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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)?

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    $\begingroup$ Well, you need lift as well, which also reduces with increasing altitude. $\endgroup$
    – Koyovis
    Commented Feb 11, 2018 at 11:29
  • $\begingroup$ Well, lift is dependent on dynamic pressure to the same degree as drag, so, theoretically, at almost any altitude, as you increase speed to that same dynamic pressure that would produce the drag you have the power (thrust) to overcome, you would have the same amount of Lift, no? $\endgroup$
    – Charles Bretana
    Commented Feb 11, 2018 at 14:18
  • $\begingroup$ Another consideration is that as you go higher, and faster, Lift required decreases due to centrifugal force. Obviously, just outside the atmosphere, 200 miles up, orbital velocity is about 18,000 mph. So airspeeds at some significant percentage of that will garner the benefits of some reduction in required Lift. (to a degree dependent on speed and what direction you travel - with or against the eastward rotation of the earth) $\endgroup$
    – Charles Bretana
    Commented Feb 11, 2018 at 14:24
  • $\begingroup$ If you remove the limitation of battery the next limitation is probably weight. At high speed and high altitude the engine would probably a jet with high exhaust velocity, where hot jet (e.g. turbo jet, ram jet, and low-bypass turbo fan) has a clear weight advantage over cold jet (e.g electric jet). IMO if you want low carbon super sonic travel implemented with reasonable amount of time and money budget, hyperloop would be slightly more practical, or hydrogen fuel. $\endgroup$
    – user3528438
    Commented Feb 11, 2018 at 16:11
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    $\begingroup$ Isn't the real limitation the amount of thrust you can generate from a fan or propellor? Which is going to depend on the density of the medium: consider the size difference between airplane & boat propellors generating the same thrust. $\endgroup$
    – jamesqf
    Commented Feb 11, 2018 at 19:50

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That electric propulsion needs no oxygen is of little help for flying high. The composition of the atmosphere does not change too much with altitude, so it is the low atmospheric density which limits maximum altitude. We had this discussion before, and indeed solar-electric propulsion helped to reach record altitudes: The AeroVironment Helios set a record at 29,524 m which will be hard to break.

Supersonic speed helps to fly high - while subsonic designs run into the coffin corner, supersonic flight helps to maintain high dynamic pressure even at altitude. However, the energy requirements for doing so will require an energy density of the batteries which is several magnitudes above what is currently possible. If you only want to go fast, the current limit with electrical propulsion and already rather generous assumptions is somewhere around Mach 2.

Flying higher does not reduce the thrust requirement since the same lift has to be generated. The best lift to drag ratio is achieved in subsonic flight. Going supersonic means crossing a drag peak, but beyond that the maximum possible lift to drag ratio is well below that at subsonic speed and decreases again with increasing Mach number.

Mr. Musk is clearly out of his competence when he claims that supersonic electric airplanes are viable, even with the progress in battery technology to be expected in the next few decades.

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  • $\begingroup$ I looked it up a bit and the available info seems very vague. The main idea seems to be that it is VTOL. I am guessing that even when supersonic it gets lift mainly by vectored thrust. And that it is more of a "potentially supersonic due to high engine power and low drag" than "actually has the range for supersonic to make sense". I guess "supersonic" is mostly because it sounds cool? It seems rather incidental to the main concept anyway. $\endgroup$
    – Ville Niemi
    Commented Feb 11, 2018 at 13:05
  • $\begingroup$ @VilleNiemi: Electric VTOL is even more challenging - the only remotely realistic concept I know of is from Volocopter, and there are quite a few out there. $\endgroup$
    – Peter Kämpf
    Commented Feb 11, 2018 at 17:42
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    $\begingroup$ @user15864: In subsonic flight it is indeed as you say (apart from density-related effects like less damping, and temperature-related effects like more friction drag and more heat engine efficiency), but when you come close to the speed of sound a new kind of drag emerges which will spoil the picture. $\endgroup$
    – Peter Kämpf
    Commented Feb 11, 2018 at 19:24
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    $\begingroup$ It's worth recognizing that many of the things that SpaceX and Tesla are doing were also decreed to be impossible or very unlikely several decades ago. That's no guarantee he will succeed at this endeavor, but worth pointing out. $\endgroup$
    – enderland
    Commented Feb 11, 2018 at 20:21
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    $\begingroup$ @enderland: McDonnel-Douglas demonstrated re-useable rockets a quarter of a century ago. However, the cosy duopoly for rockets in the US saw no need to advance to an orbital version. By hiring the best engineers from both, SpaceX had no problem to actually build the real thing. With Tesla, Musk happened to buy a company which was serious about doing EVs right, with lots of battery capacity (what their competition avoided). In both, Musk showed good engineering judgement. He does not with aircraft, however. $\endgroup$
    – Peter Kämpf
    Commented Feb 11, 2018 at 23:54

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