Air Pressure / Newton's Laws

[Michael1160]

I would like to review some principles, as well as pose some questions, to this highly intelligent community. As such, feedback of ideas, or comments, or even snotty remarks would be appreciated.


Classical physics is built on Newton's laws. As such, Newton's laws always apply somewhere, and Newton's three laws are actually one giant law if you think about it. It essentially says that objects don't change their velocity unless a net force acts on them..period.

I often read about people arguing/debating that Newton's third law is the definition of lift, and that Bernoullis's has nothing to do with it. Well, Bernoulli's principle is really a form of Newton's second law, and air pressure itself is a form of Newton's third law, which I would like to discuss a little more in detail.

Air pressure, on a submicroscopic scale, is caused by the incessant impacts of the constituent molecules on a surface (as well as on each other). The impact of these molecules (since they have mass) applies a force to the surface, and the surface applies an equal and opposite force to the molecule. These actual forces are caused by the interaction of the electrons in the molecules themselves (and that is the level we will leave it at).

Now, a low pressure (suction) just means that the pressure is lower then some other reference pressure, but it is still a positive number. In other words, the molecules are still impacting the surface, applying a force to the surface, they just are not hitting it as hard (translational velocity-temperature) or as often (density - molecules per unit volume) as a"higher" pressure would be. So, negative pressure just means that the pressure is lower then a reference pressure (usually atmospheric) but the lowest absolute pressure available would be zero, which would mean that no molecules are impacting the surface. You really can not have pressure that is an absolute (for lack of a better word) negative pressure, as the molecules can not pull on a surface, just push.

The reason I make this statement, is that I have heard people say that the top surface of a wing (airfoil) pulls the air down, therefore Newton's third says that the air pulls the wing up. But based on the definition of pressure, the air molecules caint pull on anything, Newton's third law is actually in the definition of pressure itself. What can happen is that the air pressure on the bottom of the wing, which is higher (molecules hitting the surface harder and more often) can and do create a net force on the wing. This force can be up, to support weight, sideways to turn (centripetal) or whatever. Every body always talks about conservation of momemtum. But remember, momentum is conserved in the abscence of external forces. A wing in steady, straight in level flight is actually not conserving momentum. If it were, then the impacts of the molecules should cause the wing to accelerate in the opposite direction, but the wing does not (in level, unaccelerated flight) as the lift is equal to weight. Weight is the external force in this example.

You could even think of pressure itself as an external force. The pressure gradient in the flow is what causes the mass of the fluid element, which has mass and therefore inertia, to accelerate, decelerate, and change direction. A cubic foot of air at sea level has a mass of .0023769 slugs. Therefore, it has a physical weight of .08 pounds. But, a cubic foot of air at sea level exerts a pressure of 2116 Pounds per square foot. Again, this is the result of the internal motion of the constituent molecules. If you had a solid with .0023769 slugs of mass that was one cubic foot, it would weigh .08 pounds, and since pressure is force (weight is a force) divided by area, the solid would only exert a pressure of .08 PSF vs the cubic foot of gas that exerts a pressure of 2116 PSF. This is actually the basis of the hydrostatic equation, in which the vertical pressure gradient from the surface of the Earth to the edge of space, supports the weight of the air. You have a high pressure at the surface of the earth, at the edge of space you have zero pressure (vacum) but yet the air does not rush up into space in the direction of the pressure gradient (high to low) because the air has mass, and therefore weight in the Earth's gravitational field. so, the air pressure actully supports the weight (mass). Any feedback would be highly appreciated, as I enjoy talking physics. I wil post more thoughts on similar subjects at a later date.

 

[rocketboy]

This is amazing information. I'm currently writing my IB Extended Essay in Physics on "How the Angle of Attack Affects Lift for Cambered and Symmetrical Wings". (Although I might narrow it down to just cambered wings).

Where did you learn all this? I read your other post on lift in this section and your knowledge of the subject is very impressive. Did you study aerospace engineering or physics in university?

