# The Principle of the Helicopter

The first heavier-than-air flying machines had wings whose airfoil effect provided the force of lift, due to their curvature (convex in the downward direction) which allowed air to flow more slowly along the lower surface of the wing than along the upper surface of the wing, whose curvature forced the air to traverse a longer distance, creating a partial vacuum at the trailing edge of the wing which sucked the air on the top of the wing into itself at a speed greater than that of the air at the bottom of the wing. This made the air on the top of the wing less dense than the air at the bottom of the wing, which gives the lower face of the wing a platform of dense air to rest upon, as well as a partial vacuum applying to the upper surface of the wing sucking it upwards, as long as forward motion is maintained sufficient to maintain the necessary airflow.

The wings were fixed to the fuselage, such that the only way to make the thing fly was to pull the whole aircraft, fuselage and all, through the air at a certain minimum speed.

What pulled the aircraft through the air? A propeller, which was, itself, an airfoil, curved so as to attack the air at the proper angle for lift (or, in this case, due to the axis of application of it's force, propulsion) at each point along its length (recognizing the increasing velocity of a rigid revolving body as one moves further away from the axis of rotation).

This gave some people the idea that one might liberate the fuselage from the wings, and use the propeller as the wing, by altering its axis of rotation to one perpendicular, rather than parallel, to the surface of the earth. This way, the wings move through the air without necessarily pulling the entire aircraft along with it, allowing the possibility of hovering flight.

Of course, the rotary wings create tremendous mechanical torque, such that the rotor can choose to plow through the air, or to allow the air to resist it and expend the resultant built-up energy by spinning the helicopter fuselage beneath it in the direction opposite that of the rotor's rotation. This is why you need a tail stabilizer rotor:

or twin tandem contra-rotating rotors:

or twin side-by-side contra-rotating rotors:

or twin coaxial contra-rotating rotors:

***

I hope I helped!

James Holland

## Answers and Replies

Low-Q
Gold Member
Interesting subject. I happen to be a RC-helicopter pilot. Helicopters have a main rotor which rotates at the same speed all the time - at least very close to it. The reason is that a possible change in RPM will provide a great torque on the helicopter body - more than the tail rotor can counteract. So pitch adjustment is used to rise and descent. The blades on most helicopters have an asymetrical cross section where there is a convex curve at the top, and either flat, or concave underneath. In the pro-RC world, most helicopters have a symetrical cross section of the blades, so the only thing that provide lift is a positive pitch. Positive pitch means that the leading edge of the blade is slightly higher than the other edge. In order to fly up-side-down, we must apply negative pitch. Negative pitch is absolutely not common on commercial helicopters.

Vidar

phinds
Science Advisor
Gold Member
2021 Award
Can someone explain to me how this works:

My problem is that I can't see how the rotors don't chew each other up.

Interesting subject. I happen to be a RC-helicopter pilot. Helicopters have a main rotor which rotates at the same speed all the time - at least very close to it. The reason is that a possible change in RPM will provide a great torque on the helicopter body - more than the tail rotor can counteract. So pitch adjustment is used to rise and descent. The blades on most helicopters have an asymetrical cross section where there is a convex curve at the top, and either flat, or concave underneath. In the pro-RC world, most helicopters have a symetrical cross section of the blades, so the only thing that provide lift is a positive pitch. Positive pitch means that the leading edge of the blade is slightly higher than the other edge. In order to fly up-side-down, we must apply negative pitch. Negative pitch is absolutely not common on commercial helicopters.

Vidar

Thanks!

Obviously, the pitch of a rotor blade affects its angle of attack, which, in turn, affects it's ability to transmit air along its chord (i.e., a symmetrical blade's attitude vis-a-vis pitch controls the velocity of the airflow around it just as does the asymmetrical shape of a traditional airfoil).

Great observation!

Can someone explain to me how this works:

My problem is that I can't see how the rotors don't chew each other up.

They're synchronized so that the miss each other.

