Fundamental basics of lift

[PakledHostage]

can I have you think about this suggestion.

Please give me 12-18 hours. I don't have time to respond right now, but I will get back to you (unless someone else wants to take it on before I get to it).

[cantab]

My understanding is:

The lift force on the plane is equalled by the downward force on the air. That's Newton's Third Law, there's no getting away from that.

In free air, the downward force on the air accelerates it downwards. Near the ground, or in a wind tunnel, the force is transmitted through the air into the ground/floor. Which is why you don't see the deflection in a wind tunnel.

The shape of an airfoil allows it to "pull" on the air flowing over it, as well as push the air flowing under it.

Bernoulli's principle is another side of the same coin. Perhaps it's better to regard the higher speed of air above the wing as not the cause but the consequence of lower pressure above the wing.

[Iskierka]

cantab has the best understanding of lift so far.

A question that you should consider in context of your explanation: How does an airfoil test section that spans the full width of a wind tunnel (from wall to wall) produce lift? There is no downwash from an infinite aspect ratio wing (as approximated by an airfoil test section that spans the full width of a wind tunnel). A finite aspect ratio wing that generates a downwash actually produces less lift per unit span than an infinite span wing that doesn't. How is this possible given your explanation? Does this point to an error in your understanding or can you reconcile the difference?

The first thing that I need to address is that this is absolutely false - an infinite wing may not generate tip vortices, but it absolutely does generate a downwash. It may be limited in wind tunnels, but that is because the tunnel itself rights the flow of air after it passes the wing - if you generate stream lines and observe them in a tunnel with sufficient vertical space, you can absolutely see them travel downward for some distance after an infinite aerofoil.

As for how lift is generated, while the Bernoulli effect is involved, I must point out that it provides NO contribution to lift. Lift is generated because gas moves to fill available space - around a moving object, this becomes the Coanda effect, where a pressure differential finds itself set up to push air into the constantly-opening gaps around a wing, or to leave space it fills. Above the wing, this creates a negative pressure gradient, and below a positive, as the "outside" must equal atmospheric pressure, so against the lower surface there must be high pressure to remove air, and above the upper there must be low. The flick of a wing's trailing edge does affect lift, but not significantly - most air is deflected, and most lift generated, in the first half of the wing with most curvature. Flying wings are required to have their trailing edge flick upward for stability reasons - a purely positive cambered aerofoil is both statically and dynamically unstable - yet they still generate positive lift at low AoA.

The Bernoulli effect appears in that air is accelerated because of the reduced pressure caused by the Coanda effect - Bernoulli works in both ways. At a basic physical level, there is NO reason for the air around a wing to change velocity - except for the fact that doing so provides conservation of energy as Coanda generates a pressure differential. Momentum and other factors come into play as Bernoulli plays this part, that affect how much pressure can be generated due to limiting how quickly air can accelerate, but Bernoulli is not providing lift, only providing a small manipulation on the effect that DOES generate it.

As for the acceleration on the air generated by a P-51, you're missing the fact that wings generate lift by setting up a pressure differential on a large section of air vertically around them. It would be much closer, though still incorrect, to calculate the deflection on a cylinder of air, of diameter equal to the wingspan. Running the calculations correctly, and with the two extremes of air affected at stalling speed and at maximum flight speed:

P-51 m = 3500 kg

P-51 F = 35000 N

P-51 b = 11.3 m (wingspan)

P-51 v-min = 45 m/s

P-51 v-max = 130 m/s *

air density p = 1.225 kg/m^3

* Calculated equivalent airspeed based on maximum quoted airspeed at altitude

So to remain in flight, a P-51 must affect a cylinder of air whose volume per time can vary between:

A = 11.3^2 * pi/4 = 100.3 m^2

V-min = 100.3 * 45 = 4500 m^3/s

V-max = 100.3 * 130 = 13000 m^3/s

Which means that a P-51 deflects a certain mass of air per second in flight:

m(dot)-min = 4500 * 1.225 = 5510 kg/s

m(dot)-max = 13000 * 1.225 = 15900 kg/s

If we compare this to the force generated to keep a P-51 airborne, we can calculate the velocity downward imparted on the air in order for flight to be maintained.

