Why do oblique-wing aircraft suffer from significant aerodynamic cross-coupling?

Question

Oblique-winged aircraft (which have one long wing that pivots around a central point, so that the wing is straight at low speeds but strongly-swept - one side forwards, the other side back - at high speeds), while theoretically more efficient than conventional aircraft, have a number of issues which have prevented them from seeing any significant use; one of these problems are their various unusual cross-coupling modes, including a significant tendency towards pitch-roll coupling (where pitching up or down makes the aircraft roll to one side or the other, and vice versa) and a need to hold a significant bank angle just to maintain coordinated flight and keep from slipping sideways (even with no thrust asymmetry), all of which become increasingly severe at high sweep angles.

For example (emphasis added):

McMurtry found the handling qualities were very close to the simulator, but that the aircraft’s asymmetry resulted in unusual trim requirements, asymmetric stall and inertial coupling. [...] For instance, the AD-1 required about 10° of bank in order to trim the aircraft with no sideslip at 60° wing sweep.

[...]

As hoped, the low-cost, low-speed, low-technology AD-1 successfully demonstrated the concept of a manned oblique wing aircraft, sweeping the wing to a maximum of 60°. The aircraft experienced cross coupling between pitching moment and aileron deflection. This pitch-roll coupling and the aeroelastic effects contributed to unpleasant handling qualities at sweep angles above 45°. [...] [A Summary Of A Half-Century of Oblique Wing Research, pages 20-21.]

The proposed wing pivot was also to be canted so that at 0° sweep, the wing was canted to 0°, but at 65° sweep it would be canted to 10°. The wing incidence would also have been increased (a standard feature of the F-8) with higher sweep angles. These features were expected to reduce aerodynamic cross-coupling, such as the necessity to bank the whole aircraft to trim sideslip, as found in the AD-1 flight testing. [...] _[A Summary Of A Half-Century of Oblique Wing Research, page 23.]_

Flight tests of AV1 and AV2 proved the design to be controllable in both pitch and roll. Noble states, “The elevon mixing is standard symmetric and the aircraft responds equally to left and right inputs. There is some slight roll coupling associated with up and down elevator. I believe this can be eliminated with fine tuning of the elevon mixing.” _[A Summary Of A Half-Century of Oblique Wing Research, pages 32-33.]_

Why do oblique wings come with these strange cross-couplings?

Answer 1

With the wing swept forward, a positive lift force on that wing will bend the wing upward and locally increase the angle of attack, especially to the outboard of a wing. The same thing happens on the wing swept backwards, only an upward deflection from lift force will reduce the local angle of attack, likewise to the greatest extent toward the wing tip where it is deflected upward the most. One wing will end up generating more lift than the other, which will require a rolling input from the aileron to cancel out. One could attempt to balance this out with different twist profiles of each wing, but that would only solve the issue in one g flight.

When, for example, the elevator is deflected to induce a positive pitching moment, the angle of attack on the wing increases and lift force increases. The increased lift generates an increased deflection of the wing. However, as outlined above, the impact on the local angle of attack due to that increased deflection is opposite between the left and right wings. This produces a coupled roll effect.

Finally, the asymmetric lift and therefore induced drag, in addition to the use the ailerons to counter this rolling tendency, will produce adverse yaw. To eliminate the sideslip you would need to use substantial rudder input, or a bank in the opposite direction of the adverse yaw induced sideslip.

Edit:

For a really simple visualization of the wing deflection inducing a local angle of attack change, take a piece of paper and hold it flat in the air in front of you, with the long edge facing you but turned away by 45 degrees (imagine you are looking at the leading edge of a 45 degree swept wing). Bend the short end of the paper sheet that is farthest from you (the wing 'tip') upward. Your perspective is aligned with the freestream aerodynamic flow, and by bending the tip upwards you can now see the top of the outboard wing. For a normal rear swept wing this produces washout and unloads the outboard wing. Now imagine the short end of the paper sheet that is closest to you is the wing tip. Hold the wing 'root' fixed and bend the new wing tip up. The upward deflection increases the local angle of attack at the wing tip, rather than decreasing it as before for the rear swept wing.

As an aside, this is also the reason why forward swept wings are often aeroelastically unstable. An increase in the lift force produces more lift force due to the deflection, a positive feedback that can much more rapidly lead to divergent flutter!