Last edited by a moderator:
russ_watters
Mentor
Just like a baking beater.

just like a baking beater.

exactly!!!!

phinds
Science Advisor
Gold Member
2021 Award
I think I get it now. I was assuming that one of the beaters would HAVE to hit the vertical portion of the other rotor, but I see now that they each pass OVER the other's center. Very clever.

Thanks

I think I get it now. I was assuming that one of the beaters would HAVE to hit the vertical portion of the other rotor, but I see now that they each pass OVER the other's center. Very clever.

Thanks

You're most welcome.

And one of the great things about that rotor arrangement is that it allows the rear of the fuselage to have clamshell doors which are safe from tail-rotor strike (as there is no tail rotor) for loading of stretcher cases for medevac, or offloading of rescue personnel.

Pretty neat for such a small aircraft!

The first heavier-than-air flying machines had wings whose airfoil effect provided the force of lift, due to their curvature (convex in the downward direction) which allowed air to flow more slowly along the lower surface of the wing than along the upper surface of the wing, whose curvature forced the air to traverse a longer distance, creating a partial vacuum at the trailing edge of the wing which sucked the air on the top of the wing into itself at a speed greater than that of the air at the bottom of the wing.

I've never bought this description of how a wing works. I argued against it with one of my flying instructors with the following argument:

Take a long square tube with a venturi in the middle of it. The venturi restriction is asymmetric in that there is only a lower surface that curves in towards the middle of the box section. A flow of air that passes through this square tube will [by the classic 'wing' argument] now experience a greater flow rate along the lower surface of the tube (as it is a larger surface), thus creating a vacuum on the lower surface. The box section will then experience a lift upwards as a result (even though the air coming out of the other end does so in the same direction as when it entered the tube).

He reckoned that this 'boxed wing' would, indeed, produce lift.

It is, of course, nonsense. Lift is produced by the deflection of air downwards. Without a mass [of air] being thrusted downwards, a wing will produce no lift.

The 'vacuum on top of the wing' argument has its uses in wing design because there is a relationship between the vacuum generated and the acceleration of air downwards, according to the wing profile, but is, ultimately, bogus because this is cause and effect the wrong way around.

This gave some people the idea that one might liberate the fuselage from the wings, and use the propeller as the wing, by altering its axis of rotation to one perpendicular, rather than parallel, to the surface of the earth. This way, the wings move through the air without necessarily pulling the entire aircraft along with it, allowing the possibility of hovering flight.

Not entirely sure we needed to wait until fixed-wing airplanes were in the air before this was realised:

[URL]http://darthblender.com/wp-content/uploads/2011/02/leonardo-da-vinci-helicopter-screw-concept.jpg[/URL]

"Codex on the Flight of Birds", Leonardo Da Vinci, c. 1505

Last edited by a moderator:
Low-Q
Gold Member
I've never bought this description of how a wing works. I argued against it with one of my flying instructors with the following argument:

Take a long square tube with a venturi in the middle of it. The venturi restriction is asymmetric in that there is only a lower surface that curves in towards the middle of the box section. A flow of air that passes through this square tube will [by the classic 'wing' argument] now experience a greater flow rate along the lower surface of the tube (as it is a larger surface), thus creating a vacuum on the lower surface. The box section will then experience a lift upwards as a result (even though the air coming out of the other end does so in the same direction as when it entered the tube).

He reckoned that this 'boxed wing' would, indeed, produce lift.

It is, of course, nonsense. Lift is produced by the deflection of air downwards. Without a mass [of air] being thrusted downwards, a wing will produce no lift.

The 'vacuum on top of the wing' argument has its uses in wing design because there is a relationship between the vacuum generated and the acceleration of air downwards, according to the wing profile, but is, ultimately, bogus because this is cause and effect the wrong way around.
A completely flat or rectangular wing profile will provide lift, but the wing must be pitched a bit upwards in the leading edge to do so. Profile RC planes are good examples of flying airplanes without actual lift in the wings. Any surface can fly straight through the air just by distributing 1/4 of the wing area in front of the CG, and 3/4 behind it. Try a single sheet of paper with a couple of paper clips at the leading edge. It flies perfectly.

