One of Leonardo da Vinci's flying machines appears to be a giant auger. This design would not have exploited Bernoulli's Principle, but rather used the blade's rotation to push the air below it down to keep the craft airborne.

da vinci's aerial screw

Image credit: Wikimedia

Were there any flying machines built like this that actually got off the ground?

EDIT: So maybe I have Bernoulli misunderstood, judging from the discussion.

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    $\begingroup$ paper airplanes $\endgroup$ Commented Mar 19, 2015 at 15:57
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    $\begingroup$ @Tyler - Paper airplanes are still technically Bernoulli. Just at a very small scale. $\endgroup$
    – Shawn
    Commented Mar 19, 2015 at 16:22
  • $\begingroup$ @Shawn No, there is no pressure differential on a flat wing. Of course, a paper airplane has no lift, but I would still classify it as a flying machine of a type. Another answer would be a kite. $\endgroup$ Commented Mar 19, 2015 at 16:27
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    $\begingroup$ Here is a question that clarifies why asking about Bernoulli's principle to the exclusion of other fluid-based lift generation makes no sense. $\endgroup$
    – Roman
    Commented Mar 19, 2015 at 17:11
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    $\begingroup$ @Shawn Except rockets in general; they deal with atmosphere, but in general they rely solely on the rocket for lift. In particular, the Apollo LEM didn't rely on any atmospheric effects for anything :) $\endgroup$
    – cpast
    Commented Mar 19, 2015 at 18:08

7 Answers 7


How about all lighter-than-air vehicles:

  • Hot air balloons
  • Hydrogen- or helium-filled balloons
  • Airships

If you want to restrict the choice to heavier-than-air vehicles, rockets should still qualify.

You may also include VTOL aircraft which do not rely on their wings during hover, their internal turbo machinery would still use Bernoulli's principle, however, so for me they do not qualify.

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    $\begingroup$ Interestingly airships might not pass muster here. (It depends how pedantic you want to be : They float because of buoyancy, but the propellers that move them are airfoils, so if that directional control is part of "flight"…) $\endgroup$
    – voretaq7
    Commented Mar 20, 2015 at 3:09
  • $\begingroup$ i wouldn't disqualify any answer for using bernoulli at all, but it's not responsible for the actual flight (controlled or uncontrolled). like peter's vtol example - bernoulli might be responsible for acceleration of the airflow, but the thrust vectoring downward is what actually gets it off the ground. $\endgroup$
    – Erich
    Commented Mar 20, 2015 at 3:12
  • $\begingroup$ I think if you're going to disqualify VTOL turbojets you should probably disqualify rockets as well - the turbomachinery of a liquid rocket uses Bernoulli's principle, and the nozzles of all rockets do as well. $\endgroup$ Commented Sep 16, 2020 at 8:06

Air balloons and rockets are two examples:

  • Air balloons fly by varying the density of the aircraft to lighter than air.
  • Rockets fly by redirecting exhaust gas downward.

When the F-35 hovers, it too uses engine exhaust to counter the weight. However, their internal turbines still uses Bernoulli's principle to produce thrust. enter image description here

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    $\begingroup$ It's a wonder there isn't a melted hole in the tarmac hovering at that height, what an extraordinary photo! $\endgroup$
    – Peter Wone
    Commented Mar 19, 2015 at 13:17
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    $\begingroup$ @PeterWone That happened at Oshkosh one year. They actually blew a hole in the runway and it had to be shut down! $\endgroup$
    – Lnafziger
    Commented Mar 19, 2015 at 15:32
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    $\begingroup$ That flap on the back makes it look like the canopy is open. That was confusing... $\endgroup$
    – FreeMan
    Commented Mar 19, 2015 at 16:13
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    $\begingroup$ There is the potential to melt/burn a hole in the tarmac, for the jet nozzle in the back. For the nozzle in the front, there's no jet exhaust involved. A shaft off the front of the engine spins a downward-directed turbine, which just moves air from above the plane to below the plane. This is necessary because, if there was jet exhaust coming off the forward turbine, there's the potential that the intakes could ingest too much exhaust, with too little available oxygen, and flame out. The large volume of unheated air from the forward turbine helps moderate the temperature hitting the tarmac. $\endgroup$
    – Meower68
    Commented Mar 20, 2015 at 14:23
  • $\begingroup$ Arguably rockets employ Bernoulli's principle in that the combustion chamber tapers towards the throat to accelerate the exhaust... $\endgroup$
    – Sanchises
    Commented Sep 15, 2020 at 18:15

