let's assume the holes are round shape in the middle of both wings. if the size is 1% of the whole wing, how much will be the impact? i assume this is not linear, how much will be affected if the hole becomes bigger?

i suppose this is quite difficult as bumblebee's wings are moving, and might follow a complex route. are there research on this area?

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  • $\begingroup$ OK, I have to know... why are you asking this? $\endgroup$ – John Dvorak Apr 3 at 2:07
  • $\begingroup$ @JohnDvorak just from curiosity... $\endgroup$ – athos Apr 3 at 2:09

While a full fluid dynamic and biomechanical treatment is complex, I think one can make a simple scaling argument:

Bumblebees are small. That means that the Reynolds number of fluid flow around them also gets scaled down; in fact, to a bumblebee air is a pretty viscous fluid. Hence the resistance to flowing through a small hole will be pretty big.

One can roughly estimate this by thinking of the hole as an orfice plate (in a very large pipe, so $\beta\approx 0$). Since the mass flow is proportional to the surface area of the hole we should guesstimate that a 1% hole has a pretty minor effect both on escaping air and the overall flow pattern.

In fact, looking at small moths one often finds that they have wings that are little more than a few feathers with pretty noticeable holes. This is just like how one can use a pole not just to push a punt in a river but also use it as both an oar and a rudder: in the viscous water environment the rod has enough area to matter anyway.

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    $\begingroup$ My guess is that a small hole may actually enhance vortex production, but it may also undermine wing strength. And of course, extra vortices that the insect can't control are probably not very useful. An important aspect of vortex generation is that they enhance viscosity. "Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity." - Lewis Fry Richardson. $\endgroup$ – PM 2Ring Apr 3 at 15:32

You are right. This is a spectacularly difficult problem. Considering the many assumptions that need to be made re: wing shape, wing motion, bee weight size & shape, flight profiles, and location of hole, a theoretical model will likely be woefully divergent from reality.

I suggest an empirical study. This will be necessary regardless just to verify the assumptions made, so you may as well go one step further and hole punch them too.


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