Ducted fans still run into the same issues if the airflow reaching the blades is supersonic. However with a ducted fan you can have the inlet slow the air down to subsonic speeds. In this way ducted fans are used in nearly all supersonic aircraft today. It should be noted though that these turbofans for supersonic use are way smaller than those in use for subsonic aircraft. A 3 meter diameter fan is close to the current limit for such subsonic flight fans, scaling up a supersonic fan that large is still non-trivial.

As for heating up the air and pushing it out, that concept is known as an airbreathing arcjet, which is really just a ramjet. While preventing the electrode from eroding is something of a technical challenge, it's comparatively mild. The main issue here is just power: batteries tend to discharge slowly so to get enough instantaneous power you need a very large number of batteries discharging in parallel, which are very heavy. However if you're just looking to set a speed record and not actually fly any useful distance, this may not be too much of an issue. Personally an arcjet would be my strategy of choice.

Couldn't you have a supersonic inlet widening into an area with a subsonic fan, then narrowing again to a supersonic outlet?

Sort of like medium inlet, x-large fan area, small outlet?

Yes that's exactly the principle. You can get up to about mach 3 to mach 4 before stagnation temperature (when you slow down a supersonic flow, it heats up) starts making this approach impractical.

But there's no way of getting around the fact that if you have a 3 meter diameter fan, you have at the very minimum a 7 m^2 cross sectional area that you are sticking into a supersonic airstream, and in reality that inlet is going to be pretty beefy too. That creates a lot of drag that the fan needs to overcome to produce net thrust.

> That creates a lot of drag that the fan needs to overcome to produce net thrust.

That's a great point, thank you for educating me.

Heating it would require an enormous amount of power.

A heat-producing fuel of some sort would make that more efficient. As a bonus, the aircraft would get lighter and lighter as it flew. Imagine the electricity savings!

> Would a ducted fan work better?

This comment is ironic because it initially sounds naive, but is probably the most insightful comment.

You could make a supersonic propeller-driven airplane by mounting the propeller(s) in a shroud, using a powerful engine (possibly geared), and slowing down the airstream to subsonic speed in the shroud (the same way a jet engine is designed.)

The result would be a propeller system that outwardly looks like a jet engine, but internally still has propeller(s) on a shaft(s).

The advantage would be better efficiency at low altitudes if a piston engine was used, since piston engines burn about half as much fuel as jet engines.

Nobody will build this unless high-altitude flight is banned, and thus need the efficiency of piston engines.

Rotax uses essentially a geared lawnmower engine in aviation piston applications that is half the weight of a Lycoming or Continental (because of the gearing.) So hey ... there is room for innovation.

You're not going to get a supersonic helicopter (that looks like a conventional helicopter) without retracting the blades for several reasons, starting with the advancing blade being higher speed than the retreating blade, which makes transsonic and supersonic flight with horizontal blades impractical and risky.

Current fast helicopters have stubby wings, so behave like an airplane, which is kind of cheating. To create a supersonic helicopter would mean either ducted fans instead of blades, or an entirely new technology.

Source: I study aerodynamics.

Downvoting isn't a mod-only thing.