Module: Atmospheric::Isa

Defined in:
lib/atmospheric/isa.rb

Constant Summary collapse

CONST =

2.1 Primary constants and characteristics Table 1 - Main constants and characteristics adopted for

the calculation of the ISO Standard Atmosphere

{
  g_n: 9.80665, # m.s-2
  N_A: 602.257e21, # Avogadro constant, mol-1
  p_n: 101325, # In Pascal
  rho_n: 1.225, # rho_n standard air density
  T_n: 288.15, # T_n standard thermodynamic air temperature at mean sea level
  R_star: 8.31432, # universal gas constant

  radius: 6356766, # radius of the Earth (m)
  k: 1.4 # adiabatic index, dimensionless
}
TEMPERATURE_LAYERS =

Table 4 - Temperature and vertical temperature gradients

[
  # H is Geopotential altitude (base altitude) above mean sea level, m
  # T is Temperature, K
  # B is Temperature gradient, "beta", K m^-1

  # This line is from ICAO 7488/3
  # [H: -5000, T: 320.65, B: -0.0065 ],

  # This line is from ISO 2533:1975
  {H: -2000, T: 301.15, B: -0.0065 },
  {H: 0,     T: 288.15, B: -0.0065 },
  {H: 11000, T: 216.65, B: 0       },
  {H: 20000, T: 216.65, B: 0.001   },
  {H: 32000, T: 228.65, B: 0.0028  },
  {H: 47000, T: 270.65, B: 0       },
  {H: 51000, T: 270.65, B: -0.0028 },
  {H: 71000, T: 214.65, B: -0.002  },
  {H: 80000, T: 196.65},
]

Class Method Summary collapse

Class Method Details

.air_number_density_from_H(geopotential_alt) ⇒ Object

2.10 Air number density Formula (17) n



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# File 'lib/atmospheric/isa.rb', line 248

def air_number_density_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  p = pressure_from_H(geopotential_alt)

  CONST[:N_A] * p / (CONST[:R_star] * temp)
end

.air_particle_collision_frequency_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 282

def air_particle_collision_frequency_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  n = air_number_density_from_H(geopotential_alt)
  air_particle_collision_frequency_from_temp(n, temp)
end

.air_particle_collision_frequency_from_temp(n, temp) ⇒ Object

2.13 Air-particle collision frequency Formula (20) omega



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# File 'lib/atmospheric/isa.rb', line 278

def air_particle_collision_frequency_from_temp(n, temp)
  4 * (0.365e-9 ** 2) * ((3.141592654 / (CONST[:R_star] * CONST[:M])) ** 0.5) * n * CONST[:R_star] * (temp ** 0.5)
end

.density_from_H(geopotential_alt) ⇒ Object

Calculate density for a given geopotential altitude ‘H` (m) above mean sea level Formula (14) rho



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# File 'lib/atmospheric/isa.rb', line 210

def density_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  p = pressure_from_H(geopotential_alt)

  p / (CONST[:R] * temp)
end

.dynamic_viscosity(temp) ⇒ Object

2.15 Dynamic viscosity Formula (22) mu (Pa s)



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# File 'lib/atmospheric/isa.rb', line 307

def dynamic_viscosity(temp)
  # Sutherland's empirical constants in the equation for dynamic viscosity
  capital_b_s = 1.458e-6
  capital_s = 110.4

  (capital_b_s * (temp ** (1.5))) / (temp + capital_s)
end

.dynamic_viscosity_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 315

def dynamic_viscosity_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  dynamic_viscosity(temp)
end

.geometric_altitude_from_geopotential(geopotential_alt) ⇒ Object

2.3 Formula (8) H to h h(m)



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# File 'lib/atmospheric/isa.rb', line 39

def geometric_altitude_from_geopotential(geopotential_alt)
  CONST[:radius] * geopotential_alt / (CONST[:radius] - geopotential_alt)
end

.geopotential_altitude_from_geometric(geometric_alt) ⇒ Object

2.3 Formula (9) h to H H(m)



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# File 'lib/atmospheric/isa.rb', line 46

def geopotential_altitude_from_geometric(geometric_alt)
  CONST[:radius] * geometric_alt / (CONST[:radius] + geometric_alt)
end

.gravity_at_geometric(geometric_alt) ⇒ Object

2.3 Formula (7) g(h)



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# File 'lib/atmospheric/isa.rb', line 52

def gravity_at_geometric(geometric_alt)
  temp = CONST[:radius] / (CONST[:radius] + geometric_alt)
  CONST[:g_n] * temp * temp
end

