Well , the theory that the air on top was trying to keep up with the air underneath never made sense to me. What law of physics did that idea come from? But, as someone already said, that's the only change in the idea, correct? The air does flow more quickly over the top, it's just that the reason is no longer because they need to keep up with their buddies.

I have a feeling that it came from a conservation law which was used in the derivation of Bernoulli's principle. Someone more current on it can feel free to nitpick me, but IIRC, if you evaluate it at two points, i.e. all of the top surface and all of the bottom surface, you are implying that the mass flow through the top surface and the bottom surface is equal. You can't "just ignore this", because it's implicit in the derivation of the equation.

One major issue with Bernoulli, apart from the qualitative arguments discussed previously, is that it has no accommodation for acceleration. This means that fluid velocity is the only factor in the determination of inertial forces when using it, which is incorrect.

The plane/treadmill thread was literally hundreds of pages long at RCGroups.com...

I guess it depends which theory you subscribe to. I had believed the low pressure over, high pressure under, was the cause of lift. It's the theory that more or less states aeroplanes are sucked into the air. There seems to be a lot of problems with that theory when you consider aerofoil types, AoA and of inverted flight.

The key concept (that's news to me) is that lift is generated by turning air down and away from the aeroplane (every action has an equal opposite reaction). Hence you can hang all kinds of gubbins (engines/landing gear/stores) under a wing and aslong as you can turn the air downwards as it passes the trailing edge you're good to go.

http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html

Cheers

Not to screw with your mind any more, but the thing is that a pressure differential is basically the end result of turning the air. When using applying Bernoulli's principle, it would seem that this is due to a velocity difference. When applying Newton 2nd/N-S eqns, it's due to differences in velocity, acceleration other pressure fields and anything else*. Just because in Newton's 2nd you have a force F term doesn't mean that you go from having an incorrect pressure to a mystically correct force, per sé - this force manifests itself in a pressure as well, so in both cases, as in reality, lift is generated by a difference in pressure. The key is in what generates it, which is where it gets pedantic.

The error isn't that "one uses pressure differences and one turns the air" - it's more like "one only uses velocity differences, whereas the correct one accounts for turning/accelerating the air.". The end result in *both* cases is that you get a pressure differential - lift. Note also that pressure is force divided by surface area, so you can relate Newton's 2nd to surface pressure changes.


*(the N-S equations are quite general enough for additional things, like Coriolis, magnetic field coupling, and stuff like that to be "bolted on")

"This nacent revisionism will void all previous theories of flight (however anal it may be), whilst Bournelli turns over his grave etc'

While I realize that you were joking, I also realize that it is easy to forget that his theories had nothing to do with flight, although they will be forever connected with it. He was working with water pressure.

OK, that's all ... well, confusing.

But will my plane be able to fly tomorrow ? I plan on flying into the Sun n" Fun fly-in.

That depends in which theory you believe:\

- if you think Bernouilli was right, it will fly
- if you think NASA is right, well... check your insurance papers.

Update, not sure why, but the plane still flew. So did a lot of others. Landing pattern a bit crowded.

So I guess most airplanes are still flying even if they don't know why.

It may have some relationship to magic. I've noticed that none of the aircraft can takeoff and fly until some guy in the tower performs some ritual and says the magic words. Then you can fly.

'tis indeed the truth. You must never, ever cast aspersions upon that person in the tower, as they hold much power, over life and death, and can really ruin your day.
You might also want to say a few words to ensure that the rain gods don't... rain on your parade...

I'll get my coat.

Where is this mysterious tower you write of?

In our magestic realm we have rumors of such a thing, but we have fenced off such dangerous places with the onerous requirement of The Transponder and Wireless Speech so as not to be a burden to honest flying men.

One more slap at Bernoulli - if planes were being sucked up rather than pushed away, ground effect wouldn't matter. "Pressure differential" would pull the aircraft up against the ground regardless of what was underneath.

Also, when flying through smoke or clouds, it wouldnt' be pushed downwards behind the aircraft if suction was at play. Smoke would always be higher than the aircraft after it passed as it was sucked up with the plane.

I believe that ground effects is responsible for lift because the wingtip vortices are interrupted and thus don't create drag. It is drag that is the main thing in ground effects. Less drag means better flight performance.

Aeroplane wings *are* sucked up. They are *also* pushed up from underneath. So, basically there is a net force on the wing pushing AND pulling it up. This image gives a rough idea of the pressure distribution along the surface of a wing at some positive AoA, and the resulting direction which the wing is going. Underneath the wing, it has positive gauge pressure. Above, it has a much higher degree of *negative* gauge pressure. Yup, wings suck more than they blow.

Ahh, but if the wing was sucked, what about downstream vortices in clouds? If something is sucking (and pushing) the wing *up*, then Newton's 2nd says that there must be an equal and opposite force *down*; accelerating the air down at the back of the wing, the downwash, is the result of that opposite reaction (An even greater reaction occurs at the front, - *upwash* - which is why most pressure distribution images show a big peak at the front of the wing.). What you see in pressure distribution is mirrored, not copied, by the surrounding air.