Airplanes :)


Although Bernoulli's principle is part of the reason why airplane wings generate lift, they also rely on displacing air downwards, in a similar way that the giant augur would, or in a similar way that a sail can convert a crosswind into forward momentum.

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    $\begingroup$ Else how would they fly inverted? $\endgroup$ Commented Mar 19, 2015 at 16:02
  • $\begingroup$ Although, actually, perhaps I spoke too soon. grc.nasa.gov/WWW/k-12/airplane/wrong2.html Seems like it's more complicated. Apologies! $\endgroup$
    – Nick
    Commented Mar 19, 2015 at 16:24
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    $\begingroup$ Actually, when you're sailing from close-hauled to a beam reach the sail shapes to form an airfoil that is trimmed to produce laminar flow and "lift". This is definitely bernoulli in action. $\endgroup$
    – J...
    Commented Mar 19, 2015 at 17:17
  • $\begingroup$ I read this page awhile ago and have been looking for a link to it. It's the best description of how wings work I've ever seen. $\endgroup$
    – Austin
    Commented Mar 20, 2015 at 19:36
  • $\begingroup$ The sail of a sailboat is an airfoil on most points of sail (except when running nearly directly downwind, when the boat actually slows down because the sail is less effective then), but it is an airfoil with very nearly the same path distance along the high-pressure and low-pressure sides. Neither is there any obvious constriction of the airflow on the low-pressure side of the sail. Nevertheless, a low-pressure region is developed, which (by Bernoulli) tells us the air must be accelerated as it passes around the sail. The geometry of the airflow is more complicated than that of the sail. $\endgroup$
    – David K
    Commented Mar 21, 2015 at 5:35

If I understand Bernoulli's principle correctly, it's the interaction of solid surfaces with fluids that attach and flow along. In this regard Leonardo's craft would be using Bernoulli's principle. If it were not, the air wouldn't go down but towards the outside or "up" along the blade.

In fact first propellers looked quite like that design and were used on boats. They were derived from Archimedes' screws. Experiments showed that less "propeller" created less drag in the water, i.e. running more efficiently. Extrapolating that to the lesser viscosity of air led to even slimmer propeller blades.

So it's like the other answers pointed out, alternatives to Bernoulli's principle are:

  • displacement -> lighter than air
  • impuls -> rockets
  • electromagnetism -> transrapid (although it's altitude is in the order of centimeters)

Arguably there might be some sort of antigravitation possible employing the gyroscopic effect. But I never heard of anyone successfully doing that. However I remember seeing a Youtube video that I can't seem to find again. In it was a physics professor, who spun up a heavy weight on a long stick to 10.000 RPM and then lifting it single handedly at the end of the stick. Didn't seem to be much of an effort as long as he guided the stick into a spiral motion.

On the matter of planes using the Bernoulli principle, aircraft wings do displace air, but as they are heavier than the displaced air this does not create enough lift for an aircraft to fly. I think what @Nick means with "displacing downwards" is the same as what @erich means with "push the air below it down". The actio=reactio in this is termed impulse in physics. Yes, this also contributes some lift but is also neglectible as there isn't much (mass of) air pushed down. You can see that in wind channel tests of wing profiles or when aircrafts fly through smoke. The overwhelming majority of lift is in fact generated by the difference in pressure between the upper and lower side of the wing. This pressure difference is due to Bernoulli's principle. An aircraft flying inverted adjusts its angle of attack to compensate for the mismatch in wing profile. Actually only aircrafts designed to fly inverted can safely do so. Aerobatics have almost neutral wing shapes that create lift only according to angle of attack plus they have lots of excess power to generate lift from. For more on negative lift, angle of attack and flying inverted see the answer to this : If the profile of a wing pulls a plane up, why can planes fly inverted?

