atmosphere Module

Contains the following atmospheric functions:

• density = atm_density(alt, mach)

• mach = atm_mach(alt, velocity)

• velocity = atm_velocity(alt, mach)

• pressure = atm_pressure(alt)

• temperature = atm_temperature(alt)

• sos = atm_speed_of_sound(alt)

• mu = atm_dynamic_viscosity_mu(alt)

• nu = atm_kinematic_viscosity_nu(alt)

• eas = atm_equivalent_airspeed(alt, mach)

• rho, machs, velocity = make_flfacts_alt_sweep_constant_mach(

  mach, alts, eas_limit=1000., alt_units=’m’, velocity_units=’m/s’, density_units=’kg/m^3’, eas_units=’m/s’)

• rho, machs, velocity = make_flfacts_mach_sweep_constant_alt(

  alt, machs, eas_limit=1000., alt_units=’m’, velocity_units=’m/s’, density_units=’kg/m^3’, eas_units=’m/s’)

All the default units are in English units because the source equations are in English units.

pyNastran.utils.atmosphere.atm_calibrated_airspeed(alt: float, mach: float, alt_units: str = 'ft', cas_units: str = 'ft/s') → float

Calibrated airspeed

Parameters:

altfloat

altitude in alt_units

machfloat

Mach Number

$ M

$

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

cas_unitsstr; default=’ft/s’

the calibrated airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

Returns:

casfloat

Calibrated airspeed in cas_units

https://aerotoolbox.com/airspeed-conversions/

pyNastran.utils.atmosphere.atm_density(alt: float, R: float = 1716.0, alt_units: str = 'ft', density_units: str = 'slug/ft^3') → float

Freestream Density f$ rho_{infty} f$

Parameters:

altfloat

altitude in feet or meters

Rfloat; default=1716.

gas constant for air in english units (???)

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

density_unitsstr; default=’slug/ft^3’

the density units; slug/ft^3, slinch/in^3, kg/m^3, g/cm^3, Mg/mm^3

Returns:

rhofloat

density f$ rho f$ in density_units

Based on the formula P=pRT

f[ large rho=frac{p}{R T} f]

pyNastran.utils.atmosphere.atm_dynamic_pressure(alt: float, mach: float, alt_units: str = 'ft', pressure_units: str = 'psf') → float

Freestream Dynamic Pressure f$ q_{infty} f$

Parameters:

altfloat

Altitude in alt_units

machfloat

Mach Number f$ M f$

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

pressure_unitsstr; default=’psf’

the pressure units; psf, psi, Pa, kPa, MPa

Returns:

dynamic_pressurefloat

Returns dynamic pressure in pressure_units

The common method that requires many calculations…

f[ large q = frac{1}{2} rho V^2 f]

f[ large p = rho R T f]

f[ large M = frac{V}{a} f]

f[ large a = sqrt{gamma R T} f]

so…

f[ large q = frac{gamma}{2} p M^2 f]

pyNastran.utils.atmosphere.atm_dynamic_viscosity_mu(alt: float, alt_units: str = 'ft', visc_units: str = '(lbf*s)/ft^2') → float

Freestream Dynamic Viscosity f$ mu_{infty} f$

Parameters:

altfloat

Altitude in alt_units

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

visc_unitsstr; default=’(lbf*s)/ft^2’

the viscosity units; (lbf*s)/ft^2, (N*s)/m^2, Pa*s, psf*s

Returns:

mufloat

dynamic viscosity f$ mu_{infty} f$ in (lbf*s)/ft^2 or (N*s)/m^2 (SI)

See also

sutherland_viscoscity ..

pyNastran.utils.atmosphere.atm_equivalent_airspeed(alt: float, mach: float, alt_units: str = 'ft', eas_units: str = 'ft/s') → float

Freestream equivalent airspeed

Parameters:

altfloat

altitude in alt_units

machfloat

Mach Number

$ M

$

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

eas_unitsstr; default=’ft/s’

the equivalent airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

Returns:

easfloat

equivalent airspeed in eas_units

EAS = TAS * sqrt(rho/rho0)

p = rho * R * T

rho = p/(RT)

rho/rho0 = p/T * T0/p0

TAS = a * M

EAS = a * M * sqrt(p/T * T0/p0)

EAS = a * M * sqrt(p*T0 / (T*p0))

pyNastran.utils.atmosphere.atm_kinematic_viscosity_nu(alt: float, alt_units: str = 'ft', visc_units: str = 'ft^2/s') → float

Freestream Kinematic Viscosity f$ nu_{infty} f$

Parameters:

altfloat

Altitude in alt_units

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

visc_unitsstr; default=’slug/ft^3’

the kinematic viscosity units; ft^2/s, m^2/s

Returns:

nufloat

kinematic viscosity f$ nu_{infty} f$ in visc_units

f[ large nu = frac{mu}{rho} f]

See also

sutherland_viscoscity ..

