Classes
struct	AtmosphericState
	Complete atmospheric state at a given altitude. More...

Functions
template<typename Scalar>
Scalar	density (const Scalar &altitude, double scale_height=DEFAULT_SCALE_HEIGHT)
	Exponential atmosphere - Density.
template<typename Scalar>
Scalar	pressure (const Scalar &altitude, double scale_height=DEFAULT_SCALE_HEIGHT)
	Exponential atmosphere - Pressure.
template<typename Scalar>
Scalar	temperature (const Scalar &altitude, double scale_height=DEFAULT_SCALE_HEIGHT)
	Exponential atmosphere - Temperature.
template<typename Scalar>
Scalar	speed_of_sound (const Scalar &altitude, double scale_height=DEFAULT_SCALE_HEIGHT)
	Exponential atmosphere - Speed of Sound.
template<typename Scalar>
AtmosphericState< Scalar >	state (const Scalar &altitude, double scale_height=DEFAULT_SCALE_HEIGHT)
	Exponential atmosphere - Complete atmospheric state.
double	compute_scale_height (double temperature=T_0, double gravity=G_0)
	Compute scale height from reference conditions.
template<typename Scalar>
Scalar	altitude_from_density (const Scalar &rho, double scale_height=DEFAULT_SCALE_HEIGHT)
	Compute altitude from density.
template<typename Scalar>
Scalar	altitude_from_pressure (const Scalar &P, double scale_height=DEFAULT_SCALE_HEIGHT)
	Compute altitude from pressure.

Variables
constexpr double	RHO_0 = 1.225
	Sea-level reference density [kg/m³].
constexpr double	P_0 = 101325.0
	Sea-level reference pressure [Pa].
constexpr double	T_0 = 288.15
	Sea-level reference temperature [K].
constexpr double	DEFAULT_SCALE_HEIGHT = 8500.0
constexpr double	G_0 = 9.80665
	Sea-level gravitational acceleration [m/s²].
constexpr double	R_AIR = 287.058
	Specific gas constant for air [J/(kg·K)].
constexpr double	GAMMA = 1.4
	Ratio of specific heats for air (γ = Cp/Cv).

Function Documentation

◆ altitude_from_density()

template<typename Scalar>

Scalar vulcan::exponential_atmosphere::altitude_from_density	(	const Scalar &	rho,
		double	scale_height = DEFAULT_SCALE_HEIGHT )

Compute altitude from density.

Inverse of the density function: h = -H * ln(ρ / ρ₀)

Template Parameters

Scalar double or casadi::MX for symbolic computation

Parameters

rho	Density [kg/m³]
scale_height	Atmospheric scale height [m] (default: 8500 m)

Returns: Altitude [m]

◆ altitude_from_pressure()

template<typename Scalar>

Scalar vulcan::exponential_atmosphere::altitude_from_pressure	(	const Scalar &	P,
		double	scale_height = DEFAULT_SCALE_HEIGHT )

Compute altitude from pressure.

Inverse of the pressure function: h = -H * ln(P / P₀)

Template Parameters

Scalar double or casadi::MX for symbolic computation

Parameters

P	Pressure [Pa]
scale_height	Atmospheric scale height [m] (default: 8500 m)

Returns: Altitude [m]

◆ compute_scale_height()

double vulcan::exponential_atmosphere::compute_scale_height	(	double	temperature = T_0,
		double	gravity = G_0 )

inline

Compute scale height from reference conditions.

The scale height H = R*T / g relates temperature, gravity, and the rate of pressure decay.

Parameters

temperature	Reference temperature [K]
gravity	Gravitational acceleration [m/s²]

Returns: Scale height [m]

◆ density()

template<typename Scalar>

Scalar vulcan::exponential_atmosphere::density	(	const Scalar &	altitude,
		double	scale_height = DEFAULT_SCALE_HEIGHT )

Exponential atmosphere - Density.

Computes air density using the simple exponential model: ρ = ρ₀ * exp(-h / H)

This model is suitable for quick estimates and trajectory optimization where a simple, smooth, differentiable model is preferred.

Template Parameters

Scalar double or casadi::MX for symbolic computation

Parameters

altitude	Geometric altitude above sea level [m]
scale_height	Atmospheric scale height [m] (default: 8500 m)

Returns: Density [kg/m³]

Note: For altitudes below 0, density will be greater than ρ₀. For very high altitudes, density approaches 0.