  • $\begingroup$ Good point regarding Maglevs. Microgravity will make it hard for scientific probes to move on small celestial bodies, and rotating masses are used which are stopped suddenly, letting the probe jump. But this is less flying than hopping. $\endgroup$ Commented Mar 19, 2015 at 16:22
  • $\begingroup$ To me "the interaction of solid surfaces with fluids that attach and flow along" sounds like a description of the Coandǎ effect. I think Bernoulli's principle, in its simplest form, is a relationship between total energy and pressure in an incompressible fluid flow. (I don't really know fluid dynamics, though, so this gloss may be inaccurate.) $\endgroup$
    – Vectornaut
    Commented Mar 19, 2015 at 19:46
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    $\begingroup$ Note, that the air is directed downwards and it is needed to generate (dynamic) lift due to principle of action and reaction. More of it is however pulled down from over the wing than pushed from under it unless the wing is stalled. $\endgroup$
    – Jan Hudec
    Commented Mar 19, 2015 at 20:47
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    $\begingroup$ Only aircraft designed to fly inverted can safely do so, but it is not because the wings wouldn't be able to provide lift in the other direction. The main reasons are that normal fuel systems don't work inverted (the fuel port in the tank gets above the fuel level) and due to structural load limits (elements normally under compression-loaded become tension-loaded and vice versa and are not built for that load). $\endgroup$
    – Jan Hudec
    Commented Mar 19, 2015 at 21:20
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    $\begingroup$ @Vectornaut: Yes, Bernoulli's principle is just expression of conservation of energy and is totally insufficient to explain lift. The pressure difference is due to conservation of energy, but first we need to know the flow velocity and direction and we need viscosity and inertia for that (the air flowing over upper and lower surface don't reach the trailing edge at the same time). Coandǎ effect is somewhat different though as it describes stream of fluid in a steady environment while lift is usually generated in uniform flow. $\endgroup$
    – Jan Hudec
    Commented Mar 19, 2015 at 22:03

…giant auger. This design would not have exploited Bernoulli's Principle…

Wings and propellers generate lift by exactly the same principle. The auger would work just like the slender rotating wings of a modern helicopter, just less efficiently.

Generally speaking, anything that flies flies because it generates some force that balances gravity. It can generate the force by using buoyancy or accelerating reaction mass.

Buoyancy is what balloons and airships use. It has great advantage that it does not need any energy. It has disadvantage that it needs huge structure, because air has very low density and thus provides only very little buoyancy.

The other option, moving reaction mass, can be again done in two ways: by expelling material carried for the purpose or by accelerating the surrounding air.

Expelling material carried for the purpose is what rockets do. It is the only currently working way to accelerate in space where outside reaction mass is not available, but for aircraft it is extremely impractical, because a lot of reaction mass is needed and lifting it needs more reaction mass and so on.

So what remains is accelerating surrounding air. And this always boils down to moving a slanted surface through it that always accelerates it using the same principle. Linearly moving wing, rotating wing/propeller, turbine or augur are all slanted surfaces moving through air.

The most important properties of air here are viscosity and inertia. Due to viscosity the flow tends to remain attached to the wing and due to inertia it continues downwards after flowing off the downward-slanted trailing edge.

Then you can use the simple argument of action and reaction—the air is accelerated downward, so the wing must apply force to it and therefore the air applies reaction force of the same magnitude and opposite direction to the wing, the lift—or you can use viscosity, inertia, conservation of mass and conservation of energy (that is Bernoulli's principle) to calculate how the pressure field around the wing looks and notice the lower pressure above the wing then under it.

Neither explanation is more correct than the other; laws of nature all hold at the same time and there are multiple ways to calculate most things. However, Bernoulli's principle is not itself sufficient to explain lift. It is only one of several important properties of fluids that together explain it.

