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Whenever the question "Why do airplanes fly?" is asked (e.g. »What really allows airplanes to fly?«, »How an airfoil works?«) at a certain point the following is cited:

Bernoulli's principle accounts for 20% of an airplane's lift…

In a very general formulation Bernoulli's Principle states

$p_\mathrm{total} = p_\mathrm{dynamic} + p_\mathrm{static}$

Assuming low ( $M\ll0.3$ ) velocities this can be written as (resulting in an error of 5% at $M=0.3$ due to density change):

$p_\mathrm{total} = \frac{1}{2}\rho u^2 + p_\mathrm{static}$

When Bernoulli's Principle is defined as that. Then ( in case of $M\ll0.3$ ) it does account for 100% of the lift, since it describes how the static pressure difference between suction and pressure side results into drag and lift (neglecting skin friction).

Which additional assumptions have to be made to come up with a lift which is only 20% of the actual lift? Is this the lift one would calculate when the lift-force is based on the equal-transit-time-assumption? Or is this an error occurring when a delta wing also features vortex system so that the definition of the total pressure might be difficult?

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  • $\begingroup$ The linked question from Physics seems to do a good job of explaining in detail that an airplane's lift doesn't/can't come from the pressure difference of air above and below pulling the wing upward. Your definition of Bernoulli's Principle doesn't change that at all. $\endgroup$ – hazzey Sep 29 '15 at 1:52
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    $\begingroup$ Sorry I do not unterstand. Where is the calculation/experiment showing that? Conservation of momentum does provide a way to calculate the force. But the airfoil does not know anything about the conservation laws. The only physical interaction between wing and air is pressure and friction. $\endgroup$ – rul30 Sep 29 '15 at 12:03
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The Bernoulli-Newton lift debate has been around for a long time, and now has many other theories in the mix. This hyperphysics link sums it up pretty well; http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html

There are lots of confusing explanations out there on both sides of the fence. Like the bogus “20%” claim you have come across ;-). It is a more complex topic than most people credit it and I can not say I am truly happy with any of the "book" definitions I have found over the years. I agree with your mathematical evaluation of Bernoulli's principle explaining 100% of the lift, which the equation does, but it does not explain the misconceptions surrounding the debate. It is a bit like arguing "is the world described by a Polar or Cartesian coordinate system?", because it is the same world regardless of which way you choose to describe it. I have spent a fair amount of time studding this topic and will take a shot at my own (perhaps more layman's terms) explanation. It sounds like you already have a firm understanding, but this may help you to explain it to others:

Lift is the process by which an airfoil traveling through a fluid at a velocity, transforms a small forward force into a large perpendicular force. Think of a wing/airfoil like a gear ratio between forward force and downward force. Different wings/airfoils have different gear ratios(lift coefficients). Conservation of momentum (per Newton) tells us that if we move more air down at a lower velocity, we can lift much more efficiently. You can do this math in your head, because momentum has a linear velocity term (p=mv), and kinetic energy has a squared velocity term(ke=1/2mv^2). Thus, you can see that as the velocity of the downward air increases, the power required grows exponentially (1->4->9->16->25) while lifting force only grows linearly (1->2->3->4->5). This is why a Cessna 172 can fly, but it can not fly vertical. The lift produced by the wings(low velocity, more air) is substantially more than the lift produced by the propeller(high velocity, less air), even though both scenarios have the same power input.

This insight is highly useful for explaining lift all by itself. Whatever magic occurs to make x many kg of air move down at v velocity is outside of our concern and we can still explain and evaluate lift effectively.

When we dive deeper into our understanding however, like when trying to understand why airfoils stop working at high angles of attack, we need new explanations to model reality. With our previous understanding we would have expected a nice trigonometric gear ratio change based on our angle of attack, but since airfoils do not behave that way in practice we need to understand them deeper.

Bernoulli's principle explains why the laminar flow of air over the top of the wing is critical to lift. If the angle of attack is too large or if the laminar airflow on the top of the wing is disrupted; turbulence will be generated and the airfoil will stall. In a stall, some amount of air is still being deflected downward by the bottom of the airfoil; even in the absence of negative pressure on the top of the wing. In this instance there is “lift” being generated in a “purely Newton” fashion, but the glide ratio will be that of a triangular shaped rock ;-). There is so little downward force relative to a large forward force that it is not considered lift.

A Newton perspective of lift is correct in the sense that the wing/airfoil, as a complete system, produces lift based on a gear ratio of that system. It however does not explain why we can achieve such a high gear ratio(lift coefficient) in practice. To fulfill this need we use Bernoulli's principle along with many other fluid dynamics principles to help explain the complex physics occurring. Other mathematics and theorems can be used to explain the physics in more useful and/or in more confusing ways ;-). For example I find the Kutta-Joukowski Lift Theorem to be highly irritating and unintuitive. That said, I'm sure it has saved people from some very nasty differential equations over the years ;-).

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  • $\begingroup$ Thanks for your comment, nice analogy with the coordinate systems. However, when arguing about the 'proper' coordinate system one would be puzzeles as well if someone would say: the cartesian system accounts only for 20% of the space ;-) I was wondering if there was an analytical way (including the assumptions) to come up with those 20% Bernoulli-Lift. $\endgroup$ – rul30 Oct 16 '15 at 12:52

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