.gravity_at_geopotential(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 57

def gravity_at_geopotential(geopotential_alt)
  geometric_h = geometric_altitude_from_geopotential(geopotential_alt)
  gravity_at_geometric(geometric_h)
end

.kelvin_to_celsius(kelvin) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 344

def kelvin_to_celsius(kelvin)
  kelvin - 273.15
end

.kinematic_viscosity(temp) ⇒ Object

2.16 Kinematic viscosity Formula (23) v



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# File 'lib/atmospheric/isa.rb', line 323

def kinematic_viscosity(temp)
  dynamic_viscosity(temp) / CONST[:rho_n]
end

.kinematic_viscosity_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 327

def kinematic_viscosity_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  dynamic_viscosity(temp) / density_from_H(geopotential_alt)
end

.locate_lower_layer(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 84

def locate_lower_layer(geopotential_alt)
  # Return first layer if lower than lowest
  return 0 if geopotential_alt < TEMPERATURE_LAYERS[0][:H]

  # Return second last layer if beyond last layer
  i = TEMPERATURE_LAYERS.length - 1
  return i - 1 if geopotential_alt >= TEMPERATURE_LAYERS[i][:H]

  # find last layer with H larger than our H
  TEMPERATURE_LAYERS.each_with_index do |layer, i|
    return i if layer[:H] > geopotential_alt
  end

  nil
end

.mean_air_particle_speed_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 263

def mean_air_particle_speed_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  mean_air_particle_speed_from_temp(temp)
end

.mean_air_particle_speed_from_temp(temp) ⇒ Object

2.11 Mean air-particle speed Formula (18) v_bar CORRECT



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# File 'lib/atmospheric/isa.rb', line 259

def mean_air_particle_speed_from_temp(temp)
  1.595769 * Math.sqrt(CONST[:R] * temp)
end

.mean_free_path_of_air_particles_from_H(geopotential_alt) ⇒ Object

2.12 Mean free path of air particles Formula (19) l



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# File 'lib/atmospheric/isa.rb', line 271

def mean_free_path_of_air_particles_from_H(geopotential_alt)
  1 / (1.414213562 * 3.141592654 * (0.365e-9 ** 2) * air_number_density_from_H(geopotential_alt))
end

.p_p_n_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 201

def p_p_n_from_H(geopotential_alt)
  pressure_from_H(geopotential_alt) / CONST[:p_n]
end

.pa_to_mbar(pascal) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 170

def pa_to_mbar(pascal)
  pascal * 0.01
end

.pa_to_mmhg(pascal) ⇒ Object

puts “PRE-CALCULATED PRESSURE LAYERS:” pp @pressure_layers



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# File 'lib/atmospheric/isa.rb', line 166

def pa_to_mmhg(pascal)
  pascal * 0.007500616827
end

.pressure_from_H(geopotential_alt) ⇒ Object

Pressure for a given geopotential altitude ‘H` (m) above mean sea level



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# File 'lib/atmospheric/isa.rb', line 175

def pressure_from_H(geopotential_alt)
  i = locate_lower_layer(geopotential_alt)
  lower_temperature_layer = TEMPERATURE_LAYERS[i]
  beta = lower_temperature_layer[:B]
  capital_h_b = lower_temperature_layer[:H]
  capital_t_b = lower_temperature_layer[:T]
  temp = temperature_at_layer_from_H(geopotential_alt)
  pb = pressure_layers[i]

  if beta != 0
    # Formula (12)
    pb * (1 + ((beta / capital_t_b) * (geopotential_alt - capital_h_b))) ** (-CONST[:g_n] / (beta * CONST[:R]))
  else
    # Formula (13)
    pb * Math.exp(-(CONST[:g_n] / (CONST[:R] * temp)) * (geopotential_alt - capital_h_b))
  end
end

.pressure_from_H_mbar(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 193

def pressure_from_H_mbar(geopotential_alt)
  pa_to_mbar(pressure_from_H(geopotential_alt))
end

.pressure_from_H_mmhg(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 197

def pressure_from_H_mmhg(geopotential_alt)
  pa_to_mmhg(pressure_from_H(geopotential_alt))
end

