# Newton's Third Law & aerodynamic lift

#### mmwave

I was engaged in a discussion where someone claimed that Newton's Third Law does not apply to the lift created by air flow over a wing.

My argument goes as follows:

After all the equations, etc. involving fluid dynamics and Bernoulli's principle there is an upward force on the wing. Newton's 3rd law says that if there is an upward force on the wing there must be an equal and oppposite downward force. The wing pushes downward on the air and the air pushes upward on the wing.

I'm not saying that Bernoulli is wrong, only that the 3rd law still applies here.

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#### Jonathan

The third law is very important for lift, the Bernoulli effect is commonly overrated in it's importance. I've received some trouble for stating this, so let it be known that advanced fighter jets and attack helicopters have top/bottom symetrical wings/blades, so in this case the lift is due entirly to the third law (except that sometimes some/most comes from the jet-deflecting vanes in the rear when doing manuevers.)

#### enigma

Staff Emeritus
Gold Member
Originally posted by mmwave

I'm not saying that Bernoulli is wrong, only that the 3rd law still applies here.
Newton's laws always apply. That's why they're called 'laws'. The reaction force is called 'downwash' and it's present in each and every airplane: slow, fast, jet, prop... all of them.

Jon,

The Bernoulli effect is greatly misunderstood. The internet is partly to blame, and oversimplifications in introductory physics classes are partly to blame. The Bernoulli effect states that as velocity increases, pressure decreases. That's it. It says absolutely nothing about curvature of an airfoil.

The reason the velocity increases applies to flat plate airfoils at angle of attack just as much as for non-symmetric airfoils: conservation of mass and incompressible flow effects. As the air flows around the airfoil, the streamlines become compressed. The air becomes a little bit denser (the faster it goes, the more dense it becomes), but regardless of speed, the air will need to speed up a bit to stay in the same streamline. Pictures are really needed to do the explanation justice, unfortunately.

Newton's third law always happens. It doesn't provide an underlying cause though. Downwash is an effect. The only things which can provide a change in momentum to an airfoil are pressure and friction, and the pressure differences can be modeled using Bernoulli for low speed aircraft.

#### Jonathan

I didn't intend to discredit the Bernoulli effect, it does play a part in lift, I meant that it's not as important as I always hear it is. Enigma, I think you're the first person I've ever heard to spontaneously agknowledge the importance of the third law in flight, it's usually like pulling teeth if I mention it.

#### Singularity

Yes, enigma is quite right. N III is the only deciding factor when it comes to lift. The wing exerts a downward force on the air and the air exerts an equal but opposite upward force on the wing. The interesting thing is that because of the angle of attack, even the air above the wing exerts an upward force on the wing. I actually saw a very nice demonstration about this on encarta 2000. They have a very nice little video there and everything. If you have it, take a look.

#### zoobyshoe

Singularity,

I think you have taken it too
far when you say N III is the
only deciding factor when it
comes to lift. Both
contribute to lift. What you
said about the angle of attack
causing an upward force above
the wing is Bernoulli coming
into play.

#### wimms

Bernoulli effect is a consequence of Newton laws. So there is no conflict. Bernoulli effect simplifies calculations and yields almost always correct answers. Behind it is still Newton.

I found this page quite insightful, although I've been explained it doesn't exactly follow conventional terms used in aerodynamics.
http://www.av8n.com/how/htm/airfoils.html#sec-bernoulli

#### mmwave

Great discussion. So there is a major component of lift due simply to the angle of attack. The air strikes a surface at an angle relative to the direction of motion and is pushed down. Newton III says the plane is pushed up.

Ok, for the (small) Bernoulli component of the lift, can you apply N III in the sense of air pushes on wing/wing pushes on air? or does it not apply in this case due it being a pressure difference on the top and bottom side of the wing?

The angle of attack lift explains how planes fly upside down!

#### Clausius2

Gold Member
I think it is not a good way to learn fluid dynamics or general physics only learning by heart the equations.Then one asks himself the cuestion of this post, or simply goes slepping with the doubt unsolved.
It is true Bernoulli's equation fits with the Third Law of Motion, and with the other two. It's only because Bernoulli's equation would not exist or couldn't be derived without Newton's Laws. It is a problem of math and know of where this equation is created.
The Bernoulli's equation (BE) is derived of the Momentum Equation of Fluid Mechanics under the assumptions:
a)Steady flow (Strouhal Number St<<<1 in this frame)
b)Incompressible flow (density constant in time and uniform in the space, not like i heard in this discussion, enigma talking about the differencies of density, it's impossible!)
c)Viscous efects can be neglected (Reynolds Number too large Re>>>1).
Then, BE can be derived only proyecting the Momentum Equation over a streamline. It is important to know that the Newton's Laws are applied over the fluid, NOT over the body inmersed in it.
Well, your problem about lift in an airfoil fits with Newton's Laws: of course, the wing has a weight W, so W=Lift and this is the solution (the problems always have to be real!, if not you are going to have a lot of headaches).