N = kg * m / s^2

air v-max = F / m(dot)-min = 35000 / 5510 = 6.35 m/s

air v-min = F / m(dot)-max = 35000 / 15900 = 2.20 m/s

The downwash of a P-51 in flight is somewhere between 12 mph and 4 mph. Neither are particularly exceptional velocities, and perfectly reasonable to be generated by something travelling at over 100. The downwash velocity will increase at altitude, granted, but it will increase in proportion with the increased forward flight speed, and in inverse proportion with the reduced air density, and all these equations will remain consistent. The downwash angle, the difference between the air's original path and its new path, will always remain the same for same Cl, and same equivalent air speed.

As for induced drag, I'll point out that tip shedding is a contributing part of induced drag, but not the whole. Induced drag is all drag generated by the generation of lift, as opposed to the parasite drag which is simply air being pulled along by contact with the aircraft skin. The primary part of induced drag is air deflection - lift changes the angle of the air, but it cannot accelerate air backwards behind it, so at best, the relative velocity of air and aircraft must remain equal, or reduce. As the angle changes to create a vertical deflection, some velocity is also lost in the forward dimension, and the loss of this velocity on the air acts as a drag force on the aircraft. This deflection angle is also the downwash angle mentioned above. Calculating for the P-51, the ratio of that angle is 6.3:45 at stall speed, which would mean the theoretical maximum possible L/D for it at stall speed is 45/6.3, or about 7.3. It will never come close to that L/D, as this ignores parasite drag and tip drag, but that is the maximum it could achieve simply based on how much it is having to push on the air to stay up.

The second part of induced drag is the tip shedding which creates vortices - the generation of these vortices requires energy, and the forces which provide this energy pull on the wingtips directly, creating drag. Further, once the vortex is created, the vortex itself is a low pressure zone, and pulls air into them, which creates a very small overall negative pressure behind the aircraft, pulling the overall airframe backwards. An infinite aerofoil does not experience tip drag, as there are no tips to generate the vortex, but it will always experience induced drag due to the deflection of airflow.

Edited February 6, 2015 by Iskierka

[PakledHostage]

I am not going to argue with you, Iskierka, because I have disliked the "comic bookstore guy" tone of your posts for years, but I will make a few points:

The first thing that I need to address is that this is absolutely false - an infinite wing may not generate tip vortices, but it absolutely does generate a downwash. It may be limited in wind tunnels, but that is because the tunnel itself rights the flow of air after it passes the wing - if you generate stream lines and observe them in a tunnel with sufficient vertical space, you can absolutely see them travel downward for some distance after an infinite aerofoil.

You can also see the stream lines travel upwards for some distance ahead of the airfoil. If I was to apply your own argument to the view looking forward from the airfoil test section, I could suggest that "there's no downwash, indeed there's upwash!". You can't look at them in isolation because the very images that you're referring show that there's upwash ahead of the wing as well as downwash behind it. Otherwise, you are correct that wind tunnels do affect the airflow around a test article. This is why you must apply correction factors to the measurements that you make in them.

The flick of a wing's trailing edge does affect lift, but not significantly - most air is deflected, and most lift generated, in the first half of the wing with most curvature. Flying wings are required to have their trailing edge flick upward for stability reasons - a purely positive cambered aerofoil is both statically and dynamically unstable - yet they still generate positive lift at low AoA.

I don't understand why you are bringing reflex camber airfoils into this? Why is this relevant? Did I miss where someone brought it up?

The second part of induced drag is the tip shedding which creates vortices - the generation of these vortices requires energy, and the forces which provide this energy pull on the wingtips directly, creating drag. Further, once the vortex is created, the vortex itself is a low pressure zone, and pulls air into them, which creates a very small overall negative pressure behind the aircraft, pulling the overall airframe backwards. An infinite aerofoil does not experience tip drag, as there are no tips to generate the vortex, but it will always experience induced drag due to the deflection of airflow.

