Atmo

Atmospheric conditions and density calculations

Properties

altitude: Altitude relative to sea level pressure: Unadjusted barometric pressure, a.k.a. station pressure temperature: Temperature humidity: Relative humidity [0% to 100%] powder_temp: Temperature of powder (if different from atmosphere). (Used when Ammo.use_powder_sensitivity is True) density_ratio: Ratio of current density to standard atmospheric density mach: Velocity of sound (Mach 1) for current atmosphere

Parameters:

Name	Type	Description	Default
`altitude`	`Optional[Union[float, Distance]]`	Altitude relative to sea level	`None`
`pressure`	`Optional[Union[float, Pressure]]`	Atmospheric pressure	`None`
`temperature`	`Optional[Union[float, Temperature]]`	Atmospheric temperature	`None`
`humidity`	`float`	Atmospheric relative humidity [0% to 100%]	`0.0`
`powder_t`	`Optional[Union[float, Temperature]]`	Custom temperature of powder different to atmospheric. Used when Ammo.use_powder_sensitivity is True	`None`

Example

This is how you can create an Atmo

from py_ballisticcalc import Atmo
atmo = Atmo(
    altitude=Unit.Meter(100),
    pressure=Unit.hPa(1000),
    temperature=Unit.Celsius(20),
    humidity=50,
    powder_t=Unit.Celsius(15)
)

Source code in py_ballisticcalc\conditions.py

def __init__(self,
             altitude: Optional[Union[float, Distance]] = None,
             pressure: Optional[Union[float, Pressure]] = None,
             temperature: Optional[Union[float, Temperature]] = None,
             humidity: float = 0.0,
             powder_t: Optional[Union[float, Temperature]] = None):
    """
    Create a new Atmo instance with given parameters

    Args:
        altitude: Altitude relative to sea level
        pressure: Atmospheric pressure
        temperature: Atmospheric temperature
        humidity: Atmospheric relative humidity [0% to 100%]
        powder_t: Custom temperature of powder different to atmospheric.
            Used when Ammo.use_powder_sensitivity is True

    Example:
        This is how you can create an Atmo
        ```python
        from py_ballisticcalc import Atmo
        atmo = Atmo(
            altitude=Unit.Meter(100),
            pressure=Unit.hPa(1000),
            temperature=Unit.Celsius(20),
            humidity=50,
            powder_t=Unit.Celsius(15)
        )
        ```
    """
    self._initializing = True
    self._altitude = PreferredUnits.distance(altitude or 0)
    self._pressure = PreferredUnits.pressure(pressure or Atmo.standard_pressure(self.altitude))
    self._temperature = PreferredUnits.temperature(temperature or Atmo.standard_temperature(self.altitude))
    # If powder_temperature not provided we use atmospheric temperature:
    self._powder_temp = PreferredUnits.temperature(powder_t or self.temperature)
    self._t0 = self.temperature >> Temperature.Celsius
    self._p0 = self.pressure >> Pressure.hPa
    self._a0 = self.altitude >> Distance.Foot
    self._mach = Atmo.machF(self._temperature >> Temperature.Fahrenheit)
    self.humidity = humidity
    self._initializing = False
    self.update_density_ratio()

altitude `property` ¶

altitude: Distance

Altitude relative to sea level

pressure `property` ¶

pressure: Pressure

Unadjusted barometric pressure, a.k.a. station pressure

temperature `property` ¶

temperature: Temperature

Local air temperature

humidity `property` `writable` ¶

humidity: float

Returns:

Type	Description
`float`	Relative humidity [0% to 100%]

powder_temp `property` ¶

powder_temp: Temperature

Powder temperature

density_ratio `property` ¶

density_ratio: float

Ratio of current density to standard atmospheric density

mach `property` ¶

mach: Velocity

Velocity of sound (Mach 1) for current atmosphere

density_metric `property` ¶

density_metric: float

Returns:

Type	Description
`float`	density in kg/m^3

density_imperial `property` ¶

density_imperial: float

Returns:

Type	Description
`float`	density in lb/ft^3

temperature_at_altitude ¶

temperature_at_altitude(altitude: float) -> float

Temperature at altitude interpolated from zero conditions using lapse rate. Args: altitude: ASL in ft Returns: temperature in °C

