Imagine a sphere made of a thin, ultra lightweight exotic metal of infinite strength. The entire skin of the sphere masses 1g and is 100m in diameter.
It has a valve.
You connect this valve to a pump and remove all the air from within the sphere so it contains a hard vacuum. The skin is so strong it holds itself in shape despite the removal of the air.
You release the clamps holding it in place and it flies rapidly up into the sky.
Why does it do this? Why does removing the air suddenly provide an upthrust when there was none before?
Can we draw before and after diagrams portraying the forces impinging on the sphere prior to and after evacuation of the air...
I'm really struggling to understand why it not as simple to do this as it is to draw force diagrams for 2 colliding billiard balls, and yet it clearly isn't. I guess the reason is because there are multiple forces that resolve to the upthrust and this makes a forces picture very complicated. I'd still like to see it though. There is nothing complicated about my desire to model this scenario using forces. I don't understand why the rest of the world thinks it is very strange to want to do this. Introductory mechanics is full of colliding billiard balls and force diagrams. This is just one more example...
Pressure is point forces averaged over a surface so it's just a more complicated version of force. But for me, a more difficult concept to work with because when I think about pressure I'm automatically trying to reduce it to a single point force. And if we go down that route we'll end up measuring buckets of water displaced by a body. i can already work with the Archimedes approach but, to me, while it sounds like an excellent description of what happens, it lacks step by step explanatory power. I don't need to reduce things to quantum field theory, but point forces seems like a good explanatory level.
It's what we use to explain rocket ships, a balloon should be easy!
Can you imagine gadzillion of point forces, originating at almost same point (infinitesimal sphere) and directed at all directions? (This roughly corresponds to movement of molecules in tiny water volume.)
David, as You've already probably caught, the problem with Your model is because You treat the layers of liquid/gas like solid layers, which transfer outer forces only directionaly. This is not the case.
In general, forces between particles may be attracting or reppelling, depending on the kind of molecules and their relative distances. It's a complex matter and I don't feel able to explain it in short anyway. But there are some consequences of them that create 3 states of matter: solid, liquid and gas.
In solids, the final effect of intermolecular forces is that molecules maintain their positions. With some tolerance for thermal vibrations and some elasting shift caused by directional force. If You press a solid by directional force, it will cause some elastic deformation, mostly directional, but also sideways, both will be counteracted by by intermolecular forces, trying to stabilise molecular distances and positions. So any global directional force to the piece of solid (external or its own weight) will be transfered directionaly by the interaction between its molecules, because forces between them try to maintain their relative location (and globaly the shape of solid body).
In liquid or gas it goes other way. Molecules can move and change their position constantly, due to weaker intermolecular forces. In liquid their distances are smaller, so there's constant strong interaction. It doesn't stop the movement, just holds average distances between them. In gas interaction is so weak, that in "perfect gas" model we assume that happens only at close encounters (so called "collisions").
In both cases volume of liquid/gas doesn't maintain its shape. So any global force on the volume is transfered within in absolute random directions by intermolecular forces. It maintains the intensity, but not the direction.This leads to Pascal law. Pressure in liquid (both external or internal) can act creating forces in any direction. In case of contact with a solid object, the force created by liquid pressure (which is just constant "bombardment" of that surface by moving fluid molecules) is just perpendicular localy to that surface. So if this surface is on the top of the object, the force would be pointed down, if on its bottom - up. If on the side - to the side. etc.
Why this force from fluid pressure is perpendicular to the solid surface? Simply: only perpendicular component of molecular hits do not cancel out in average. Side/parallel component of a hit from one molecule would be canceled out by another going from other side at the same angle & speed statistically.
Regards,
-J.
It's not actually true that I treat fluids as if they are solids, even if that is how it might seem. My initial model used only the kinetic motion of molecules to explain buoyancy and was roundly laughed at (not here). My new model is intended to avoid that laughter. Perhaps I have thrown out the baby with the bathwater.
