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It's a very widely held myth that 'the laws of aerodynamics say that bumblebee can't fly, but no-one told the bee.'
Probably this is based on a simple linear treatment of oscillating aerofoils. This assumes small amplitude oscillations without flow separation, ignoring the effect of dynamic stall which causes an airflow separation inducing a large vortex above the wing. This vortex briefly produces several times the lift of the aerofoil in regular flight. The bumblebee flies because its wings encounter dynamic stall on every down stroke.
Bees beat their wings approximately 200 times a second, which is up to 20 times as fast as nerve impulses can fire. They achieve this because their thorax muscles don't expand and contract on each nerve firing, but rather vibrate like the string on a musical instrument.