Source code in py_ballisticcalc\conditions.py

def temperature_at_altitude(self, altitude: float) -> float:
    """
    Temperature at altitude interpolated from zero conditions using lapse rate.
    Args:
        altitude: ASL in ft
    Returns:
        temperature in °C
    """
    t = (altitude - self._a0) * cLapseRateKperFoot + self._t0
    if t < Atmo.cLowestTempC:
        t = Atmo.cLowestTempC
        warnings.warn(f"Temperature interpolated from altitude fell below minimum temperature limit.  "
                      f"Model not accurate here.  Temperature bounded at cLowestTempF: {cLowestTempF}°F."
                      , RuntimeWarning)
    return t

update_density_ratio ¶

update_density_ratio() -> None

Updates the density ratio based on current conditions

Source code in py_ballisticcalc\conditions.py

def update_density_ratio(self) -> None:
    """
    Updates the density ratio based on current conditions
    """
    self._density_ratio = Atmo.calculate_air_density(self._t0, self._p0, self.humidity) / cStandardDensityMetric

pressure_at_altitude ¶

pressure_at_altitude(altitude: float) -> float

Pressure at altitude interpolated from zero conditions using lapse rate. Ref: https://en.wikipedia.org/wiki/Barometric_formula#Pressure_equations Args: altitude: ASL in ft Returns: pressure in hPa

Source code in py_ballisticcalc\conditions.py

def pressure_at_altitude(self, altitude: float) -> float:
    """
    Pressure at altitude interpolated from zero conditions using lapse rate.
    Ref: https://en.wikipedia.org/wiki/Barometric_formula#Pressure_equations
    Args:
        altitude: ASL in ft
    Returns:
        pressure in hPa
    """
    p = self._p0 * math.pow(1 + cLapseRateKperFoot * (altitude - self._a0) / (self._t0 + cDegreesCtoK),
                            cPressureExponent)
    return p

get_density_factor_and_mach_for_altitude ¶

get_density_factor_and_mach_for_altitude(altitude: float) -> Tuple[float, float]

Ref: https://en.wikipedia.org/wiki/Barometric_formula#Density_equations Args: altitude: ASL in units of feet. Note: Altitude above 36,000 ft not modelled this way. Returns: density ratio and Mach 1 (fps) for the specified altitude

Source code in py_ballisticcalc\conditions.py

def get_density_factor_and_mach_for_altitude(self, altitude: float) -> Tuple[float, float]:
    """
    Ref: https://en.wikipedia.org/wiki/Barometric_formula#Density_equations
    Args:
        altitude: ASL in units of feet.
            Note: Altitude above 36,000 ft not modelled this way.
    Returns:
        density ratio and Mach 1 (fps) for the specified altitude
    """
    # Within 30 ft of initial altitude use initial values to save compute
    if math.fabs(self._a0 - altitude) < 30:
        mach = self._mach
        density_ratio = self._density_ratio
    else:
        if altitude > 36089:
            warnings.warn("Density request for altitude above troposphere."
                           " Atmospheric model not valid here.", RuntimeWarning)
        t = self.temperature_at_altitude(altitude) + cDegreesCtoK
        mach = Velocity.MPS(Atmo.machK(t)) >> Velocity.FPS
        p = self.pressure_at_altitude(altitude)
        density_delta = ((self._t0 + cDegreesCtoK) * p) / (self._p0 * t)
        density_ratio = self._density_ratio * density_delta
        # # Alternative simplified model:
        # # Ref https://en.wikipedia.org/wiki/Density_of_air#Exponential_approximation
        # # see doc/'Air Density Models.svg' for comparison
        #density_ratio = self._density_ratio * math.exp(-(altitude - self._a0) / 34122)
    return density_ratio, mach

standard_temperature `staticmethod` ¶

standard_temperature(altitude: Distance) -> Temperature

Note: This model only valid up to troposphere (~36,000 ft). Args: altitude: ASL in units of feet. Returns: ICAO standard temperature for altitude

Source code in py_ballisticcalc\conditions.py

@staticmethod
def standard_temperature(altitude: Distance) -> Temperature:
    """
    Note: This model only valid up to troposphere (~36,000 ft).
    Args:
        altitude: ASL in units of feet.
    Returns:
        ICAO standard temperature for altitude
    """
    return Temperature.Fahrenheit(cStandardTemperatureF
                                  + (altitude >> Distance.Foot) * cLapseRateImperial)

standard_pressure `staticmethod` ¶

standard_pressure(altitude: Distance) -> Pressure

This model only valid up to troposphere (~36,000 ft).

