How does altitude affect the TAS and thrust of an electric fan powered aircraft? I'm confused about the relation between IAS, TAS, thrust, and shaft power, for an electric application. Yes, higher air is thinner, and thrust goes down due to higher airspeed. What I've researched uses only air breathing engines for calculations.
Gas turbines either are limited to lower altitudes or higher altitudes with high speed, to intake enough air to maintain combustion. The other limiting factor is they have very strict maximum rpm. Modern turbofans do not have a variable transmission to counteract this. The same concept applies to electric motors, to a lesser degree.
For example, an electric driven ducted fan has a tip speed of Mach 0.85 and was set to maintain the same power output of say 50kw no matter the altitude.

What would happen to the TAS, IAS, thrust and the shaft rpm of the motor as well as tip speed of the ducted fan as the altitude increases?

Is the power necessary for an increase in TAS and a constant IAS the same up to the point where the increase in rpm (less load) due to thinner air causes the fan blades to see supersonic tip speeds?

If an aircraft can fly at 60 knots with 50 kw at sea level, does that mean at 50,000 ft it can realistically fly at 185 knots TAS for the same given power? (I used this calculator).


Also, how does thinner air affect static thrust?  Is the same thrust maintained as long as the same amount of power is given to spin the fan?
The Helios was an electric powered prop driven aircraft that achieved an altitude of over 96,000 feet and maintained it in level flight for more than 40 minutes.

as altitude increases

You maintain wing lift with constant IAS until the wing airflow approaches the speed of sound (TAS increases).  Shaft power output must increase to spin prop faster to maintain thrust or... changing prop pitch is helpful instead of increasing rpm.  This helps avoid the &quot;sound barrier&quot; for the prop.

as motor rpm increases

Even when not limited by supersonic prop tips, increased engine bearing friction from higher rpm requires a greater power draw.  Again, the ability to vary prop pitch is enormously helpful to maintain optimal prop AOA as TAS increases.

can I fly with the same amount of power at 50,000 feet as I can at sea level

You can get a lot closer by designing your aircraft to fly at 50,000 feet by:
 1.  Reducing wing loading by removing weight
 2.  Increasing wing aspect ratio and/or increasing wing area
 3.  Increasing the **area** of your prop so you can push more air at the same rpm.

With props, you must compensate for thinner air, but higher rpm is not the only way.