Jan Peter Apel

How Insects Fly 

Of course, also insects can only fly on the basic principle of flying at all, the downward acceleration of air mass. But they have their flight aligned to that, that they can fly on a point in the air without moving forward.
Nevertheless, they too moves plates horizontally through the air, as it makes airplanes. They do this with special designed very light wings, which they easily can swing fast enough back and forth through the air.

But now it is no longer enough to set the wings front edge towards the rear edge only so a little higher like on an airplane, where it can only hardly be seen (about 6 degrees). Insects positioned them with about 45 degrees and swing they back and forth horizontally, while of course during the back swing they rotate the blades so that the angle is 45 degrees again in this direction. The top on the forward swinging wing is then the bottom during the reverse swing.

The picture shows a bumblebee as the heaviest insect relative to its wing size in that moment, in which the forward swing of the wings has arrived just at the end. At this moment, these air flows have revealed, which brings 
aerodynamicist to despair. They see no more relationship to the movements of air, which are previously caused by airplane wings.

The picture of the air motions is determined by two large vortices. Out of this was born a vortex theory, even though vortex never can be active. Vortices must produced at all once. Vortices are only the consequences of something, never the cause for something! On bumblebee wings they are the consequence of the fact, that the wing moves too crossway through the air.

Although the wings of the bumblebee moved half crossways through the air, air will be accelerated in the perpendicular direction to the wing downward. The vertical component of this air force is lift force. But it is not quite enough. It is only so much how on an airplane in state "stall".
Fortunately some more adds. To  move the wings half crossways through the air, the drag against this direction of movement will be considerably greater by the generation of the vortices. However, this drag force also acts perpendicular to the surfaces of the wings, with respect to the vertical 45 degrees from bottom to top, ie in the same direction as before the air moving down "normal" by its angles of the blades.

It does not matter for which reason air exerts a force on surface, it is always perpendicular to the surface. Gases cannot exerts shear forces. 

The combined product of the two forces generates
enough vertical lift for flying. All air forces interact perpendicular to the wings surfaces. Because lift is the vertical proportion of air force, by 45 degrees results a lift force from 71% of the total air force on the wings. With this  bees and all insects and the bumblebee can fly easily! Even pigeons rotate their wings so to the back side like insects, if they must start strong vertically. The upper wings surface shows during the back move down.

The total amount of air that is accelerated by insect wings down, also includes the drawn vortices: everything flows together down. Even the little wasp produces an air flow downwards, which is clearly noticeable in humid weather and near flight over the back of the hand.
More clearly than by the the flight of the bumblebee can the principle of flying nowhere seen, namely that it is a purely mechanical process and no mysterious effects such as Bernoulli or Coanda.

Why swings a bumblebee from side to side if they in fact want to stand still  on a place? Because otherwise it would fall in its self-induced downwash. Therefore it hovers alternately to rest air to the sides.