Wednesday, January 8, 2014

A Hovering Darner, Part III

The previous two installments on this topic focussed on the vertical motion of the darner as it hovers.  We've seen that it bobs up and down with a frequency of about 4.5 bobs per second, with roughly 4 strong wingbeats alternating with 4 weak wingbeats for each cycle of the bobbing motion.  These installments can be found at the following links:

We now include the horizontal motion in our analysis.  I didn't know what to expect when I started, but it turns out that the darner is making a series of "orbits" as it hovers.  Here's an example of an orbital cycle:

The orbits are traversed in the counterclockwise direction, but this is not significant because the orbits would be clockwise if viewed from the other side of the darner.  What is significant is that the darner moves forward as it drops in altitude, and moves backward as it rises.  This is the same regardless of the side from which it is viewed.

Here's another example of an orbital cycle.

The series of bobbing cycles shown below is interesting in terms of the corresponding orbits.  You can see that cycle 2 rises higher, and takes more time to complete, than the other cycles.  Is this difference reflected in the orbits?  Let's see.

First, for comparison, let's look at the orbits for cycles 1, 3, and 4.  As we can see below, these orbits are quite typical in shape.

When we look at the orbit for cycle 2, however, we see something quite different.  As shown below, the cycle 2 "orbit" consists of two loops – a sort of loop-the-loop orbit – with both loops orbited in the counterclockwise direction.  Thus, cycle 2 does have a different type of orbit, after which normal bobbing cycles continue as before.

Finally, I've collected below a number of orbits in a 3x3 grid.  The center square shows the takeoff of the darner, and the surrounding squares show a variety of different orbits, including the loop-the-loop in the lower right square.

What's particularly interesting to me about this figure is that it was drawn by the dragonfly itself.  Each orbit was traced out by the darner during one of its up-and-down bobs.  Nice work, Mr. Happy-face!

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