Questions about density and being in the air

[Androo]

Hello all, I have been arguing about this for a few days. My friend is telling me that a helicopter flies in the air because there is a difference in density on top of the propeller and below the propeller.The air on top of the helicopter has less density and the bottom has more density. This generates a force to push the helicopter up from difference in density. He is calling this a fundamental principle of physics. I am trying to tell him that the helicopter creates a wind aka force push in the air to push it up and there is no change in density. He also has been trying to convince me for days that if i am holding a box in the air, it is a fundamental law of physics that my body density is greater than the air above it, so it stays up. I believe the box stays up because my hand pushes with a force upward greater than gravity, and thus is not pushed down, unrelated to a density difference between my body and the air. Another case he has just tried to convinced me I am certainly incorrect about is that if I blow a piece of paper into the air, he says I have manually changed the density of the air below the paper and the air above the paper is less dense and thus is moves upward. In his explanation, anytime there is a force or pressure the density has to change. I am saying absolutely not, sometimes density will cause things like a helium balloon to float, sometimes it is a force independent of density. Thank you for any explanations.

 

[Student100]

A helicopters rotors act much like an airplanes wing. The shape of the rotors causes the air underneath to travel further than the air on top. The air traveling on top of the rotor moves faster, creating an area of low pressure, pulling the aircraft towards it. This is the basic method through which lift is generated. The wind/downward thurst from the rotors does not produce the lift.

He also has been trying to convince me for days that if i am holding a box in the air, it is a fundamental law of physics that my body density is greater than the air above it, so it stays up.

Unless I'm reading this wrong, this is blatantly incorrect. When you lift a box you aren't generating lift.

. Another case he has just tried to convinced me I am certainly incorrect about is that if I blow a piece of paper into the air, he says I have manually changed the density of the air below the paper and the air above the paper is less dense and thus is moves upward.

There will be some lift generated, simply due to the fact that paper is falling through the air/you blew it.

 

[Androo]

A helicopters rotors act much like an airplanes wing. The shape of the rotors causes the air underneath to travel further than the air on top. The air traveling on top of the rotor moves faster, creating an area of low pressure, pulling the aircraft towards it. This is the basic method through which lift is generated. The wind/downward thurst from the rotors does not produce the lift.
Unless I'm reading this wrong, this is blatantly incorrect. When you lift a box you aren't generating lift.
There will be some lift generated, simply due to the fact that paper is falling through the air/you blew it.

Hey thanks for the reply, I am not talking about lift so much as he is telling me all lift, pressure, or change in force is caused by a change in density which I find impossible.

 

[ToastedMitch]

I did an experiment that will actually defies the law. If you put a flat surface under the propellers like say 2 inches below the propellers the area of dense pressure pushing down (Lift) has no place to push upon because if the flat surface below it wasn't there the area of dense pressure would push against the area of regular pressure creating lift but the flat surface so when it hits the flat surface the air has no place to go except outwards instead instead of creating lift. It basically creates an fan that "fans" 360.

 

[Student100]

I did an experiment that will actually defies the law. If you put a flat surface under the propellers like say 2 inches below the propellers the area of dense pressure pushing down (Lift) has no place to push upon because if the flat surface below it wasn't there the area of dense pressure would push against the area of regular pressure creating lift but the flat surface so when it hits the flat surface the air has no place to go except outwards instead instead of creating lift. It basically creates an fan that "fans" 360.

Huh? Lift has nothing to do with "pushing down" only the speed at which the air is flowing over the top and bottom of the wing.

 

[ToastedMitch]

One thing Helicopters have propellers and your correct but the area that the propellers are pushing down create an area of dense pressure pushing down making lift.

 

[stedwards]

One thing Helicopters have propellers and your correct but the area that the propellers are pushing down create an area of dense pressure pushing down making lift.

You're not making sense Toasted Dude. The gate keeps may show up and ban your behind.

 

[Chestermiller]

In the case of the box, your explanation is correct. In the case of the other examples, the net force of the air pressure on the object is upward. Of course if the air pressure is higher, it's density is also higher, but this is a secondary byproduct, and not a cause of anything.

 

[nasu]

He also has been trying to convince me for days that if i am holding a box in the air, it is a fundamental law of physics that my body density is greater than the air above it, so it stays up. I believe the box stays up because my hand pushes with a force upward greater than gravity, and thus is not pushed down, unrelated to a density difference between my body and the air

You can push the box up against a steel ceiling. The density of your hand is less than that of steel. What happens? Will the box fall through your hand?

