In my scifi setting small utility robot swarms are used for many purposes. I'm currently trying to estimate how much energy such a swarm would need to operate. Since biology, robotics and nanotechnology have pretty much merged into one thing in the setting I decided that taking bees as an example for a standard mircobot is as good as starting point as I'm going to get. So how much power ($W$) does a bee nee to fly?
Or to put a more hard-science spin on it, how much power ($W$) does a flying object of a mass ($m$) need to fly with a speed of ($v$) in an environment with an airpressure of ($p$), which might be anything from 0 to 25 bar, and a gravity of ($g$), which might be anything from 0 to 5 times that of Earth?
I know that a precise answer to this is probably extremely hard to give, but that isn't really my goal. I need to know the order of magnitude of energy these droneswarms will consume, so I can figure out if the powessource of the swarm should be batteries, chemical fuels or small nuclear reactors. This information is just here to give some context, it is irrelevant for the actual question.
A great answer would provide me with a formula and a right estimate for the bee-sized mircobot. The bee value is supposed to be a sanity check.