Todo

better debug ..

pyNastran.utils.atmosphere.atm_mach(alt: float, V: float, alt_units: str = 'ft', velocity_units: str = 'ft/s') → float

Freestream Mach Number

Parameters:

altfloat

altitude in alt_units

Vfloat

Velocity in velocity_units

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

velocity_unitsstr; default=’ft/s’

the velocity units; ft/s, in/s, knots, m/s, cm/s, mm/s

Returns:

machfloat

Mach Number f$ M f$

f[ large M = frac{V}{a} f]

pyNastran.utils.atmosphere.atm_pressure(alt: float, alt_units: str = 'ft', pressure_units: str = 'psf') → float

Freestream Pressure f$ p_{infty} f$

Parameters:

altfloat

Altitude in alt_units

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

pressure_unitsstr; default=’psf’

the pressure units; psf, psi, Pa, kPa, MPa

Returns:

pressurefloat

Returns pressure in pressure_units

Note

from BAC-7006-3352-001-V1.pdf # Bell Handbook of Aerodynamic Heatingn page ~236 - Table C.1n These equations were used b/c they are valid to 300k ft.n Extrapolation is performed above that.n

pyNastran.utils.atmosphere.atm_speed_of_sound(alt: float, alt_units: str = 'ft', velocity_units: str = 'ft/s', gamma: float = 1.4) → float

Freestream Speed of Sound f$ a_{infty} f$

Parameters:

altfloat

Altitude in alt_units

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

velocity_unitsstr; default=’ft/s’

the velocity units; ft/s, m/s, in/s, knots

gamma: float; default=1.4

the specific heat ratio Cp/Cv; gamma=1.4 for air

Returns:

speed_of_sound, afloat

Returns speed of sound in velocity_units

f[ large a = sqrt{gamma R T} f]

pyNastran.utils.atmosphere.atm_temperature(alt: float, alt_units: str = 'ft', temperature_units: str = 'R') → float

Freestream Temperature f$ T_{infty} f$

Parameters:

altfloat

Altitude in alt_units

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

temperature_unitsstr; default=’R’

the altitude units; R, K

Returns:

Tfloat

temperature in degrees Rankine or Kelvin (SI)

Note

from BAC-7006-3352-001-V1.pdf # Bell Handbook of Aerodynamic Heatingn page ~236 - Table C.1n These equations were used because they are valid to 300k ft.n Extrapolation is performed above that.

pyNastran.utils.atmosphere.atm_unit_reynolds_number(alt: float, mach: float, alt_units: str = 'ft', reynolds_units: str = '1/ft') → float

Returns the Reynolds Number per unit length.

Parameters:

altfloat

Altitude in alt_units

machfloat

Mach Number f$ M f$

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

reynolds_unitsstr; default=’1/ft’

the altitude units; 1/ft, 1/m, 1/in

Returns:

ReynoldsNumber/Lfloat

the Reynolds Number per unit length

f[ large Re_L = frac{ rho V}{mu} = frac{p M a}{mu R T} f]

Note

this version of Reynolds number directly calculates the base quantities, so multiple calls to atm_press and atm_temp are not made

pyNastran.utils.atmosphere.atm_velocity(alt: float, mach: float, alt_units: str = 'ft', velocity_units: str = 'ft/s') → float

Freestream Velocity f$ V_{infty} f$

Parameters:

altfloat

altitude in alt_units

machfloat

Mach Number f$ M f$

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

velocity_unitsstr; default=’ft/s’

the velocity units; ft/s, m/s, in/s, knots

Returns:

velocityfloat

Returns velocity in velocity_units

f[ large V = M a f]

pyNastran.utils.atmosphere.cas_to_mach(alt: float, vcas: float, alt_units: str = 'ft', cas_units: str = 'ft/s')