Anyways, keep posting because I'm sure everybody is learning tons. Unfortunately I don't know enough about the subject to "discuss" the topic with you (yet).

-Jon

 

[Michael1160]

Rocketboy:

Thank you for your compliments. Yes, my degree is actually in Aeronautical Science which actually deals with the physics of flight and applied flight mechanics. I have also completed courses in aircraft flight testing and evaluation, aircraft performance and design, and other miscellaneous stuff. I am also a professional pilot. However, I do not claim to be any kind of guru, my posts are really to stimulate thinking and conversation in the community.

I really enjoy talking about physics. I just found out about this forum about a week ago.

The thing to remember is that Newton's laws always apply. Newton's three laws are really just one giant law that says: things don't just change their velocity...there must be a net force. Newton's laws also do not stipulate the origin of this force. Under Newton, a force is a force is a force. However, there must be an origin of this force, forces don't just magically appear. A 10 pound force of friction will cause the same deceleration (negative aceleration) as 10 pound force of air pressure (assuming equal masses). Whether the force is generated by "internal" conservative forces (such as air velocity changing into pressure) or is caused by "external" dissipative forces (such as friction) will be determined by the system. Just saying Newton's third law is not good enough...there has to be an origin of the force. Let me know if I can be of further assistance.

 

[FredGarvin]

Bernoulli's principle is really a form of Newton's second law

Bernoulli is a statement of conservation of energy under specific constraints. I guess I am not seeing the correlation right now.

You really can not have pressure that is an absolute (for lack of a better word) negative pressure, as the molecules can not pull on a surface, just push.

That is absolutely correct.

The reason I make this statement, is that I have heard people say that the top surface of a wing (airfoil) pulls the air down, therefore Newton's third says that the air pulls the wing up.

I can't say I have heard anyone say it that way (which doesn't mean that no one says that by any means). Of course I strongly disagree with anyone that states it in those words. The way I heard it growing up and am used to hearing it today is the higher pressure underneath pushes upward in the direction of the lower pressure.

I'd suggest doing a search in the physics forums for lift generation. Not too long ago there was quite a discussion on this topic. It brings in other topics such as circulation into the fray. It is worth the time to read.

 

[Nam_Sapper]

but the lowest absolute pressure available would be zero, which would mean that no molecules are impacting the surface. You really can not have pressure that is an absolute (for lack of a better word) negative pressure, as the molecules can not pull on a surface, just push.

On the contrary, since attractive Electromagnetic forces are real, it is conceivable that for instances there might be slight negative pressures (pulls) resulting from (near) instantaneous imbalances of forces, although this may be statistically rare.
So negative pressure (attraction) is possible between massive systems.

You are right to insist however, that the force of lift on a wing comes from below, and is a result of pressure (repulsion/collision).

Every body always talks about conservation of momemtum. But remember, momentum is conserved in the abscence of external forces. A wing in steady, straight in level flight is actually not conserving momentum. If it were, then the impacts of the molecules should cause the wing to accelerate in the opposite direction, but the wing does not (in level, unaccelerated flight) as the lift is equal to weight. Weight is the external force in this example.

This statement does not seem clear to me at all. The conservation of momentum in this case refers primarily to collisions, and the collisions certainly obey the conservation of momentum principle. The energy is transferred in an orderly way according to Newton's 3rd law. While energy/momentum is perhaps leaving the 'local' environment of the moving wing in a plane, (exchanging energy with the surrounding environment moving past), nonetheless Conservation of Momentum is preserved as far as I can see both in the subsystems, and between the systems. Perhaps in a nuclear reaction one could conceive of energy being 'created' or converted out of destroyed mass and disrupting the Newtonian version of the Law of Conservation, by adding to the system a surplus of energy/momentum unaccounted for, this is not the case in a normal exchange of momentum between the wind and the wing. (?)