 

[russ_watters]

Of course if the air pressure is higher, it's density is also higher, but this is a secondary byproduct, and not a cause of anything.

To put a finer point on it, lift is calculated in two basic ways:
1. "Pusing down the air" = momentum chage or f=ma.
2. Pressure change/difference.

The first method is totally blind to density changes.

When using pressure change/difference, density is often assumed to be constant because at low speed, the density change is too small to matter. It is totally ignored in the calculations.

 

[Khashishi]

Your friend is wrong on all of these things. Your friend probably confused the concepts of density and pressure. A helicopter hovers by exerting a downward force on the air. There's an equal opposite reaction by the air on the helicopter blades holding the helicopter up (against gravity). The propeller is basically a fan pointed downward. The blades cut through the air at an angle which forces air to move downward.

 

[Student100]

Your friend is wrong on all of these things. Your friend probably confused the concepts of density and pressure. A helicopter hovers by exerting a downward force on the air. There's an equal opposite reaction by the air on the helicopter blades holding the helicopter up (against gravity). The propeller is basically a fan pointed downward. The blades cut through the air at an angle which forces air to move downward.

The rotor isn't a fan pointed downward. The rotor is a rotating wing. You can't put a "big fan" on helicopter and expect it to fly.

The "downward force on the air" isn't the full story. From the rotors reference the movement of the air a small distance from the rotor is inconsequential. The pressure differences explain 100% of the lift.

There is a method to calculate lift from newtownian laws. That method can get far more complicated and is of no real use to anyone outside of wing design, in my opinion.

There's really no consensus on how lift is generated or the best method to use, even between two AE's working for Boeing.

Take the newtownian method, pilots and students will neglect the flow deflection on the leeward wing surface. Which leads to the incorrect conclusion that the windward flow deflection from hitting the curved wing surface is producing the lift by simply pushing the air downward. This is false, if it were true stalls (flow separation) wouldn't exist, angle of attack wouldn't matter, and vortex shedding wouldn't even be a thing. Airplanes would fly like kites.

That's why the rotor isn't simply a big fan, if it were it couldn't generate the needed lift. I prefer the pressure differential method, and think it's the better soultion to this question. As its easier to understand conceptually and works for these speeds.

I could be wrong, if so someone correct me please so I can learn something. :)

 

[Khashishi]

A fan blade is basically the same as a wing. The blades on a propeller are thinner than a house fan because it is engineered to spin faster but it's not that different. (A thick fan blade would cause some problems with cavitation as the air could not replace itself after the path of blade in time for the next blade.)

Air is not a perfect fluid, and the concept of pressure is an idealization. But Newton's third law is not an idealization. Push air down and you go up. That's the ONLY way you can generate lift with a wing.

 

[Student100]

A fan blade is basically the same as a wing. The blades on a propeller are thinner than a house fan because it is engineered to spin faster but it's not that different. (A thick fan blade would cause some problems with cavitation as the air could not replace itself after the path of blade in time for the next blade.)

Air is not a perfect fluid, and the concept of pressure is an idealization. But Newton's third law is not an idealization. Push air down and you go up. That's the ONLY way you can generate lift with a wing.

A fan blade has nothing in common with a wing. A fan blades job is to move large volumes of air around, not generate lift or reduce drag.

A rotor isn't an engineered fan blade that moves faster. It is there to provide high aspect ratios, produce lift, and minimize drag.

Huh on the last paragraph? That makes no sense. Newtonian flow is an idealization.

 

[russ_watters]

A fan blade has nothing in common with a wing. A fan blades job is to move large volumes of air around, not generate lift or reduce drag.

A fan* moves air by generating lift: Khashishi is correct that a fan, rotor and wing are fundamentally the same device.

*That is, an "airfoil fan". A centrifugal fan utilizes a different operating principle...

 

[nasu]

Huh on the last paragraph? That makes no sense. Newtonian flow is an idealization.

Newton's third law is not about Newtonian flow.

 

[Student100]

Newton's third law is not about Newtonian flow.

Newton's third law is an idealization as well.

A fan* moves air by generating lift: Khashishi is correct that a fan, rotor and wing are fundamentally the same device.

*That is, an "airfoil fan". A centrifugal fan utilizes a different operating principle...

Thanks Russ, I had just assumed they all operated like blowers.