This is an oversimplified explanation. It doesn't account for why higher aspect ratios result in lower induced drag. How could such a strong vortex be created at the tip when the lift on a 3D wing (and the pressure differential between lower and upper surfaces) falls to zero at the tip? It also doesn't account for why the tip vortices don't form directly behind the wing tip. The initial distance between tip vortices is typically about 85% of the wing span.

An airfoil (and indeed a wing) generates circulation about itself when moving through a viscous fluid like air through a combination of the shear forces that occur in the fluid at the sharp trailing edge (ref. the Kutta condition that I mentioned in one of my earlier posts) and conservation of angular momentum. Conservation of angular momentum requires that net circulation in the fluid must be conserved. Where a wing creates circulation, equal and opposite circulation must be created elsewhere. That circulation is fundamental to the production of lift because it results in a pressure field about the wing being created as a result of conservation of momentum and conservation of energy.

Vortices also can't just begin or end in a fluid. A wing will shed a small part of its bound vortex with every change in lift along its span. In a 3D flow, the lift on a wing is not uniformly distributed from root to tip; the lift per unit span decreases all the way out to the tip. In a viscous flow, all of these minute vortices roll up to form a trailing vortex that is located inboard of the tips. The sum of these shed vortices results in a net downwash behind the wing in addition to the aforementioned trailing vortices.

If readers of this thread have any doubts about what I've written, they can do their own experiment to learn more about circulation about a lifting surface in a viscous fluid. All it takes is some chicken broth (or similar fluid with low viscosity oil on the surface to aid flow visualization).

1. Take a knife and insert the blade into the broth at a small angle of attack

2. Suddenly accelerate the knife through the broth, maintaining the small angle of attack. Note that a little "whirlpool" forms where the knife started moving from. This is a starting vortex. It is related to the natural occurrence of the kutta condition on the knife's trailing edge in a viscous fluid due to conservation of angular momentum and shear forces in the viscous fluid at the knife's trailing edge.

3. Let the broth settle down for a few seconds and then move the knife smoothly through the broth at an angle of attack again. This time stop it suddenly. Note that a little whirlpool is shed by the knife and continues to move towards the edge of the bowl at the speed that you were moving the knife? This is the bound vortex/lifting vortex being shed by the knife when it stops producing lift.

4. The bound vortex changes in intensity with every change in lift. Increasing the angle of attack of the knife will also increase circulation about the knife. If you do it carefully and suddenly enough, you will be able to see a second starting vortex generated in the broth at the location where you increased the knife's angle of attack. This starting vortex conserves the angular momentum of the new opposite circulation that has been created about the knife.

5. And while you can't see it in the broth, there is a vortex under the surface that connects the starting vortex and the bound vortex. This is the same vortex that you see trailing from the wings of an airplane. In a real fluid, the trailing vortex will break up into little eddies and dissipate, but overall, angular momentum is still conserved.

[Iskierka]

You can also see the stream lines travel upwards for some distance ahead of the airfoil. If I was to apply your own argument to the view looking forward from the airfoil test section, I could suggest that "there's no downwash, indeed there's upwash!". You can't look at them in isolation because the very images that you're referring show that there's upwash ahead of the wing as well as downwash behind it. Otherwise, you are correct that wind tunnels do affect the airflow around a test article. This is why you must apply correction factors to the measurements that you make in them.

Which I'd expect you to realise is a completely false concept, as ahead of the aerofoil is ahead in time, and does not reflect the final momentum imparted to the airflow, thus is not a consideration for the final force generated (though it is very significant in the torque and aerodynamic centre, which was not being discussed).

I don't understand why you are bringing reflex camber airfoils into this? Why is this relevant? Did I miss where someone brought it up?

... On top of that explanation, the excuse I hear most often now is the Newtonian flow deflection theory about air being deflected downward off the trailing edge to create downwash; ...

