Is the weight of the aircraft flying in the sky transferred to the ground? Is the weight of people swimming in the pool also transferred to the ground? How can we prove it?
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25$\begingroup$ “How to prove it?” Put a beaker partly full of water on a beam balance. Balance the system. Float a cork. Observe how the balance behaves. Try it again but this time lower a dense object in on a string, not letting it touch the bottom. $\endgroup$– dmckee --- ex-moderator kittenDec 13, 2019 at 23:49
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21$\begingroup$ @dmckee The plane is not in the sky with buoyancy. $\endgroup$– enbinDec 14, 2019 at 5:30
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4$\begingroup$ @enbinzheng I was always wondering whether the overall volume of affected air around the airplane plus the airplane itself is not, in fact, as dense as the air surrounding that volume (there is a volume of lower-density air above the wings); since pressure differentials are the only thing which can lift anything, in the end. $\endgroup$– Peter - Reinstate MonicaDec 14, 2019 at 11:33
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3$\begingroup$ @enbinzheng Well, anything suspended in a fluid. $\endgroup$– Peter - Reinstate MonicaDec 14, 2019 at 16:26
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3$\begingroup$ The increase in pressure on the ground due to a plane of mass $M$ flying at an altitude of $h$ is approximately $$P = \frac{2 M g h^4}{\pi (h^2 + d^2)^3}$$ where $d$ is the distance on the ground from the point directly below the plane. $\endgroup$– Count IblisDec 15, 2019 at 4:05
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7 Answers
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Is the weight of the aircraft flying in the sky transferred to the ground?
Yes, at approximately the speed of sound.
Is the weight of people swimming in the pool also transferred to the ground?
Yes
How to prove it?
The swimming one can be quantitatively proven with a kitchen scale. Weigh an object that will float. Fill a bowl partway with water. Weigh it without and then with the object.
The airplane one can be qualitatively seen in pictures of aircraft flying low over water.
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11$\begingroup$ The illustration isn't quite convincing to me. A closer analogy to the object floating in water is an object floating in the air, a balloon, and there will not be visible waves from the balloon floating over the ocean. $\endgroup$ Dec 15, 2019 at 23:11
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13$\begingroup$ Sound is a pressure wave, so pressure waves travel at the speed of sound. The pressure increase on the ground cannot increase instantaneously, but rather must propagate as a wave from the aircraft and that wave moves at the speed of sound. $\endgroup$– DaleDec 16, 2019 at 0:48
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10$\begingroup$ If you have a small drone, you can also hover it over a kitchen scale and see that it shows the same weight as if the drone was sitting directly on the scale. $\endgroup$ Dec 16, 2019 at 8:31
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4$\begingroup$ @Jeeped see youtube.com/watch?v=lVeP6oqH-Qo for a quick version of the MythBusters episode where they tested this $\endgroup$– DaleDec 16, 2019 at 16:40
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1$\begingroup$ @Jeeped I immediately thought of that old joke too! In reality, though, assuming that the back of the truck is more or less closed (not airtight, or the budgies are in trouble!) then the budgies' weight would be transferred to the floor of the truck. If it was an open cage then the pressure wave could pass through, and some of that weight would thus transfer to the road outside the truck. So, with a tall enough truck and big enough gaps in the cage, it might actually work. $\endgroup$ Dec 16, 2019 at 16:43
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If the planes flew higher, to avoid air friction and at much greater speeds, they would orbit, and no weight would be transferred to the ground.
But at 900 km/h, the centripetal acceleration (V$^2$/R) is about 0,1% of g. So its weight is 99,9% transferred.
The weight of floating objects on water is obviously transferred. Just put lots of ice on a water jar to verify.
answered Dec 14, 2019 at 1:51
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28$\begingroup$ Note that while the weight of the plane is transferred, it is spread over a very large area beneath, so the pressure difference at ground level is negligible. $\endgroup$ Dec 14, 2019 at 20:11
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1$\begingroup$ In the orbital case there absolutely is a force between the vehicle and the ground, but what is fun is that while in low speed, level, atmospheric flight the aerodynamic forces balance the gravitational ones, in orbit we wind up with only the gravity in play, so the vehicles mass pulls the earth towards it, as it is pulled towards the earth, but there is no counteracting aero force, it is just going fast enough to keep missing the planet. Thus the orbital case is actually the one with the net forces between the bodies, the atmospheric flight has everything cancel. $\endgroup$ Dec 15, 2019 at 11:38
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$\begingroup$ @Dan Mills You are right. The gravitational force between earth and a orbit object can be measured through its effect on the acceleration of both bodies. But it is not transferred to the ground in the usual meaning of the expression. If the plane could really accelerate closer to an orbit velocity, the atmospheric pressure would decrease in the process. $\endgroup$ Dec 15, 2019 at 16:26
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3$\begingroup$ @WorldSEnder is it possible to approximate how large of an area? based on airplane height? (and speed??) $\endgroup$– AequitasDec 16, 2019 at 0:35
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2$\begingroup$ Am I making a math mistake? 900km/h = 250m/s. Earth radius = 6,371,000m. I get the accel at 0.1% of g $\endgroup$– MarsDec 17, 2019 at 3:04
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Yes the supporting force is ultimately transferred to the ground, for a theoretical "proof" (=calculation) one would likely employ the concept of control volume in fluid dynamics, and calculate the momentum balance and pressure balance around the surface of the control volume.
