# Wing surface area

1. Apr 1, 2014

### physical n00b

Hello,

I'm new here, but I have some questions which i'd like to ask.

I had this idea about corrugated wings to increase the wing surface area (thus increasing lift), but quickly realised that this would also increase the wings drag as it would have a larger cross section breaking through the air. I was wondering if you could use 'pores' on the wings surface to increase the surface area to the low air pressure beneath, but without increasing the wings induced drag?

I have been searching the internet for the answer but haven't really been satisfied with what I found. I'm sure someone somewhere has tried this out but I'm very curious to know if it could work or not.

Thanks guys

2. Apr 1, 2014

There are a couple things here:

1) The pressure is higher beneath the wing, or else the net force would point down, which would be a decidedly bad thing.

2) The force on any given point of the wing due to the pressure is going to be normal to the surface at that point. This means that unless the wing surface is perfectly normal to the upward (lifting) direction, then that pressure force is going to contribute slightly to lift and slightly to drag. By increasing the area just by putting corrugation or pores on the surface, you are going to be introducing no net gain because ultimately the pressure forces will always have a counteracting direction that you will have also reduced, all the while likely just adding to drag due to an increased cross-section or else increased surface area for viscous drag. To increase lift by increasing surface area, you just have to make bigger wings.

3) There are legitimate uses for corrugated-type structures on wings but it has to do with more complicated flow physics than just the pressure distribution over the wing. You can do a lot of fancy things with the boundary layer using structures like that.

3. Apr 1, 2014

4. Apr 1, 2014

### physical n00b

Thanks I noticed my mistake on the pressures (oops). I think I understand what you mean here with the no net gain.

I'm fairly new to engineering but flight really does fascinate me, I have been reading quite an outdated book on the mechanics of flight which was written in the 70's at some point (brilliant book) as I've had no internet access. Don't suppose you could recommend anything more up-to-date which isn't to advanced?

I have several more questions which have been bugging me, concerning the Venturi principle, although I am unsure weather or not i should start a new thread.

Thanks for the reply mate! :)

5. Apr 1, 2014

### Staff: Mentor

Not a stupid question at all. That's how we learn -- by asking reasonable questions & researching them.

I remembered something about small holes in wings being used to increase lift or something similar, and found a few things via Google:

2006 -- http://www.avionews.com/index.php?corpo=see_news_home.php&news_id=66965&pagina_chiamante=index.php

6. Apr 1, 2014

### physical n00b

Thanks man, the PF thread was great!

7. Apr 1, 2014

That PF thread you linked was bananas. There are a lot of people on there who just say random things they don't know. Some of it is correct and more of it has some correct conclusions with weird/ridiculous reasoning.

Anyway, as for a book, the one they use for a lot of introductory-level aerospace programs is https://www.amazon.com/gp/aw/d/0073380245. I don't know what your education level is but that's a pretty low-level book. It's a textbook so it's pretty pricey, though.

Last edited by a moderator: May 6, 2017
8. Apr 1, 2014

### physical n00b

Cheers mate its abit price though!

Which is the updated edition of the one I had been reading! :)

Just a quick question concerning the Bernoulli Principle if you don't mind. I know that the velocity of the air flow will increase over the wing of an aircraft, relative to the airflow beneath the wing, causing the pressure differences.

What I'm finding hard to grasp is that its the decrease in pressure which 'causes' the velocity to increase. Although from what I understand, its the increase in the air speed over the wing that actually causes the pressure difference in the first place.

I would have guessed that there would have to be an external force to accelerate the airflow over the wing to cause the low pressure above the wing in the first place??

Thanks guys

9. Apr 1, 2014

### Staff: Mentor

Oops, sorry. I didn't read through it -- thanks for checking it out!

10. Apr 1, 2014

### AlephZero

Correct. That's why planes have engines - to keep the wings moving through the air. (That may be more obvious if the "wings" rotate, as in a helicopter.)

People can get tied in knots trying to assign "causes" and "effects" to what is going on here. Bernouilli's principle is just Newton's laws of motion, applied to a fluid. It doesn't "explain" why the air flow pattern is what it is.

