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Can we stop talking about quadcopters as if they're the only kind of drone on the planet? There are other kinds of drones with far better endurance, e.g. Predator drones which can stay in the air for 24 hours.
The usable energy density of fossil fuel is hard to beat, especially in a weight-constrained application like a drone. I'm surprised more of these haven't hit the market yet. The refueling advantage is substantial in a fleet application, too.
Weight-constrained and energy-hungry. Fixed wing drones can stay up for much longer.
Have both, a quadplane.. (or triplane in the below case).

VTOL (Vertical Take Off & Landing) plus the economy of fixed wing flight. In the case below, flown automatically by ArduPilot. https://youtu.be/hDG-KlYyYDU?t=65

Something that has been on my mind for a while is how much efficiency is needed (and how far from that are we) to have a drone hold itself aloft on it's own solar power.

It's probably a bit tricky to get data on solar panel efficiency by weight.

You can have an easier time if the solar panels are mounted on the bottom of the drone, and you shine a large laser at them. Disclaimer: I am involved with a company that does it this way.

Nasa has built[0] a drone awhile back that flies on solar power, though it was limited to flights during daylight hours as not enough mass was available for enough batteries to last the night.

[0]: https://www.nasa.gov/centers/dryden/history/pastprojects/Era...

This is something I've wondered about for a long time. Good to see it happen :)

Could it go even longer if the motors burned the fuel directly?

Could fuel motor speeds be controlled with enough bandwidth to remain stable like electric ones?

Four separate gasoline engines would be very heavy and a single engine with distribution driveshafts would be mechanically complicated. For fuel-powered rotary wings the speed cannot be varied fast enough to maintain control, so you'd use a collective pitch control on the rotor blades to achieve stable flight.
That's a super weird camera angle. I wonder if it's in ground effect?