When I was studying aircraft design we used xflr5 which has xfoil built in. It's a simulation software. What you are asking isn't a good idea to use just one lift equation because your answer will be wrong and here is why:
1. There are many airfoil shapes with lift data such as a lift coefficient. When you extrude a wing from an airfoil it's data changes a lot. It adds a third dimension that you have to compensate for.
2. There are also 2 main theories to aproximate wings based on what is called the aspect ratio, AS, which is the ratio between length and surface area.
3. You talked about a simulation. This requires ranges of ∝, angle of attack, when this changes the airfoil lift coefficient changes and the wing coefficient changes as well. I highly recommend writting a program to calculate for you or use software. Note: Coefficient of lift also changes with altitude and mach speed
4. You can model them separately as individual wings but when combined in a tail configuration there are vortex effects at the corners, tips, and disrupted flow from the aircraft body. These are not easily calculated by hand.
As for "slipping" effects, I believe you mean viscous effects. At subsonic speeds it can be ignored and often time is. Now, transonic and supersonic speeds can be an issue. When supersonic the lift actually increases a lot due to the viscous effects.
Depending on the scope of your analysis you can simplify and ignore points that I mentioned but I'd have to know the full scope in order to tell you which.
SteamKing said:
Most airfoil shapes used on aircraft will 'stall', i.e. lose the ability to provide lift, when the angle of attack reaches about 15 degrees. If a wing stalls when the aircraft is taking off, for example, there is usually insufficient altitude to maneuver the aircraft to recover from the stall and a crash results.
That's not exatly true. Jet fighters, or other high performance aircraft, are designed for large angles of attack around 30° and are capable of going vertical mid-flight. They can only due this because of the massive thrust to weight ratio. I believe takeoff angle is over 25° for aircraft carrier launches which is about a 27-30° aoa for the wings depending on tilt of the wing.