Most, if not all, new airplanes are required to have stall warning systems to (as the name should make clear) provide the pilots with a warning when the airplane is about to stall. Most stall warning systems work not by directly detecting the rapid increase in airflow separation near the stall point, but, rather, by measuring the airplane’s angle of attack and giving an alarm if it is greater than some threshold value. However, as the attack angle at which the wing stalls can vary by a great deal, these older stall warning systems have multiple thresholds; for instance, a particular system might sound an alarm at 15º in a clean configuration, but lower the threshold to just 5º if icing is detected (as icing promotes airflow separation, and, thus, lowers the wing’s stall angle), while waiting until 30º if the slats are extended (as leading-edge devices, such as slats, delay airflow separation, and, thus, increase the allowable attack angle).
With all this in mind, how do stall warning systems handle situations in which one wing is stalled, or close to stalling, but the other wing is not?
I can think of a number of scenarios under which this might occur:
Category 1 - The two wings have different stall angles, such as could result from...
Scenario 1: ...asymmetrical icing, or damage to the leading edge of one wing but not the other, which would increase the roughness of the damaged or more-iced wing, thereby increasing the tendency for the airflow to separate from said wing, and, therefore, cause it to stall at a lower attack angle than the undamaged or less-iced wing.
Scenario 2: ...asymmetrical leading-edge device (non)deployment, such as from failure during takeoff of the hydraulic system powering one wing’s outboard slats, resulting in the retraction of said slats, which would decrease the stall angle of the wing with non-extended or less-extended leading-edge devices.
Category 2 - The two wings are at different angles of attack relative to the airflow around them, such as could result from...
Scenario 3: ...violent, fine-grained turbulence, which could result in the airspeed of one wing being considerably lower than that of the other wing, thereby causing the horizontal component of the airflow around that wing to be considerably decreased while leaving the vertical component of said airflow unchanged, thus resulting in the lower-airspeed wing encountering the oncoming air at a much steeper angle than the higher-airspeed wing, and, as a result, possibly causing the lower-airspeed wing, but not the higher-airspeed wing, to exceed its stall angle; for instance, if an airplane is flying at an indicated airspeed 30 knots above its stall speed, and is hit by an asymmetric gust that causes the left wing to experience a 45-knot tailwind while the right wing sees a 15-knot headwind, the left wing will be 15 knots below its stall speed at the same time as the right wing is 45 knots above its stall speed, and, therefore, the left wing will stall, but not the right wing.
Scenario 4: ...a rapid yaw to one side, possibly as a result of overenthusiastic piloting or a mechanical failure, causing the airspeed of one wing to increase and that of the other to decrease, possibly causing an asymmetric stall via the same mechanism as in scenario 3 (for instance, a sudden rudder hardover would produce an extremely high yaw rate, and, thus, airspeed differential, before the pilot(s) had time to react, which could easily bring one wing, but not the other, below its stall speed).