Edit: Sorry. I misunderstood your reply. Well, a venturi should be shaped and aligned correctly in order to provide lift of that square tube...

Vidar

A completely flat or rectangular wing profile will provide lift, but the wing must be pitched a bit upwards in the leading edge to do so.

Exactly. It is the displacement of air that provides lift.

In fact, it was following experiments on lift and wings that lead Sir George Cayley to state "lift shall be achieved by the application of power against the resistance of air" in 1799 (but who also went on to publish that lift was generated by a region of low pressure above the wing, in 1809). I guess I am having my cake and eating it there, but you don't need an aerofoil section to generate lift, therefore it would be wrong to claim it is due to low pressure arising from the shape of the wing. Aerofoil section makes the wing more efficient, and more capable in a wider range of angles [of attack] to the flow of air.

Edit: Sorry. I misunderstood your reply. Well, a venturi should be shaped and aligned correctly in order to provide lift of that square tube...

It cannot produce lift, if the air coming out of the tube is flowing in the same direction as the air entering it. It doesn't matter at all how fast the air is travelling over any surfaces during its transit between entering and exiting the tube. This is exactly the same for a wing; all that matters is the flow of air ahead of and behind the wing. If your wing generates a net motion downwards, you get lift. Doesn't matter what the wing does, or how it does it, so long as more air is moving downwards behind it than ahead of it.

One further means of counteracting the aerodynamic torque generated by the helicopter blades spinning through the air:

a contrarotating coaxial counterweight, which has the advantage of making your tail rotor a much more efficient mechanism of intentional yaw:

(it's the "stick" above and perpendicular to the rotor blades in this photo:

Last edited:
Not entirely sure we needed to wait until fixed-wing airplanes were in the air before this was realised:

[URL]http://darthblender.com/wp-content/uploads/2011/02/leonardo-da-vinci-helicopter-screw-concept.jpg[/URL]

"Codex on the Flight of Birds", Leonardo Da Vinci, c. 1505

That was NEVER realized.

Its weight-to-power ratio was abysmal, and its rotor design was the product of wishful thinking and lack of understanding of aerodynamic principles.

Last edited by a moderator:
One further means of counteracting the aerodynamic torque generated by the helicopter blades spinning through the air:

a contrarotating coaxial counterweight, which has the advantage of making your tail rotor a much more efficient mechanism of intentional yaw:

(it's the "stick" above and perpendicular to the rotor blades in this photo:

That's just sooo WRONG!

Please delete the post. Someone might actually believe you.

This is a rotor stabilising bar and is not contra-rotating.

You should be sure you know your subject before making such statements.

That was NEVER realized.

I meant 'realised' as in 'had the idea', contrary to your statement;

What pulled the aircraft through the air? A propeller, which was, itself, an airfoil.... This gave some people the idea that one might liberate the fuselage from the wings

Are you saying Leonardo ddin't have the idea to liberate the fuselage from the wings, then?

boneh3ad
Science Advisor
Gold Member
The first heavier-than-air flying machines had wings whose airfoil effect provided the force of lift, due to their curvature (convex in the downward direction) which allowed air to flow more slowly along the lower surface of the wing than along the upper surface of the wing, whose curvature forced the air to traverse a longer distance, creating a partial vacuum at the trailing edge of the wing which sucked the air on the top of the wing into itself at a speed greater than that of the air at the bottom of the wing. This made the air on the top of the wing less dense than the air at the bottom of the wing, which gives the lower face of the wing a platform of dense air to rest upon, as well as a partial vacuum applying to the upper surface of the wing sucking it upwards, as long as forward motion is maintained sufficient to maintain the necessary airflow.

Wrong. This is not how lift is generated. Cambered (curved) wings and symmetric wings can both produce lift. A cambered airfoil will just provide the same lift with less drag penalty. The reason the air moves over the top of the wing faster has nothing to do with having to travel a greater distance. This is a common misconception, but still incorrect.

