Dragonflies' flight capabilities are prodigious. They dash, they dart, they manoeuvre, they cross oceans. At least four distinct flight styles are recognised in Odonata: counter-stroking (where fore- and hind-wings move up and down about 180 degrees out of phase), phased-stroking (where the hind-wings cycle about 90 degrees - a quarter cycle - before the fore-wings), synchronised-stroking (where fore- and hind-wings move in unison), and gliding.
Counter-stroking is the normal mode for Zygoptera except some Calopterygidae, and for Anisoptera when they are hovering or flying very slowly. This is a very powerful and efficient way of flying and generates a lot of lift.
Phased-stroking is used by Anisoptera when flying about. This method generates more thrust but less lift than counter-stroking.
Synchronised-stroking is used by Anisoptera when maximising thrust to change direction quickly. It is also used by calopterygid Zygoptera as a display flight, showing off the coloured wings.
Gliding is used by some Anisoptera and a few of the very largest Zygoptera (mostly in the family Pseudostigmatidae). Three kinds of gliding can be recognised: free gliding, where an animal just stops stroking with its wings and glides slowly down for a few seconds; updraft gliding at hill crests, where the animal adjusts its wing positioning to float in the air without the need to beat its wings; and gliding in towed females, where a female in the wheel position holds her wings out and glides while the male provides the motive force.
Dragonfly flight is powered by muscles attached directly to the wing bases. Efficient muscle action depends on temperature and many dragonflies spend considerable time and energy in maintaining a near constant elevated temperature for their flight muscles. When at rest the dragonfly thorax appears skewed, but in flight the head is held low and the stroke of the wings is about parallel to the long axis of the flight muscles, providing mechanical efficiency. Small controller muscles operating on the wing base adjust the wing shape and angle of attack of the wing during each stroke.
Thrust generating mechanisms in dragonflies are complex. Whereas aircraft use only two methods for generating lift (and one of these only for very short periods) dragonflies use at least four distinct physical processes: classical lift, supercritical lift, vortices, and vortex shedding. There is also something funny happening during take-off by some perching libellulids. Classical lift is the stuff that keeps aeroplanes up, and is well understood. Supercritical lift ocurs when the attack angle of the wing passes a critical value. Very high lift is generated for a short distance then the wing "stalls". By using short wing strokes dragonflies can use this effect continuously. The study of the use of vortices and of shed vortices in insect flight is a field that is only just opening up. Thrust is generated both by the movement of the wing through the air and by the twisting of the wing (supination/pronation) at the ends of each stroke. Almost all Zygoptera use the 'clap-and-fling' lift-generating mechanism (Weis-Fogh 1975) in take off, calopterygids also use it during normal flight. A remaining conundrum is the libellulid dragonflies that perch with their wings low, pointed well forward, and twisted to be near vertical. These animals launch themselves into the air very quickly. High speed filming needs to be done to see what is happening. Dragonfly flight is very powerful in terms of the body mass of the animals - accelerations to 4g in a straight line and 9g in turns are documented in high speed videotapes of free-flying dragonflies as they pursue, or break off attacks on, prospective prey - indicating a very respectable power/weight ratio.
Dragonfly wings are very dynamic structures. They are not simple planar objects. The corrugations in the wing hold an aerofoil of air around the physical wing, lowering friction, and the wings flex around several axes, responding both to muscle actions and to inertia effects. The pterostigma on the leading edge near the tip is a weight that causes the wing tip area to flex during a wing stroke, improving aerodynamic efficiency.
To make things more impressive, dragonflies can fly with different wings doing quite different things, even using different methods to generate thrust. Asymmetric wing stroking in damselflies permits wings on one side to drive forward, and the other side to drive back, spinning the animal on its axis in a single combined stroke. All dragonflies achieve their mastery of flight by varying what their wings are doing in a coordinated fashion. They can adjust wing shape, stroke length, angle of attack, move a wing forward (or backwards) of its "usual" position, stop one or two wings, adjust relationships between any two wings on either side of the body ... the list goes on.