Validate atmospheric calculations

[dbookstaber]

During testing (the old test_danger_space unittest), with an absurdly dense atmosphere (1000 hPa) that led to a trajectory drop through 4000ft, the t in conditions.py::get_density_factor_and_mach_for_altitude() went negative. As best I can tell this is a temperature, so this shouldn't be possible no matter how extreme the variables. This function is probably supposed to do calculations in Kelvin, but it appears to be doing them in whatever Temperature units were set. So we need some test cases here.

Specific values found in this test case:

• t = -.008055
• _p0 = 1000
• _t0 = 15
• cP = -5.255876
• ta = 57.82
• tb = 72.8
• altitude = -3878
• x = 1038
• y = -4208

[dbookstaber]

The cIcaoFreezingPointTemperatureR is wrong: °R = °F + 459.67. Freezing point in °F = 32, so freezing point in °R = 491.67. However, making this correction breaks test_computer.py::test_temp_atmo. Actually it looks like the variable is just misnamed: It appears that everywhere in the code it is used to convert units between Rankine and Fahrenheit.

References for validation of the remaining logic:

• https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html
• https://en.wikipedia.org/wiki/Atmospheric_pressure#Altitude_variation
• https://en.wikipedia.org/wiki/Barometric_formula#Pressure_equations
• https://physics.stackexchange.com/questions/333475/how-to-calculate-altitude-from-current-temperature-and-pressure
• https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf

[dbookstaber]

C_d (drag coefficient) is a function of Mach number. Drag force is a function of air density * C_d.

drag = density_factor * velocity * self.drag_by_mach(velocity / mach)

where

density_factor, mach = atmo.get_density_factor_and_mach_for_altitude(alt0 + range_vector.y)

and

density_factor = density / cStandardDensity

Atmo.get_density_factor_and_mach_for_altitude() returns incorrect density. The adjusted pressure equation there is just wrong.

[dbookstaber]

References to validate:

• Calculator
• Another Calculator

Others:

• Mach number by temperature
• Standard atmosphere (temp, pressure, and density) by altitude
• Pressure at altitude or this calculator or this
• Density by temperature, std sea level
• Moist air density by temperature and pressure
• Density by temp, pressure, humidity, or this calculator or here
• Vapor pressure of water by temperature
• Water saturation pressure and review of models and another model

Python package: https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.density.html#metpy.calc.density