 

[rootone]

You could make a helicopter with flat rotor blades, as long as they have some angle of attack.
It would still result in air being pushed down and therefore lift would be produced.
This would be very inefficient though, a lot of the energy delivered to the rotor would be wasted in producing unnecessary air turbulence and some heat.
The point of the aerofoil shape is to get the air to flow in a way that minimizes 'drag' - (which translates as energy wastage.)

 

[Khashishi]

True, but house fan blades are also not flat.

 

[nasu]

They are, on the fan in my kitchen.
But they are not horizontal.

 

[rootone]

True, but house fan blades are also not flat.

Sure, but why waste electricity on pushing a blade around in an inefficient way, when a simple technology can be applied with low cost to produce a more effective result it a more efficient way.

 

[Khashishi]

Oh, then it's to reduce cost

 

[Chestermiller]

Newton's third law is an idealization as well.

Why did you feel it was necessary to respond to Nasu in this way when he corrected you about not recognizing the difference between Newton's third law and Newtonian fluids /Newtonian flow? He was just trying to prevent the OP from being subjected to misinformation. What is this response even supposed to mean? Your response perpetuates the idea that Newtonian flow and fluids might still be a key factor. My "misinformation warning" finger is getting itchy.

Chet

 

[rootone]

Oh, then it's to reduce cost

Not really that, it's to do with making best use of energy.

 

[Student100]

Why did you feel it was necessary to respond to Nasu in this way when he corrected you about not recognizing the difference between Newton's third law and Newtonian fluids /Newtonian flow? He was just trying to prevent the OP from being subjected to misinformation. What is this response even supposed to mean? Your response perpetuates the idea that Newtonian flow and fluids might still be a key factor. My "misinformation warning" finger is getting itchy.

Chet

I was pointing out that it's an idealization as well to simply say the downward force of the air produces lift and that using Newton's 3rd law is somehow not an idealization in this case. The entire movement of the fluid is an idealization in both cases (pressure and reactionary). I thought my reply to Khashishi was clear and conveyed what I was thinking in context. When Nasu mentioned the third law, I also stated it was an idealization in the context of the conversation. To apply it to something that is inherently non-inertial is an idealization, if I'm wrong then I apologize to Nasu and I could conveyed my idea better.

 

[rcgldr]

If you put a flat surface under the propellers like say 2 inches below the propellers ... air has no place to go except outwards instead instead of creating lift.

The air from above is still accelerated downwards. Radio control helicopters can hover and climb upwards while inverted while almost touching the ground. With a large thrust to weight ratio, some impressive stunts are possible.

Low inverted "grass trimming" hover at 2:15 into this video:

In the case of the box, your explanation is correct.

In the case of a sealed box, the total weight of the box, air inside the box, and a model helicopter inside the box remains the same regardless if the helicopter is resting on the bottom of the box, hovering within the box, or hovering inverted and pushing upwards on the top of the box. First note absent the helicopter, the pressure at the top of the box is less than the pressure at the bottom of the box, with the net downwards force related to the pressure differential within the box corresponding to the weight of the air in the box. If the helicopter is hovering within the box, the pressure gradient from top to bottom is increased so that the downwards force on the box equals the weight of the helicopter and the air inside the box. If the helicopter is hovering inverted and pushing upwards against the box, the pressure gradient is greater still so that the net downwards force on the box remains equal to the weight of the helicopter and the air inside the box.

airfoils

Almost all helicopters full size and scale use symmetrical airfoils. Cambered airfoils produce a downwards pitching torque, which would be too much stress on the bearings. Also unlike a propeller, helicopter rotor blades are "flat", not twisted (issues with collective / cyclic / horizontal flight). This means the inner part of a rotor blade contributes little to lift, but it doesn't contribute much to drag either.

 

[Chestermiller]

I was pointing out that it's an idealization as well to simply say the downward force of the air produces lift and that using Newton's 3rd law is somehow not an idealization in this case. The entire movement of the fluid is an idealization in both cases (pressure and reactionary). I thought my reply to Khashishi was clear and conveyed what I was thinking in context. When Nasu mentioned the third law, I also stated it was an idealization in the context of the conversation. To apply it to something that is inherently non-inertial is an idealization, if I'm wrong then I apologize to Nasu and I could conveyed my idea better.

So where does your allusion to Newtonian flow and Newtonion fluids fit in with all this?