A while back I found an independent description of my kinetic model from someone else who had put numbers to it. To me this model seemed to explain everything I wanted about buoyancy in a way that Archimedes did not (to me). I showed this to a physicist/mathematician friend and he poured scorn on it. I could never quite work out what was wrong with it, but I assume there was something. I'll see if I can locate it again and reproduce it here. Perhaps you can tell me what's wrong with it and combined with what's wrong with my current model, I'll be able to home in on what really happens. Got to be optimistic!
EDIT: Here we go. So what is wrong with this model?
If a balloon rises there must be a net upward force on it that is greater than its weight. What produces this force?
It must be the atmosphere. The atmosphere, made of gases moving at approximately 1000mph at 25 deg. Celsius striking the balloon produce a large surface force on the sphere. A balloon of diameter 30cm (~ one foot) has a surface area of 2826 cm^2. Each cm^2 experiences a force of 2.3 pounds (~10 newtons) for a total force on the balloon surface of about 6500 pounds. All from colliding gas molecules.
What is missing in my calculations is the difference between the collisions on the bottom of the balloon compared to the top of the balloon. Because of gravity the atmosphere varies in density as the altitude changes. This results in a density gradient. Maximum density at sea level. Minimum at 60mi, considered the edge of space. The atmospheric pressure is directly proportional to density so, maximum pressure is at sea level decreasing to a minimum at 60mi. Even with an altitude difference of one foot there is a difference in the force upward on the balloon and the force down at the top of the balloon due to density of colliding gas molecules.
If we change our balloon to a box with sides of 30cm (nearly a cubic foot), we can explore the force difference more easily.
Since the density/pressure gradient is vertical the sides of the box experience the same horizontal forces due to colliding gas molecules resulting in a net force of zero horizontally. The box will not drift left or right.
Vertically the atmospheric pressure changes about 0.035 mbar/1 ft. (near sea level) so the box bottom experiences a pressure of 1013.250 mbar pressure and the top would be 1013.215 mbar (- 0.035 mbar). Converting this pressure to force produces about 0.000078 pounds /cm^2 difference. For our box of 900cm^2 top and bottom areas results in a force difference of 0.070 pounds or 0.311 newtons or the weight of about 20 large paper clips.
If the box and its contents weigh less than this difference it will rise.
Good, it looks like this: ✴ (No references to Kurt Vonnegut intended.)
Now I start with first model under some assumptions:
we have homogenous fluid or gaseous environment (our environment is not infinite, but boundaries are very far away and do not affect our model)
our environment is anisotropic - no preferred direction /edit: no one noticed terminology error here🙃/
we analyze only static conditions
we have no gravity or any other outside forces present
I marked some virtual boundaries around really small volumes and few of your tiny forces on those boundaries on next drawing - note that all forces are numerically equal (boundary lengths on picture are same) and perpendicular to boundaries. I hope these claims do no need explanations, they are based on our assumptions alone - but if required, I can explain more.
Also I hope that despite my image being 2D and I'm talking about boundaries length, we can safely assume that in reality situation is 3D and boundaries have same surface area - this does not change overall picture.
Is such image/situation agreeable and understandable?
OK, now we take two more steps (maybe they are side steps, but I think they may help later), continuing without gravity.
We can safely assume that virtual boundaries are real boundaries (surfaces), infinitely thin, weightless, rigid and elastic (elastic here means there will not be absorbtion of collision energy) - entire picture will look exactly the same.
We remove water from one "cell", resulting in next situation:
Now we have similar looking forces, but their meaning is somewhat changed.
Green arrows are your tiny forces from previous model - water molecules colliding with something.
Red arrows are reaction forces to water molecules impacts. (They are of electrostatic nature as well - as are almost all forces between molecules.)
As we have no gravitation, overall picture does not change - cell walls elastic reaction replaces previous water molecules action.
We can leave cell empty or put anything inside evacuated cell, this does not affect surrounding fluid/gase behavior at all.
David, once again the same old mistake: remove density greadient from Your model. It has nothing to buoyancy itself (as it exist both in gas and in liquid, right?), just is one of the causes (together with temperature) to buoyancy change with altitude of flight within atmosphere.
This is only pressure gradient due to fluid column height differenc around the floating object that causes buoyancy, nothing more.