Airplane in stable horizontal flight:
In simple terms, the pressure distribution around the airplane (mainly the wings) generates the lift, while at the same time pushing air downwards, to satisfy the momentum balance. This in itself is enough to provide lift.
The downwards directed airstream will gently flow towards the earths surface and excert a pressure increase there, because there it will get redirected, hence applying the same lift force on the ground.
For an airplane flying at high altitude, this airstream will be dragging surrounding air with it due to friction inside the airspace, and hence widen up. Since the momentum is conserved, the larger the moving mass, the slower the velocity will be. By the time this air flow gets redirected on the ground, it's a large mass at low velocity, so the pressure increase for redirection will be very low, and wide spread out.
For a low-flying airplane, the airstream directed downwards is significantly more concentrated, leading to a higher pressure increase on the ground. (key word "ground effect", and the things visibly in the picture of the F18 seen above.)
Buoyancy of a swimmer in a pool:
This is somewhat simpler - no need to check momentum balances. The ground will have to support everything that's inside the pool, otherwise the pool would accelerate towards earth center. As analogy, you could put a pot with water ("model of a pool") on a scale, and then add an apple ("model of a swimmer"), and check what the scale shows in the two cases.
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3$\begingroup$ What if there is a plane flying in the water of the swimming pool? $\endgroup$– enbinDec 14, 2019 at 16:07
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7$\begingroup$ @enbinzheng A submaplane? $\endgroup$ Dec 14, 2019 at 16:27
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4$\begingroup$ @enbinzheng The "plane" pushes down on the fluid (water, air, metallic hydrogen) under the wing. That's what lift is. $\endgroup$ Dec 14, 2019 at 18:03
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4$\begingroup$ @enbin zheng, buoyancy also provides lift. The difference to heavier-than-air vessels is that the lift is "dynamic". And that airplane would be a "water plane" then.. (seriously - that exists and is called hydrofoil) $\endgroup$ Dec 14, 2019 at 21:40
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4$\begingroup$ @enbinzheng Indeed, and the only reason ships use buoyancy and planes use lift is because buoyancy is a function of the displaced mass, and with the density of water being significantly higher than the density of air it is far easier to displace a required volume of water for a given lift requirement than it is to displace a required volume of air for a similar lift requirement. This is a key reason we mostly use buoyancy for water and lift for air. Blimps/hot air balloons rise through the air using buoyant forces, hydrofoils rise in water using lift. The fluid doesn't care. $\endgroup$– James TDec 16, 2019 at 11:57
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This seems like an application of Newton's Third Law: For each action there is an equal and opposite reaction.
The airplane flies because the air beneath it exerts an upward force on the wings. There's also a downward force from the air above, but the wing shape takes advantage of Bernouli's principle so that the upward force will be greater. The net force is upward, and must be equal to the aircraft's weight when cruising or rising at a constant upward velocity (it will be greater when it's accelerating upward).
Therefore, the wings are exerting a net downward force on the air below it of an equal magnitude. And each volume of air similarly exerts force on the volume below it, going all the way down to the ground.
In effect, the column of air below the plane acts like enormous stilts connecting the plane to the ground.
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1$\begingroup$ The lift force and the the weight force (m*g) are also equal during constant climb or descent. Otherwise the airplane would undergo an acceleration in the direction of the lift (could be e.g a turn) $\endgroup$ Dec 14, 2019 at 21:46
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$\begingroup$ Thanks for the clarification, I've updated. $\endgroup$– BarmarDec 14, 2019 at 21:52
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2$\begingroup$ Stick to Newton and leave superstition out of it. The wings push the air down so the air pushes the wings up. To push the wings up the air must push the ground down. $\endgroup$ Dec 16, 2019 at 0:04
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Flying Aircraft
Logically: the aircraft is supported by reactions with the surrounding air; the air is supported by the ground, so yes, the weight of a flying aircraft is transferred to the ground. Although winged aircraft fly due to aerodynamics, interactions between air molecules ultimately represent the weight of the aircraft in their interactions with the ground. The closer an aircraft is to the ground, the more localized the effect (there is a noticable downwash as an aircraft passes over); the higher its altitude, the more it diffuses out. This is a twist on the "birds in a truck" riddle.
Swimmer
Does the weight of the water in a pool transfer to the ground? Obviously yes.
