The answer to another question mentions the rather unusual pivot wing. From an aerodynamical standpoint, what are the benefits of an oblique wing compared to a delta, a trapezoid or a forward swept wing?
Are there any other differences?
Note that I am asking about the oblique wing when it is oblique. The advantages of variable-sweep aircraft have already been discussed at length.
The pivot wing, also called oblique wing is a type of wing design that tries to minimize the drag over the entire speed range of the aircraft.
At low speeds, the main concern is the induced drag, which can be reduced by increasing the aspect ratio. That is why low speed aircrafts like gliders have very long slender wings.
As the speed increases, the induced drag falls off quickly and the wave drag comes to dominate at supersonic speeds. This is the reason why supersonic aircrafts have highly swept wings with very small aspect ratios.
One way to reduce the drag at high speeds is to sweep the wing. The velocity component perpendicular to the wing is reduced, reducing the drag.
The delta wing is a highly swept wing used in supersonic combat aircrafts. A good example is the Eurofighter Typhoon, which is a tailless delta. The delta wing provides excellent supersonic performance and has a high stall angle. However, the wing 'bleeds' energy rapidly during turns and the requires high takeoff and landing angles.
"Eurofighter Typhoon line drawing" by Inductiveload - Own work. Licensed under Public Domain via Commons.
The trapezoidal wing is a version of high speed wing with small aspect ratio. The most famous example of the use of trapezoidal wing was the Lockheed F-104 Starfighter, which had excellent high speed performance. However, the aircraft had high takeoff and landing speeds and comparatively less low speed performance.
"Lockheed F-104C Starfighter" by Kaboldy - Own work. Licensed under GFDL via Commons.
Almost all the swept wings in use are swept towards the rear. One disadvantage of this kind of wing is the th airflow is from the root to the tip and as a consequence, the (outboard) ailerons stall before the inboard portion of wing and this results in loss of roll control in high angles of attack. This can be prevented by sweeping the wing forward. However, the bending stress in the wing root is increased due to aeroelastic twisting.
source: NASA
The issue with fixed sweep wings is that what is efficient in one regime will not be so in the other. One way to reduce the drag in all speeds is to change the sweep and aspect ratio of the wing.
The variable sweep wings change the aspect ratio by rotating a part of the wing.
"Three F-111s with different wing configurations" by Jason B from Australia - 3 Configs. Licensed under CC BY 2.0 via Commons.
The pivot wing is an extreme version of the swept wing where the entire wing is rotated. So far, it has only been implemented in one aircraft, the NASA SD-1.
"AD-1 ObliqueWing 60deg 19800701" by NASA - http://www1.dfrc.nasa.gov/Gallery/Photo/AD-1/HTML/ECN-15846.html. Licensed under Public Domain via Commons.
The main aerodynamic advantage of the oblique wing is that by adjusting the sweep progressively, the aircrafts can be optimized for drag reduction over a wide range of Mach numbers. Also, the AD-1 was designed with elliptical wing for minimizing induced drag.
However, on the downside, as the entire wing is rotated, one side of the wing is swept forward, while the other side is swept towards the rear. This means that their stalling characteristics are entirely different. On one side (forward swept side), the inboard region stalls first, while its the opposite on the other side. This makes controlling the aircraft difficult. A follow on project of AD-1, the Northrop Grumman Switchblade was canceled over control difficulties.
The aircraft also exhibited aeroelastic and pitch-roll coupling effects that adversely affected the aircraft's handling qualities at over 45 degrees sweep. Also, the aircraft exhibited unusual trim requirements and inertial coupling. For instance, it was reported tha the AD-1 required about 10° of bank in order to trim the aircraft with no sideslip at 60° wing sweep.
Though the pivot wing aircraft had excellent aerodynamic characteristics, its poor and unusual control characteristics prevented further development.
The pivot wing and the variable sweep wing both enjoy the same benefits to any non variable wing design which is the ability to adjust the sweep angle and aspect ratio of the wing and the relative thickness of the airfoil. All of which helps to optimize the wing for different airspeeds. When flying at low speeds, a high aspect ratio keeps the induced drag low, which takes up the majority of drag. In addition, the greater relative thickness gives the airplane the ability to fly at relatively low angles of attack which helps when landing or taking off and keeps drag low. At higher speeds especially when approaching Mach 1 wave drag takes up the majority of drag. To reduce wave drag thin wings with a low aspect ratio are required.