Additionally, there is no density difference that, in general, explains lift. Below Mach 0.3, the flow is incompressible anyway and the density can be treated as a constant, so with that in mind, if the density really explained lift, the Wright brothers would never have gotten off the ground.

So where does lift come from? The Kutta condition. If you place an object with a sharp trailing edge at angle of attack in a steady, inviscid flow, you will have a forward stagnation point and a rear stagnation point which would on an airfoil be located on the top side an arbitrary distance from the sharp trailing edge. This configuration produces no net lift (or drag for that matter, see: D'Alembert's Paradox). Clearly this isn't what happens in real life. However, the inviscid theory does predict that the flow successfully curves around the sharp trailing edge and finds its own natural stagnation point.

Now, place it in a viscous flow (any real-world fluid) and you see a totally different situation. When the object initially starts moving, the flow can successfully find that natural rear stagnation point, but this is not sustainable. The governing equations predict that to do this, the velocity would have to be infinite at the trailing edge, which is obviously not possible. In essence, the trailing edge represents a singularity in the flow (and in fact is modeled as one on Kutta-Joukowski airfoils). What this means is that a vortex forms and is shed (see: starting vortex). This leads to a net circulation over the wing, as vorticity must be conserved. This circulation manifests itself as fast-moving flow over the wing and slow-moving flow under the wing, which translates to a lower pressure above the wing and a net lift force.

That is how a subsonic wing really works.

A supersonic wing is both more an less complicated, but suffice it to say that camber no longer matters and the lift relies on the pressure differential generated by shocks and Prandtl-Meyer expansions.

I've never bought this description of how a wing works. I argued against it with one of my flying instructors with the following argument:

And you should, because the way BadBrain explains it is incorrect.

Take a long square tube with a venturi in the middle of it. The venturi restriction is asymmetric in that there is only a lower surface that curves in towards the middle of the box section. A flow of air that passes through this square tube will [by the classic 'wing' argument] now experience a greater flow rate along the lower surface of the tube (as it is a larger surface), thus creating a vacuum on the lower surface. The box section will then experience a lift upwards as a result (even though the air coming out of the other end does so in the same direction as when it entered the tube).

He reckoned that this 'boxed wing' would, indeed, produce lift.

It is, of course, nonsense. Lift is produced by the deflection of air downwards. Without a mass [of air] being thrusted downwards, a wing will produce no lift.

It cannot produce lift, if the air coming out of the tube is flowing in the same direction as the air entering it. It doesn't matter at all how fast the air is travelling over any surfaces during its transit between entering and exiting the tube. This is exactly the same for a wing; all that matters is the flow of air ahead of and behind the wing. If your wing generates a net motion downwards, you get lift. Doesn't matter what the wing does, or how it does it, so long as more air is moving downwards behind it than ahead of it.

The fact is that your "boxed wing" would actually produce lift. If you built it out of a material that was light enough and you got the air moving fast enough, you could most certainly lift that box off the ground. This is the same principle as blowing over the top of a sheet of paper that is loosely hanging and watching the paper rise up. You lower the static pressure above the object when you force the air to move faster, meaning that there is a higher pressure below the surface leading to a net force. This net force is your lift. This is, of course, assuming that this box was not sitting flat on the ground where there is effectively no air under it. Then there can be no force from below.

Again, it absolutely does matter how fast the air is moving over a given surface. Your last line there should read "If you have lift, your wing will generate a net motion downward."

The 'vacuum on top of the wing' argument has its uses in wing design because there is a relationship between the vacuum generated and the acceleration of air downwards, according to the wing profile, but is, ultimately, bogus because this is cause and effect the wrong way around.

Both of the arguments you have here have the cause and effect wrong. The vacuum effect and the downward motion of the air leaving the wing are actually effects of what really leads to the velocity differential over a wing, which is the Kutta condition.

