rod?
[/QUOTE]
Machine A doesn’t have to know that Machine B is there.

When Machine A is turned off, there is a consistent atmospheric pressure both inside and outside the machine itself, and no net force. When Machine A is turned ON, there is no longer any atmospheric pressure inside the machine. The result is that the actual force, on the total surface of the machine itself, is no longer balanced. Ergo, the machine moves along the rod.

The only thing Machine B does in this scenario is prevent the rod from moving. In the same situation without Machine B, BOTH the rod and machine would move, in inverse proportion to their masses (in the absence of friction). That’s getting a bit far afield from the spaghetti, though.

91

[QUOTE=zut]
First of all, viscous drag does not equal pressure.

Second of all, “wind” (air velocity, I assume you mean) is not caused by drag; drag is caused by the velocity. “Wind” can perfectly well exist in an inviscid environment.

Third of all, you’re quoting my statement out of context, and, apparently, not reading the rest of the thread.

Fourth of all, meaningless soundbytes don’t add much to the general conversation, as John W. Kennedy has already ably demonstrated.

Care to try again, with a little extra explanation?
[/QUOTE]

I did read the whole thread, but still managed to misunderstand your position. I somehow failed to realize that it is not an implication of your view that the air pressure at every point on a sphere is equal to the pressure at every other point. I knew you didn’t actually believe this, but I thought it was nevertheless an implication of what you were saying. In that, I (am now pretty sure I) was mistaken.

Tell me what, if anything, is supposed to be wrong with the following explanations of the spaghetti’s movement:

By sucking, I cause a wind to blow inwards toward my mouth.
Wind pushes things.
Indeed, it is this wind that is pushing the spaghetti near my mouth inwards toward my lungs. The rest of the spaghetti is dragged along.

But what is this “wind”? (See a thread in GQ I’ve started, asking about this)

Perhaps wind is bodies of air moving around.
Then when I inhale, I cause a body of air to move toward my lungs.
Since the body of air is moving toward my lungs, in aggregate, the molecules in that body of air tend to be moving toward my lungs.
This means that when a molecule of air hits the spaghetti near my mouth, it will be moving toward my lungs more often than not.
This means the kinetic energy applied to the spaghetti near my mouth is directed toward my lungs.

However, perhaps wind is pressure differentials and the forces these differentials end up causing to be applied to objects inside the body of air containing these differentials.
Then the area inside my lungs and mouth is relevantly characterized as having lower pressure than the area outside.
This is either due to temperature or density.
If it is due to density, then there are fewer air molecules inside me per volume than there are outside me.
This means that at the boundary between the inside and the outside of me (i.e. right around my lips) air molecules are more likely to be travelling toward my lungs than away from my lungs–for there are more molecules outside than inside, and so any given molecule at the boundary is more likely to have originated outside than inside, and so any given molecule at the boundary is more likely to be moving toward my lungs than away from them.
This would mean the kinetic energy applied to the spaghetti around the area of my mouth tends to be directed toward my lungs rather than away.
But what if the pressure differential is due to temperature instead?
Then the molecules outside me are more energetic than the molecules inside.
This means that a molecule at the boundary is more likely to originate from outside rather than from inside. For since the outside molecules are more energetic, they will cross the boundary more often than the inside molecules.
And so in this case, as well, the kinetic energy applied to the spaghetti near my mouth is going to be, in the aggregate, directed toward my lungs rather than away from them.

-FrL-

92

[QUOTE=Frylock]
Tell me what, if anything, is supposed to be wrong with the following explanations of the spaghetti’s movement:

By sucking, I cause a wind to blow inwards toward my mouth.
Wind pushes things.
Indeed, it is this wind that is pushing the spaghetti near my mouth inwards toward my lungs. The rest of the spaghetti is dragged along.
[/QUOTE]

What is wrong here is that you’re not, in general, drawing air into your mouth when you suck on a piece of spaghetti.

And, even if you were, the next problem is implicit in your last statement: if the spaghetti is “dragged along”, that implies (quite correctly) that if there is a wind, it must be moving faster than the spaghetti. I think you should be able to demonstrate to yourself (particularly at that moment where the spaghetti is almost, but not quite moving) that there is no column of wind howling into your mouth.

93

[QUOTE=zut]
What is wrong here is that you’re not, in general, drawing air into your mouth when you suck on a piece of spaghetti.
[/quote]

The way I suck on spaghetti, I am drawing air into my mouth. Is this not how everyone does it?

