Electric aircraft have certain advantages and disadvantages, Casey Handmer notes:
Advantages include mechanical simplicity and reliability, reduced noise, reduced cost, increased efficiency, and reduced engine weight. The major disadvantage is that battery energy density is still, at best, about 50 times less than gasoline. Even factoring in other efficiency gains, electric aircraft have greatly reduced flying time and range.
The underlying reason that I believe electric aircraft can break the sound barrier is that electric motors can deliver far higher power-to-weight ratios than piston engines, jets, or turbines. The F-4 Phantom is a textbook example of high thrust, being able to (just) achieve a vertical climb. In contrast, for $100 I can buy a racing drone that can accelerate vertically at 10 gs. There are other factors at play but a power-to-weight ratio of 10 screams possibility.
In terms of fundamental physical limits, let’s consider the Concorde. While most fighter jets can fly supersonic for at most a few minutes, the Concorde couldn’t do in-flight refueling and had to cross the Atlantic in a single hop. It could cruise at Mach 2 for 201 minutes! Let’s say that when battery energy density and electric motor efficiency are factored in, electric systems with present technology would have 10x less range. Still, an electric Concorde could fly for 20 minutes, covering almost 450 miles. That’s more range than a Tesla!
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Of course it should be possible to develop a better configuration than a Concorde clone, but it’s an interesting starting point. In particular, many supersonic aircraft use delta wings because of relatively consistent lift characteristics over a range of speeds. It’s not that Concorde needs that enormous wing to fly at Mach 2 at 60,000 feet. Concorde needs the huge, draggy wing to fly slowly enough to land on a runway. But electric aircraft can deliver the necessary power and control to take off and land vertically (VTOL) like a helicopter, obviating the need for much wing at all.
Before diving into the specifics of different subsystems, I will motivate an example point design by appealing to the obvious. A supersonic electric aircraft must have a lot of thrust and minimal drag. When we think about what it might look like, the F-104 Starfighter comes to mind. Long, pointy, and with the barest minimum of a wing.
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Ordinarily, fast planes use jet engines for propulsion. Their compressor stages operate at subsonic speed so all supersonic jets have complex intake systems designed to decelerate inrushing air with a series of shocks prior to impacting the turbine. Building a turbine to ingest a supersonic stream ordinarily seems like a recipe for disaster. Jets need subsonic flow because combustion typically occurs subsonically. Electric propellers have no such constraint, and nor do they care that 80% of the atmosphere isn’t oxygen.