I guess I am having my cake and eating it there, but you don't need an aerofoil section to generate lift...

True.

...therefore it would be wrong to claim it is due to low pressure arising from the shape of the wing. Aerofoil section makes the wing more efficient, and more capable in a wider range of angles [of attack] to the flow of air.

This is a logical fallacy. Just because you don't need an airfoil to generate lift doesn't mean that the pressure differential doesn't arise on other surfaces that aren't airfoil sections. A flat plate at an angle can generate lift and yes it will deflect the air downwards, but if you measured the flow above and below it you would find a difference in velocity and pressure that can't be explained simply by saying the air was deflected. It comes from the circulation generated by having a sharp trailing edge. This sharp trailing edge is why the air is deflected downward and leads to the net circulation around the lifting body and therefore the pressure differential. You could put an ellipse at an angle in the flow and as long as it wasn't too elongated, you would not produce lift because the flow would just curl around the trailing edge and find its own preferred rear stagnation point. By adding a sharp trailing edge to something, you are enforcing your own stagnation point.

The fact is that your "boxed wing" would actually produce lift.

No. It would produce no lift at all if it causes no air to be displaced downwards.

Sounds like you want to raise a 3rd notion of how a wing works.

Any way you swing it, if you don't cause a displacement of air downwards, you get no lift. Air is a fluid and as such the only way to stay straight and level in it is to push a steady stream of it down. I'm not particularly bothered what the finery details of what various aero-structures can do that, but lift is acheived by thrusting air downwards.

This is a logical fallacy. Just because you don't need an airfoil to generate lift doesn't mean that the pressure differential doesn't arise on other surfaces that aren't airfoil sections.

I'm not aware I argued that point. How did you come to a conclusion otherwise? I dispute nothing about what pressures are, or are not, on wings, only that this is not a fully-consistent explanation for how lift is generated (because pressures could also be made on a wing that does not generate lift).

"A wing pushes air down to generate lift" is a complete description (because if, and only if, it pushed air down then it will generate lift), albeit missing out on how it actually does that.

boneh3ad
Science Advisor
Gold Member
No. It would produce no lift at all if it causes no air to be displaced downwards.

I am sorry, but you are just not correct here. Check any aerodynamics textbook.

Sounds like you want to raise a 3rd notion of how a wing works.

No, I wanted to explain the real reason a wing works. As a result of this reason, the other two postulated explanations in this thread are a byproduct of the correct explanation.

Any way you swing it, if you don't cause a displacement of air downwards, you get no lift. Air is a fluid and as such the only way to stay straight and level in it is to push a steady stream of it down. I'm not particularly bothered what the finery details of what various aero-structures can do that, but lift is acheived by thrusting air downwards.

Again, this just isn't true. True, aerodynamic lift is generated in any situation where there is a net upward force. You do not need to deflect any air downward to generate this force. The underlying reasons for generating aerodynamic lift often (not always) lead to a downward deflection of the flow, but this is not a necessary condition for generating lift. A circulation about a lifting body is both necessary and sufficient.

I'm not aware I argued that point. How did you come to a conclusion otherwise? I dispute nothing about what pressures are, or are not, on wings, only that this is not a fully-consistent explanation for how lift is generated (because pressures could also be made on a wing that does not generate lift).

"A wing pushes air down to generate lift" is a complete description (because if, and only if, it pushed air down then it will generate lift), albeit missing out on how it actually does that.

You did argue that point when you argued (and are still arguing) that the lower pressure on the upper surface of the lifting body does not lead to lift. That is what lift is. It is flow-normal force that arises from a pressure differential on two opposing surfaces. Here is lift as defined by Katz and Plotkin, 2001:

$$L = -F_x \sin \alpha + F_z \cos \alpha$$
where
$$F_x = \int_{\mathrm{wing}} \left( p_u \frac{\partial \eta_u}{\partial x} - p_l \frac{\partial \eta_l}{\partial x} \right)dx\;dy$$
$$F_z = \int_{\mathrm{wing}} \left( p_l - p_u \right)dx\;dy$$
$\alpha$ is the angle of attack
$p$ is pressure
Subscripts $u$ and $l$ denote upper and lower surfaces
$\eta$ is the surface profile of the lifting body