Regards,
-J.
So which bits of that description are physically wrong? The author, Greg, is certainly correct that there is an atmospheric pressure gradient otherwise no one would need to carry oxygen to climb Everest.
If there is physically an atmospheric gradient, how can we ignore it? I would have thought that anyone looking at Greg's description would think it must be true, how could it be otherwise? It's sounds perfectly logical. An atmospheric gradient exists therefore there must be a pressure difference even over the short distance of the height of the balloon.
I can't help but feel that if this model is incorrect, it needs to be explained why it is incorrect before we move on. I assume there are misunderstandings about the exact physical conditions present or there are omissions. But we need to falsify it in detail, otherwise, all we are left with is an unexplained pre-knowledge that your last sentence is correct. I'm not wedded to the Greg model. Something about it "feels" as if it can't be right. But I want to understand in detail (rather than by assertion) why it doesn't work. I've been unable to explain it away myself, but no one I've asked has been able or willing to do so either, so far. Instead, they dismiss it as nonsense without actually refuting it.
I'm sure it must be wrong, but why?
p.s.
This thread does show how subtle physics it and how easy it is to come up with incorrect or misunderstood explanations. It took 10,000 years of civilisation to arrive at the current understanding, it's hardly a surprise that trying to re-invent the ideas from scratch can run into difficulties.
If the green arrows represent a force acting towards the open space and there is nothing there to apply an opposite force, will that cause the cells surrounding that space to move into it? Or are those molecules locked in place so the green force just distorts the "wall" facing the open void?
p.s.
I'm leaving today (Thurs) on an overnight trip and probably won't be looking at this thread again until Sat morning. Please carry on if you are happy to do so, it's most appreciated.
From p1 - we replaced virtual boundaries with real solid walls, wall molecules are locked and just react to water molecules impacts - red arrows. Nothing can flow through these walls.
My main point was to show that at least in static conditions without gravity we can replace any volume of environment (water/gas) with some hard object and absolutely nothing will change in surrounding water or gas environment - all forces remain the same.
David, You now writing about pressure gradient (which is correct both in liquid and gas under gravity), but before (and this is what I was reffering to) You have written about density gradient which is severe only in gas (air/atmospfere) and has no meaning for creating buoyancy itself. Just for its changes with altitude (and temperature). In fact those changes exist also in liquids, but are minimal compared to gas and more dependant upon temperature than pressure.
So don't put density change into understanding buoyancy as it is. It of course and only explains the change of buoyancy with altitude. But not the very existence of buoyancy.
Regards
-J.
Blow-Up a1966 mystery thriller film directed by Michelangelo Antonioni, has this very thing throughout it. Watch it if you haven't already- true classic!
Been staring at this thread title for a few days, muddling through the "proper exposure" thread l'd say I can't explain every single photograph I've ever taken... 😆
I may be writing about pressure gradient but if so, only by accident. It's quite clear the "Greg" piece is about a density gradient. The whole argument rests on the idea that there is a density gradient present and the consequences of that is that there are more molecules at the bottom of the balloon than at the top and the consequence of that is even if each molecule hits the balloon with exactly the same force irrespective of its position, the the overall effect is more forces applied at the bottom than the top.
My intuition today is that this can't be right. And many people over the years have queued up to say it isn't right. But I'm not sure why it isn't right, it sounds right, but none of them so far has gone beyond "that is not right". Nobody seems willing to able to explain exactly why it isn't right in terms of the behaviour of individual molecules. There must be an obvious error or an unspoken error or something is omitted but if that is the case, why can't people just explain it very simply: "Those 4 molecules at the bottom that provide the lift in this model don't exist, or their forces operate at right angles to the direction the model suggests", or something of this nature. My take away from this situation is that there are a lot of people who struggle to accurately describe physical situations, even those who believe they have a good understanding. Probably because physics is subtle.
No doubt, when someone finally hits on the correct microscopic description, it will be face palm time and I'll be saying "Ah, of course, that's how it works. How obvious and how silly of me to think otherwise". I'm looking forward to that moment of enlightenment but I've been waiting 20 years so far, patience is a virtue...