  • $\begingroup$ i think of a simple household oscillating fan. how much is bernoulli involved in the rotation of the angled blades pushing air? i would think very little. $\endgroup$
    – Erich
    Commented Mar 20, 2015 at 2:09
  • $\begingroup$ on the other hand, in putting your hand behind the fan, very little acceleration of air on the back side of the fan can be detected (compared to the front). is the increased airflow coming off the front of the fan an effect of a resultant higher pressure (a la bernoulli)? $\endgroup$
    – Erich
    Commented Mar 20, 2015 at 2:11
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    $\begingroup$ @erich: The principle is still the same—the air flows along the slanted blades and gets accelerated and reduced pressure above the blades is what transfers the energy. $\endgroup$
    – Jan Hudec
    Commented Mar 20, 2015 at 6:03
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    $\begingroup$ @erich: The acceleration upstream of the fan is lower, because the air is drawn from all directions. That is the case with any kind of propeller. $\endgroup$
    – Jan Hudec
    Commented Mar 20, 2015 at 6:05

No. "Flying" has come to refer to the non-intuitive or 'magical' mechanisms of travel through air - and that 'miracle of flight' is Bernoulli at work.

Rockets and balloons can only go straight up, they cannot fly (ie. travel horizontally). Well I suppose jet packs count. I do not think we should call that flying. "Jetting" maybe ...

We could categorise ways of getting about in air as:

  1. Flying. Bernoulli pressure differential devices (including propellors).
  2. Scooping. Things which mechanically displace the air to support or propel them - paddles/scoops/augers/blades/flat wings (are there any working examples which do not also use Bernoulli? Maybe insects? Did anyone work out yet how bees fly?)
  3. Positive Impulse. Things which create new air [or gas] to support or propel them - Rockets, steam jets, photon rockets
  4. Negative Impulse. Things which destroy air in front to support or propel them - not sure if anyone has made a supercooler negative impulse engine but I presume it works in theory (it would have to squirt out liquid air which would be type 2 thrust as it expanded ..)
  5. Anti gravity devices. Would move sideways by interacting with planets.
  6. Magnetic levitation - close range only.
  7. Floating. Balloons do not really count as flying though because they cannot move sideways without using other principles.
  8. Riding. Wind (kites,leaves) , convection currents (house dust) or thermals (gliding, clouds).
  9. Jumping ( or getting from a to b quick before gravity kicks in ). I think in this category we also have electromagnetic radiation - which does a good job of 'flying' long distances very quickly and has been around a long time.

So 'No' is probably the answer.


Planes (physics.stackexchange.com)

Basically planes fly because they push enough air downwards and receive an upwards lift thanks to Newton's third law.

And Bernoulli effect is the consequence, not the cause. Or:

Air is still (speed 0). Then a wing arrives. Air over the wing says "Oh, I was stopped, but now I'm over the wing. So, let's accelerate to back, hence low pressure is created for pulling the wing up." This is absurd.

What makes the air move faster to rear above the wing? Itself? No, a lower pressure. Thus, cause: lower pressure. Effect: air moves.

And what does it cause the lower pressure? Not its effect (air moving), of course. Now, there is only one suspect left: deflection of air.

In sum:

Wing deflects air (downwash) => this causes simultaneously lift and pressure changes (lower pressure above the wing). Lower pressure over the wing causes the higher speed of air on that side.

Also note

It is worth to mention that the Bernoulli equation is valid to calculate the amount of lift. Here we are estimating lift not by measuring the downwash itself, but by measuring a direct consequence of it: pressure changes.

  • $\begingroup$ Your text says Physics, but the link is to Aviation, is that in error? Also, I'm not sure I'm following your logic, you might want to add a bit more detail instead of using terse, incomplete sentences. $\endgroup$
    – FreeMan
    Commented Sep 15, 2020 at 17:35
  • $\begingroup$ @FreeMan Sorry the link and cite is to physics. Now it's right. $\endgroup$ Commented Sep 15, 2020 at 18:06

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