How can I figure out how much energy a hummingbird expends while hovering?

I don’t know all the formulas, but the approach to solving it is lift = load

Since F= mA, and m = mass of a hummingbird and A = acceleration of gravity (32ft/sec/sec), the lift energy must be equal to the load force.

According to this article 3–7 calories daily,

Hmm, I can find a lot more research on oxygen consumption than I can caloric use.

Oh, wait, this looks promising.

Hummingbirds appear to be well studied

I tried to come up with a witty analogy, and they all have holes.

- imagine the hummingbird/drone/helicopter is in a stream and wants to stay stationary
– imagine the h/d/h is in space, but is caught in the gravity of something other than Earth, that just happens to be accelerating it at 9.8 m/s/s
– imagine the h/d/h is twice as heavy, etc….

So I resorted to google, “physics of hovering” gives some good links

Amount of energy required to hover is good but assumes the air is giving a gliding bird the energy instead, as I understand it. That link has a link to why does holding something up cost energy while no work is being done.

From the abstract, The physics of flight: III. Hovering sounds like a paper created very similar to your own search. But I didn’t access it ;)

Regarding the work done, I think it depends on how big you make your system. No work is being done on the overall system, but in reality the lack of motion is because work is being done in smaller pieces of the system. Rotors are turning and wings are flapping to create the lift needed to offset gravity.

How much energy is needed really gets into efficiency, but it sounded like you were looking for a generalized answer.

These are great answers!!! The physicist in me says if I am not lifting the mass I am not doing work and therefore do not need to expend energy. But the engineer in me says that hummingbird is flapping wings at 250 beats per second, the drone is spinning the prop at 1000 rpm, the helicopter is spinning its prop at 120 rpm. That all expends energy. A lot of energy!

I am watching 4 hummingbirds at my 3 feeders arguing and fighting to prevent the others from feeding. One male hovers in front of the feeder to scare off the others. He is wasting so much energy being a prick protective. Their lives wold be so much better if they all shared.
I hope the females don’t mate with the bully.

@syz Did you see the hummingbirds muscle efficiency is only 4% to 15%!? No wonder those little buggers need to feed so often. And yet they can fly to Mexico. WTH?!?!?!

The physicist/engineer/nitpicker in me says that you can’t measure the energy it expends, because no real system is anywhere near 100% efficient, so an animal or machine always expends more energy than it is able to convert towards its intended task. There will be inefficiency in the physical systems, and inefficiency in the air friction and other side-effects of the movement used to generate the desired effect. You can only calculate the minimum resulting energy needed, which is just a function of mass * gravity + energy lost to all the inefficiencies.

Others have noted the apparent paradox that, since the hummingbird (or Helo) isn’t moving in a hover, the force countering gravity does no work, therefore there is no change in energy. This, of course is an illusion, based on an incorrect definition and analysis of the system in question. Both the Hummingbird and the Helo are accelerating a mass of air downwward, an action generating an opposing force which counteracts the force of gravity for the hovering object. A force is indeed appllied to the air mass by the bird’s wings ( Helo rotor) and the air mass does move. The work done on the air mass in this manner plus the losses in the bird’s body (helo engine & transmission) does indeed equal the energy expended.