# Forces on an airfoil

I'm building an airplane (Super Baby Great Lakes) and I'm wondering something about airfoils. In particular (this plane is fabric covered), I'm wondering about the lifting forces on the main wings. I've read something about it being very important that the fabric adheres very well on the top of the wing to the ribs so that the fabric doesn't separate when lift is generated.

My question is this: how much lift is generated by direct pressure of the slipstream against the bottom of the wing because of high angle of attack vs. how much "sucking" force is generated due to low pressure on the top of the wing? Is the vacuum on the top of the wing simply a lack of atmospheric pressure, or is it genuinely a sucking force, like a powerful vacuum cleaner which could actually tear the sheet out of a notebook, for example?

Thanks, Jay

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@Pygmalion it's valid. Why not? Can you find an exact duplicate? –  Manishearth Apr 24 '12 at 15:15
Only in last two days we've discussed this stuff twice: physics.stackexchange.com/questions/24201, physics.stackexchange.com/questions/24221, and since I am here for two weeks at least another two times. Plus this is such a complex question nobody really knows the exact question. Even aeronautic engineers don't. That's why they are still building wind tunnels and do experiments. And who cares after all, I don't have the privilege to vote for closing anyway. –  Pygmalion Apr 24 '12 at 15:43
Even if I did have privilege to vote for closing I might not vote that way. After all there are even much more close deserving questions that remained open, so what? I just feel fed up of flight questions, and if expressing that feeling means being asshole, I apologize. –  Pygmalion Apr 24 '12 at 15:58
@Pygmalion "nobody really knows the exact answer" Well, we know that air is strongly deflected downward at the trailing edge and that this is due in part to the positive angle of attack and in part to differences in how the boundary layers separate from the top and bottom sides. Of course, boundary layer separation is one of those topics in general fluid flows that is only partially understood and particularly amenable to simulation either. Sigh. –  dmckee Apr 24 '12 at 17:13
@tmac: Complaining about duplicates (or reasonably possible duplicates) is encouraged no matter what tags they bear. –  dmckee Apr 25 '12 at 1:35

I've never seen actual figures but, in general, articles I've seen about flight state that "most" lift is generated from the angle of attack and relatively little from the Bernoulli effect. I suspect the exact figures are rather variable and probably depend on whether the plane is climbing, descending, banking, etc and will also vary from plane to plane. Maybe this is why exact figures seem not to be quoted.

The pressure difference between the top and bottom of the wing is quite real, though note that on the top of the wing it's not a vacuum as the pressure doesn't decrease that much. The lowered pressure above the wing will indeed tend to pull the skin off the wing, or more precisely the air within the wing that is at normal atmospheric pressure will try to push the skin off. Once again I can't give you exact figures - I must admit I thought ballpark figures would be easy to calculate, but Google has failed me.

Incidentally, there's a good NASA article on this subject at http://www.grc.nasa.gov/WWW/k-12/airplane/wrong1.html and it even includes a Java applet for you to play with the details of the wing. A longer slightly more staid article is at http://www.free-online-private-pilot-ground-school.com/aerodynamics.html

Later:

If an approximate answer would be OK then you could could use Bernoulli's equation as described in http://en.wikipedia.org/wiki/Bernoulli%27s_equation#Incompressible_flow_equation. Although this really only applies to incompressible fluids, and air is obviously compressible, the article suggests it would be a reasonable approximation for low speeds.

Rewriting the equation to make it more useful for our purposes gives:

$$P = \rho A - \rho \frac {v^2}{2} - gh$$

where $A$ is some constant and $h$ is the height. We don't know the constant, but let $P_{bot}$ be the pressure below the wing and $P_{top}$ be the pressure above the wing then we can take the difference between them i.e. the pressure drop between the bottom and top of the wing. If we assume the height is constant i.e. we can ignore the thickness of the wing we get:

$$\Delta P = P_{bot} - P_{top} = 0.5 \rho (v_{top}^2 - v_{bot}^2)$$

I don't know what speed you plane flies at, but let's guess at 30 m/s and let's guess that there's a 10 m/s difference between the air speed at the top and bottom of the wing, so that's $v_{bot} = 30$ and $v_{top}$ = 40. Google gives the density of air at ground level as 1.225 kg/m3.

$$\Delta P = 0.5 \times 1.225 \times (40^2 - 30^2) = 429 Pa$$

429 Pa is 4.29 grams per square cm or 0.06 pounds per square inch, so it's completely insignificant.

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I still find myself wanting something concrete regarding with what force nature will be trying to tear away the covering off the tops of my wings. Having said that, John, your text and the links you provided did help me gain a bit better understanding of what's going on. Thanks. –  birdus Apr 24 '12 at 16:50
Well, OK, I've updated my answer and tried to do a calculation, but frankly until someone actually measures the pressure difference I'm not sure I believe a word of it! –  John Rennie Apr 24 '12 at 17:26
More good food for thought. Thanks, John. –  birdus Apr 24 '12 at 20:30
You can't really distinguish between angle of attack and Bernoulli. The angle of attack causes air to be deflected into a downwash, and that can't happen without a pressure differential, and Bernoulli is just a way of explaining how that pressure differential arises. If the angle of attack is high enough, the flow detaches from the top of the wing & Bernoulli no longer works, so much less downdraft, and that's known as stalling the wing. The critical angle of attack is typically around 19 degrees. –  Mike Dunlavey Apr 26 '12 at 16:52
There's a nice video here showing with bits of yarn what happens when a wing stalls. The pilot reduces power and pulls the nose up to maintain altitude. When the critical angle of attack is reached, the yarn no longer lies flat against the top of the wing. –  Mike Dunlavey Apr 26 '12 at 17:13

John Rennie made a pretty good estimate, 0.06 pounds per square inch is 8.6 pounds per square foot. The Great Lakes Super Baby has a wing loading of 9.6 pounds per square foot at max gross weight. In the worst case, where all the lift is provided by sucking on the upper surface, the sucking force would therefore be 9.6 lb/sq ft in level flight. during a 3G maneuver it would be 29 lb / sq ft. So that is an upper bound. Your typical vacuum cleaner pulls about 20 kPa suction, or about 400 pounds per sq foot.

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Please don't say "sucking" in this context. It's just painfully wrong. –  dmckee Apr 25 '12 at 1:35
You've got funny issues with the word sucking. –  user1631 Apr 25 '12 at 16:53