To elaborate: Let us suppose the wing is traveling at a constant speed and altitude in a virtual straight line (at least locally). The force of gravity is balanced by the force of lift, and there is no net external force disrupting the system from the viewpoint of the inertial frame of the wing and plane. There may be air entering and leaving a given cubic volume, but overall, the energy/momentum leaving the scene balances that entering, minus the small amount of energy needed to counteract gravity, which has been absorbed by the wing from the passing air.

From the inertial frame of the wing, the air leaves at a slightly lower velocity than the air arrives. The wing has absorbed the energy and stays in the air. In fact, the air has a large reservoir of excess energy due to its velocity relative to the wing. This direct high-speed impact (600 mph wind) is easily milked for enough lift by the asymmetry of the wing.

From the inertial frame of the earth, we see that air standing still has been dragged and imparted a velocity roughly in the same direction as the plane, air flow which disorganizes quickly due to turbulence, but nonetheless has stolen energy from the passing plane: this would slow the plane down, but energy is added by the thrust of the engines to compensate. Thus some of the thrust of the engine is directly converted to lift by asymmetrical collision with the air at 600 mph.

However we look at it, the plane and air collide at 600mph, and some of that impact of collision is converted to lift, just enough to balance the weight of the plane. Some energy from the engine has been diverted upward. In any inertial frame, energy has been released via fuel, and converted into an equal amount of momentum lifting the plane up, and driving the air down. However, since an incredible amount of air is moving past, each air molecule only needs to take on a small amount of downward energy, as large quantities of air collide with the wing. The exact same amount of momentum is transferred upward to the wing, but in this case, a relatively small number of molecules are available to contain a lot of momentum (enough to lift a plane!).

In the exchange of energy between air and wing, directionally speaking, there is a slight net force upward due to asymmetry in the wing shape, which is just enough to keep the plane in the air. In reaction, obeying Newton's 3rd law, the air is given a slightly downward net motion, which dissapates in turbulence rather quickly.

 

[Michael1160]

NAM SAPPER

Thanks for the feedback! However, I must disagree with you on some points.

Let's look at an example:
You have a cylinder, with a piston in it. You have a molecule that is traveling towards the piston in the positive X direction. The molecule strikes the piston, applying a force to it and causing the piston to rebound with some velocity. According to the conservation of momentum, the molecule must rebound with less velocity than it had before the collision. Momentum has been conserved. Even though the molecule is traveling in the negative X direction now, the addition of the momentum of the now moving piston, and the molecule, will equal the total momentum before the collision. The key here is that the piston is now moving. Some of the momentum of the molecule has been transferred to the piston. The momentum of the system is still the same, although the momentum of the molecule has changed. If you were to consider the molecule as the only part of the system, then the force applied by the piston (Newton's 3rd) would be considered an outside force, thus changing the momentum of the system.

From an energy standpoint:
The molecule strikes the piston, applying a force to the piston and moving it thru a distance, therefore work has been done on the piston, which represents a transfer of energy out of the molecule, again the piston is now moving.

If the piston does not move:

since a force has been applied to the piston, it should accelerate. If the piston does not accelerate, it must be because of a force external to the system.

Momentum in this case is not conserved, the molecule which had a momentum in the positive X direction before, now has momentum in the negative X direction, but the piston has no momentum in the positive X direction. Therefore, the momentum of the system has been changed. Newton says that if the momentum of a system changes, it must have been caused by an external force.

Any absorbtion of energy by the wing has to do with drag, not lift. It is true that the wing produces drag while producing lift, but that is a consequence, and that force is aligned with the velocity of the airplane. Lift, by definition is perpendicular. Since lift be definition is always perpendicular to the relative wind and hence the velocity, it is by definition centripetal force. Centripetal force can only change the direction of the velocity, not the magnitude. From basic mechanics, a force perpendicular to the velocity can do no work, in other words it can not change the total mechanical energy of the system. So how is it that you say the lift of the wing is absobing energy?If the wing was accelerating then it would be changing the total energy level, but how can lift do this if it always acts perpendicular to the velocity? If you are saying that the wing is absorbing energy, in what form is this energy appearing?