Get Mach Number from calibrated airspeed

Parameters:

altfloat

Altitude in alt_units

vcasfloat

Calibrated airspeed in cas_units

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

cas_unitsstr; default=’ft/s’

the calibrated airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

Returns:

altfloat

Altitude in alt_units

cas = a0 * mach_comp

mach_comp = vcas/a0

mach_comp = np.sqrt(5 * ((qc/p0+1)**(1/3.5) - 1))

qc = p0 * ((1 + 0.2*mach_comp**2)**3.5 - 1)

qc = p * ((1 + 0.2*mach**2)**3.5 - 1)

mach = sqrt(5 * ((qc/p+1)**(1/3.5) - 1))

pyNastran.utils.atmosphere.constant_alt_line_alt_mach(alt: float, mach0: float, mach1: ndarray, num: int = 20, alt_units: str = 'ft', eas_units: str = 'knots') → None

creates a constant altitude line between two mach numbers

pyNastran.utils.atmosphere.constant_mach_line_alt1_alt2(mach: float, alt0: float, alt1: ndarray, num: int = 20, alt_units: str = 'ft', eas_units: str = 'knots') → tuple[ndarray, ndarray, ndarray]

creates a constant mach line between two altitutdes

pyNastran.utils.atmosphere.create_atmosphere_table(quantities: list[str], mach: float, alt_min: float, alt_max: float, nalt: int = 0, dalt: float = 0.0, alt_units: str = 'ft', density_units: str = 'slug/ft^3', pressure_units: str = 'psf', temperature_units: str = 'R', velocity_units: str = 'ft/s', dynamic_viscosity_units: str = '(lbf*s)/ft^2') → array

Parameters:

quantities list[str]

alt_minfloat

alt_maxfloat

naltint

daltfloat

alt_unitsstr; default=’m’

the altitude units; ft, kft, m

velocity_unitsstr; default=’m/s’

the velocity units; ft/s, m/s, in/s, knots

density_unitsstr; default=’kg/m^3’

the density units; slug/ft^3, slinch/in^3, kg/m^3, g/cm^3, Mg/mm^3

pressure_unitsstr; default=’psf’

the pressure units; psf, psi, Pa, kPa, MPa

temperature_unitsstr; default=’R’

the altitude units; R, K

dynamic_viscosity_unitsstr; default=’(lbf*s)/ft^2’

the dynamic viscosity, mu; (lbf*s)/ft^2, (N*s)/m^2, Pa*s, psf*s

out = create_atmosphere_table(

quantities, mach, alt_min=0, alt_max=10000, dalt=1000.)

out[:, 0] # alt

[0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000]

pyNastran.utils.atmosphere.eas_from_alts_machs(alts: list[float] | ndarray, machs: list[float] | ndarray, alt_units: str = 'ft', eas_units: str = 'knots') → ndarray

pyNastran.utils.atmosphere.get_alt_for_density(density: float, density_units: str = 'slug/ft^3', alt0: float = 0.0, alt_units: str = 'ft', nmax: int = 20, tol: float = 0.1) → float

Gets the altitude associated with a given air density.

Parameters:

densityfloat

the air density in slug/ft^3

density_unitsstr; default=’slug/ft^3’

the density units; slug/ft^3, slinch/in^3, kg/m^3, g/cm^3, Mg/mm^3

alt_unitsstr; default=’ft’

sets the units for the output altitude; ft, m, kft

nmaxint; default=20

max number of iterations for convergence

tolfloat; default=0.1

tolerance in alt_units

Returns:

altfloat

the altitude in feet

pyNastran.utils.atmosphere.get_alt_for_eas_with_constant_mach(equivalent_airspeed: float, mach: float, velocity_units: str = 'ft/s', alt_units: str = 'ft', nmax: int = 20, tol: float = 0.1) → float

Gets the altitude associated with an equivalent airspeed.

Parameters:

equivalent_airspeedfloat

the equivalent airspeed in velocity_units

machfloat

the mach to hold constant

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

velocity_unitsstr; default=ft/s

the velocity units; ft/s, m/s, in/s, knots

nmaxint; default=20

max number of iterations for convergence

tolfloat; default=5.

tolerance in alt_units

Returns:

altfloat

the altitude in alt units

pyNastran.utils.atmosphere.get_alt_for_mach_eas(mach: float, eas: float, eas_units: str = 'knots', alt_units: str = 'ft', nmax: int = 20, tol: float = 0.1) → float

Gets the altitude associated with an equivalent airspeed.