If that isn't defined in terms of pressures, I don't know what is. Of course, that is just a force balance description. If you want a source on what I explained earlier, check out Karamcheti, 1966 There he discusses the Kutta-Joukowski theorem and how it was such a landmark in aerodynamics, illustrating the key role that circulation plays in generating lift. In fact, you can take a circular cylinder, which obviously doesn't produce lift, and then generate your own circulation by spinning it when it is in a flow and you will suddenly have lift despite the fact that all the streamlines in the system approach the cylinder and leave the cylinder at the same height. There is no net downward deflection. In fact, there is actually a temporary upward deflection of the flow (see: Karamcheti, page 384).

You will find a similar account in Abbott and Doenhoff, 1959, Anderson, 1984 or any other reputable reference on the subject of aerodynamics.

Last edited:
I am sorry, but you are just not correct here. Check any aerodynamics textbook.

I am sorry but you are not correct here. Actually I don't think any text book really mentions this.

But anyhow, this isn't about aerodynamics, this is simple Newtonian mechanics. There is no way a thing will stay suspended in, and by, a fluid unless the fluid is providing an upwards force to hold the thing against gravity.

There is always an equal and opposite reaction. The fluid, in providing an upwards force, therefore receives on it a downwards force. As it is a fluid, this therefore MUST result in a mass flow downwards.

If you deny this, you deny basic Newtonian mechanics.

My point being that there is, therefore, never lift without a downwards force on the fluid, therefore there is always a downward mass flow. The 'box wing' has no such downward flow, so you can see immediately that it won't fly (unless, as mentioned, it is tilted so that it is used as a duct to re-direct air downwards).

Lift is absolutely and exactly proportional to the downwards dispacement of the mass of air. Zero displacement of air, zero lift. This isn't aerodynamics, this is Newton's 3rd law.

boneh3ad
Science Advisor
Gold Member
I am sorry but you are not correct here. Actually I don't think any text book really mentions this.

But anyhow, this isn't about aerodynamics, this is simple Newtonian mechanics. There is no way a thing will stay suspended in, and by, a fluid unless the fluid is providing an upwards force to hold the thing against gravity.

In case you missed it, fluid mechanics is an extension of Newtonian mechanics and thermodynamics as the governing equations are derived from first principles in these fields. It is actually directly a branch of continuum mechanics except in the case of rarefied gases. Of course the fluid must be imparting a force in order to suspend it. I haven't at any point claimed otherwise. What I have claimed is that a fluid need not change direction in order to impart such a force.

Now, the fluid can (and does) provide a force without changing directions. Pressure is, after all, just a host of molecules impinging on a surface, so the bulk motion of a fluid does not have to change direction to impart a force. You can have two stagnant fluids on either side of a membrane not moving at all but at different pressures and the fluids will impart a force on said membrane. Not surprisingly, the fluid in this case has no change in momentum yet applies a force anyway.

Now take the example of an airplane wing. Now you have the same fluid on both sides in an open system, so you can't just have the two sides and different pressures stagnantly. That is, of course, why a plane will fall from the sky if it stops moving. However, it has long been known theoretically and been borne out theoretically that when a fluid increases in bulk velocity, the static pressure in the fluid decreases. This is often enumerated through Bernoulli's principle. As long as something causes the fluid to move over the wing faster above than below, there will be a net force regardless of what direction the fluid moves before or after passing the object. It is a simple force balance. You have the pressure integrated across the bottom surface resulting in one force and the pressure integrated across the top surface resulting in another. As long as one is larger than the other, you have a net force, and if the bottom surface force is larger as in the case of a wing, you have lift. If that resultant lift is greater than the weight of the object, they object can take off.

That all fits neatly inside of Newton's laws without requiring the flow to change direction.