Ref: https://en.wikipedia.org/wiki/Barometric_formula#Pressure_equations

Args: altitude: Distance above sea level (ASL) Returns: ICAO standard pressure for altitude

Source code in py_ballisticcalc\conditions.py

@staticmethod
def standard_pressure(altitude: Distance) -> Pressure:
    """
    Note: This model only valid up to troposphere (~36,000 ft).
        Ref: https://en.wikipedia.org/wiki/Barometric_formula#Pressure_equations
    Args:
        altitude: Distance above sea level (ASL)
    Returns:
        ICAO standard pressure for altitude
    """
    return Pressure.hPa(cStandardPressureMetric
        * math.pow(1 + cLapseRateMetric * (altitude >> Distance.Meter) / (cStandardTemperatureC + cDegreesCtoK),
                   cPressureExponent))

icao `staticmethod` ¶

icao(altitude: Union[float, Distance] = 0, temperature: Optional[Temperature] = None, humidity: float = cStandardHumidity) -> Atmo

Note: This model only valid up to troposphere (~36,000 ft). Args: altitude: relative to sea level temperature: air temperature Returns: Atmo instance of standard ICAO atmosphere at given altitude. If temperature not specified uses standard temperature.

Source code in py_ballisticcalc\conditions.py

@staticmethod
def icao(altitude: Union[float, Distance] = 0, temperature: Optional[Temperature] = None, humidity: float = cStandardHumidity) -> 'Atmo':
    """
    Note: This model only valid up to troposphere (~36,000 ft).
    Args:
        altitude: relative to sea level
        temperature: air temperature
    Returns:
        Atmo instance of standard ICAO atmosphere at given altitude.
        If temperature not specified uses standard temperature.
    """
    altitude = PreferredUnits.distance(altitude)
    if temperature is None:
        temperature = Atmo.standard_temperature(altitude)
    pressure = Atmo.standard_pressure(altitude)

    return Atmo(altitude, pressure, temperature, humidity)

machF `staticmethod` ¶

machF(fahrenheit: float) -> float

Parameters:

Name	Type	Description	Default
`fahrenheit`	`float`	Fahrenheit temperature	required

Returns: Mach 1 in fps for given temperature

Source code in py_ballisticcalc\conditions.py

@staticmethod
def machF(fahrenheit: float) -> float:
    """
    Args:
        fahrenheit: Fahrenheit temperature
    Returns:
        Mach 1 in fps for given temperature
    """
    if fahrenheit < -cDegreesFtoR:
        fahrenheit = cLowestTempF
        warnings.warn(f"Invalid temperature: {fahrenheit}°F. Adjusted to ({cLowestTempF}°F)."
                      , RuntimeWarning)
    return math.sqrt(fahrenheit + cDegreesFtoR) * cSpeedOfSoundImperial

machC `staticmethod` ¶

machC(celsius: float) -> float

Parameters:

Name	Type	Description	Default
`celsius`	`float`	Celsius temperature	required

Returns: Mach 1 in m/s for Celsius temperature

Source code in py_ballisticcalc\conditions.py

@staticmethod
def machC(celsius: float) -> float:
    """
    Args:
        celsius: Celsius temperature
    Returns:
        Mach 1 in m/s for Celsius temperature
    """
    if celsius < -cDegreesCtoK:
        bad_temp = celsius
        celsius = Atmo.cLowestTempC
        warnings.warn(f"Invalid temperature: {bad_temp}°C. Adjusted to ({celsius}°C)."
                      , RuntimeWarning)
    return Atmo.machK(celsius + cDegreesCtoK)

machK `staticmethod` ¶

machK(kelvin: float) -> float

Parameters:

Name	Type	Description	Default
`kelvin`	`float`	Kelvin temperature	required

Returns: Mach 1 in m/s for Kelvin temperature

Source code in py_ballisticcalc\conditions.py

@staticmethod
def machK(kelvin: float) -> float:
    """
    Args:
        kelvin: Kelvin temperature
    Returns:
        Mach 1 in m/s for Kelvin temperature
    """
    return math.sqrt(kelvin) * cSpeedOfSoundMetric

calculate_air_density `staticmethod` ¶

calculate_air_density(t: float, p: float, humidity: float) -> float

Calculate the air density given temperature, pressure, and humidity.

Parameters: t (float): Temperature in degrees Celsius. p (float): Pressure in hPa. humidity (float): The relative humidity as a fraction of max [0%-100%]

Returns:

Name	Type	Description
`float`	`float`	Air density in kg/m^3.