If you added an amount of water to a pool equal to the weight of a swimmer, would that added weight transfer to the ground? Obviously yes.
If you add a swimmer to a pool, why would you treat the addition of their weight differently? You don't.
So, yes, the weight of a swimmer transfers to the ground. However, as water is a fluid, the weight isn't applied directly under the swimmer; it is evenly distributed over the entire bottom surface.
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$\begingroup$ If the pool is of a type that has a constant water level, the swimmer displaces some water from the pool and the water equivalent to their weight is transferred to the overflow tank. $\endgroup$– JasenDec 15, 2019 at 4:51
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1$\begingroup$ @Jasen Okay, so some water moves to an overflow tank, but this distracts from the key point: the swimmer's mass becomes part of the mass of the pool's contents thus contributes to the water's overall weight, thus is represented in the forces applied by the water to the bottom surface of the pool. $\endgroup$ Dec 15, 2019 at 15:59
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Airplane Shell
Let's do a thought experiment: what if we increase the number of planes in the air until they blot out the sky1? If pressure transmitted to the ground is not holding them up, then what is? Does the air itself have some kind of magical inertia that allows it to suspend planes without themselves transmitting the force? Does the density of this magical air matter? Could we thin out the atmosphere and still maintain this "airplane shell"?
Let's do just that. Let's put all the planes on the ground, and cover the surface with runway, so the planes are rolling around on their wheels. Do we agree that the ground is holding them up? Now, let's gradually add air until they lift off. Note that as their speed increases and they generate lift, the suspension will hold up less and less of the aircraft weight. Where does this lift come from, and what is it pushing against? The wheels are pushing against the ground, so if the air isn't also pushing against the ground, you need to invoke some magic to tell us what the air is doing differently than the wheels to counteract gravity.
Ground Effect
Now, it turns out that the lift near the surface does something special, called ground effect. This increase in lift is so pronounced that entire vehicles have been built to take advantage of it. One of the largest such "planes" was the Russian-built ekranoplan. @Dale's dramatic picture of an F-18 skimming the ocean looks awesome, but doesn't directly imply ground effect, because we know these jets can fly at tens of thousands of feet. Whereas, the ekranoplan couldn't even get 100' into the air, because it is completely dependent on ground effect, which is the increased lift from air pushing against a nearby surface (like the ground, usually).
Escape
Now, if you got a big metal plate and tried to float it in a swimming pool, if the plate exactly fit the surface of the pool, then the water should be able to hold it up. But what if the plate didn't exactly fit the shape of the pool? Or what if it had a hole in it? Well, obviously, it would sink, and water would spurt up every opening it could find. Huh.
So let's think about this for a minute. Gravity is pulling the plate down, along with the water. And the water molecules are kind bouncing around near each other mostly not going too far2. But when the plate-with-a-hole begins to sink, we don't just have metal pushing on water pushing on ground. We also have metal pushing on water, pushing on a water jet that shoots upwards, opposite of the plate's direction of travel!
Now technically, the falling metal plate is not directly accelerating any water molecules upwards. Rather, the plate is increasing pressure on the water beyond the gravitational weight, and the water molecules simply escape through whatever free path they can find. The fact that liquids don't hold their shape allows them to convert the downward force of the plate into an upward force on some of the water molecules. So, even though most of the weight of the plate is being transmitted by the water to the bottom of the pool, some of it is actually causing water to escape from the pool.
In the same way, if our "airplane shell" were "floating" on our atmosphere, but were not air-tight, then some of the lift would actually go towards forcing the air between the cracks, and accelerating it away from earth. So even though most of the force must eventually get to the ground to support the weight of the airplanes, the slippery nature of gases ensures that we cannot direct all of the lift exactly downwards.
Note: all of the weight of the airplanes must be ultimately transferred to the ground, or they will not be able to maintain level flight. However, the "weight" of the airplane also causes forces to be transmitted in all other directions as well, including upwards.
Notes
1 Let's ignore the fact that there isn't a feasible flight path for all those planes, assuming straight and level flight, or that they don't perfectly tile the surface of a sphere, or that aerodynamic effects would prevent them from flying so close together, etc. Just pretend they are spherical cows.
2 If they were going far, you would notice them as currents, although, diffusion of dye in the pool should show you that a single molecule could make it all the way across the pool eventually, just from Brownian motion.
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Short version: the weight of the atmosphere, the oceans, and everything in them presses on the earth. This includes the plane, whether flying or not.
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$\begingroup$ If the swimmer is swimming, will he have more pressure on the bottom? So the bottom is put on more weight? $\endgroup$– enbinDec 14, 2019 at 22:21
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$\begingroup$ If I go into the ocean, there is immediately ninety kilograms transferred from the land to the ocean. $\endgroup$– WGroleauDec 15, 2019 at 2:25