# Does flying an airplane upside down imply negative AoA? Why?

I saw the statement below in this answer:

Note that for normal level unaccelerated flight $$C_L$$ is always > 0. The minimum $$C_L$$ is a negative value for negative AoA, and would mean that the aeroplane is flying upside down.

This would seem to me to imply that flying an airplane upside down implies a negative angle of attack.

But the typical illustration and explanation of angle of attack is that it is the angle between the airstream and a reference line, the latter of which in airplanes is normally the wing chord.

How can the two be reconciled? Alternatively, what am I missing?

• I don't understand why the two statements need reconciling. – Fred Larson Aug 14 '19 at 18:37
• Negative AOA to generate negative lift. So flip it upside down and you have positive AOA... – JZYL Aug 14 '19 at 19:09

Level flight (no change in altitude) upside down, with an airfoil with a zero-lift AoA of less than or equal to zero degrees, requires a negative AoA to get upwards lift.

This is assuming the AoA is measured in the body frame of the aircraft, aligned with the chord line of the airfoil.

Also this assumes there is no thrust/drag or thrust/drag do not meaningfully contribute to vertical net forces.

It depends on what you are using for your coordinate system. If you are using a coordinate system relative to the airfoil where the top of the airfoil points towards the postive y direction and the bottom of the airfoil points to the -y direction, then inverting the airplane will cause a negative AOA since the airfoil would be fixed in this coordinate system. In this case the negative AOA would cause negative lift as defined in this coordinate system. However, if I defined the coordinate system relative to the ground where -y points towards the ground and postive y points towards the sky, then the AOA would remain the same in both normal and inverted flight and the AOA would be positive with positive lift in both cases.

We could pick the system of co-ordinates where AoA does not depend on which side of the plane is the "upper side": the side facing the sky could be the upper side, regardless if that side has landing gear on it or not.

This would look more intuitive for human to understand. However various algorithms of computer simulation would have difficulties at the 90 degrees roll. At this angle the AoA would reverse the sign, because the "upper side" is now the opposite. Such changes make tasks like calculating derivatives over this point awkward.

The math is much easier without the badly-behaving points. This is generic everywhere in mathematical modelling.

"The minimum Clift is a negative AOA value" means that positive lift is still being generated at a negative angle of attack. Go to Airfoil Tools on the net and study the graphs. Many cambered airfoils do this down to a few degrees negative AOA.

For aerobatic planes, symmetrical airfoils are used to get similar lifting properties when trying for sustained inverted flight. They will generally will have 0 lift at 0 angle of attack.

So "negative" or "positive" lift really depends on which direction you want the WING to generate lifting force.

For example, if you enter a loop, you may be inverted but pulling back on your stick to complete the loop. AOA is still positive. However, if you do a half loop and wish to fly straight away inverted, you now push your stick forward, to negative AOA, creating lifting force towards the bottom of your wing (which is now "up").

When you half roll back to upright, then pull the stick back for positive lift. This is the "Immelmann" maneuver, from early in the last century.