quote:Original post by Malone1234
The particles traveling over the top (curved) of the wing exert a certain amount of force downward, while the particles traveling along the bottom (flat) of the wing exert a certain amount of force upward.

The pressure force on the to of the wing actually can be negative relative to the ambient atmospheric pressure, and therefore effectively is a suction, e.g., the negative pressure on the upper surface of the wing pulls the wing up instead of trying to push it down. You can test this by taking a sheet of notebook paper, holding it up to your mouth, and blowing over the top surface. The paper will rise with no additional pressure from below pushing it up. A cool little experiment you can try at home! NOTE: the paper will droop down until you start blowing, but you should blow horizontally for this to work, NOT down onto the paper. Here''s a sort of diagram:

--  \   \  -    -------> blow air in this direction, not onto the paper |     /--\--         \            \You    Paper 

There is a property of the airflow around a wing called "circulation," which represents the rotation of air around the wing. Imagine, say a cylinder, moving through the air at constant speed. In this case, the air on the top and bottom will move at the same speed. The air will move faster at the top and bottom than the speed of the cylinder itself, but the air on the top will not move faster than the air on the bottom. But, suppose the cylinder rotates, and that there is friction so that the air right at the surface sticks to the surface and moves at the same speed as the cylinder. In this case, the air on either the top or bottom of the cylinder will move faster and it will move slower on the other side. Effectively, the velocity of the cylinder surface is added to the air velocity that would be present without the rotation. This added velocity is the air circulation. A nonzero circulation is always present when there is lift. BUT, it isn''t required that the object surface be rotating! The relationship between lift and circulation is called the Kutta-Joukowski theorem, but it isn''t useful unless you''re doing computational aerodynamics, which is usually overkill for flight simulators.

quote:Original post by Malone1234
Because of frictional effects and the fact that the plane is displacing volume, the particles on the top move faster along the curved surface than the particles on the bottom move along the flat surface. Hence, the upward pressure from the bottom is greater than the downward pressure from the top, which "lifts" the wing. That''s what we learned in high school physics anyway. We never got as far as air friction in my college course.

Lift actually can be generated in the complete absense of friction. The required circulation can be generated purely by making the air conform to an odd, asymmetric shape, such as an airfoil that is angled relative to the wind. You can''t get this frictionless situation exactly in real life, but is predicated by theory and essentially proven experimentally (experiments can produce results that correlate VERY closely to frictionless calculations, and well-understood adjustments to the calculations account accurately for the added friction in the experiment). In fact, friction can have an adverse effect and reduces the degree to which the air on top of the wing can move faster. In a twisted way, without getting into the theory, this make sense. If there is no friction, then the particles can move even faster and therefore a large negative relative pressure can be generated on the top surface without friction than with friction. As in the case of the rotating cylinder, friction can be used to create the circulation that is required to generate lift, but just having an asymmetric shape can generate circulation as well, without friction. Circulation can also be created by blowing air artificially over a surface, such as the notebook paper test above.

quote:Original post by Malone1234
Of course, you could just write a mathematical function that takes the speed and angle of the plane as parameters. Specify a value of this function to be a sort of equilibrium (the plane neither ascends nor descends) <-- the function should probably have at least two of these points. If you''re clever you could design the function so that this value is zero, which would be ideal.

Such a function exists, and it is the "CL-alpha" curve, which defines the variation of lift with angle of attack (angle of the wing relative to the wind, NOT relative to the ground). For small angles of attack (less than, say, 10 degress plus or minus), for conventional airplanes, the CL-alpha curves is linear, and looks like this:

CL = CL_0 + dCL/dalpha * alpha

Where CL is the lift coefficient, CL_0 is the lift coefficient at zero angle of attack (it is not zero for wings airfoils that have different curvature on the top than on the bottom, and for finite-span 3-D wings in general), dCL/alpha is the lift curve slope (approximately 0.1 / degree for very long wings, e.g. wings of high aspect ratio, less than 0.1 for stubby wings, and for swept wings), and alpha is the angle of attack in degrees.

It is insufficient to model lift only. Even for purely 2-dimensional flight you need to model drag, and also the pitching moment to deal with the effect of aerodynamics on aircraft rotation.

quote:Original post by Malone1234
Also, if your plane is ok when you fly straight up, I don''t see why it shouldn''t work at other angles. Any upward-pointing angle should have a positive y component of velocity which would act against gravity.

I think he may be using the propulsion system (propeller, jet engine) thrust to counteract weight in this case, and not wing lift. Which is wrong unless he''s also modeling drag that would act in the same direction as weight for vertical flight. Even without lift, there is a component of thrust in the upward direction that counteracts weight. But it is insufficient to completely balance the weight without lift.


Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Some useful gamedev.net threads:

http://www.gamedev.net/community/forums/topic.asp?topic_id=131995

http://www.gamedev.net/community/forums/topic.asp?topic_id=124303 - includes more detailed formulas for lift

http://www.gamedev.net/community/forums/topic.asp?topic_id=109341

http://www.gamedev.net/community/forums/topic.asp?topic_id=58187 - discusses drag, and adjustments to the CL-alpha curve due to having a finite length wing

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.