 

[Chestermiller]

The air from above is still accelerated downwards. Radio control helicopters can hover and climb upwards while inverted while almost touching the ground. With a large thrust to weight ratio, some impressive stunts are possible.

Low inverted "grass trimming" hover at 2:15 into this video:



In the case of a sealed box, the total weight of the box, air inside the box, and a model helicopter inside the box remains the same regardless if the helicopter is resting on the bottom of the box, hovering within the box, or hovering inverted and pushing upwards on the top of the box. First note absent the helicopter, the pressure at the top of the box is less than the pressure at the bottom of the box, with the net downwards force related to the pressure differential within the box corresponding to the weight of the air in the box. If the helicopter is hovering within the box, the pressure gradient from top to bottom is increased so that the downwards force on the box equals the weight of the helicopter and the air inside the box. If the helicopter is hovering inverted and pushing upwards against the box, the pressure gradient it greater still so that the net downwards force on the box remains equals the weight of the helicopter and the air inside the box.

The OP never said anything about a helicopter being inside the box. This was just another unrelated example.

Chet

 

[rcgldr]

The OP never said anything about a helicopter being inside the box. This was just another unrelated example.

I thought it might be a response to the rotors being 2 inches above the ground, which clearly isn't an issue as seen in the videos above. Now that I read it again, I'm not sure where the sealed box issue came up, but I decided to cover the explanation for that as well.

Newton third law - idealization

This is not an idealization. Forces only exist in Newton third law pairs, in this case, the Newton third law pair is the force that the rotor exerts on the air, coexistent with an equal in magnitude but opposing force that the air exerts onto the rotor.

 

[Student100]

So where does your allusion to Newtonian flow and Newtonion fluids fit in with all this?

That we are treating air as a Newtonian fluid in the discussion, and that it will flow "Newtonianally"? For the air to push downward it must flow? To thereby use Newton's third law?

 

[Chestermiller]

That we are treating air as a Newtonian fluid in the discussion, and that it will flow "Newtonianally"? For the air to push downward it must flow? To thereby use Newton's third law?

The OP never mentioned anything about a Newtonian fluid in his post. In fact, I doubt if he even knows what a Newtonian fluid is. For all we know, the fluid could be an Euler fluid, and everything that was said in the responses applies equally well to Euler fluids. So why did you feel it was necessary to defend what you wrote when Nasu pointed out your error? Everyone reading this thread recognized right away that you were confusing Newton's third law with the flow relationship for Newtonian fluids. We wouldn't have held that against you. Everybody has these mental lapses. Why couldn't you just let it go at that? Now you've called attention to it for the third time.

Chet

 

[rcgldr]

For the air to push downward it must flow? To thereby use Newton's third law?

Separate issues. Going back to the sealed box example, imagine a fan mounted within a vertical duct in a horizontal plane inside the box so that the only flow within the box is through the fan. After the initial transition, there is no vertical component of flow, just an increased pressure differential within the box maintained by the fan.

Newton's third law still applies even if there is no flow, but just a pressure differential.

 

[russ_watters]

Thanks Russ, I had just assumed they all operated like blowers.

Note that even blowers can be different types and use mixtures of different operating principles. You can reverse the curvature of the blades or even spin a blower backwards and it will still move air in the same direction (just not necessarilly as well)!

https://www.cincinnatifan.com/blower-wheels.htm

 

[Student100]

Separate issues. Going back to the sealed box example, imagine a fan mounted within a vertical duct in a horizontal plane inside the box so that the only flow within the box is through the fan. After the initial transition, there is no vertical component of flow, just an increased pressure differential within the box maintained by the fan.

Newton's third law still applies even if there is no flow, but just a pressure differential.

Seems like an apple to oranges comparison. One that in itself applies idealizations to the box, blower, and flow- physics itself is an idealization of nature. I don't understand why this is so controversial.

I still don't understand how you apply N3 to lift and not call it an idealization, but then call pressure differentials an idealization. Flows are non-inertial - the entire system is non-inertial. The entire idea behind Navier-Stokes is apply N2, with viscosity and turbulent flows. You simplify the calculations by looking at a time average for turbulence, and further simplify it by treating the air as a Newtonian fluid with linear viscosity. To use N2, you then introduce the fictitious forces. If this is the case, as far as I understand it, using N3 to calculate lift must be an idealization, as much so as the pressure differential treatment.

