Now if only I could find an explanation of how some planes can fly inverted.
I can take care of that for you. Please bear with me as I'll get a little technical but I think going the extra distance will give you a better understanding of what's happening. I will take a few shortcuts though but feel free to ask questions, I'll answer them to the best of my abilities.
Welcome to Ghetto Aerodynamics 101!
In order to understand fluid flow over an airfoil and thus a wing, we start at the most basic case, which is flow over a flat plate. We do well here to define some quantities:
FLAT PLATE FLOW / BOUNDARY LAYER
- Uinfinity is the "relative wind speed". Imagine the object is stationary, then this is how fast the fluid moves over the object (we will assume uniform flow for this discussion).
- Viscosity (absolute) is usually denoted by the Greek letter nu. High viscosity fluid would be molasses, low viscosity would be air. High nu = bad, that's why we don't fly through molasses, much less swim through them!
- Density is rho and you know what that is.
For the diagram above, BL stands for boundary layer. Anytime that a viscous fluid interfaces with something else (a solid, another fluid, a gas, whatever), you'll have this boundary layer thing form up, of which the thickness delta(x) is a function of the distance parallel to the fluid flow.
The boundary layer is the volume of flow in shear stress and as mentioned will always occur at an interface. The velocity profile inside the boundary layer is classically given as a parabolic distribution as a distance perpendicular to the flow motion, thus u(y). Velocity at the boundary (y=0) will always be zero; the fluid is stagnant here. Velocity at the BL boundary (y=delta(x)) will be Uinfinity. The fluid that is not in shear is called "potential flow". That means we can ignore the viscous terms
in that region and that leaves our governing equations as first order derivatives, much easier to solve than before (viscous terms are second order).
OKAY! NEEEEXT!
Now we can talk about flow over a flat plate with some angle of attack, for both inviscid and viscous cases.
FLAT PLATE FLOW AT SOME ANGLE OF ATTACK
- Alpha is the angle of attack of the object relate to the relative wind. Mouthful.
A flat plate in inviscid flow can produce lift because Mr. Newton says that if you cause a displacement in the fluid (in this case, you making it change directions and then letting it exit at a different position) you'll get some net resultant force. Super.
However there is also a viscous explanation for lift and the both have to be incorporated as one. Remember the boundary layer thing? Now it's formed up on the top surface of the flat plate, but the bottom is being bombarded by fluid so it doesn't get to grow like the other does. So if you're a fluid molecule and you're coming to this thing, to you it doesn't look like a flat plate anymore, it looks more like a flat bottomed half eclipse thingy. This incurs even more fluid displacement. This fluid displacement translates to a pressure gradient, which we'll talk about soon. Anyway asAlpha gets bigger, your BL gets bigger and bigger to the point where you get something called separation. When separation occurs, the fluid isn't adhered to the surface anymore and usually that spells trouble (s form of stall).
This is why paper airplanes can "fly". There are many explanations for lift, and a lot of the ones that you will find on the internet (gasp Wiki gasp) may be erroneous.
ALMOST THERE! TWO MORE STEPS!
FLOW OVER CYLINDERS
Alright now picture these cylinders as being infinite in and out of your screen, and you have some uniform flow over them. If the cylinder is stationary, you would expect the streamlines in the flow to look identical on the top and on the bottom. The cylinder produces drag but no useful lift. If you start spinning the cylinder at some rotational velocity Omega, now you're doing something. The flow will remain attached to the surface longer in the direction of the spin (think of this as the BL being dragged by the cylinder) and shorter in the opposite direction of the spin. So now you're displacing the fluid in a useful way! You're generating a change in pressure, which is lift. This is why baseball pitchers and ping pong players can curve balls. This is called the Magnus Effect.
AIRFOIL ANATOMY
- LE is the leading edge. Velocity here is zero (stagnation point).
- TE is the trailing edge.
- c is the chord of the airfoil, or the length from LE to TE.
- mc is the Mean Camber line, and is a measure of the curvature of the airfoil. An airfoil with no camber is symmetrical (top and bottom halves are identical). Camber can be measure locally as the distance between mc and the chord line.
- t is the local thickness.
- AC is the Aerodynamic Center. All aerodynamic forces occur about this point (lift, drag, etc). Generally it's at about 0.25c but not always.
I keep saying lift (and drag too) is all about a change in pressure. Let's talk math. If you were to take the surface integral over the spinning cylinder (or over your airfoil or over your wing!) of all the local pressures, in and out of the screen and in the vertital direction, you'd get lift. You can do the same thing to get drag but you integrate in the direction in and out of the screen and in the horizontal direction. This is only one for of drag, called pressure drag, or drag due to lift.
These equations can be easily rewritten in algebraic form as follows,
L = 1/2 * rho * Uinfinity^2 * S * Cl
D = 1/2 * rho * Uinfinity^2 * S * Cd
- S is the wing surface area.
- Cl is the coefficient of lift
- Cd is the coefficient of drag, both of which are dimensionless parameters and can be found experimentally or numerically. They are usually functions of the Reynolds Number, the Mach Number, the angle of attack and of course the geometry of the airfoil.
This is for a wing. For an airfoil, the S term becomes only c, so that you have force per unit depth. Side note, if you go up too high, rho goes down, you might not produce enough lift. If you go too slow, you might not produce enough lift either (another form of stall).
I'm sure you've seen these, but they really do stem from an approximation of those surface integral equations.
ALRIGHT!!!
A plane is in equilibrium (not accelerating, not falling out of the sky, just straight and level flight) when the summation of all resultant forces (Lift, Weight, Thrust and Drag) equals zero.
Haha so HOW can airplanes fly upside down?
Some have symmetrical airfoils. Since they're symmetrical, they produce no lift at 0deg AOA. You just slide your nose up a little smidgen if any at all and you still get positive lift. If you have huge jets strapped onto your rig you can use brute force to keep you in the air.
Some planes have cambered airfoils. Now that gets tricky, so you have to use your elevator (horizontal stabilizer) to give yourself "nose up attitude". What that does for you is really more about the thrust than anything else. You're pointing your engines a bit down so now your thrust has a vertical and horizontal component which can be expressed as a trig function of your angle of attack. The vertical component is the bit that will say "no" to your weight and "negative" lift and thus keep your airborne. Yeehaw.
Either way that's usually why you don't see airplanes fly inverted too slow, they basically rely on thrust to get them going.
Sorry I got soooo carried away. It's my passion. Sorry if the little pictures are hard to understand. Anyway hope this helped or if anything, spurred some interest.
The main issue with doing a side view flying game is that you can only see about 3 seconds in front of you. So dogfighting and bombing is impossible without always looking at radar, which is no fun imho.
Yeah Dogfight uses a little trick where when you get going fast the camera shifts a bit so you can see further ahead. I forget if it zooms out some too to give you greater perspective? But that would be a way to deal with that problem. Challenging nonetheless. That game is pretty hard man =/
All said and done, if aerodynamics and how airplanes (or helis) fly is a subject of interest and you wanna learn some cool crap, I suggest this book:
http://www.amazon.com/Model-Aircraft-Aerodynamics-Martin-Simons/dp/1854861905/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1211533249&sr=8-1You can get it used for like $15 and it's totally worth it. Don't let the title fool you, this stuff works for any aircraft and the book does and awesome job at introducing all sorts of very neat and important aerodynamic concepts. I'm Audi 5k.
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