In the reference frame of the wing, the slowing down of the air, in the boundary layer, will appear as unusable heat. The slowing down of the air in the potential flow region outside the boundary layer, will be accompanied by an increase in static (local) pressure as defined by the equation of state of a gas. The kinetic energy is recovered as an increase in pressure (pressure differential supports the weight) However, energy has been conserved, not absorbed. At the trailing edge of the wing, as the air readjusts to atmospheric pressure, this energy will reappear as an increase in velocity (kinetic energy).

In the reference frame of the earth. The air was standing still prior to the airplane moving thru it. But after the airplane leaves, and the air has readjusted to atmospheric pressure, the air now has a velocity (Kinetic energy) in the direction that the airplane is moving, then that is a loss that the airplane's engine must sustain (drag). However, this loss comes about due to the friction in the boundary layer, not from the potential flow region.

Remember, a fluid element has mass and therefore must obey Newton's laws. However, a fluid element is not a solid. A solid cannot flow. The internal energy (temperature) of a solid is associated with molecular vibrations, but the molecules all maintain their positions with respect to each other. In a fluid, especially a gas, the molecules are free to move about, they do not maintain the same positions relative to each other. The tempature of gas is a measure of the average translational kinetic energy of the molecules. A cubic foot of air at sealevel, that is static (mass velocity of zero) on a molecular scale has molecules zooming around at very high speed. These molecules have mass and velocity, therefore they have momentum and kinetic energy at a molecular level, even though the air mass as whole is not moving.

If the aircraft is manuvering (accelerating) then there will be a drag incured, even in a 2D case, as the pressure distribution is distorted (D'Alembert's paradox no longer valid) However, the airplane is losing energy (not absorbing). Remember, the air was still prior to the airplane passing. After the airplane leaves, if the air now has kinetic energy,it must have come from somewhere. Indeed it has, from the airplane. This energy loss must be sustained by the thrust of the engine if the velocity (magnitude) is to be maintained.

From a 3D standpoint, the wingtip vortices, a by- product of lift, will distort the pressure distribution and cause a drag, even when the aircraft is not accelerating (maneuvering)

Momentum is a vector quantity..it has both magnitude (speed) and direction. The magnitude of a moving object does not have to change in order to change momentum. A change in direction, but with the speed staying the same, according to Newton, is a change in momentum, and therefore must have been caused by a force.

As far as the power from the engine is concerned, the fuel that is burned in the combustion chamber (we will use a receiprocating engine as an example) goes into delivering torque (power) to the crankshaft ( it is actually a linear motion converted to rotational motion by the connecting rods) which in turn delievrs that power to the propeller. The propeller in turn converts that rotational motion into a force (thrust) by interacting with the fluid (air) that it is imersed in. In the abscence of a fluid medium, such as air, the only time you need a force or torque is to change the velocity, not sustain it. When energy in the form of torque has to continually be supplied to the propeller to maintain (sustain) its RPM, the energy consumed must end up somewhere in the fluid. And it does end up in the slipstream of the propeller, which is actually wasted energy. Now, if the thrust of the propeller is at an angle to the velocity vector of the aircraft, there will be a vertical component of thrust (thrust X sin angle) to help support the weight of the aircraft.

 

[Michael1160]

FredGarvin:
Thank you for the feedback.