The aspect ratio is the ratio between the wingspan of the aircraft and the wing area. The wingspan changes with sweep angle on a variable sweep or pivot wing, whereas the wing area stays the same. This causes the lower aspect ratio of the swept wing.
The relative thickness is the ratio between the thickness of the airfoil and the chord line.
To get the chord line you measure from the leading to the trailing edge of the wing. When you do this in swept wing configuration you will find out that the chord line is longer than when the wing is straight. Therefore the thickness ratio is lower when the wing is swept.
Trapezoidal wings like those on the F-104 Starfighter had very bad low speed characteristics and could not hold any fuel because they were so thin. To achieve enough lift high angles of attack as well as a high landing and take off speed were needed. At high speeds however these wings had very low drag enabling the Starfighter to fly Mach 2 even though its engine was relatively weak compared to modern ones.
The delta wing achieves the low supersonic drag by choosing a higher sweep angle. It is easy to build and fuel tanks can be placed inside the wing. The delta wing has a very high stall angle, so that high lift coefficients for slow flight or for tight turns are possible. This is because vortices along the wings leading edge create additional lift at high angles of attack. However, that comes at the cost of extremely high drag. Depending on the sweep angle it can be chosen for which speed the wing is optimized. Todays fighters use all kinds of tricks in order to adapt the wing to the desired airspeed. One example is the use of strakes. Strakes are basically wings with a higher sweep angle than the rest of the wing placed in front of the actual wing to create the beneficial vortices without having to compromise with a low aspect ratio. The advancements in those and other designs as well as more powerful engines have made the variable sweep wing requiring complex sweep mechanics obsolete.
The main advantage of a pivot wing compared to a swept wing, that I can think of, is the lower trim drag of the pivot wing when the wings are swept. While pitching moment changes with sweep angle for variable sweep wing designs, it remains the same for pivot wing designs.
On a typical variable sweep wing design the aerodynamic center moves aft when the wings are swept back. This is because most of the wing surface moves aft when the sweep angle of the wing increases. The aerodynamic center is the point on which all aerodynamic forces of the aircraft are imagined to act upon. So When the aerodynamic center of the wing moves back the distance between the center of gravity and the aerodynamic center will get larger (for stable aircraft designs). Flying supersonic moves the aerodynamic center even more towards the tail.
The torque around the pitch axis (pitching moment) acting on the aircraft can be calculated by multiplying the total force on the vertical axis (basically lift) by the distance between the aerodynamic center and the center of gravity.
To compensate for the greater magnitude of pitching moment more positive trim needs to be applied when the wings are swept back in order to maintain level flight or even to pitch up. More trim results in more drag.
The difference in pitching moment is why many early variable sweep wing designs had longitudinal stability problems.
To compensate the difference in pitching moment the F-14, for example, introduced little retractable lifting surfaces in front of the wings in its later versions. These would extend when the wings were swept to move the aerodynamic center forward reducing the trim drag.
On a pivot wing design the aerodynamic center remains exactly the same no matter the wings sweep angle.
When pivoted, the aerodynamic center of one wing will move a certain distance to the rear, and the aerodynamic center of the other wing will move an equal distance to the front. Thus the aerodynamic center of the entire wing will not move when the wing is pivoted and the pitching moment remains the same.
No additional trim is required on a pivot wing for changing the sweep angle and thus no additional trim drag. However, a pivot wing has numerous other major aerodynamic problems as have been depicted in other answers and is therefore not really practical for aircraft in operational service.
I think the main difference between a swept and a straight wing is that the straight wing has a lower landing speed, whereas the swept wing can fly closer to the speed of sound without compressibility problems. So a pivot wing gives the benefit of both, the disadvantage being extra weight of the pivot mechanism.
Peter Garrison explains the benefits of a swept wing here: http://www.flyingmag.com/why-are-wings-swept