This is an oversimplified explanation. ...

Yes, it is. The topic is about the generation of lift, not drag, and I was simply quickly addressing someone who appeared to me to be confused about the difference in definition between induced drag and vortex drag, and as they're likely aware of the cause and effect of vortex drag, I focussed on the factors that are part of induced drag but not part of the vortices, ie; the forward axis component to wing downwash.

[Vanamonde]

Please do not make the argument personal, people.

[K^2]

Bernouli effect across the airfoil is zero, because boundary layer is stationary. Bernouli effect is not responsible for lift That is a very naive view. It is one of the components that set up an air flow around the foil. That, along with separation layer and continuity will result in a pressure differential in boundary layer.

[Mattasmack]

Bernouli effect across the airfoil is zero, because boundary layer is stationary. Bernouli effect is not responsible for lift That is a very naive view. It is one of the components that set up an air flow around the foil. That, along with separation layer and continuity will result in a pressure differential in boundary layer.

But once you go through the boundary layer to the surface of the airfoil the Bernoulli equation becomes irrelevant, because it applies only as long as viscous forces are negligible.

In conversations at this level, it is usually taken for granted that we are talking about a high-Reynolds-number flow (and flow that isn't separated from the surface) so that the boundary layer is thin compared to the airfoil and there isn't a significant pressure difference across the boundary layer. Then one needs to deal only with the irrotational flow outside the boundary layer (where the Bernoulli equation does hold) to get a reasonable approximation of the lift an airfoil produces.

Though I agree with the larger point, that simply naming an effect is not an explanation. There's no law that says the behavior of a reasonably complicated system must be able to be accurately explained in a few words of english.

[K^2]

I agree that if you treat air as almost inviscid, almost incompressible fluid, you can get good approximation for lift by using Bernouli near airfoil. And this works for low mach numbers. But saying that Bernouli principle is the cause of lift is fundamentally wrong. It is wrong precisely because you cannot take it past boundary layer. And taking flow to be perfectly inviscid takes away separation layer. Lift of a foil in perfect inviscid flow is exactly zero.

[Bill Phil]

Both are effective descriptions separately, but in real life they both work together to provide lift.

[Bryce Ring]

have either of you discussed this on RCGroups. sounds familiar.

http://www.rcgroups.com/forums/showthread.php?t=1539175

http://www.rcgroups.com/forums/showthread.php?t=1610771

http://www.rcgroups.com/forums/showthread.php?t=1479190

some nasty buggers in that group.

Not like here. I like KSP's attitude towards grumpy attitudes etc. though I dislike how it can close a thread.

Here is a nice little short one.

http://www.rcgroups.com/forums/showthread.php?t=1227290

Edited February 6, 2015 by Bryce Ring

[K^2]

No, but this argument tends to happen frequently wherever enthusiasts and some professionals gather. Unfortunately, aeronautical engineers are frequently responsible for the worst nonsense in such discussions. There are a lot of very well qualified engineers out there who, unfortunately, do not understand the difference between, "This is a very good model that approximates behavior," and "This is why it works."

[Bryce Ring]

K^2 true true.

I almost always jump in. I tend to learn more that way. been wrong many times and right for reasons I didn't fully understand. made corrections to my assumptions and corrections to those. it takes time. but in the end we can all stick out hand out the window and form a shape and feel the effect, we know it as push or a force.

I have been thinking these last few days, How would some one go about describing all the motions and forces involved on and around an airfoil and the air that is affected as a result of its motion through the air, without using one key concept, that key concept is Pull, or Suck, or any other word that suggests attraction (Particularly between the wing and the air)

Maybe I should start a thread,

Does Aerodynamics Suck?

or

do wings suck ?

Or to address the ultimate question., What sucks?

I'm sure it may attract a few, but .... it will probably get pull down in the end.

But I can't see them coming out well, and no doubt I would get flamed for trying to create some "New Politically Ccorrect Hippy Lovin "Its all circular!" Aerodynamic Theory.

Any thread name suggestions ?