 

[stedwards]

A fan blade is basically the same as a wing. The blades on a propeller are thinner than a house fan because it is engineered to spin faster but it's not that different. (A thick fan blade would cause some problems with cavitation as the air could not replace itself after the path of blade in time for the next blade.)

Hmm. This is not very right. The blades on a typical box fan are a fairly thin, and the blades on an aeroplane propeller thicker.

The thin box fan blades fulfill to criteria. They are less expensive to produce than thick blades, and can be nearly as efficient as they operate at a nearly constant angle of attack. The thicker blades of an airplane propeller, in general, will have the airflow attached over a greater length of the cord, thus less drag, more lift and more efficient.

Airplane propellers do not suffer cavitation. In addition, cavitation in ship propellers is not a result of interference between blades. Cavitation results from local low pressure areas generating gas voids.

 

[rcgldr]

I still don't understand how you apply N3 to lift and not call it an idealization.

I never claimed that you could calculate or model lift solely based on Newton's third law, only that it applies to all forces, since all forces only exist as one part of a Newton third law pair of forces.

 

[Student100]

I never claimed that you could calculate or model lift solely based on Newton's third law, only that it applies to all forces, since all forces only exist as one of a Newton third law pair of forces.

In inertial frames. This isn't an inertial frame of reference.

 

[rcgldr]

... all forces only exist as one part of a Newton third law pair of forces.

In inertial frames. This isn't an inertial frame of reference.

If the ambient air (the air unaffected by an aircraft) is used as a frame of reference, it is an inertial frame. If an aircraft is not accelerating, then the wing as a frame of reference is an inertial frame.

 

[Student100]

If the is air is used as a frame of reference, it is an inertial frame. If an aircraft is not accelerating, then using the wing as a frame of reference is an inertial frame.

Then why introduce fictitious forces into the proper calculations of lift if we could simply agree on an inertial frame of reference?

Flows I thought could never be considered inertial frames.

Inertial frames are all just approximately inertial frames correct?

 

[rcgldr]

Flows I thought could never be considered inertial frames.

I updated my prior post. It's the ambient air (air unaffected by an aircraft) that can be used as an inertial frame of reference, or the ground in a no-wind situation.

 

[Student100]

I updated my prior post. It's the ambient air (air unaffected by an aircraft) that can be used as an inertial frame of reference, or the ground in a no-wind situation.

Even that air is subject to the fictitious forces to apply N1 & N2, is this not correct?

 

[rcgldr]

... the ambient air (air unaffected by an aircraft) that can be used as an inertial frame of reference, or the ground in a no-wind situation.

Even that air is subject to the fictitious forces to apply N1 & N2, is this not correct?

Ignoring issues related to the rotation of the earth, the ambient air (the air unaffected by the aircraft), is not accelerating. The only idealization here is assuming that ambient air would not be accelerating. The same idealization is also made when using the wing as a frame of reference, as the oncoming flow approaching a wing is considered to have constant velocity. I don't see how any fictitious forces could exist from the perspective of an inertial frame.

 

[Student100]

Ignoring issues related to the rotation of the earth, the ambient air (the air unaffected by the aircraft), is not accelerating. The only idealization here is assuming that ambient air would not be accelerating. The same idealization is also made when using the wing as a frame of reference, as the oncoming flow approaching a wing is considered to have constant velocity. I don't see how any fictitious forces could exist from the perspective of an inertial frame.

But you have to make assumptions about the fluid to make it inertial. That's my entire confusion here, is that not an idealization? Would such an event ever occur in nature? Then is it not an idealization to apply N3 to lift?

That's all I'm trying to clear up.

 

[rcgldr]

you have to make assumptions about the fluid to make it inertial.

I'm not sure I understand your point here, but I'm going to guess that you're thinking that if a fluid is not a Newtonian fluid, then it doesn't follow Newtonian physics, which isn't true. A Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate. It's a idealization of viscosity, not about Newton's laws of physics. Wiki article

http://en.wikipedia.org/wiki/Newtonian_fluid

Regardless of viscous effects, in an inertial frame of reference, then all fluids would be "inertial". A force exerted onto the air, results in a change in pressure and/or temperature and/or acceleration, and the reaction follows Newton's laws of physics.

