Two questions though, what's the benifit of the under camber? I understand that the standard teaching about different leangths of travel on different side of a wing isn't entirely correct, but wouldn't an under camber make the top and bottom almost the same length and thus negate any effect of the pressure differential? If so, what's holding the glider up(angle of attack is the only other thing I can think of...)? Sorry if that's misinformed or confusing...
<SNIP question already answered>
I think I have some time to try to answer this one. Real aero engineers feel free to step in and correct as needed. I switched to Metallurgy as a Junior in college. More inspiring prof. Of course I came back to it in my masters where turbine engine design was a minor. For lift and airfoils same stuff, less of the stability stuff that drove me nuts at the time. Anyway...
Warning, high level stuff coming.
I’ll start with a summary. Gliders tend to spend most of their time at a single operating condition. Gliding near stall. Turns out a highly undercambered wing has the best lift-drag ratio in this condition so it gets used when you can get away with it in the other conditions (launch).
Unfortunately that standard teaching is worse than not entirely correct. It's mostly flat wrong. If you want to know the right mathematical way to describe things, look up circulation theory, Richard von Mises, Ludwig Prandtl and Theodore von Karman. They really established the rigorous theory and math of flow around a wing. Bernoulli’s theories were important to that work, but not as commonly understood.
The following is an attempt to describe that non-mathematically.
Let’s start at a high level of detail where you don't have to worry about the airfoil and how it works, but look at the wing as a system. That way we can look at inputs and outputs only for a moment. The wing becomes a black box. We'll assume straight and level flight. Hold the wing stationary and consider the air to be flowing past the wing.
Start with an empty box.
- Air goes in and out with the same velocity, let’s make it horizontal for now. Note, VELOCITY, not speed. This is vector stuff, direction is important.
- Since there is no change in the air flow in and out, there is no force on the system
Now, we want to get some lift out of this system.
- Insert wing. Details unimportant at the moment, but to get lift (force upwards on the wing) you have to push DOWN on the air.
- This changes the air’s velocity. Now the air goes in horizontal, and comes out at the same mass flow rate, but with a DOWNWARDS pointing velocity vector.
- To maintain the mass flow balance (what goes in has to come out, conservation of matter and all), you have to slow the air in the horizontal direction too so you get drag (force forwards on the air, backwards on the wing, vectors).
o This is even IF you could create a theoretically dragless wing shape. Which you can't.
o But you can imagine it. Which is why aeronautical types tend to break drag up into induced and form (sure of the first, not sure of the second term, might be parasitic, hmm… might be three pieces, one from things like surface roughness, hmm… Oh well, later), one from the basic creation of lift (induced) and one from the form.
OK, that’s the basic lift model.
- It shows why speed increases lift (more mass flow, F=mA after all)
- Angle of attack increases lift (more A or change of wind velocity vector) and wing area (more mass intersected).
- It also shows why more lift means more drag. Irregardless of airfoil shape.
Now, let’s look a little closer and look at that airfoil. Because to fill out that lift equation, you need a constant which IS influenced by the shape of the wing.
- Its ONLY purpose is to turn that airflow with as little FORM drag as possible adding to the basic induced drag from lift.
- But how does it work?
o Turns out, its not that stuff about Bernoulli and speed differences. The Bernoulli stuff works great on air flowing through a tube of varying cross section, but not so much in free stream. Otherwise a flat plate wing wouldn’t work, and they perfectly good wings (in some conditions).
o Coanda had a MUCH better model. A fluid flow tends to follow nearby surfaces.
o Assuming non separated flow (more on that in a moment, but it’s almost always bad stuff) the amount of air deflection tends to be the average of the top and bottom of the TRAILING edge of an airfoil. That flow following the surfaces
o That’s why a flat plate wing works. For small angles of attack the flow comes off the trialing edge at the angle of attack and lift vs form drag is just fine.
- But you are going to say, “Mr Anderson, what about the REST of the wing. Lots of different shapes in the real world, can’t be totally unimportant.” Of course it isn’t. That’s where we get back to form drag and flow separation.
o Lets go back to the flat plate.
It is fine at low angles of attack, air stays attached, is deflected with little turbulence. But only creates a little change in flow.
Unfortunately, it goes to garbage at high because the flow separates from the top surface,
This messes up Coanda flow something fierce, the air flow tumbles in random directions.
Causing LOTS of drag and lift no longer follows angle of attack directly.
If it gets TOO bad, lift goes away entirely and you’ve stalled.
o So, what do we do.
I’ll start with a simple curve shape. Think of a metal venetion blind slat. Kind of like that undercambered wing, but thinner.
Set that slat so the leading edge is parallel to the incoming flow.
For reasonable conditions, the flow will nicely follow the top and bottom surfaces with little drag. But lots of flow turning, lots of lift. You still get the induced drag of course.
For that specific condition, it turns out you get about the lowest form drag.
For minor variations, it works OK, but then, like the flat plate, drops of sharply for too large variations of the conditions.
In fact, the blades in a turbine where the operating conditions tend to be fairly constant are shaped mostly on that model with just enough thickening to meet structural requirements.
- Again, you’ll say “Mr Anderson, that’s not what modern wings are like. They tend to have flat or convex bottoms. Why?”
o Well, that gets back to operating conditions. Remember I mentioned the above shapes operate under only limited conditions,
o Airplane wings on the other hand have to work under a much larger range of conditions and the shapes you are familiar with give up ideal lift to drag at one condition to gain OK lift to drag under a wide range of conditions.
o And let’s not even talk about speeds near sound. Air starts doing really weird stuff there and that affects wing shape again.
o And finally, I’ll point out slats and flaps. Modern jets when landing extend slats and flaps. This does two things. One it increases area. Second, if you looked at the wing in cross section you would see that undercamber airfoil. They need that to get enough lift at the slower speeds!
Note, I’ve left out MOST of the math. It becomes important in describing the details of forces and pressures and velocities and modeling airflow and performance of a specific airfoil under specific and varying conditions. Here, you need to look at something called circulatory flow and Richard von Mises, Ludwig Prandtl and Theodore von Karman. They really established the math of flow around a wing. Bernoulli was only a part and not as commonly understood.
So, why do low ceiling gliders tend to have undercamber wings? Well, they spend most of their time at a single, slow speed (gliding) and need to have the best lift/drag properties at that speed.
Why does a low ceiling glider have flaps that straighten? Because that nice slow speed undercamber is too dragging at launch velocity, you’d never get to the ceiling.
Why might a high ceiling glider have LESS undercamber, or none? Two reasons. More time climbing, so you need an airfoil to compromise on launch vs glide conditions. Structural, much larger launch forces, that thin wing just won’t hold up.
Hmm, way too much, I've spentmore time that I really have already. Probably some errors or oversimplifications, hopefully not to egregious, experts feel free to correct.