Ohhh, never mind, I cant see anyone actually learning anything new from it, But I just know some one would (After having read that that thread) jump into a forum discussion about lift and use the very concept to describe.

Hang on wait. Am I wrong. is it true that you can describe lift without using that concept ?

[PB666]

Correct me if I'm wrong. My understanding after I read this post is somewhat shattered.

I tried my best to express my beliefs of why airplanes fly in MS Paint (forget my madskillz), but I always thought that lifting force is produced by this (not to scale):

http://dumpt.com/img/files/1bh326a81s51ecwsyw1g.png

Have I been wrong all along?

The deflection force acting on the wing is only about 10% of the lift, and it produces high drag to lift. Bernoulli's 'force' produces most of the lift. A stall for example is not cause by the slowing of an aircraft, it occurs because the angle of attack exceeds (typically 18 degrees IIRC) causes air to separate from the airfoil on the tailing edge of the wings causing turbulence and a loss of pressure differential. Even though the deflective lift is greater, it is insufficient to compensate for the loss of Bernoulli's 'force' and the aircraft begins to fall at angles tangential to the wing direction.

Ending a stall is not immediate, turning a wing exactly on the to zero angle of attack is followed by the replacement of disorganize air to laminar air flow over the wing, and then lift is restored. Near ground stalls are often catastrophic since there is in adequate vertical distance to reestablish lift and also change vertical vectors.

In addition stalls are associated with shuttering (extreme turbulence) which make control surface function marginal.

This behavior is the reason that aircraft are equipped with flaps. Flaps increase bernoullis but also drag (they create a large wind profile), but they reduce the need for high angles of attack which are both draggy and risky. As a craft speeds up its angle of attack for level flight or climb declines, it can retract flaps and through this repeated process the aircraft 'trims'. Eventually the elevator can be trimmed and the craft is mainly relying on its wingshape to keep altitude. By speeding up aircraft, despite greatly increasing the potential for drag actually reduce drag because Benoulli's lift allows them to trim deflecting surfaces that produce the most drag. The point is that there are many ways to create lift (engine Angle of attack and verticle thrust vectors, deflective lift, etc) but Bernoulli's 'force' is the most efficient lift per drag unit produced.

Point of order here though. Why are we talking about level flight dynamics in KSP. The most important force that acts on launches is the pressure wave that builds up on ascending craft as they surpass the speed of sound, real world forces acting on non-aerodynamic designs far exceed bernoulli's force, deflective lift. I using MSFS with over 10,000 hours of flight from supercubs to SR71 blackbird (favorite is DC6B), kerbal has nothing on FS, the wings are boxy shaped and lack proper shape, they are pretty much driven by brute force rockets, that if you get pitch high enough the rockets vertical vector provides sufficient lift. The lift surfaces act more like sheets of plywood with defectors on the back. I suppose you could use small wing strips to make a inverted concave surface that resembles an aircraft's, but I wonder if the physics engine would recognize it and deliver lift?

[YNM]

Maybe lift have a connection with ideal gas law a bit, most noticeably over the pressure difference ?

[K^2]

The deflection force acting on the wing is only about 10% of the lift, and it produces high drag to lift. Bernoulli's 'force' produces most of the lift.

As explained above, Bernoulli Effect does not produce any force on the wing. It is, however, part of what shapes the airflow around the wing.

And 100% of the lift corresponds to deflection. Newton's 3rd, etc. What you can say is that majority of the deflected air is not swept by the wing directly. Again, see the illustrations of flow patterns around the wing to see how much air is actually being deflected in the flow.

This behavior is the reason that aircraft are equipped with flaps.

Not really. Plain flaps reduce critical AoA. However, they give you higher C_L at the same AoA at the cost of increased C_D and reduced glide ratio. Furthermore, they typically have higher AoA at the same attitude, so you don't have to flare nearly as much during approach.