Parameters:

machfloat

the Mach number

easfloat

the equivalent airspeed in eas_units

eas_unitsstr; default=’knots’

the equivalent airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

nmaxint; default=20

max number of iterations for convergence

tolfloat; default=0.1

altitude tolerance in alt_units

Returns:

altfloat

the altitude in alt_units

pyNastran.utils.atmosphere.get_alt_for_pressure(pressure: float, pressure_units: str = 'psf', alt_units: str = 'ft', nmax: int = 20, tol: float = 0.1) → float

Gets the altitude associated with a pressure.

Parameters:

pressurefloat

the pressure lb/ft^2 (SI=Pa)

pressure_unitsstr; default=’psf’

the pressure units; psf, psi, Pa, kPa, MPa

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

nmaxint; default=20

max number of iterations for convergence

tolfloat; default=0.1

altitude tolerance in alt_units

Returns:

altfloat

the altitude in alt_units

pyNastran.utils.atmosphere.get_alt_for_q_with_constant_mach(q: float, mach: float, pressure_units: str = 'psf', alt_units: str = 'ft', nmax: int = 20, tol: float = 0.1) → float

Gets the altitude associated with a dynamic pressure.

Parameters:

qfloat

the dynamic pressure lb/ft^2 (SI=Pa)

machfloat

the mach to hold constant

pressure_unitsstr; default=’psf’

the pressure units; psf, psi, Pa, kPa, MPa

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

nmaxint; default=20

max number of iterations for convergence

tolfloat; default=0.1

tolerance in alt_units

Returns:

altfloat

the altitude in alt_units

pyNastran.utils.atmosphere.get_mach_for_alt_eas(alt: float, eas: float, eas_units: str = 'knots', alt_units: str = 'ft', gamma: float = 1.4) → float

Gets the altitude associated with an equivalent airspeed.

Parameters:

altfloat

the altitude in alt_units

easfloat

the equivalent airspeed in eas_units

eas_unitsstr; default=’knots’

the equivalent airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

alt_unitsstr; default=’ft’

the altitude units; ft, kft, m

gammafloat; default=1.4

gas constant

Returns:

altfloat

the altitude in alt_units

pyNastran.utils.atmosphere.make_flfacts_alt_sweep_constant_mach(mach: float, alts: np.ndarray, eas_limit: float = 1000.0, alt_units: str = 'm', velocity_units: str = 'm/s', density_units: str = 'kg/m^3', eas_units: str = 'm/s') → tuple[NDArrayNfloat, NDArrayNfloat, NDArrayNfloat]

Makes a sweep across altitude for a constant Mach number.

Parameters:

machfloat

Mach Number

$ M

$

altslist[float]

Altitude in alt_units

eas_limitfloat

Equivalent airspeed limiter in eas_units

alt_unitsstr; default=’m’

the altitude units; ft, kft, m

velocity_unitsstr; default=’m/s’

the velocity units; ft/s, in/s, knots, m/s, cm/s, mm/s

density_unitsstr; default=’kg/m^3’

the density units; slug/ft^3, slinch/in^3, kg/m^3, g/cm^3, Mg/mm^3

eas_unitsstr; default=’m/s’

the equivalent airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

pyNastran.utils.atmosphere.make_flfacts_alt_sweep_constant_tas(tas: float, alts: ndarray, alt_units: str = 'm', velocity_units: str = 'm/s', density_units: str = 'kg/m^3', eas_limit: float = 1000.0, eas_units: str = 'm/s') → tuple[ndarray, ndarray, ndarray]

Veas = Vtas * sqrt(rho/rho0) Vtas = Veas * sqrt(rho0/rho) Vtas = sos * Mach Mach = Vtas / sos = Veas/sos * sqrt(rho0/rho)

pyNastran.utils.atmosphere.make_flfacts_eas_sweep_constant_alt(alt: float, eass: list[float], eas_min: float = 0.0, alt_units: str = 'm', velocity_units: str = 'm/s', density_units: str = 'kg/m^3', eas_units: str = 'm/s') → tuple[NDArrayNfloat, NDArrayNfloat, NDArrayNfloat]

Makes a sweep across equivalent airspeed for a constant altitude.