Ok..a view of how Bernoulli can be seen as a form of Newton's second law F=ma
according to the work-energy theorum. in order to change the kinetic energy of an object, work must be done. Work=Force X Distance

Wether the force comes from internal consevative forces or external forces will depend on the system. in Bernolli's equation, when the velocity increases, the static pressure decreases. Looking at a fluid element, traveling along a streamline from an area of high pressure to low pressure, will have its velocity increasing. If you look at the sides of the element, let's say the left side of the element has a higher pressure than the right side. Since Force= pressure X area then the element will have a force on it, it is traveling thru a distance, therefore work is done. Now, does the velocity increase because the static pressure is decreasing or does the static pressure decrease because the velocity is increasing? Depends how you look at it. Since Newton's second law says that the velocity will change if there is a net force, we will look at it from this standpoint

Let's say that we had an object, with a mass of 2 slugs, traveling at 100 feet per second (fps). We want to bring it to a stop in 5 feet. Now, to travel 5 feet at 100 fps will take .05 seconds.
Now, I realize that as the object is decelerating the velocity will be changing, and the time to travel the 5 feet will not be .05 seconds, but actually longer. But I will address that in a minute.

So. if the object has a Mass of 2 slugs, an acceleration of 100/.05 = 2000 f/s^2 from Newton's second law, a force of 4000 lbs is required. However, the time to travel that 5 feet is actually longer than .05 seconds, because as soon as the object starts to decelerate, the velocity is changing, and the time will be longer. So, we will cut it in half. Forces required = 2000 pounds. This can actually be proven using integral calculus, but I will keep this simple.

Energy:
an object witha mass of 2 slugs traveling at 100 fps has a kinetic energy of 10,000 ft-lbs
now since F X D = Kinetic energy. An object with 10,000 ft-lbs of energy, to be brought to a stop in 5 feet, 10,000 ft-lbs / 5 feet = 2,000 lbs of force. The same as above using Newton's second law.

Also, you probably remember this next equation from basic kinematics:

V^2(2) = V^2(1) + 2AS where S = distance and A = aceleration
However, we can write A in the form of Newton's second as: A = F/M
substitution in the above equation yields:
M(V^2(2)-V^2(1) / 2 = F X S which is Kinetic Energy (work)

 

[Michael1160]

[

Perhaps in a nuclear reaction one could conceive of energy being 'created' or converted out of destroyed mass and disrupting the Newtonian version of the Law of Conservation, by adding to the system a surplus of energy/momentum unaccounted for, this is not the case in a normal exchange of momentum between the wind and the wing. (?)

Nuclear reaction?...creation of energy?...where are you getting that from?

We are talking about regular everyday physics here...Im not sure how you interperted momentum not being conserved as having anything to do with nuclear physics.

Every basic physics books explains how momentum is not conserved in the presence of forces external to the system. You don't need to split an atom for this to happen.

 

[Nam_Sapper]

[
Nuclear reaction?...creation of energy?...

We are talking about regular everyday physics here...Im not sure how you interperted momentum not being conserved as having anything to do with nuclear physics.

Every basic physics books explains how momentum is not conserved in the presence of forces external to the system. You don't need to split an atom for this to happen.

<smile>* I merely meant to say that barring some unforseen mysterious 'source' of energy, it is hard to imagine how momentum is not 'conserved' in the simple activity of molecular collisions (wind & wing).

Momentum *is* conserved of course in all reactions. It is only the appearance of a failure of conservation when we make artificial divisions in the physical environment (we define our own 'subsystems' inside the System=universe).

Thus we can say that if we take the plane, or the plane and a finite cubic space around it as one 'subsystem', we can see energy/momentum entering or leaving the subsystem, and so we extrapolate 'exterior' forces outside the boundary.

In this process we of course are actually insisting that Conservation of Momentum *is* conserved, but energy/momentum is being exchanged between subsystems. This allows us to precisely define and quantify the external 'forces' we have artificially created by drawing an invisible boundary between arbitrary 'subsystems'.

 

[Michael1160]

).

In this process we of course are actually insisting that Conservation of Momentum *is* conserved, but energy/momentum is being exchanged between subsystems. This allows us to precisely define and quantify the external 'forces' we have artificially created by drawing an invisible boundary between arbitrary 'subsystems'.