Notes: - Divide result by cDensityImperialToMetric to get density in lb/ft^3 - Source: https://www.nist.gov/system/files/documents/calibrations/CIPM-2007.pdf

Source code in py_ballisticcalc\conditions.py

@staticmethod
def calculate_air_density(t: float, p: float, humidity: float) -> float:
    """
    Calculate the air density given temperature, pressure, and humidity.

    Parameters:
    t (float): Temperature in degrees Celsius.
    p (float): Pressure in hPa.
    humidity (float): The relative humidity as a fraction of max [0%-100%]

    Returns:
        float: Air density in kg/m^3.

    Notes:
    - Divide result by cDensityImperialToMetric to get density in lb/ft^3
    - Source: https://www.nist.gov/system/files/documents/calibrations/CIPM-2007.pdf
    """
    R = 8.314472  # J/(mol·K), universal gas constant
    M_a = 28.96546e-3  # kg/mol, molar mass of dry air
    M_v = 18.01528e-3  # kg/mol, molar mass of water vapor

    def saturation_vapor_pressure(T):
        # Calculation of saturated vapor pressure according to CIPM 2007
        A = [1.2378847e-5, -1.9121316e-2, 33.93711047, -6.3431645e3]
        return math.exp(A[0] * T ** 2 + A[1] * T + A[2] + A[3] / T)

    def enhancement_factor(p, T):
        # Calculation of enhancement factor according to CIPM 2007
        alpha = 1.00062
        beta = 3.14e-8
        gamma = 5.6e-7
        return alpha + beta * p + gamma * T ** 2

    def compressibility_factor(p, T, x_v):
        # Calculation of compressibility factor according to CIPM 2007
        a0 = 1.58123e-6
        a1 = -2.9331e-8
        a2 = 1.1043e-10
        b0 = 5.707e-6
        b1 = -2.051e-8
        c0 = 1.9898e-4
        c1 = -2.376e-6
        d = 1.83e-11
        e = -0.765e-8

        t = T - cDegreesCtoK
        Z = 1 - (p / T) * (a0 + a1 * t + a2 * t ** 2 + (b0 + b1 * t) * x_v + (c0 + c1 * t) * x_v ** 2) \
            + (p / T) ** 2 * (d + e * x_v ** 2)
        return Z

    # Temperature in Kelvin
    T_K = t + cDegreesCtoK

    # Calculation of saturated vapor pressure and enhancement factor
    p_sv = saturation_vapor_pressure(T_K)
    f = enhancement_factor(p, t)

    # Calculation of partial pressure and mole fraction of water vapor
    p_v = humidity / 100 * f * p_sv
    x_v = p_v / p

    # Calculation of compressibility factor
    Z = compressibility_factor(p, T_K, x_v)

    density = (p * M_a) / (Z * R * T_K) * (1 - x_v * (1 - M_v / M_a))
    return 100 * density

Vacuum

Bases: Atmo

Vacuum atmosphere has zero drag

Source code in py_ballisticcalc\conditions.py

def __init__(self, 
             altitude: Optional[Union[float, Distance]] = None,
             temperature: Optional[Union[float, Temperature]] = None):
    super().__init__(altitude, 0, temperature, 0)
    self.cLowestTempC = cDegreesCtoK
    self._pressure = PreferredUnits.pressure(0)
    self._density_ratio = 0

update_density_ratio ¶

update_density_ratio()

Source code in py_ballisticcalc\conditions.py

def update_density_ratio(self):
    pass

Atmo

altitude property ¶

pressure property ¶

temperature property ¶

humidity property writable ¶

powder_temp property ¶

density_ratio property ¶

mach property ¶

density_metric property ¶

density_imperial property ¶

temperature_at_altitude ¶

update_density_ratio ¶

pressure_at_altitude ¶

get_density_factor_and_mach_for_altitude ¶

standard_temperature staticmethod ¶

standard_pressure staticmethod ¶

icao staticmethod ¶

machF staticmethod ¶

machC staticmethod ¶

machK staticmethod ¶

calculate_air_density staticmethod ¶

update_density_ratio ¶

altitude `property` ¶

pressure `property` ¶

temperature `property` ¶

humidity `property` `writable` ¶

powder_temp `property` ¶

density_ratio `property` ¶

mach `property` ¶

density_metric `property` ¶

density_imperial `property` ¶

standard_temperature `staticmethod` ¶

standard_pressure `staticmethod` ¶

icao `staticmethod` ¶

machF `staticmethod` ¶

machC `staticmethod` ¶

machK `staticmethod` ¶

calculate_air_density `staticmethod` ¶