I found a lot of references to the question but no definite simple answer. What would be the influence on true airspeed (TAS) for same airplane at same throttle setting flying straight and level at higher altitude? Would it change for Jet engine vs internal combustion engine?
The answer to your question largely depends on what you mean by "constant throttle setting".
For propeller propulsion, if "constant throttle setting" means "constant power setting" as in a fixed output BHP, TAS will increase almost linearly with altitude (up to the altitude where constant power output can no longer be maintained).
For a normally aspirated reciprocating engine with a fixed pitch propeller, a constant throttle position will mean a decreased manifold pressure with increased altitude resulting in less power output, less thrust (T), and thus decreasing TAS (assuming the decrease in thrust is larger than the decrease in drag (D) resulting from the decreased density at higher altitude, this generally holds true). For a supercharged engine, depending on how the supercharger is controlled, "constant throttle setting" can have the charge control maintain a constant manifold pressure. In this case, the power setting will be maintained (up to the maximum altitude where the supercharger can maintain the manifold pressure), and TAS will increase.
For a jet propulsion engine, once again it depends on what is implied with "constant thrust setting". For example, for low/no bypass engines, a constant EPR should roughly correspond to constant T with altitude, hence with D decreasing with altitude, TAS will be higher before T = D. If "constant thrust" means "constant N1", thrust will actually decrease with altitude, how quickly it decreases with altitude will determine the effect on TAS (once again, where T = D).
If "constant throttle setting" simply implies "constant thrust". Resulting TAS will always be higher (as for a given TAS, T remains constant and D once again decreases).
The true airspeed (TAS) is determined by adjusting the indicated airpseed (IAS) for altitude and outside air temperature (OAT).
Faster small airplanes have a TAS calculator built in to the ASI. To use it, the pilot dials in the pressure altitude read off the altimeter (ALT), and sometimes the OAT, and reads the TAS off a separate dial on the ASI. In this photo, the IAS is 105kts, and the TAS is 129kts @14,000ft, 147kts at 16,000, 164kts @ 18,000ft, 182kts @ 20,000.
In one airplane I fly, the cruise setting is 34" MP and 2400 RPM. This setting produces a higher TAS at higher altitudes.
For airplanes that don't have such a dial, the pilot can estimate the TAS by adding 2% per 1,000ft of altitude to the IAS. For example, 100kts IAS at 10,000 ft pressure altitude is 100kts * 20% = 20kts. So the TAS would be 120 kts.
True airspeed calculations become less accurate as altitude increases and the planes flies faster, but a jet and a plane both flying at the same indicated airspeed at 10,000ft will read the same TAS off the dial.
At higher altitudes, jets and turboprops use an "air data computer," such as this one, which states:
Air data computers are used by aircraft to acquire and process data from sensors (such as pitot tubes and avionics buses) to obtain key air data parameters such as altitude, airspeed, height deviation and temperature to ensure safe and accurate flight detail, on both rotary and fixed wing aircraft.