Parameters:

altfloat

Altitude in alt_units

easslist[float]

Equivalent airspeed in eas_units

alt_unitsstr; default=’m’

the altitude units; ft, kft, m

velocity_unitsstr; default=’m/s’

the velocity units; ft/s, in/s, knots, m/s, cm/s, mm/s

density_unitsstr; default=’kg/m^3’

the density units; slug/ft^3, slinch/in^3, kg/m^3, g/cm^3, Mg/mm^3

eas_unitsstr; default=’m/s’

the equivalent airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

pyNastran.utils.atmosphere.make_flfacts_eas_sweep_constant_mach(mach: float, eass: np.ndarray, gamma: float = 1.4, minus_eas: list[float] | None = None, alt_units: str = 'ft', velocity_units: str = 'ft/s', density_units: str = 'slug/ft^3', eas_units: str = 'knots') → tuple[NDArrayNfloat, NDArrayNfloat, NDArrayNfloat, NDArrayNfloat]

Makes a sweep across equivalent airspeed for a constant altitude.

Parameters:

machfloat

Constant mach number

easslist[float]

Equivalent airspeed in eas_units

alt_unitsstr; default=’m’

the altitude units; ft, kft, m

velocity_unitsstr; default=’m/s’

the velocity units; ft/s, m/s, in/s, knots

density_unitsstr; default=’kg/m^3’

the density units; slug/ft^3, slinch/in^3, kg/m^3, g/cm^3, Mg/mm^3

eas_unitsstr; default=’m/s’

the equivalent airspeed units; ft/s, m/s, in/s, knots

gammafloat; default=1.4

the gas constant

minus_easfloat; default=0.0

tag the velocity with a -1

Veas = Vtas * sqrt(rho/rho0)

a * mach = Vtas

a = sqrt(gamma*R*T)

p = rho*R*T -> rho = p/(R*T)

Vtas = Veas * sqrt(rho0 / rho)

Veas = mach * sqrt(gamma*R*T) * sqrt(p/(R*T*rho0))

Veas = mach * sqrt(gamma*p / rho0)

Veas^2 / mach^2 = gamma * p / rho0

p = Veas^2 / mach^2 * rho0/gamma

pyNastran.utils.atmosphere.make_flfacts_mach_sweep_constant_alt(alt: float, machs: list[float], eas_limit: float = 1000.0, eas_min: float = 0.0, alt_units: str = 'm', velocity_units: str = 'm/s', density_units: str = 'kg/m^3', eas_units: str = 'm/s') → tuple[NDArrayNfloat, NDArrayNfloat, NDArrayNfloat]

Makes a sweep across Mach number for a constant altitude.

Parameters:

altfloat

Altitude in alt_units

machslist[float]

Mach Number

$ M

$

eas_limitfloat

Equivalent airspeed limiter in eas_units

alt_unitsstr; default=’m’

the altitude units; ft, kft, m

velocity_unitsstr; default=’m/s’

the velocity units; ft/s, in/s, knots, m/s, cm/s, mm/s

density_unitsstr; default=’kg/m^3’

the density units; slug/ft^3, slinch/in^3, kg/m^3, g/cm^3, Mg/mm^3

eas_unitsstr; default=’m/s’

the equivalent airspeed units; ft/s, in/s, knots, m/s, cm/s, mm/s

pyNastran.utils.atmosphere.make_flfacts_tas_sweep_constant_alt(alt: float, tass: ndarray, eas_limit: float = 1000.0, alt_units: str = 'm', velocity_units: str = 'm/s', density_units: str = 'kg/m^3', eas_units: str = 'm/s') → tuple[ndarray, ndarray, ndarray]

TODO: not validated

pyNastran.utils.atmosphere.sutherland_viscoscity(T: float) → float

Helper function that calculates the dynamic viscosity f$ mu f$ of air at a given temperature.

Parameters:

Tfloat

Temperature T is in Rankine

Returns:

mufloat

dynamic viscosity f$ mu f$ of air in (lbf*s)/ft^2

Note

prints a warning if T>5400 deg R

Sutherland’s Equationn

From Aerodynamics for Engineers 4th Editionn

John J. Bertin 2002n

page 6 eq 1.5bn