One way to "explain" it is that the shape of the wing causes the air to move downwards, and the change in momentum of the air causes an upwards force on the wing. The "details" of the pressure and velocity around the wing have to be consistent with that "global" behavior, or else Newtonian mechanics is wrong.

Beware of web sites that claim the air speed "must be" higher above the wing than below, because the top surface is "longer" (more curved) than the bottom surface. That argument is usually complete nonsense - and in any case, it doesn't explain how planes can fly upside down!

11. Apr 1, 2014

### SteamKing

Staff Emeritus
Flying, after all, is a dynamic activity. Planes just don't jump off the ground by themselves.

This diagram shows the basic forces acting on an aircraft in flight:

12. Apr 2, 2014

Heh, it's okay. Aerodynamics is one of those subjects that gets misunderstood quite a bit. I won't pretend to know everything, of course, but there are a number of things in there that are just silly. But, that is what you get on a web forum sometimes. There's no way around that. There are a few nice anecdotes in that discussion, though, even if the people didn't always properly understand what the physical mechanisms for them were.

A few times they mentioned applying suction to small holes. There are definitely some interesting uses for this, though not really for high lift. If you apply a small amount of suction to those holes near the leading edge, you can stabilize the boundary layer considerably and delay the transition to turbulence over the wing sometimes even nearly to the trailing edge depending on the wing design. That can reduce drag on the plane considerably. It doesn't really help you with lift, though. For high speed flows (roughly Mach 4 and higher), a micro-porous surface (no need for suction) can reduce drag and heating by absorbing the acoustic waves traveling through the boundary layer and, again, preventing the transition to turbulence. Still, it really doesn't help with lift.

There have also been studies on streamwise channels or corrugations. They can help prevent the spread of turbulent spots and delay transition. Similar but different are wing fences, which can help control spanwise flow along the wing and increase in low-speed situations but preventing stall. That's not quite the mechanism the OP was considering, though.

13. Apr 2, 2014

### physical n00b

yeah, my problem is understanding why the air moves faster over the top than the bottom. I understand its often better to just accept that this is simply 'how it is', but I would much rather nail down my understanding of this subject.

consider this as an example, a model aircraft is traveling inside a train carridge. The train carridge represents the net airflow and velocity and the model aircraft represents the aircraft. If the train carridge (airflow) is travelling slightly faster than the aircraft, how can the aircraft catch up with this airflow, and get enough air to flow at a high enough velocity (in the opposite direction to the way it was traveling initially) to generate lift?

it really seems like a chicken/egg problem to me.

thanks bonehead, i've learnt abit about wing fences. What I was getting at is if it were possible to increase surface area without causing more drag as a result, which doesn't seem to be the case. (universe doesn't give out free meals) haha :)

thanks

14. Apr 2, 2014

The reason the air moves faster is rather complicated. Basically, though, there is one important feature of an airfoil that enables this: the sharp trailing edge. Imagine you have a circle moving through the air. You will have a stagnation point at the front and back where the air slows to zero velocity and attaches to or leaves the surface respectively. Now, start squishing that circle into an ellipse and you will start to have two pointier regions. If the ellipse is still pointed so that its long axis is aligned with the flow, the stagnation points will still be on those tips.

So, now you have to think, if Newton's laws imply that air must be deflected downward in order for the plane to be pushed up, then how do we go about accomplishing that? The idea then is to turn the ellipse slightly so that it acts sort of like sticking your hand out the window and exposing a bit of the long side to the oncoming flow. We call this angle it makes the angle of attack. As it turns out, though, in an inviscid sense and also a viscous sense for large enough tip radius, even at angle of attack, the flow will just turn around the small tips and your stagnation points will still be at the front and the back and will not be deflected downward at all. This is where the sharp trailing edge comes into play. In an inviscid sense, to navigate a sharp trailing edge, the velocity would have to go to infinity, which is impossible (or near infinity, as nothing is perfectly sharp). Instead, viscosity ensures that at the sharp trailing edge, the flow simply leaves the surface there. Basically, if you take your ellipse and continue to flatten it a bit and then squish the trailing edge into a point, you are enforcing the location of that rear stagnation point. Now when you put that shape at an angle of attack, you are deflecting the air nearby downward.