WHY DOES AN AIRPLAIN FLY?. One can treat to resolve this problem mathmatically (too difficult!) or merely with BE. In my opinion, it's imposible that a symmetric wing with no weight have a lift exerted on it by the flow. Why?: you only have to think of the symmetry of the problem. If it has weight my opinion is not the same, but in order to the weight could act upon the fluid, the airplain must be on air. You have noticed that an airplain taking off has to have their flaps heading up, but in the flight it is not necessary. In the take off the weight is absorbed by the wheels, but in the flight it is absorbed by the fluid that cancel it with the lift. Therefore, when the flow reaches the frontal part of the wing there is just in this point an stagnation point that divides the flow in two streamlines, one above an another below the wing. We suppose the wing is asymmetric and atacched (the weight doesn't act) for an easier problem. Then p+(&roU^2)/2=constant over the streamlines. In the rear part the velocity U has to be common for the two streamlines, which join in this point. So the fluid has to pass over the two sides of the wing in the same time, in order to the Continuity of the flow. Therefore the velocity U must be different on both sides. Depending on the curvature of the wing the lift will be exerted in z or -z direction, because of a difference of pressure (not density) is created between both sides (difference of velocities implies a difference of pressures). In order to create a lift on the z direction, the curvature of the wing has to be negative at the bottom (like a cup of coffee upside down).
Enigma, you can check on the Euler's Equation (Momentum Equation with Re>>>1) that the usually flow of gas with small velocities (Mach Number too small Ma<<1) is isobaric (non barotropic if T=constant, i.e. &ro=density=constant).

The angle of attack is involved in the Boundary Layer Theory. It works playing with the width of the gap of the boundary layer, creating a difference of pressure in the rear of the wing. But it is nothing to do with Bernoulli's Equation, because this change of angle creates a turbulent non-steady flow. The lift and drag forces are proportional to the circulation of the velocity. But it would be another topic to be posted. Do somebody know about D'Alembert Paradox?. Perhaps one day i'll write about it.

I hope that I answer your cuestion; but you can discuss my opinion (of course!).

#### enigma

Staff Emeritus
Gold Member
Again: NIII isn't a cause of lift.

The only ways for any force to be transmitted are friction and pressure distributions.

d/dt(mV) = [sum] F

NIII is the explanation for the downwash, but it doesn't provide the formulas for determining how much lift is generated. It is an effect - not a cause.

#### Clausius2

Gold Member
And from where do you think the pressure distribution is generated? It does'n come from Mars, it has to have a cause, and the cause is an external force (W) in the case of a weighting wing. If the aeroplane is flighting steady (height=constant), then the Second Law of Motion in z axis is W=Lift.
Is there Weight?Yes---->There is Lift although the wing is symmetric.
It is not a symmetric wing?yes---->There is Lift because of geometry.

#### enigma

Staff Emeritus
Gold Member
I just realised that quite a bit of this post was directed at me. Clausius, my last statement was crossposted, and directed at the previous poster.

Originally posted by Clausius2
It is true Bernoulli's equation fits with the Third Law of Motion, and with the other two. It's only because Bernoulli's equation would not exist or couldn't be derived without Newton's Laws.
You're right, Bernoulli is N-2 applied to fluids.

b)Incompressible flow (density constant in time and uniform in the space, not like i heard in this discussion, enigma talking about the differencies of density, it's impossible!)
There are always differences in density. In reality, there is no such thing as an incompressible flow. For M# ~= 0.3, it is a decent approximation, though: ~ 95% accurate.

p0/p = (1+( &gamma; -1)/2*M2)^(1/( &gamma;-1))

I got sidetracked in my description of the situation, which is why I brought that up.

WHY DOES AN AIRPLAIN FLY?. One can treat to resolve this problem mathmatically (too difficult!) or merely with BE.
This is one thing that I don't agree with. Yes, for low speeds, BE gives the pressure at each point if you know the velocity. It doesn't give you that velocity, though. That was the point I was trying to make earlier. You need to look at conservation of mass assuming incompressible flow (or do it easier by running a windtunnel test ) to get a velocity distribution.

In the rear part the velocity U has to be common for the two streamlines, which join in this point. So the fluid has to pass over the two sides of the wing in the same time, in order to the Continuity of the flow.
No it doesn't. Slipstreams occur when you have two streamlines moving next to each other at different velocities.

In general, the flow on the upper surface takes less time than the flow on the bottom surface to travel the length of the chord. See Introduction to Flight by John D. Anderson, Jr. Section 5.19 for an explanation and illustrations.

