enginesrus said:
And again what about a symmetrical wing with the same curvature on the bottom as the top?
Symmetrical wings can fly because they operate at a non-zero angle of attack.
'Regular' non-symmetrical wings sections also operate at some not-zero angle of attack; they don't perform well inverted because the way they are shaped for high efficiency in the mode of operation they are designed for means that if you flip them upside down, you would need huge angles of attack for them to work properly.
Symmetrical wings work on aerobatic planes because they are designed to function at relatively small angles of attack which are still possible to achieve when the fuselage is upside-down, without putting the airframe into some crazy attitude which would cause damage or generate a boatload of drag.
The two surfaces which form the rear section of an airfoil are not parallel, whether the section is symmetrical or not. As a result, for any possible symmetrical airfoil section, there is a range of AoA values from zero up to the divergence angle of the trailing edge where no part of the airfoil is oblique to the flow, BUT the length of the streamline over the top is longer than the streamline over the bottom - meaning there will be a pressure differential generated if the airfoil is moving. Pressure differential means lift.
Next time you watch an aerobatic plane flying, pay attention. You'll notice that the mean camber line - for a symmetrical airfoil, the centerline - of the wing is not parallel to the centerline of the airframe. It's angled down a few degrees in the rear, so that in level forward flight the airframe is parallel to the direction of travel and the wing has a few degrees of positive AoA. In inverted level flight, the airframe will be 'tail low' to the point where the airfoil is moving at roughly the same AoA as it was when not inverted. The airframe is tail low because the mean camber line and airframe centerline are not parallel to each other. In the real world, in inverted level flight, the ailerons will be trimmed slightly nose-down as well, which reduces the necessary AoA to keep the aircraft level. So the amount of 'tail down' attitude you would expect to see in level inverted flight would be slightly less than the angle between the airfoil centerline and the centerline of the airframe.