[/QUOTE]

I will agree that if you include "everything" in your system that momentum will be conserved. However, this would eventually lead to us including the mass of the earth, which due to its "masssive" size would lead to velocity changes so extremely small, as to be negligible.

Also, as in the case of a fluid, "dissipative forces" such as viscosity or turbulence would lead to us including "momenta" of of individual particles.

Did you read my full response to your post about three posts up? There were some questions that I had for you about things you stated in your post that seemed a little "odd" to me. In the interest of physics conversation, I am curious as to your response.

 

[arman]

I don't have a level of understanding about aerodynamics as the people discussing this topic, so I'm trying very hard not to say anything stupid. To simplify, as far as I understand the turbines (which can be considered as sources of force) propel the plane in a horizontal direction, and then the wings essentially translate some of that horizontal momentum into vertical momentum (which ofcourse incurs some losses in the form of heat, sound and momentum imparted on the air).

The question I'd like to ask, is why isn't it more efficient to avoid that loss of translation by directly having the turbines impart a degree of downward thrust?

 

[Michael1160]

ARMAN

That is not a stupid question at all!

Helicopters due just that, the weight of the aircraft is supported by the thrust of the rotor (which is nothing more than a horizontal propeller) Also, various airplanes have tried this approach...Harrier...V-22 Osprey..etc. The problem is the power required. It takes a lot less power from an "engine" to compensate for the atmospheric drag, than it does to actually support the entire weight, or even a component of weight of the aircraft. VTOL aircraft, like the Harrier, use a "running" jump start most of the time in order to divide the weight of the aircraft between the engines thrust, and the wings. This allows them to take off at a lot higher weight, than if they were try to take off vertically just using engine thrust alone.

Now, wings/airfoils are actually quite "efficient" at what they do. A ratio called the lift over drag ratio (L/D) rates how much lift a wing will produce as compared to the drag. A typical number would be about 10/1. This means that the wing will produce 10 pounds of lift for every 1 pound of drag.

So, an airplane that weighs 10,000 pounds would create 1,000 pounds of drag. The drag force is what the engine must overcome in level flight (not considering climb requirments at the present time). So, you can see the "engine" to maintain its horizontal velocity would only need to generate 1,000 pounds of thrust. If you used the engine to support/help support the weight of this aircraft, it would have to produce a lot more thrust (which would lead to a higher power requirment)

 

[Rocketa]

I haven't got time to go through everything.

If you are arguing over the LIFT, I remember that I see the clear definition in one of David Japikse's book, maybe centrifugal compressor. He also mentioned that many books have wrong definition about lift.

 

[Gokul43201]

Mike, Newton's 2nd and 3rd Laws are not derivable from each other. I know this is not the core of the discussion here, but since you've made that statement at least twice that "Newton's three laws are really just one giant law", I thought I'd chime in on that.

The third law, however, is nothing but a restatement of momentum conservation, which results from continuous translational symmetry (via Noether's Theorem).

PS : An excellent thread on lift : https://www.physicsforums.com/showthread.php?t=57710

 

[Michael1160]

[

QUOTE=Gokul43201]Mike, Newton's 2nd and 3rd Laws are not derivable from each other. I know this is not the core of the discussion here, but since you've made that statement at least twice that "Newton's three laws are really just one giant law", I thought I'd chime in on that.

Sure, I agree that they are not derivable from each other, I guess I should have stated it as follows:

First Law : The velocity of objects don't change unless there is a net force.
Objects just don't spontaneously change their velocity at will.

Second law: If an object does change its velocity it is because of a net force and the rate of change of velocity will be equal to the amount of the force divided by the mass

Third law: if an object does change its velocity as a result of a net force the changed momentum does not just disappear, it must appear somewhere else. Or, the momentum of a system (defined) is constant unless acted on by a force external to the system.

I guess I should have clarified better what I meant by " one giant law"

Thank you for the feedback