Other than by completely closing one’s lips around the noodle and also one’s throat, and then using one’s tongue to increase the volume of the cavity in one’s mouth, I can not think of any other way to suck spaghetti noodles into my mouth.

[/quote]

You’ve completely lost me. There is a colomn of wind howling (hissing anyway) into my mouth, when I suck things into my mouth.

Are we talking about the same thing here?

-FrL-

94

Ah.

Reading the original column this thread is about shows that we are thinking of different things.

I’m thinking of noodle sucking Japanese style…

My mistake, my mistake!

-Kris

95

[QUOTE=Mangetout]
Are you saying what I think you’re saying - that a piece of limp spaghetti is pushed into your mouth from the very end furthest away from you?

If so, that’s patently absurd.
[/QUOTE]
We’re still talking about a vertical piece of spaghetti, right? That is what I was saying – if the force of air pressure is normal to the spaghetti at every point, then along the length of the spaghetti it only acts to hold the strand straight, while the difference between the forces at the two ends propels it. I can’t see any other way this could work if we assume air pressure exerts a force normal to the surface.

But I’ve just thought of an objection to my own hypothesis: Say one end of the spaghetti is glued to the plate. If I suck hard enough, the spaghetti will break, right? That suggests the force is being applied close to my mouth, and doesn’t make sense with my idea that air pressure is normal to the surface everywhere.

So now I’m just confused. :frowning:

96

I think the force is acting at the joint that has formed between my lip and the noodle. Not near that joint as Cecil’s article theorizes, but at that joint.

For the momentum towards my mouth of a particle colliding with the lip/noodle complex at that joint is not cancelled out by the momentum of any hypothetical particle tracing its path in reverse–in fact, such a second particle would add to the momentum toward my mouth, not subtract from it.

And the number of molecules hitting this joint on the outside of my mouth will be greater than the number hitting the corresponding joint on the inside of my mouth–since the pressure is greater outside than it is inside.

One problem with this idea: There is no such explicit joint, but rather, a very complicated surface with lots of room for bouncing back and forth and such and whatnot. But it seems like there must be a set of areas inside all this complication which play the role of such an idealized “joint” or “corner” as the one I mentioned above.

Another possible problem: Can there be enough molecules hitting such a set of areas to account for the ability of the noodle to move across my lips?

-FrL-

97

Let’s recap what we know:

(1) A person sucking on a piece of spaghetti produces a force close to the point where the spaghetti enters the mouth. This is demonstrated by the fact that two people sucking on opposite ends can tear a spaghetti strand in two.

(2) If the force were applied normal to the spaghetti surface at every point, this couldn’t be the case. Picture two people of equal heights sucking on a spaghetti strand that’s horizontal between their mouths. For simplicity, lets say the air pressure is reduced to zero inside their mouths. Nowhere along the length of the spaghetti does the normal vector point towards either person, except inside the mouths where the pressure is zero. Yet, the strand tears in two.

(3) If we still believe air-pressure is what moves the spaghetti (which I do), one can only conclude that the force of air pressure is not normal close to the mouth, but rather directed somewhat towards the mouth. (That’s what I was saying at first – I should have stuck to my guns instead of reversing myself.)

However, I can’t really understand how such a force is produced. zut’s objection makes sense: for every particle striking obliquely one way there’s one striking obliquely the other way. Either it hits the strand, then the lip, or it follows the reversed path and hits the lip then the strand. (I’m sticking with the horizontal piece of spaghetti between two mouths here, because that avoids any confusion about the bend in the spaghetti playing a role.) Unless it hits right at the corner – this seems to be what Frylock is saying – and bounces back exactly as it came in. It seems like that would be a very small fraction of the air molecules, though.

98

[QUOTE=tim314]
But I’ve just thought of an objection to my own hypothesis: Say one end of the spaghetti is glued to the plate. If I suck hard enough, the spaghetti will break, right? That suggests the force is being applied close to my mouth, and doesn’t make sense with my idea that air pressure is normal to the surface everywhere.