Leading edge flaps, slats in particular, can be used to increase critical AoA, but they typically reduce C_L, so they are only ever really used on large airliners together with Fowler flaps, because the later dramatically increase wing area compensating for a C_L drop. Naturally, all of that comes at a cost of a lot of drag, but that's what the airliner's engines are for.

[Mattasmack]

I agree that if you treat air as almost inviscid, almost incompressible fluid, you can get good approximation for lift by using Bernouli near airfoil. And this works for low mach numbers. But saying that Bernouli principle is the cause of lift is fundamentally wrong. It is wrong precisely because you cannot take it past boundary layer. And taking flow to be perfectly inviscid takes away separation layer. Lift of a foil in perfect inviscid flow is exactly zero.

Sure, viscosity is necessary, no disagreement here. In the context of ideal flow, the way I usually see it argued is that viscosity is what explains / enforces the Kutta condition, which can't really be proved or explained purely within the ideal flow model.

But it seems to me that if you're concerned about the Bernoulli principle being invoked as the fundamental cause of lift, the problem isn't that it neglects viscosity, the main problem is that the principle, by itself, doesn't explain anything! The lift force is a result of the flow field around the airfoil and the Bernoulli principle can't explain what that field should be. You need the full Navier-Stokes equations. But, if you've already determined the velocity field by other means (e.g. a wind tunnel), you can invoke the Bernoulli principle to explain the regions of high and low pressure that add up to the lift force. (And that works! Though you could also use the pressure gradient normal to curved streamlines and avoid talking about Bernoulli at all.)

-- edit --

Whoops, ninja'd several times over.

...

And 100% of the lift corresponds to deflection. Newton's 3rd, etc. What you can say is that majority of the deflected air is not swept by the wing directly. Again, see the illustrations of flow patterns around the wing to see how much air is actually being deflected in the flow.

That deserves repeating, especially since I think I've seen it said otherwise in this thread.

Edited February 7, 2015 by Mattasmack

[K^2]

But, if you've already determined the velocity field by other means (e.g. a wind tunnel), you can invoke the Bernoulli principle to explain the regions of high and low pressure that add up to the lift force. (And that works! Though you could also use the pressure gradient normal to curved streamlines and avoid talking about Bernoulli at all.)

Even if you know the velocity field, Bernoulli only gives you correct lift at low mach numbers. The reason is that you have to take pressure differential outside of boundary layer, and at high mach numbers, pressure gradient across boundary layer is very high. So pressure in the region where Bernoulli applies doesn't agree with pressure on the wing's surface.

If you have velocity field, just use Kutta-Joukowski. That's what it's for.

In the context of ideal flow, the way I usually see it argued is that viscosity is what explains / enforces the Kutta condition, which can't really be proved or explained purely within the ideal flow model.

I don't think there is a way to prove that viscous flow gives rise to Kutta condition, but it is possible to show that inviscid flow is laminar, and that it results in no separation layer. So yeah. No viscosity, no Kutta condition, no lift.

[Bryce Ring]

Anyone know about this.

I want to play with it

[K^2]

CUDA is awesome. And with modern cards, you don't even need a TESLA to handle fluid simulations. You can run something like this on most modern nVidia GPUs.

[Iskierka]

I have been thinking these last few days, How would some one go about describing all the motions and forces involved on and around an airfoil and the air that is affected as a result of its motion through the air, without using one key concept, that key concept is Pull, or Suck, or any other word that suggests attraction (Particularly between the wing and the air)

Maybe I should start a thread,

Does Aerodynamics Suck?

or

do wings suck ?

Or to address the ultimate question., What sucks?

Nothing sucks, or pulls, on air in wing aerodynamics. Air attempts to follow a surface that moves away from or towards it - this isn't due to some magical pulling force, this is simply because there's empty space, or an object in the way. When the wing appears, air cannot occupy that space any longer, and the particles bounce off the wing, leaving the area. Those particles then bounce off other particles, pushing a larger volume of air away, then back off the wing once again, rinse, repeat. The greater number of particle collisions here as the air is forced away results in the higher pressure gradient of the leading edge and the lower surface.