Enigma, you can check on the Euler's Equation (Momentum Equation with Re>>>1) that the usually flow of gas with small velocities (Mach Number too small Ma<<1) is isobaric (non barotropic if T=constant, i.e. &ro=density=constant).
I'm not sure what point you're trying to make here. Can you please elaborate?

#### Clausius2

Gold Member
Enigma, sorry for my bad english!. If you cannot understand some pieces of my text, it doesn`t matter. If i could speak english very well i probably don't understand too what clausius want to tell me!
It's all right your assumption of compressible flow, but you have to modify the classical Bernoulli's equation, just like you did in this post (taking into account the Mach Number).
Ok! You have continuity equation which relates velocity and density, the momentum equation which relates pressure, density and velocity (in the form of BE too) and the equation of state of your gas, which relates pressure, temperature and density. The problem is determined except for temperature.
I was trying to tell you that Euler's equation & rhov(& nablav)=-& nablaP say to us the order of the pressures differences on the flow is the order of the density multiplied speed powered to two. Then, at low velocities (Ma<<<1) the flow can be considered incompressible if the temperature remains constant.
But no problem, if you want to take temperature as an unknown, you should equate the energy equation too. You would have four unknowns for four equation, the boundary conditions for pressure, velocity, temperature and density, and the problem will seem to be solved. I recommend you to have a software for computing fluid dynamics. If not, this problem could be transformed into a hell !.
Merely, i was supposing an incompressible flow.
I don't understand what are you telling me when you say "No it doesn't. Slipstreams occur when you have two streamlines moving next to each other at different velocities." Sorry I'm not sure what point you're trying to make here. Can you please elaborate?

#### enigma

Staff Emeritus
Gold Member
This may be better suited being pulled into its own thread

Originally posted by Clausius2
Enigma, sorry for my bad english!.
Not a problem. I'm sure your English is about a million times better than my Spanish! I just know the dirty words...

I don't understand what are you telling me when you say "No it doesn't. Slipstreams occur when you have two streamlines moving next to each other at different velocities." Sorry I'm not sure what point you're trying to make here. Can you please elaborate?
OK. You said that the velocities of the streamlines above and below the wing at the end of the chord have to be equal. This is not true. In almost all cases, they are different. It doesn't last long past the wing, because turbulence 'blends' the streams together, but right at the end of the chord, the two streamlines 'slip' past each other at different velocities.

I'll be honest that my studies haven't focused on low speed flows. I'm in a space track, so my coursework has focused on supersonic flows through nozzles (rocket engines), and slipstreams play a much greater role in those situations. Still, there is nothing about a fluid that prohibits approximating adjacent flows as 'slipping' past each other (i.e. velocity gradient so steep that it can be modeled as two adjacent flows).

Always happy to talk with other aeronautics/aerospace heads!

#### Clausius2

Gold Member
Eeeey! It would be my sweetest dream (apart of one in which jennifer lopez appears) study a course of rocket engines or a space track!.
Well, to be honest i have to say also that i'm not an expert in supersonic flow, and in nothing that has to do with aeronautics, wings, or flight dynamic. I'm only studying industrial engineering specialized in which you usually name power plants, here in Spain.
I wish i were studying aeronautical engineering (here it doesn't exists aerospatial engineering, it is only a part of aeronautical one). After all fluid mechanics, spacecrafts an aircrafts are my favourites subjects!.
This year i'm going to fight with supersonic flow, and situations a little bit real involving flight dynamics, so perhaps i'll return over here and you and me will have a sweet quarrel talking about things flying .
Till then, i should believe that you are correct in your opinion about slipstreams.
I am too lazy now to take a book and check your answer! Uff![zz)]

#### enigma

Staff Emeritus
Gold Member
If you do get time to hit the library, check out the book I cited earlier in the thread. It describes the situation in the section I mentioned.

If you think about it, there isn't anything which would prohibit a slipstream from occuring. Intermolecular 'friction' wouldn't let it last very long, but there isn't a reason why they couldn't happen.

Another book by the same author: "Fundamentals of Aerodynamics" has a huge amount of information on compressible flow through rocket nozzles (along with tons of other topics).

#### Clausius2

Gold Member
I always heard about the continuity of the velocity field, even near of the walls (i.e. v=0 is a non-sliping condition on the wall), but never about discontinuity inside it. The internal friction of the flow (i.e. Rayleigh's function) implies a micro-discontinuity on the molecules of each side of the frictioning surfaces, but it doesn't show a discontinuity on the macroscopic field of velocity. Perhaps it is possible in supersonic flow.
I belief it was a hard assuption in the equation of fluids the continuity, and these equations were built under it.

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