.pressure_layers ⇒ Object

Base pressure values given defined ‘TEMPERATURE_LAYERS` and constants



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# File 'lib/atmospheric/isa.rb', line 126

def pressure_layers
  return @pressure_layers if @pressure_layers

  # assuming TEMPERATURE_LAYERS index 1 base altitude is zero (mean sea level)
  p = []

  TEMPERATURE_LAYERS.each_with_index do |x, i|
    last_i = (i == 0) ? 0 : i - 1
    last_layer = TEMPERATURE_LAYERS[last_i]
    beta = last_layer[:B]

    if last_layer[:H] <= 0
      pb = CONST[:p_n]
      capital_h_b = 0
      capital_t_b = CONST[:T_n]
    else
      pb = p[last_i]
      capital_h_b = last_layer[:H]
      capital_t_b = last_layer[:T]
    end

    current_layer = TEMPERATURE_LAYERS[i]
    geopotential_alt = current_layer[:H]
    temp = current_layer[:T]

    p[i] = if beta != 0
      # Formula (12)
      pb * (1 + ((beta / capital_t_b) * (geopotential_alt - capital_h_b))) ** (-CONST[:g_n] / (beta * CONST[:R]))
    else
      # Formula (13)
      pb * Math.exp(-(CONST[:g_n] / (CONST[:R] * temp)) * (geopotential_alt - capital_h_b))
    end
  end

  @pressure_layers = p
end

.pressure_scale_height_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 240

def pressure_scale_height_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  (CONST[:R] * temp) / gravity_at_geopotential(geopotential_alt)
end

.pressure_scale_height_from_temp(temp) ⇒ Object

2.9 Pressure scale height Formula (16) H_p



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# File 'lib/atmospheric/isa.rb', line 236

def pressure_scale_height_from_temp(temp)
  (CONST[:R] * temp) / CONST[:g_n]
end

.rho_rho_n_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 217

def rho_rho_n_from_H(geopotential_alt)
  density_from_H(geopotential_alt) / CONST[:rho_n]
end

.root_rho_rho_n_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 221

def root_rho_rho_n_from_H(geopotential_alt)
  Math.sqrt(rho_rho_n_from_H(geopotential_alt))
end

.specific_weight_from_H(geopotential_alt) ⇒ Object

Specific weight Formula (15) gamma



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# File 'lib/atmospheric/isa.rb', line 229

def specific_weight_from_H(geopotential_alt)
  density_from_H(geopotential_alt) * gravity_at_geopotential(geopotential_alt)
end

.speed_of_sound_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 298

def speed_of_sound_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  speed_of_sound_from_temp(temp)
end

.speed_of_sound_from_temp(temp) ⇒ Object

2.14 Speed of sound Formula (21) a (ms-1) CORRECT



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# File 'lib/atmospheric/isa.rb', line 292

def speed_of_sound_from_temp(temp)
  # `kappa` (ratio of c_p / c_v) = 1.4 (see 2.14)
  kappa = 1.4
  Math.sqrt(kappa * CONST[:R] * temp)
end

.temperature_at_layer_celcius(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 80

def temperature_at_layer_celcius(geopotential_alt)
  kelvin_to_celsius(temperature_at_layer_from_H(geopotential_alt))
end

.temperature_at_layer_from_H(geopotential_alt) ⇒ Object

Formula (11) T



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# File 'lib/atmospheric/isa.rb', line 70

def temperature_at_layer_from_H(geopotential_alt)
  lower_layer_index = locate_lower_layer(geopotential_alt)
  lower_layer = TEMPERATURE_LAYERS[lower_layer_index]
  beta = lower_layer[:B]
  capital_t_b = lower_layer[:T]
  capital_h_b = lower_layer[:H]

  capital_t_b + (beta * (geopotential_alt - capital_h_b))
end

.thermal_conductivity_from_H(geopotential_alt) ⇒ Object 



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# File 'lib/atmospheric/isa.rb', line 339

def thermal_conductivity_from_H(geopotential_alt)
  temp = temperature_at_layer_from_H(geopotential_alt)
  thermal_conductivity_from_temp(temp)
end

.thermal_conductivity_from_temp(temp) ⇒ Object

2.17 Thermal conductivity Formula (24) lambda



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# File 'lib/atmospheric/isa.rb', line 335

def thermal_conductivity_from_temp(temp)
  (2.648151e-3 * (temp ** (1.5))) / (temp + (245.4 * (10 ** (-12.0/temp))))
end