Flight at high altitude
Flight at high altitude
Some information is summarized in the main page already, in the aircraft section.
Gas properties and altitude
Density is a very useful property in aeronautics. It's for example used to calculate the lift and the drag of an aerofoil, the thrust of an engine or even the heat transferred by air. We must know, at least approximately, what air density will be faced in order to design everything. An atmosphere model should be used for design, but can also be used at runtime to verify that the actual atmosphere is within prediction range. The most used model is the ISA (International Standard Atmosphere) from 1975. It is quite simple and provides temperature, pressure and density as function of altitude, between -2km and 86km. A calculator for the model is available here (example values). We use this model to estimate the heat transfer to cryogenic tanks during rocket ascension to ignition altitude. Our implementation can be found here: File:ISA atmospheric model.c.
Air density depends on pressure and temperature, and thus on altitude. Some pressure values can be found in this table or this one. We can see that a tenth of sea level atmospheric pressure (1atm: 101.325kPa) is met at around 16km altitude, and a hundredth of it at around 31km altitude.
Air density in the atmosphere is also related to the ratio of water vapour in it, as indicated on this page. The page also contains lots of formulas and calculators, most importantly the air density calculator that we'll use right below for the examples. Water vapour is much less abundant when temperature goes down, as it does in the higher troposphere or low to mid stratosphere that we're aiming. The calculator gives us, with temperature and pressure values taken from the table mentioned above, values for density of:
- 1.214 kg/m^3 at sea level (15°C)
- 0.1877 kg/m^3 at 15km altitude (-57°C)
- 0.0441 kg/m^3 at 25km altitude (-52°C)
- 0.017 kg/m^3 at 30km altitude (-46°C)
Turbofan engine's Mass flow rate calculation
One way of calculating the MFR is to use the continuity equation. The mass of gas leaving the engine is the same than the mass of gas entering the engine, for which we know the density, plus the mass of the fuel, which is much lower than the mass of air. It's the velocity difference between input and output that creates the thrust.
Supersonic flight - high engine power
Is it possible to have a low total pressure ratio engine operating at subsonic inlet speeds and low air density? The MiG 25 has supersonic inlet, which allows him to have a significant pressure increase before the compressor actually gives energy to the flow. A subsonic input air flow in the high-altitude conditions is likely to not provide enough oxygen for the combustion to maintain by itself, or a too poor mass flow rate to the turbine. The SR-71 is another example for high-service ceiling (25900m, M3.2).
Subsonic flight - high lift
High engine power in low air density generally means supersonic flight, or at least, high flight speeds, which in return increase the lift of the aircraft or decrease its wingspan. Our next step is to make some calculations of the required winged area for subsonic low-density air travel, and assess the feasibility of our air launch to orbit project.