There is always an equal and opposite reaction. The fluid, in providing an upwards force, therefore receives on it a downwards force. As it is a fluid, this therefore MUST result in a mass flow downwards.

If you deny this, you deny basic Newtonian mechanics.

Of course there is always an equal and opposite reaction. That reaction does not have to come in the form of the fluid changing direction. Like I said before, consider a circular cylinder rotating in a fluid flow. The streamlines in the far field are undisturbed, yet there is a net lift. This is borne out mathematically and experimentally, yet doesn't conform to your rule here.

http://www.grc.nasa.gov/WWW/k-12/airplane/cyl.html
https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=fl&chap_sec=07.4&page=theory

My point being that there is, therefore, never lift without a downwards force on the fluid, therefore there is always a downward mass flow. The 'box wing' has no such downward flow, so you can see immediately that it won't fly (unless, as mentioned, it is tilted so that it is used as a duct to re-direct air downwards).

Then explain to me how a rotating cylinder has lift? Without meeting your criterion? If you can't do that, your whole argument is disproven.

Lift is absolutely and exactly proportional to the downwards dispacement of the mass of air. Zero displacement of air, zero lift. This isn't aerodynamics, this is Newton's 3rd law.

Downward displacement of air is often (if not usually) a result of lift generation. There are, however, instances where lift is present without downward deflection of the flow do exist, and the downward flow is therefore not a necessary condition. As far as I know, however, it is a sufficient condition.

I see a picture showing air flow where all the lines are pointed up to the left, and all the lines are pointed down to the right. A net mass displacement, just as I have been discussing.

I see pictures at the bottom demonstrating lift where a net mass movement of air is shown pointing downwards on the left, then flowing across the cylinder and flowing up on the right. Lift is described as -ve in the y axis (vertical), just as I have been describing.

Then explain to me how a rotating cylinder has lift? Without meeting your criterion? If you can't do that, your whole argument is disproven.

It does meet my criterion. A rotating cylinder, as well-demonstrated in the links you've provided, gives a net mass vector displacement to a flow of air coming towards it. Lift is the reaction to that mass vector displacement.

I am sure I am not going to convince you that Newton's 3rd law applies here, so I will have to leave you to believe what you want on this. it seems fairly clear we are not going to be able to convince each other.

You simply can't have a mass flow of air over a lifting body that is vector-identical to that after it. The gravitational force of the lifted mass must ultimately be due to additional pressure on the ground, transferred there by the air. You can argue all detail as you see fit that there is 'extra pressure' under the wing, and I will not contest that. But for there to be additional pressure under the wing then air must have flowed from above it to below it. If anyone wishes to argue that it is lower pressure on top of the wing, then, still, air must have flowed from above the wing to below the wing. You could conceivably argue that the pressure differential is due to differentials of speed. Well, the same kinds of thing apply - if you have the top side of a volume moving faster than the bottom side, then it will rotate downwards, about a horizontal axis.

As I say, I'm not going to convince you, so we should call it quits. I have tried, and failed, to persuade people who, in the modern terms and conventions of 'lower pressure over the wing' know everything about this there is to conventionally know.

What concerns me more about this thread is that nonsense about the rotor stabiliser being a contra-rotating mass. I really hope the op will delete it. This lift-thing is an arguable discussion - but this other thing is just wrong!!! I suppose I should explain what it actually does, but there are too many in this thread that know so much better!

boneh3ad
Science Advisor
Gold Member
cmb said:
I am sure I am not going to convince you that Newton's 3rd law applies here, so I will have to leave you to believe what you want on this. it seems fairly clear we are not going to be able to convince each other.

