Say you're in a right sideslip. What happens to tip vortices? I'm fairly sure that it would just reduce the strength of the vortex (for the left wing), because there is a force trying to keep the high pressure under the wing, if that makes sense. That force is the freestream because the wing is at an angle.
The right wing vortex would probably grow in strength, because that same force is helping the air escape from under the wing. (if I had to guess)
The following quote is from "Oblique Flying Wings: An Introduction and White Paper" from Desktop Aeronautics, Inc., available at https://www.desktop.aero/library/ofwwhitepaper.pdf.
2.2.2 Effect of Oblique Sweep on Spanwise Lift Distribution
A well-known effect of wing sweep is the variation of induced downwash along the span from the trailing wake that produces an additional lift distribution characterized by increased loading on the aft wing and reduced additional lift on the forward wing. For a wing with no twist or bend, this results in a significant rolling moment, tending to roll the forward wing downward. There is also a yawing moment from the asymmetrical distribution of induced drag that tends to unsweep the wing.
Keep in mind that by "wing sweep" the authors are talking about obliquely sweeping both wings together as a unit, like in the photo in this other answer to the present question. We have essentially the same effect when we sideslip. The direction of the roll torque generated is toward the "forward" wing, which in a sideslip is the "upwind wing". In a steady-state non-turning sideslip this would also be the "lowered" wing. This is an anhedral-like effect.
In the paper they recommend adding a small amount of dihedral to the outboard portions of an oblique-wing aircraft to counteract this, with the amount of dihedral being dependent on the lift coefficient that the aircraft is intended to fly at.
I'd suggest that this effect due to "the variation of induced downwash along the span" falls within the scope of the question's focus on "tip vortices".
The anhedral-like (upwind) roll torque generated by an unswept, zero-dihedral wing in a sideslip was also the subject of a post on an aerodynamics subforum of the"RCGroups" model-airplane on-line forum by a prolific, knowledgeable contributor with the username "ShoeDLG". Some excerpts from his post:
I used a Vortex Lattice Method to explore the impact of various Radian Pro wing design features on apparent dihedral effect.
The cases I looked at (all without any twist):
- Untapered / Unswept / Zero Dihedral Wing (flat AR 10 rectangular wing)..."
and then
The results are shown in the first attachment. A couple of observations:
- A flat rectangular AR 10 wing has negative apparent dihedral effect at positive AOA and positive apparent dihedral effect at negative AOA..."
and then
The dihedral effect associated with an untapered, unswept, zero dihedral wing is interesting. The span loading for an AR 10 rectangular wing at 5 degrees AOA and 20 degrees sideslip (to exaggerate the asymmetry) is shown in the second attachment."
These conclusions are consistent with the "Oblique Flying Wings" white paper-- during a sideslip, on an aircraft with flat (no dihedral or anhedral) wings with no sweep, the lift distribution is changed in a way that creates an "upwind" roll torque-- i.e. an anhedral-like effect.
Here are the two attachments:
However, a web page called www.flightlab.net by Bill Crawford came to the opposite conclusion, stating that during a sideslip, tip vortices shifted in a way that increased the angle-of-attack of the upwind wing and decreased the angle-of-attack of the downwind wing, contributing a dihedral-like roll torque component, toward the downwind wing. A full page of text devoted to the topic, along with an illustration, may be seen on page 14 of his generally excellent PDF "Flightlab Ground School: 4. Lateral/Directional Stability", now viewable only on this link on the Wayback Machine. This content is well worth reading through.
Crawford goes on to reach the following conclusion: (footnotes added)
"Since downwash strength is a function of CL, pulling or pushing on the stick will affect roll moment due to sideslip in a manner similar to the swept-wing example already described.1 (Our trainers’ rectangular planforms tend to promote strong tip vortices. Other straight-wing planforms with different lift distributions might not be as effective.)"
followed by:
From all the above, an under-appreciated yet nevertheless great truth of airmanship emerges: For a swept or a straight wing, pulling the stick back tends to increase rolling moments caused by sideslip (and by yaw rate), pushing decreases them.
(In the specific case of an unswept wing, Crawford is obviously assuming that there is some aspect of the aircraft's overall geometry, such as a high wing position, or actual dihedral, or perhaps just the tip vortices themselves, that results in an overall dihedral-like roll torque during a sideslip. The comment above wouldn't make sense for, say, a low-wing airplane with no sweep and a great deal of actual anhedral, because then the effect that he is claiming for the wingtip vortices, which are most pronounced at high Cl, would be acting in the wrong direction.)
So Crawford is reaching the opposite conclusion on the effect of tip vortices on the balance of roll torque during a sideslip than the other sources cited above-- he is claiming that they contribute a dihedral-like roll torque component, toward the downwind wing. I can't account for this discrepancy at present. Is it possible that Crawford's conclusions are valid for wings of a certain geometry, such as the low-aspect ratio wings with broad wingtips found on many trainers? Or is he simply mistaken in the idea that tip vortices, and the associated larger upwash / downwash flow field around the wings, tend to contribute a dihedral-like, downwind roll torque component during a sideslip? Should his observation of increased rolling moments due to sideslip at high lift coefficients versus at low lift coefficients, even in unswept wings, be explained by other means entirely?
Footnotes:
In consideration of level flight, if we think about dihedral, the wing yawed into the wind would develop increased lift relative to the other wing, and we would expect the lift-induced vortex on the wing yawed into the wind to be stronger than on the other wing. This would occur in gliding flight and can be easily demonstrated in general, even though this is not exactly level flight. However, in powered flight with a single-engine propeller on a mid-wing aircraft, the propeller slipstream may increase lift on the down-wind wing more than dihedral would increase lift on the upwind wing in a side slip. The consequence will likely cause a roll in the direction of the upwind wing. Now the question remains, in this circumstance which vortex would be increased? If we consider the total-potential circulation to be more strongly shifted toward the down-wind wing as a consequence of the propeller slip stream, then we would expect that the down-wind wing would have the stronger tip vortex. Nevertheless, this result is counterintuitive and seemingly unexpected.
There are relatively few in-depth resources discussing in detail this aspect of flight. quiet flyer will likely have a more informed perspective.
Or do you mean something mostly like this?
Robert T. Jones, at NASA, rather extensively investigated this aspect of flight. Various summaries and perspectives of his work in this area are readily available on the internet, particularly via NASA. This particular configuration of the wing is termed oblique. In this case, for level flight, there is no apparent asymmetry in the relative distribution of lift.
A crucial difference between slip and oblique data is that slip data (for roll behavior) must include(net) dihedral effect from relative wind on wing, fuselage and vertical stabilizer, whereas oblique tests only change the orientation of the wing.
This allows us to isolate the effects of oblique sweep on roll behavior and analyze them more accurately.
It is possible the "upwind" or "reverse swept" wing's airstream flow into the fuselage degrades the low pressure area over the wing, but the "sweep" of the downwind wing's airstream flow helps preserve it, resulting in a roll (from lift imbalance) into the upwind wing.
This is supported by winglet studies and bird-like aircraft design.
Amazingly, the data supports 2 major features which could help make the design viable:
Other concerns are with fluttering tendencies of reverse swept wing tips, which, if overcome, could lead a path to a practical, economical way to increase to flight envelope of an aircraft into the transonic, and even supersonic regimes.
What happens to tip vortices in a sideslip?
Going for brevity, and with thanks to another member here:
The relative wind may push the vortex further into the upwind wingtip and further away from the downwind wingtip.