So now I’m just confused. :frowning:
[/QUOTE]

Fret not, O Tim! Chris, the guy in the cell… er, cube next to mine, has cleared up the issue to my satisfaction, and maybe yours and Zut’s, so we can finally end this blessed thread! He says:

[ul]
[li]Yes, the force of the air pressure is normal to the noodle’s surface at all points.[/li][li]Yes, the force of the air pressure is equal at all points where the pressure is the same.[/li][li]But yes, the air molecules on the sides of the noodle are forcing it into your mouth! For that matter, the molecules on the opposite end do their bit, too.[/li][li]So yes, the noodle is being stretched if you suck on both ends, and yes, it will break if it’s weak enough.[/li][li]Because Lo! The noodle is being squeezed into your mouth by the outside air pressure like toothpaste being squeezed out of a tube![/li][/ul]
But wait, I said, what if it’s something solid, like a case-hardened steel rod?

Doesn’t matter, he said. A case hardened steel rod is made up of molecules (well, atoms), that distort just enough to convert the force of air pressure squeezing on its sides to a force along its length. Admittedly, the force on the other end of the rod will be a big player, if that end’s free.

In my experiment with the two sucking machines, the air pressure is squeezing the rod longitudinally into both chambers, which looks a lot like the ends are being pulled. In fact, the narrowing and lengthening distortion that the pressure creates is the same as if you clamped the rod’s ends and pulled with the same force.

Admittedly, Chris is only an electrical engineer (so far as I know; he might have a wall full of PhDs), but he says you could work it all out with Maxwell’s equations. I don’t know Maxwell’s equations. I know the chorus of Maxwell’s Silver Hammer, but I guess that doesn’t help.

Anyhow, what do y’all think of that? Can we argue about something else now?

99

mwbrooks, I think that’s got to be basically right.

The more I think about it, it can’t be about the direction of individual air molecules hitting the strand. Because even if the air molecules were just resting on top of the strand, moving the strand into the vacuum of your mouth allows the air molecules to fall into the position previously occupied by the strand, lowering their potential energy. So even for air molecules that are pushing straight down it’s energetically favorable for the strand to move into the mouth.

Plus, I just can’t see any reason for the force not to be exerted normal to the surface.

And certainly in my example where we suck on both ends and the strand breaks, we’d expect it to first stretch and thin out around the point where it breaks, right?

So I think what we’re left with is this:

As the air presses down on the strand, the strand distorts in such a way that its radius decreases slightly and its end extends further into the mouth. If its being sucked at both ends, this keeps going until it breaks – or if the pressure isn’t great enough, until the attractive forces between the atoms of the strand are great enough to keep it from stretching any further. (The attraction increases as it stretches, like springs between the atoms trying to pull them back to their equilibrium position.) For a stronger strand the attractive forces are greater, making it harder to break.

Now, if it’s only being sucked at one end, the strand stretches asymmetrically – air pressure on the other end keeps it from stretching, and it only stretches in the direction of the mouth. The attractive forces between the atoms eventually overcome this and shrink the atoms back together – the shrinking is also asymmetric, with everything shrinking towards the end that isn’t being pushed on (the one in the mouth). So basically, the spaghetti strand shimmies into the mouth like a slinky (oscillating longitudinally).

If it’s a more rigid material, you can’t stretch it as much before it snaps back, so you have faster longitudinal oscillations with a smaller amplitude. But you can still suck it.

In any case, Cecil’s explanation is wrong.

Maybe we can move on to solving other mysteries, like why the content of this thread makes Google ads want to sell me a “skin cone” to undo my circumcision.

100

[QUOTE=mwbrooks]
Fret not, O Tim! Chris, the guy in the cell… er, cube next to mine, has cleared up the issue to my satisfaction, and maybe yours and Zut’s, so we can finally end this blessed thread! He says:

[ul]
[li]Yes, the force of the air pressure is normal to the noodle’s surface at all points.[/li][li]Yes, the force of the air pressure is equal at all points where the pressure is the same.[/li][li]But yes, the air molecules on the sides of the noodle are forcing it into your mouth! For that matter, the molecules on the opposite end do their bit, too.[/li][li]So yes, the noodle is being stretched if you suck on both ends, and yes, it will break if it’s weak enough.[/li][li]Because Lo! The noodle is being squeezed into your mouth by the outside air pressure like toothpaste being squeezed out of a tube![/li][/ul]
But wait, I said, what if it’s something solid, like a case-hardened steel rod?

Doesn’t matter, he said. A case hardened steel rod is made up of molecules (well, atoms), that distort just enough to convert the force of air pressure squeezing on its sides to a force along its length.
[/QUOTE]

All of which, I should point out, I said three weeks ago, way back in post five; the post that ultimately instigated this thread snowball.

I imagine there’s a lesson in that, somewhere, but I’m not sure what it is. At least the story arc has a satisfying symmetry.