Conversely, when the upper surface moves away from the air and leaves space, there's nothing pushing the nearest air particles up any more - those then bounce off the particles above, and as there's no resistance below, move to fill the gap. They still reach and bounce off the surface below, but in far smaller quantities than usual, as the air cannot immediately fill the space, and so much fewer particle collisions occur as fewer particles are around, resulting in a much reduced pressure. The relative pressures then set up the lift force.

There is no "pulling" or any similar effect - there is simply air expanding into gaps and being forced out of others, which is how it always tries to behave. Add gas to a vacuum flask, and it distributes evenly within. Push a wing through air, and air tries to distribute itself evenly around the moving body, which results in motion in the air, which results in net useful lift force.

[Bryce Ring]

Nothing sucks, or pulls, on air in wing aerodynamics. Air attempts to follow a surface that moves away from or towards it - this isn't due to some magical pulling force, this is simply because there's empty space, or an object in the way. When the wing appears, air cannot occupy that space any longer, and the particles bounce off the wing, leaving the area. Those particles then bounce off other particles, pushing a larger volume of air away, then back off the wing once again, rinse, repeat. The greater number of particle collisions here as the air is forced away results in the higher pressure gradient of the leading edge and the lower surface.

Conversely, when the upper surface moves away from the air and leaves space, there's nothing pushing the nearest air particles up any more - those then bounce off the particles above, and as there's no resistance below, move to fill the gap. They still reach and bounce off the surface below, but in far smaller quantities than usual, as the air cannot immediately fill the space, and so much fewer particle collisions occur as fewer particles are around, resulting in a much reduced pressure. The relative pressures then set up the lift force.

There is no "pulling" or any similar effect - there is simply air expanding into gaps and being forced out of others, which is how it always tries to behave. Add gas to a vacuum flask, and it distributes evenly within. Push a wing through air, and air tries to distribute itself evenly around the moving body, which results in motion in the air, which results in net useful lift force.

PEace love n Equilibrium Bro.

[Mattasmack]

Even if you know the velocity field, Bernoulli only gives you correct lift at low mach numbers. The reason is that you have to take pressure differential outside of boundary layer, and at high mach numbers, pressure gradient across boundary layer is very high. So pressure in the region where Bernoulli applies doesn't agree with pressure on the wing's surface.

...

Ah, perhaps we were talking past each other a bit. My background is mostly in incompressible flow and the OP posted those diagrams of subsonic flow around airfoils, so, yes, I defaulted to talking about low Mach number, incompressible flow.

Could you recommend a reference that expands on / explains "...at high mach numbers, pressure gradient across boundary layer is very high"? That's outside of my experience, and outside most of my references which deal with incompressible flow, and I'd like to learn more.

[Bryce Ring]

Ah, perhaps we were talking past each other a bit. My background is mostly in incompressible flow and the OP posted those diagrams of subsonic flow around airfoils, so, yes, I defaulted to talking about low Mach number, incompressible flow.

Could you recommend a reference that expands on / explains "...at high mach numbers, pressure gradient across boundary layer is very high"? That's outside of my experience, and outside most of my references which deal with incompressible flow, and I'd like to learn more.

Hi Matt.

big side note here. Just wondering, been wondering this for a long long time actually.

would it be better to have a CPU GPU fan blow air over a heat sink radiator, or to have the fan turned around so that it allows air to accelerate over the heat sink radiator on its way to the fan where the fan then blows the air away.

PS no doubt a new heat sink radiator design which takes advantage of this would need to be used.

Your thoughts ?

Curiously yours

Bryce.

[K^2]

Could you recommend a reference that expands on / explains "...at high mach numbers, pressure gradient across boundary layer is very high"? That's outside of my experience, and outside most of my references which deal with incompressible flow, and I'd like to learn more.

This might be a cliche, but I still haven't found a better text on fluid dynamics that deals with general cases, rather than simplify it all down to incompressible/inviscid.

Landau Lifshitz: Fluid Mechanics - Not familiar with this particular translation/edition, though.