# Which law explains the best why an aircraft can fly?

#### Andre

Just a little question again. Which law explains the best why an aircraft can fly?
A The ideal gas law of Boyle Gay Lussac.
B The secound law of Newton.
c The basic law of aerodynamics of Bernouilli.

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#### enigma

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Newtons second, along with a little of the ideal gas law and thermodynamic principles.

Bernoulli's equation only works for low speed aircraft. It breaks down past Mach#= 0.3. (Bernoulli's equation is also just a derivation drawn from Newton's second to begin with)

Ideal gas law alone doesn't give any information into why the pressure is lower on the top of the wing (although when used with thermodynamics it does). Newton's second takes the values for pressure & friction given by gas law / thermo and gives you lift and drag.

EDIT: If this is homework for a physics class, then Bernoulli may be what your prof is looking for. Just keep in mind that it only applies for low speed, and it follows from further derivations of newtons law

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#### Andre

No homework, just trying to have some discussion. Yes I agree, Newtons second albeit somewhat differently. And this:
If this is homework for a physics class, then Bernoulli may be what your prof is looking for
is too sad for words. That was the objective of the question, to expose the lazy thinking of the bulk of the best. If Bernouilli was best describing the flight of aircraft, then a/c flying upside down would crash immediately.

Actually the shape of the wings only contributes a little. It is the angle of attack that creates a downdraft. Air mass accelerating downwards creates a force in opposite direction. That's the bulk of your lift. The lower pressure over the wing is just a very small portion. An aircraft flying upside down is still flying, The angle of attack is still forcing air downwards and still generating lift by accellerating an air mass.

Symmetrical air foils (like most jet aircraft) don't use Bernouilli at all. Kites neither.

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#### enigma

Staff Emeritus
Gold Member
Originally posted by Andre
And this:
If this is homework for a physics class, then Bernoulli may be what your prof is looking for
Well, the thing to note is the timeframe. When I took physics 1, Bernoulli's equation wasn't even a full day's lecture. It was a sidebar in a lecture which covered several other things as well. Bernoulli also doesn't generate the value for lift. The typical problem goes: pressure & velocity at pt1, pressure at pt2, what is velocity at pt2. Integrating the pressure distribution is a whole other can of worms.

For those who aren't going to be working with aircraft or other high speed applications, Bernoulli is all they would EVER need. In addition, the derivation is too complex for your typical first semester physics student. I didn't see it until my second semester sophomore year. A lot of complex thinking growth occurs in those first two years. How can you expect someone to understand integrating pressure distributions in three dimensions when they just learned about forces earlier in the semester and they are -at best- taking multivariable calculus at the same time (I took it a semester later)!

Actually the shape of the wings only contributes a little. It is the angle of attack that creates a downdraft. Air mass accelerating downwards creates a force in opposite direction. That's the bulk of your lift. The lower pressure over the wing is just a very small portion.
Well, sort of. The only way that nature can 'touch' a wing is through pressure or friction. The air being accelerated downward causes a high pressure region. So, the pressure is what causes the lift, but the conservation of momentum is what causes the pressure.

Symmetrical air foils (like most jet aircraft) don't use Bernoulli at all. Kites neither. [/B]
If the plane is going slow enough, you could use Bernoulli to approximate wind velocity or pressure. The shape of the wing doesn't matter. What does matter is the incompressible flow approximation.

And actually, many jets aren't symmetrical. Most subsonic jets have supercritical airfoils, which allows them to fly faster before the streamlines seperate from the airfoil near Mach 1.

Supersonic jets may have really flat wings, but they still have some camber.

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#### enigma

Staff Emeritus
Gold Member
I apologise for the extremely long post...

I just read the page you posted, and getting a little confused about what they were talking about, went back and reread the related chapters in my textbooks. If you want to read along with what I'm going over, the book I'm using is "Introduction to Flight, Fourth Edition" by John D. Anderson, Jr.

I believe that the people talking in that correspondance were a little confused about what exactly the "Bernoulli effect" is, and why and when it applies.

The Bernoulli effect is not a lift produced by a difference in curvature. To say it is, is a misinterpretation of the math. All Bernoulli says is that a faster moving flow will have a lower pressure. That's it.

Nyal Williams in the last post on the linked page says that: "I believe Bernoulli is incomplete and I prefer Newton."

