So I was thinking about Elon Musk's supersonic electric jet idea. Assuming we have sufficiently energy-dense batteries, where would the limits be in terms of speed and altitude.
His logic seems to be: electric (fan?) propulsion doesn't need oxygen -> can go higher -> less friction -> need less power and thrust to maintain airspeed compared to traditional jet
Question: is there some kind of limit for altitude and TAS? I mean suppose the Concorde would be retrofitted with batteries and electric fans. Instead of mach 2 cruising at 18300 meters, assume it would climb to 30km, or even 40km. Air density at 18.3km is 0.115 kg / m^3, at 30km it's 0.018 kg / m^3 and at 40km it is 0.0039 kg / m^3.
So 0.0039 / 0.115 = 3.4%. Meaning the resistance at 40km would only be 3.4% compared to 18.3km. Would that mean the power or thrust requirement to maintain mach 2 would only be 3.4%? Or is induced drag becoming significant at that point? Or maybe it would even stall at mach 2 if flying 40km high?
I mean somehow there must be limits, otherwise we could just fly higher and higher and fly with 0 thrust and still maintain mach 2 (not talking about space flight here)?