Ironically, ground effect is something that you can, to some degree, be predicted using Bernoulli's principles if you're just looking at lift, and not drag (although not by comparing the top and the bottom of the wing's surfaces). Basically, being in ground effect bounds the bottom surface of the wing, so if you look at it from the side, it's like a pipe that shrinks in cross-section as you go along, especially at higher pitch angles. Based on that, you can that the smaller downstream end of the pipe will be a bit smaller, so you get higher velocity, and higher pressure, which is *part* of your cushion effect.
Interruption of the airflow by the runway around the wing is what reduces the drag, but I don't want to get too much into that. Also, don't get me started on tip fences...


Just further food for thought - Car diffusers. Think of a simple wedge-diffuser like at the back of a 'vette C6R. If you can use Bernoulli to explain lift, explain why diffusers create downforce at a diffuser. Air entering the diffuser is fast, whereas it slows down across the diffuser (because the cross-sectional area is increasing) and leaves the diffuser *slower* because the exit is larger. Bernoulli says this will actually *increase* pressure, pushing the back of the car off the ground... but we know it doesn't...

Pardon my sins for the tl:dr-ness of this.

I'm more confused than ever.

Looking at that image, I presume the lines are vector quantities? NASA's lift modeling applet (http://www.grc.nasa.gov/WWW/k-12/airplane/right2.html) shows that while the velocity difference of the air passing over and under the aerofoil is huge (10 degree AoA/under=60mph/over=120mph) the pressure difference is minimal (under=14.7 psi/over=14.6 psi). If you expanded those figures to an entire aeroplane, wouldn't it mean that just to lift the weight of the surface area of the aeroplane you'd need a surface area that weighs less than .1 psi? And that's before you've worried about gravity.

I get a slightly bigger pressure differential with a classically shaped aerofoil but it still appears marginal when compared to the huge difference in velocity.

http://www.grc.nasa.gov/WWW/k-12/airplane/foil2.html

To the simple brain of a layman like me, flow turning is appealing. It 'seems' like thrust vectoring. Although of course with flow turning you're not vectoring thrust, you're vectoring the air as you come into contact with it.

Cheers

Yes, but they are quite useless for AD's purposes (school teaching, if I understand correctly) as pupils will be hopelessly overburdened by the advanced maths required to understand them. They're also completely inappropriate to provide hands-on examples, as not even Grigori Perelman can solve them analytically - you'd further have to teach sophisticated numerical integration approaches. It's just not going to happen!



Nope, Bernoulli can accommodate ground effect perfectly fine. The proximity of the ground changes the air velocity distribution on the bottom surface and hence, according to Bernoulli's equation, the static pressure distribution there. This will change lift.

The problem is that Bernoulli's principle is NOT an end-to-end explanation for the creation of lift. It requires you to know, from some other consideration, the distribution of flow velocity on the airfoil - Bernoulli does NOT explain why air goes faster on top and slower on the bottom. This is where many attempts to explain lift based on his principle go awry, they either sweep this gap in their chain of argument under the rug or fudge a crude and inaccurate explanation such as "equal transit time".

To understand how the difference in flow velocity between top and bottom comes about you'd have to study the concept of circulation and the Kutta-Joukowsky theorem ("Joukowsky", as in Zhukovsky, lent his name to Russia's world-famous flight test centre!). Both are pretty heavy stuff to be taught at school, so one can somewhat understand the oversimplifications sometimes perpetrated to get around them, but it is always bad policy to make up non-scientific band-aids like "equal transit time".

Don't for a moment believe that the Newtonian approach is necessarily more elegant and intuitive either. Like Bernoulli, it cannot by itself explain HOW an airfoil turns the flow, so you need to know the nature of the change in momentum (air mass boundaries, flow vectors in and out) from some other source.

Bernoulli: A simplified expression for conservation of energy. Calculates correct lift for a given velocity distribution (which you need to have obtained elsewhere).

Newton: Based on conservation of momentum. Calculates correct lift for a given change in flow momentum (which you need to have obtained elsewhere).



Bernoulli's principle makes no predication one way or the other about what happens to the direction of the air after it leaves the airfoil trailing edge - this is a process which is outside its scope, so you cannot deduce whether it is right or wrong on that basis. OTOH, Newton does not explain this:

http://upload.wikimedia.org/wikipedia/commons/5/5a/Cloud_over_A340_wing.JPG

But it's ok - it makes no attempt to do so in the first place and remains valid regardless. There's quite simply more than one way to skin this cat, both approaches are based on sound physical principles (conservation of energy or momentum, respectively) and will return accurate results if applied correctly.

In wind tunnels which do not mount the model on a balance to measure forces and moments directly, lift (and lift coefficient) is calculated from static pressure taps all around the airfoil - the pressure difference is VERY real indeed!