So what does this have to do with the speeds and pressures on the surfaces? You can look at it a few ways. Either you can say that Newton's laws show that there should now be an upward force, meaning there must be a pressure differential, meaning there must be a speed differential. Otherwise, you can say that if you look at the actual equations that fully describe continuum fluid motion, the Navier-Stokes equations, they will predict a faster flow over the top as a result of that geometry. In fact, you don't even have to artificially set the trailing edge as the rear stagnation point, as the Navier-Stokes equations sort that out for you since they include viscosity. In practice, it is also very common to simplify that problem and treat the flow without viscosity and just mathematically set that trailing edge as the stagnation point, and then even much simpler equations can get a pretty close answer.

So then, the bottom line is that you can look at it one of two ways:
• The sharp trailing edge allows the airfoil to deflect the flow, and Newton's laws require that there is a pressure differential and therefore a velocity differential. This won't help you calculate the actual values of the pressures and velocities at every point, but it should be rather intuitive in helping you reason out why there must be a pressure and velocity difference.
• With a sharp trailing edge, the more complete equations of motion (and, of course, nature itself) show that the velocity must be moving much more quickly over the top of the airfoil, thereby signalling a pressure difference.
How you prefer to look at it depends on what helps convince you of what is going on and just how in-depth you are trying to get here.

15. Apr 2, 2014

### physical n00b

Thanks again bonehead, really appreciate the help. I've had a quick look over the Navierâ€“Stokes equations, it will take me a while to understand these (maybe forever) but they are exactly what I was looking for. :)

The stagnation makes sense to me, and that the downward deflection of air causes an equal and opposite reaction, what we call lift?

"With a sharp trailing edge, the more complete equations of motion (and, of course, nature itself) show that the velocity must be moving much more quickly over the top of the airfoil, thereby signalling a pressure difference."

but from my understanding for something to gain velocity it needs an accelerating force? (I may have missed something)
Is it correct to say that the airs density above the wing is less (due to the low pressure), which allows it to travel faster?

16. Apr 2, 2014

That depends entire on the speed of travel. Below about Mach 0.3, the air flow is effectively incompressible and the density is not going to change. Once you get faster than that, the density can and will change.

As for the accelerating force, that comes from the pressure gradient. The pressure on the surface of the wing is not constant and lift can be calculated from integrating the pressure field over the entire wing surface. The pressure gradient is a result of the movement of the wing through the air, and when a parcel of air moves over the wing from a region of high pressure toward one of lower pressure (favorable pressure gradient), it will accelerate. When it moves from a region of low pressure to high pressure (adverse pressure gradient), it will decelerate.

The problem with looking for one that explains the other (pressure and velocity) is that in the governing equations (and thus the physics), the two cannot be decoupled. If you change the pressure, it necessarily changes the velocity and vice versa, so you really can't, in general, separate the two and call one the cause and the other the effect.

17. Apr 3, 2014

### physical n00b

Thanks for your time, I'm afraid I am one of those people who is constantly looking for cause and effect haha.

Gonna have to knuckle down and read up on more theory.

Take care

18. Apr 3, 2014

### rcgldr

To produce lift, a wing moves through the air with an effective angle of attack that diverts the air flow (relative to the wing) downwards. This results in the air being accelerated downwards (lift) and a bit forwards (drag). On the lower surface air is usually deflected downwards (even flat bottom airfoils typically fly with some angle of attack). As a wing passes through a narrow (front to back) column of air, the air tends to follow the upper surface downwards, otherwise a void would be created, as long as the angle of attack isn't excessive (otherwise the air will form a vortice in order to fill in what would otherwise be a void). This results in downwards acceleration of air, and since the air has momentum, that acceleration co-exists with a pressure differential, with the pressure being lower than ambient above the wing surface. This lower than ambient pressure results in air being accelerated towards the low pressure zone above a wing from all directions, except that the air can't flow upwards through the wing.

Above the wing, the speed of the air increases when ever it accelerates from a higher pressure area to a lower pressure area, and absent external (to the air) forces, Bernoulli's equation approximates the relationship between speed and pressure (ignoring issues like viscosity and turbulence, and the fact that a wing performs some work on the air, changing the total energy).

Under the wing, there's usually a higher pressure area, so it tends to decelerate the air as it's pressure increases from ambient to the pressure under a wing.