Getting back to the original posters question, a change in pressure coexists with a change in density. Wiki article:

http://en.wikipedia.org/wiki/Compressibility_factor#Compressibility_of_air

In the case of a wing, a density differential coexists with the pressure differential, but it's the net pressure differential on a wing that corresponds to lift and drag forces exerted by the air onto the wing. For level flight, you can calculate the net pressure differential by the wing loading divided by the wing area.

http://en.wikipedia.org/wiki/Wing_loading

Take the example of a large commercial aircraft, the MD-11F, at 173 lbs / ft^2 wing loading, this is equal to about 1.2 psi (lbs / in^2) net pressure differential. Say this is distributed as +0.4 psi below the wing and -0.8 psi above. At near sea level where ambient pressure is about 14.7 psi, these differences are relatively small: +0.4/14.7, -0.8/14.7. At 35,000 feet, ambient pressure is only 3.2 psi, so the relative differences in pressure (and density) are greater, but the net pressure differential is the same. At higher altitudes, due to the lower density of the air, a greater speed and/or greater angle of attack is needed to maintain level flight.

 

[Student100]

Going back to the original point made:

Air is not a perfect fluid, and the concept of pressure is an idealization. But Newton's third law is not an idealization. Push air down and you go up. That's the ONLY way you can generate lift with a wing.

My point, Newtons third law is an idealization.

To apply it we have to consider an inertial frame of reference. This doesn't exist in lift calculations. Therefore, to apply N3 we make assumptions about the fluid and the plane, or an idealization of an otherwise complex interaction.

The discounting of pressure because it's an idealization, is therefore, flawed.

 

[olivermsun]

I must be missing something -- what is the difficulty here?

An airfoil and a typical (box) fan blade and a ship's propeller all operate on essentially the same principle. Toy helicopters are in fact found with blades very similar to house fans, and they fly. There are also sails, which have basically no thickness at all and are found in all sorts of widths and aspect ratios.

Is there some controversy about whether Newton's 3rd law is true?

 

[rcgldr]

My point, Newtons third law is an idealization. To apply it we have to consider an inertial frame of reference.

Newton's third law is not something you apply as part of a calculation, it simply exists. As stated before all forces only exist as one of a pair of Newton third law forces. In this case, the aircraft exerts a force onto the air, and the air exerts an equal in magnitude but opposing force onto the aircraft.

This doesn't exist in lift calculations.

Generally 3d lift calculations divide the upper and lower surfaces of a wing into a very large number of tiny squares, and calculate the pressure at each square, then sum up these pressures to determine the net pressure differential that corresponds to the force that the air exerts onto the wing. Newton's third law still applies, it would be the force that the wing exerts onto the air.

 

[nasu]

Going back to the original point made:
My point, Newtons third law is an idealization.

To apply it we have to consider an inertial frame of reference. This doesn't exist in lift calculations. Therefore, to apply N3 we make assumptions about the fluid and the plane, or an idealization of an otherwise complex interaction.

The discounting of pressure because it's an idealization, is therefore, flawed.

You mean that the Earth is not good enough as an inertial system for lift calculation? What assumption do you need to make about fluid in order to apply Newton's third law?
Are you thinking about the effect of Coriolis forces in lift calculations?

It's not clear why did you even bring in the discussion the inertial systems. It looked like you did it just to keep arguing about the "idealization" of Newton third law.

This seem to go around in loops. :)
Or rather in spiral, getting more and more remote from the original question.

 

[Ariel24K]

I like the N3 explanation better than the pressure difference explanation simply because my daily observation said so

Why does a toy helicopter goes higher when I put my palm about 5 inches under it ? Saying that the pressure difference becomes higher as the volume of air under the heli becomes smaller can't be true as my hand won't change the volume. It goes higher because it exerts force on my palm, which will push the toy upward.

And why can't helicopters climb as high as aircraft ? Some may say that the air density would be too low for it to generate lift, but hey, the decrease of air density under the rotor should be directly proportional with the decrease of air density above the rotor, it should still be able to generate lift right ?

thus I concluded at too high of altitude, the air under the rotor becomes too light to exert force on, which result in the helicopter unable to climb no more

And excuse me for my English.. Its not my first language

 

[Chestermiller]

And why can't helicopters climb as high as aircraft ? Some may say that the air density would be too low for it to generate lift, but hey, the decrease of air density under the rotor should be directly proportional with the decrease of air density above the rotor, it should still be able to generate lift right ?

How much lift do you think a helicopter could generate on the moon where the air density is zero?

Density is not a force, so it can't be directly associated with lift (which is a force). On the other hand, pressure is a force per unit area normal to surfaces, and so pressure differences are the direct cause of lift.

Chet