Simplistic. The diffuser is supposed to enable a smooth transition for the air flowing below the car from fast below the floor (up-stream of the diffuser) to slow, matching the ambient conditions behind the car (downstream of the diffuser). Without a diffuser, flow would separate and create "blockage", slowing the air up-stream and reducing downforce according to Bernoulli. It is rather analogous to the trailing edge area of a wing (where the air is also decelerating).

For once, Wikipedia has it entirely correct:

Trident:
Okay, my gut feeling is that as Bernoulli's principles are based on laminar flow, it wouldn't predict the blockage caused by uneven flow transitions without a-priori existence of them, so if you just apply it to a diffuserless back end, it won't see separation nor blockage, because as you mentioned earlier, it makes no attempt to do so - this is outside of the scope of the equation. I would expect the results of this analysis to be quite different from experiment (overprediction of reality).

Conversely, my gut feeling is that adding a diffuser would reduce the suction given by Bernoulli, but this would be closer to an experimental result, as the flow is "more laminar".

I'm not a vehicle aerodynamicist, so point me in the right direction if I'm falling really far off base. The thing I'm trying to point out here is that straight application of the equation would not predict this stuff of its own accord - knowledge of flow blockage, separation, and other correction factors would have to be applied to bring it into line in what actually happens.

AD:
Don't try and pull numbers off of that. What you *can* do is understand more general ideas about it - gauge pressure on the bottom is higher than atmospheric; gauge pressure on the top is lower than atmospheric. The difference between gauge and atmospheric pressures is, on average much larger on the top surface than the bottom (it sucks more than it pushes).

Also, the biggest changes appear at the leading edge of the aerofoil - velocities are much higher than on the TE, as is the pressure differential. Another thing is that air in front is being turned upwards, and the air behind is turning back to the flat - so, the aerofoil doesn't just affect what is immediately above and below it.

Yep, "vectoring the air" isn't a bad way of thinking about it. The air nearest the wing gets vectored the most; air a metre above the wing less so, and 10m above the wing even less.

Bernoulli's principle does indeed not handle separation (neither does the proposed simplified form of Newton's law though), but again - the velocity distribution (including possible regions of separation) needs to come from elsewhere anyway. Only once you've established that in some other way does Bernoulli come into play and even with a diffuserless back end you should still get a pretty decent downforce estimate out of it. If you have an accurate prediction of the velocity distribution up-stream of the back end separation to work from the error should be small, since the contribution from this limited area is minor compared to the rest of the underbody. Think of the diffuser or back end as a device which alters the velocity distribution up-stream but doesn't (locally) contribute much itself.



If there is no separation thanks to the diffuser, you can apply Bernoulli's principle along the entire length of car's floor, including the diffuser itself.



Again, the same is true for all other simplified methods - if you want your modelling approach to *predict* things like separation with no additional assumptions you'll need either a computer to numerically solve the full equations or a wind tunnel (preferably both).

As always, there is no free lunch - the more general and versatile you want your method to be the more complicated it gets.

I see where you're coming from now. For some reason, when you mentioned about having a prescribed velocity field defined elsewhere, I didn't quite catch onto what you were doing. In that case, then you're essentially using a known velocity field with the right hand of the Euler variation of the N-S equations.

But yes, both in methodology and equations, we've gone a long way away from the original intentions of this post, plus I agree, there isn't any free lunch, and we haven't even gone onto turbulence modelling. :o)

Gopher, your pressure distribution diagram is horrible... A better idea of the pressure field and it's influence on flight is given from decent aero-texts ~ while I haven't browsed the whole of the site linked this page of pressure distributions seems a reasonable schematic overview: Note that you have a suction over most of the wing perimeter, and a high pressure area near the front stagnation point. Tbh I'm not 100% convinced they have the lift forces summed entirely correctly... And of course at higher AOA the lower surface will have a higher pressure - possibly a positive pressure differential.

http://www.dynamicflight.com/aerodynamics/pres_patterns/

A very good overview of flight and aero for the non-mathematical is:

See How It Flies
Avoids most of the dafter things said about aerodynamics and flight, and from what I remember, I don't think you'd kill yourself with believing any of it with a dollop of common sense added in.

I agree it wasn't totally accurate - it was meant to be illustrative - specifically that you get a crapload more force at the LE and less so at the TE, and that in general, the lower surface pushes less than the upper surface sucks. And yes, I know, the force "vectors" weren't accurate in direction either - not surface normal.
If you want *accurate*, I could whip up a simple pressure field of a 2D NACA 0012 at say 5 degrees in a fluid solver, but then depending on where your bar is, that might not be accurate enough either (plus everyone is bored of those colourful diagrams these days...).

The hardest part here is striking a good balance between simplistic and correct explanations, which isn't helped by the fact that the mathematics of many of the models are actually chips off the same block.