The pressure above or below a wing isn't constant, it varies as the air flows from front to back along the wing, and ideally for low drag, the pressures above and below a wing at the trailing edge would be the same, but in the real world, the pressure above is usually lower than the pressure below at the trailing edge, resulting in some trailing edge upwash (and trailing edge vortices) during the transition where the two air streams merge at the trailing edge.

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

http://home.comcast.net/~clipper-108/lift.htm [Broken]

Last edited by a moderator: May 6, 2017
19. Aug 21, 2014

### FactChecker

A plane flying upside down has to tilt the nose up enough to tilt the wing up (toward the floor of the plane) The air going over the top (normally the bottom) moves faster. It is still the same principle.

http://commons.wikimedia.org/wiki/File:Flying_upside_down.jpg

20. Aug 21, 2014

### FactChecker

A shortcut explanation is that Bernoulie's equation relates velocity to pressure. The lower pressure and higher velocity over the top of a curved wing with a positive angle of attack has been extensively studied and verified. Most people conceptually think that the shape and angle of attack of the wing forces a higher velocity over the top. That then causes the decreased pressure on the top.

A detailed, point by point, understanding of what is going on is possible with the Navier-Stokes equations. It explains the behavior of a tiny part of air in an understandable way. Then computational fluid dynamics (CFD) can be applied to the thousands (millions?) of Navier-Stokes equations for the entire flow around the wing to see how it all fits together. The CFD calculations are difficult, but the concept is understandable. Modern computer power allows fairly good CFD results.

EDIT: I forgot to mention that a very idealized airflow (incompressible, irrotational) around a two dimensional wing section can be solved with complex analysis and conformal mappings. The equations give the velocities and pressures of the airflow. The ideal solution can be fairly close to reality at low speeds. This can be done with first-year complex analysis. So it is possible to get a feel for the velocities around a wing without CFD or experimental measurements.

Last edited: Aug 21, 2014
21. Aug 21, 2014

### AlephZero

I wasn't commenting about the fact that the velocity over the upper surface is higher, but the (incorrect) explanation.

The warning was about people who write websites explaining flight, but whose ideas about what shape wings ought to be hasn't changed since 1920.

22. Aug 23, 2014

### FactChecker

I should have described this differently. Navier-Stokes explains the behavior of a tiny part of air based on the behavior of the neighboring tiny air parts. So it is like piecing together a giant jigsaw puzzle. In fact, it is worse. The behavior of those neighbor parts are not completely known because they depends on the behavior of the original piece of air. So the calculations have to keep going around and around trying to get closer and closer to a solution that all fits together from beginning to end. That is why so much computer power is needed.

But CFD is really the gold standard as far as really understanding air flow around a wing. It can deal with turbulance, compressability, etc. CDF results still need to be experimentally verified for any particular airplane.

23. Aug 23, 2014

CFD actually has an extraordinarily difficult time dealing with turbulence. This is why so much time and effort is devoted to the field of turbulence modeling. Turbulence is both time- and space-dependent and feature eddies ranging from the tiny Kolmogorov length scale all the way up to the integral length scale, all of which must be resolved by the computational grid in order to solve for a turbulent flow. Further, the only way to capture all of this is with a direct numerical simulation (DNS), where the full Navier-Stokes equations are solve with no simplifying assumptions.

As it turns out, the number of computations required to compute a DNS grows with Re3. For any meaningful Reynolds number comparable to flight or a car or many other common aerodynamic situations, we have no hope of carrying out a DNS. For that reason, CFD usually relies on turbulence models whereby the Navier-Stokes equations are averaged or otherwise simplified, using empirical correlations to try to predict the turbulence statistics for some or most of the turbulent phenomenon rather than directly solving for them to save time with varying degrees of success.

24. Aug 23, 2014

### FactChecker

Thanks for the clarification. I see that I had a naively underestimated the turbulence problem.

25. Aug 23, 2014

### rcgldr

Note that a thin trailing edge is more efficient, but not required to produce lift. In the case of the M2-F2 and the M2-F3, the trailing edge was a blunt edge, where the rocket nozzels were placed in the case of the M2-F3 (M2-F2 was glider only):