Understanding How Airfoil Shape Affects Airflow and Lift in Plane Flight

[bobsmith76]

I've watched a lot of youtube videos on how planes fly and they all gloss over one detail that I can't understand. They say that the foil is shaped such that the air on top must travel faster than the air on the bottom. By Bernouille's equation, this creates higher pressure on the bottom than on the top since if

P₁ + v₁² = P₂ + v₂²

then if P decreases on one side, then it must be compensated by higher velocity on the other side of the equation. I get that part. But what I don't understand is why the foil causes the air on top to go faster. I have an idea, but I want to be sure if it's right. It's the same reason why water flows faster in a narrow pipe than in a wide pipe. It relates to the equation of continuity:

A₁v₁ = A₂v₂

The area above the wing becomes less so this must be compensated for by a higher velocity. I realize it's a bit hard to imagine how a foil could actually decrease the amount of space, since the amount of space above the wing is so large, effectively all of the Earth's atmosphere, but that is the only explanation I can think of.

 

[rcgldr]

They say that the foil is shaped such that the air on top must travel faster than the air on the bottom.

The foil doesn't have to be "shaped", a flat board at some angle of attack will also produce lift, with air on top moving faster than air on bottom. A "shaped" airfoil will be more efficient, producing the same amount of lift with less drag than a flat board. Some small balsa gliders use flat air foils.

Bernoulli ... equation of continuity:

A₁v₁ = A₂v₂

... it's a bit hard to imagine how a foil could actually decrease the amount of space.

That's sort of an indirect effect. If the air didn't follow the downward sloping surface of a wing, a void (vacuum) would be created, so the air tends to follow the upper surface of a wing, even if the wing is curved and/or angled "downwards", as long as the curvature and/or angle isn't too large (otherwise, what would be a void is filled in with turbulent flow mostly consisting of large vortices (like horizontal tornados)).

The air has momentum, so it can't immediate change direction, so pressure is reduced as air accelerates in order to follow the upper surface of a wing. This reduction in pressure will correspond to an increase in velocity and a narrowing of "streamlines", and the 'streamline" follow the equation of continuity you mentioned. The narrowing of "streamlines", is towards the wing's upper surface, so the "void effect" extends past the immediate vicinity of the wing, and air is accelerated downwards and pressure is reduced to fill in what would otherwise be a void.

The air below a wing is normally deflected downwards to due a effective angle of attack of a wing.

link to a website with a simplified description of how wings work:

http://www.avweb.com/news/airman/183261-1.html

 

[bobsmith76]

thank you for this. I'm too tired to look this over but when i finish sleeping i'll take a look at it and if i have any questions i'll repost.

 

[Vanadium 50]

This is a difficult way to think about it. A better way is to realize that what a wing does is deflect air down, and thus receive a force up.

This is true even in the Bernoulli limit (which is not a very good model for a physical wing) where a difference in pressure between the top and bottom of the wing indicates more air molecules on the bottom, which means in turn they must have experienced a force down.

 

[Alpha Floor]

There are a lot of incorrect theories around the web on how planes fly, the most common and most "incorrect" one is the "pair of friends fluid particles". It's the one that says that two fluid particles separating from each other at the leading edge, must get magically together again at the trailing edge and since the distance around the upper part of the wing is supposed to be longer than the lower part (which is false, in general) then the upper flow is faster etc etc... , this is completely false.

The lift that an airfoil generates is proportional to the circulation that it induces in the air around it (Kutta-Yukovski Theorem). Circulation is the line integral of velocity over a given path (any path that encloses the airfoil).

To explain why an airfoilf induces circulation is more complicated. It involves the Bjerknes-Kelvin theorem on conservation of circulation, it involves the air being viscid (if it wasn't planes would never fly) etc...

 

[and7barton]

If you could inject or force a layer of air over an aircraft wing at a high enough velocity, possibly through a set of rearward-facing slots just aft of the upper leading edge of the wings, then it should be possible for an aircraft to take off at zero ground speed, doing away with the requirement for long runways.
This would be the Coanda effect which can be utilised to generate lift in disc-shaped aircraft.

 

[bwood01]

http://www.infoocean.info/avatar1.jpg The foil doesn't have to be "shaped".

 

[Ken G]

The usual explanation is wrong for all the reasons mentioned. What's more, note that planes can fly upside down. You can use a tilted angle of attack to deflect air downward, just as you can use a flat board as a sail. But the curved shape increases efficiency, which means more lift per drag. Drag dissipates energy, which mostly shows up in turbulence in the air as the plane passes, but you can't eliminate turbulence because it is also important for generating lift. It turns out that having a very sharp edge at the back of the wing is quite important, because it keeps the air from wrapping around the wing before it separates. A sharp edge at the back of the wing forces separation at the back, which angles the air downward and creates lift, but it also produces turbulence and drag. So a lot of the engineering is to increase the ratio of lift to drag, but not to eliminate either drag or turbulence, as both are crucial.

 

[rcgldr]

It turns out that having a very sharp edge at the back of the wing is quite important, because it keeps the air from wrapping around the wing before it separates.

A sharp edge can reduce drag, but depending on the factors, wing loading, wing size, air foil, speed, angle of attack, ... , it's common to have some upwash at the trailing edge of a wing because the pressure is still lower above and higher below as the two streams rejoin. A blunt trailing edge will result in more drag, but such an airfoil can still work, as seen in this old photo of a pre-shuttle lifting body prototype (M2-F2), in this case a glider version (there was also a rocket powered version called M2-F3):

 

[Alpha Floor]

Generating lift is very easy, the difficult part is maximazing the lift/drag ratio (maximazing efficiency), that's where aerodynamics is important.

 

[Ken G]

A blunt trailing edge will result in more drag, but such an airfoil can still work, as seen in this old photo of a pre-shuttle lifting body prototype (M2-F2), in this case a glider version (there was also a rocket powered version called M2-F3):

Looks like a flying bar of soap! It must be very interesting to scan the parameter space in search of the ideal solution for given flight characteristics. I recall hearing that a "flying wing" design was once found to be an extremum in fuel efficiency, but it was later determined to be a minimum not a maximum! I don't know if that's true, it's often cited as motivation for understanding what a second derivative is.

 

[rcgldr]

Looks like a flying bar of soap!

Since it was a pre-shuttle prototype, the M2-F2 was designed to handle re-enry from orbit from space. The last version of the series, M2-F3, was able to achieve mach 1.6, so either a lot of rocket power, or it's not as draggy as it looks. The front top portion is flat, while the front bottom portion is shaped like 1/2 of an expanding cone. The tail end of the M2-F2 is tapered, with the taper starting sooner on the top and the trailing blunt edge is somewhat below the nose. There's a flap than can be deployed off the bottom of the tail end, my guess it that is for slower glide speed. I like the M2 series because the hump is on the bottom, dispelling common mis-conceptions about how wings generate lift. Also I think it looks cool and unusual.

Wiki articles include a history of all 3 versions:

http://en.wikipedia.org/wiki/NASA_M2-F1

http://en.wikipedia.org/wiki/Northrop_M2-F2

http://en.wikipedia.org/wiki/Northrop_M2-F3

Link to wiki image of the M3-F3 at the Smithsonian Institution:

http://en.wikipedia.org/wiki/File:M2F3museum.JPG

 

[bobsmith76]

very good website recommended by rcg, all my questions are answered.