No need to get snippy. I assure you I have the utmost faith in Newton's laws applying everywhere where classical mechanics are valid, including here. It is more the cause and effect that we are arguing. I still maintain that the downward deflection is the effect of lift rather than the cause. If you take a wing with a sufficiently rounded trailing edge and move it at an angle of attack through the air, there would still be no lift. You have to have that sharp trailing edge and therefore bound circulation in order for the flow to be deflected downward.

cmb said:
But for there to be additional pressure under the wing then air must have flowed from above it to below it. If anyone wishes to argue that it is lower pressure on top of the wing, then, still, air must have flowed from above the wing to below the wing. You could conceivably argue that the pressure differential is due to differentials of speed. Well, the same kinds of thing apply - if you have the top side of a volume moving faster than the bottom side, then it will rotate downwards, about a horizontal axis.

I 100% agree with this portion of that paragraph, and in fact that is what I have been describing (though with different words). The flow does move up and around the leading edge for any airfoil at an angle of attack (leading to what is commonly called a suction peak, but I digress). This behavior amounts to the very circulation about the wing that I have been talking about and is the reason why the air does in fact move faster over the top and why the pressure is in fact lower. Like you said before, though, the simple notion of higher pressure on bottom or higher speed on top is not enough to explain where lift comes from. I think we are in 100% agreement there as well.

cmb said:
As I say, I'm not going to convince you, so we should call it quits. I have tried, and failed, to persuade people who, in the modern terms and conventions of 'lower pressure over the wing' know everything about this there is to conventionally know.

Many, many people attribute lift straight to Bernoulli's principle and then make up whatever they want about how the air along the top moves faster, usually involving the fictitious notion of equal transit time. The simple fact is that regardless of which one of us is right (and I would argue that we are very nearly arguing semantics at this point minus a few smaller issues), the nature of lift is very commonly oversimplified to the point of just being flat wrong as in the original post here.

boneh3ad:

Thanks for the correction, the info, and the equations.

Just one follow-up: the explanation for the wing that I gave in my original post is what I was taught everywhere from school to the boy scouts, and it's, frankly, the only one I've ever been taught until now.

Seeing as that explanation is as wrong as I now realize it to be, why is it so widely taught?

Last edited:
cmb:

You're right about the UH-1 post. I no longer stand by it, but can no longer delete it, because too much time appears to have passed since I posted it.

OK, I'm glad you acknowledge the error.

For interest, the reason those masses are there is to balance cyclic loads on the rotor. The loads change as the blades rotate, and when you have just two blades the effects become even more noticeable.

A helicopter rotor works in an interesting way. When a helicopter is moving forwards, one blade is going forwards and one is going backwards. (This is why the speed of a helicopter is limited - eventually one cannot go backwards fast enough to generate any lift at all!)

For both sides to have equal lift, the pitch of the advancing blade is lower than the pitch of the blade going backwards. This balances the L-R lift.. This is achieved by a device called a 'swash plate' that is angled according to the pilots inputs that achieves this oscillating function as the rotor rotates. As these are cyclic variations, that control is called 'the cyclic'. The pitch of the blades can be biased to be greatest either one side or the other, or forwards or backwards. Clearly, if you bias left or right you roll, and f-b you pitch.

To go forwards, you create a pitch by biasing the angle of attack towards the rear of the disc. This would simply cause you to lose height if that was all there was. There is a second pilot control which alters all the pitch angles, at any rotor rotation angle, collectively. This control is therefore called 'the collective'. It moves the whole swash plate up or down, rather than tilting it about its centre like the cyclic.

The rotor balancing shaft helps damp these cyclic blade-pitch variations, and also, so I believe, should therefore ease the loads on the cyclic control.

(I have not flown such helicopters but I seem to recall the stabiliser bar is sometimes dubbed a 'Chinaman's Hat'? Don't take that as a fact unless someone can corroborate it, maybe that was just a 'local' nick-name I over-heard, or mis-heard.)

Many, many people attribute lift straight to Bernoulli's principle and then make up whatever they want about how the air along the top moves faster, usually involving the fictitious notion of equal transit time. The simple fact is that regardless of which one of us is right (and I would argue that we are very nearly arguing semantics at this point minus a few smaller issues), the nature of lift is very commonly oversimplified to the point of just being flat wrong as in the original post here.

I think we have a consensus on this!