Bernoulli's Equation is:

p2+ 1/2*[rho]*V22 = p1 + 1/2*[rho]*V12

Which means that p + 1/2*[rho]*V2 is constant along a streamline. (Anderson, 119)

Bernoulli is incomplete. It only applies for incompressible, frictionless flows (which don't exist, although low speed comes close enough to approximate). It also doesn't give you lift.

The thing that Nyal Williams missed is that Bernoulli is a direct result of Newton's second law applied to fluid dynamics! A complete derivation can be found in Anderson p116-9 starting with good old F=ma.

Why does Bernoulli lead to lift?

Bernoulli's equation by itself is not enough to describe what happens when air flows over a wing. There is absolutely nothing in the equation itself that needs the shape of the wing before you can compute it. All the equation can do is relate the values between two points in a flow.

What you can do to find quantitative results requires wind tunnel experiments to find velocities at various points along the wing. Those can then be converted to pressures which are then integrated along the bottom and top surfaces to give you a resultant lift and drag force.

Qualitatively, you can use Bernoulli to come up with general results, but again, Bernoulli by itself is not enough to give you those results - you need the mass continuity equations as well.

Mass conservation and the 'Stream Tube' concept (Anderson, 112)

The best way to think about air flowing around an airfoil in low speed flight is to think of it as a 'tube' of air. What goes in one end of the tube, comes out the other end of the tube. This leads to the concept of a 'streamline' which is a graphical representation of those 'tubes'. The amount of mass in a certain differentially small piece of the tube is:

dm = [rho]*A*V*dt

or, the density times the cross sectional area of the tube, times the velocity of the flow, times the differentially small duration of time it took to sweep out the volume.

the mass flow, dm/dt, is the amount of mass which flows past an arbitrary point in the tube in a unit time.

dm/dt = [rho]*A*V

Since mass cannot be created or destroyed, dm/dt1 = dm/dt2 = constant.

What that means, is that if the area of a tube gets smaller, either the density gets larger or the velocity increases. At low speed and near surface conditions, air is nearly incompressible. It can be shown through thermodynamic principles that an incompressible approximation holds to within 95% accuracy up to Mach 0.3 (Anderson, 174-5). This means that the Velocity must increase, since the density cannot increase. You can see this effect in action by partially covering the nozzle of a hose and spraying your siblings or children with it.

Tying it all together

I apologise for the poor quality of this drawing. There is a better one in Anderson, p 321 in the section entitled "How lift is produced".

http://www.wam.umd.edu/~dpullen/Bernoulli.jpg [Broken]

So why is the lift produced for an airfoil in level flight? Introducing a disturbance into a flow causes the stream tubes to deflect.

What does this mean?

The stream tubes closest to the top side of the wing must get smaller. There is no other way for the air to get out of the way. From the mass continuity equation, that means that the Velocity increases in that portion on the top near the leading edge.

On the bottom side of the wing, the wing is trying to fly into the flow (as opposed to under the flow on the top side). This causes the flow velocity to decrease along that portion. This increases the pressure on the bottom half.

From the Bernoulli effect, the increased velocity means that the pressure is reduced at the top, and the decreased velocity on the bottom results in an increased pressure.

The result is a net upward force.

Newton's Third?

Action/Reaction?

Yes, the plane's upward acceration do to lift is coupled with a downwash of the air surrounding it. This is an effect of the airfoil passing, but not the cause of it. The fact that the air is moving downward does not explain why the airplane is moving upward.

Again, the only way for nature to reach out and touch anything is through pressure or friction. The differing velocities around the wing are what cause those pressure differences, leading to the lift and the downwash.

Other notes re: the page you cited

Someone asked how a thin airfoil produces lift when it is at an angle of attack, guessing that Bernoulli can be discounted.

The answer is: the same way a normal wing does. The airfoil's bottom surface slows down the flow, which increases the pressure. Bernoulli.

The same thing applies to the 'kites' question. Box kites are not at zero angle of attack.

Airfoils which are mirror images on either side produce no lift when they are at zero angle of attack. No contradictions there.

Flying upside down does provide some lift. Unless the plane is designed to fly upside down though, it will lose altitude if it is at zero angle of attack.

Remember: Bernoulli is Newton's second law applied to fluids.

EDIT: Can't get the picture to show in-post. A link will have to do...

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