Partial-span flaps increase strength of trailing vortices
This thread was drawn to my attention a few days ago. It is now eleven months since the thread was active, and maybe no-one is watching, but here is my contribution. I am an aeronautical engineer specialising in aerodynamics and airplane performance. I think I was the author of the comment in Wikipedia saying wingtip vortices are strongest with flaps extended.
Most of the comments on this thread focus on angle of attack in an attempt to explain the relationship between trailing vortices and trailing-edge flaps. This is forgivable because it works when explaining the change in strength of vortices when there is a change in airspeed or lift. However, as Brian Abraham pointed out correctly, the strength of vortices and induced drag is a function of the lift coefficient, not the angle of attack. Using angle of attack in an attempt to relate trailing vortices and flap settings leads to the incorrect conclusion because changing flap setting causes a significant change in angle of attack but no significant change in lift coefficient. I will attempt to explain.
Vortices represent kinetic energy and they don’t occur spontaneously in the atmosphere. The law of conservation of energy requires that a force must act on the atmosphere to cause a vortex. In the case of trailing vortices behind an airplane the generating force is the reaction to the induced drag on the airplane. If the induced drag on an airplane increases by one percent, the rate at which energy is added to the trailing vortices also increases by one percent. Therefore the energy in the trailing vortices is known once the induced drag on an airplane and its true airspeed are known.
The lift on a wing is not generated uniformly across the span. Pressure difference between top and bottom surfaces is greatest near the wing root, falling to zero pressure difference at the wingtip. The lift should reduce gradually and smoothly from the center section to the tips. To achieve the minimum induced drag a fixed-wing airplane needs a wing whose spanwise lift distribution is in the shape of an ellipse. That is why R J Mitchell designed the Supermarine Spitfire with an almost elliptical planform so that its spanwise lift distribution with the flaps retracted would always be close to perfect.
The key to unlocking the mystery of partial-span flaps and trailing vortices is neither angle of attack nor lift coefficient. The key is the aspect ratio and the Oswald Efficiency Number (often called Span Efficiency Factor). The Oswald Efficiency Number for typical airplanes with flaps retracted is somewhere between 70% for the least efficient, up to 85% for the most efficient. This means that the effective aspect ratio of the wing of typical airplanes is only 70% to 85% of the actual aspect ratio. An airplane with a perfectly elliptical spanwise lift distribution would have an effective aspect ratio equal to its actual aspect ratio. The higher the aspect ratio of an airplane wing, the lower is the induced drag. The standard formula for aircraft drag coefficient contains the aspect ratio and the Oswald Efficiency Number in the denominator of the induced drag term.
In Daniel P. Raymer’s book "Aircraft Design: A Conceptual Approach" (AIAA Education Series) in Section 12.5 it states "deflection of flaps changes the spanwise lift distribution so that a flap deflection actually increases the induced drag"
When partial-span flaps are extended, extra lift is generated on the part of the wing with the flaps, and less is generated on the part of the wing with the ailerons. In Section 12.6, Raymer states "This extra lift in the vicinity of the flap affects the spanwise lift distribution, and therefore the drag-due-to-lift. Our hard-won elliptical lift distribution is ruined, and we must adjust the drag-due-to-lift upward."
Extending partial-span flaps ruins the gradual and smooth shape of the spanwise lift distribution. This causes a significant fall in the Oswald Efficiency Number, and that in turn causes a significant increase in induced drag coefficient. Even the lift distribution of the Spitfire is severely disrupted when flaps are extended. Induced drag and trailing vortices both increase as the result.
All of the above is in conflict with several websites and FAA Advisory Circular AC 90-23F "Aircraft Wake Turbulence". In section 5 of AC 90-23F it states "The greatest vortex strength occurs when the generating aircraft is heavy-clean-slow." Sadly, the authors of 90-23F appear to have been unaware of the significance of what they have written. Stating that the greatest vortex strength occurs with flaps retracted is contrary to everything known and published about trailing vortices and induced drag, so it demands a careful and detailed explanation of what they meant and why. Section 5 also says "The vortex characteristics of any given aircraft can also be changed by extension of flaps or other wing configuring devices." The authors knew that flaps influence vortex characteristics but they were conspicuously reticent about declaring in which direction the characteristics change, and why.
Perhaps the authors of 90-23F know something that aerodynamicists don’t. Aerodynamicists would be willing to accept the knew knowledge if only the authors would divulge what it is.
If it were true that trailing vortices are strongest in the clean configuration, why wouldn’t airplane designers create airplanes with fixed trailing edge flaps so they would benefit continually from weaker trailing vortices and therefore weaker induced drag? Why wouldn’t pilots fly all the way to their destination with flaps in the takeoff position to benefit from weaker trailing vortices and lower fuel burn? The answer is that trailing vortices and induced drag are stronger with trailing-edge flaps extended, and that is why the designer, the operator and the pilots are all keen for the flaps to be retracted as soon as it is safe to do so.
Classical aerodynamic theory and many decades of airplane design lead us to predict that trailing vortices increase in strength as trailing-edge flaps are extended. If someone knows that the opposite occurs, that someone should explain why the theory and the practice fail.