◆ pressure()

template<typename Scalar>

Scalar vulcan::exponential_atmosphere::pressure	(	const Scalar &	altitude,
		double	scale_height = DEFAULT_SCALE_HEIGHT )

Exponential atmosphere - Pressure.

Computes pressure using the simple exponential model: P = P₀ * exp(-h / H)

Uses the same scale height as density for consistency with an isothermal atmosphere assumption.

Template Parameters

Scalar double or casadi::MX for symbolic computation

Parameters

altitude	Geometric altitude above sea level [m]
scale_height	Atmospheric scale height [m] (default: 8500 m)

Returns: Pressure [Pa]

◆ speed_of_sound()

template<typename Scalar>

Scalar vulcan::exponential_atmosphere::speed_of_sound	(	const Scalar &	altitude,
		double	scale_height = DEFAULT_SCALE_HEIGHT )

Exponential atmosphere - Speed of Sound.

Computes speed of sound from temperature: a = sqrt(γ * R * T)

Since temperature is constant in this model, speed of sound is also constant.

Template Parameters

Scalar double or casadi::MX for symbolic computation

Parameters

altitude	Geometric altitude above sea level [m] (unused)
scale_height	Atmospheric scale height [m] (unused)

Returns: Speed of sound [m/s] - constant at ~340.3 m/s

◆ state()

template<typename Scalar>

AtmosphericState< Scalar > vulcan::exponential_atmosphere::state	(	const Scalar &	altitude,
		double	scale_height = DEFAULT_SCALE_HEIGHT )

Exponential atmosphere - Complete atmospheric state.

Returns all atmospheric properties in a single evaluation. Efficient for trajectory optimization where multiple properties are needed.

Template Parameters

Scalar double or casadi::MX for symbolic computation

Parameters

altitude	Geometric altitude above sea level [m]
scale_height	Atmospheric scale height [m] (default: 8500 m)

Returns: AtmosphericState containing T, P, ρ, a

◆ temperature()

template<typename Scalar>

Scalar vulcan::exponential_atmosphere::temperature	(	const Scalar &	altitude,
		double	scale_height = DEFAULT_SCALE_HEIGHT )

Exponential atmosphere - Temperature.

Returns the reference temperature (isothermal assumption). The exponential atmosphere model assumes constant temperature, which is why both density and pressure decay with the same scale height.

Template Parameters

Scalar double or casadi::MX for symbolic computation

Parameters

altitude	Geometric altitude above sea level [m] (unused)
scale_height	Atmospheric scale height [m] (unused)

Returns: Temperature [K] - always returns T_0 = 288.15 K

Variable Documentation

◆ DEFAULT_SCALE_HEIGHT

double vulcan::exponential_atmosphere::DEFAULT_SCALE_HEIGHT = 8500.0

inlineconstexpr

Default atmospheric scale height [m] Approximately 8.5 km based on RT/g at sea level

◆ G_0

double vulcan::exponential_atmosphere::G_0 = 9.80665

inlineconstexpr

Sea-level gravitational acceleration [m/s²].

◆ GAMMA

double vulcan::exponential_atmosphere::GAMMA = 1.4

inlineconstexpr

Ratio of specific heats for air (γ = Cp/Cv).

◆ P_0

double vulcan::exponential_atmosphere::P_0 = 101325.0

inlineconstexpr

Sea-level reference pressure [Pa].

◆ R_AIR

double vulcan::exponential_atmosphere::R_AIR = 287.058

inlineconstexpr

Specific gas constant for air [J/(kg·K)].

◆ RHO_0

double vulcan::exponential_atmosphere::RHO_0 = 1.225

inlineconstexpr

Sea-level reference density [kg/m³].

◆ T_0

double vulcan::exponential_atmosphere::T_0 = 288.15

inlineconstexpr

Sea-level reference temperature [K].

Classes

Functions

Variables

Function Documentation

◆ altitude_from_density()

◆ altitude_from_pressure()

◆ compute_scale_height()

◆ density()

◆ pressure()

◆ speed_of_sound()

◆ state()

◆ temperature()

Variable Documentation

◆ DEFAULT_SCALE_HEIGHT

◆ G_0

◆ GAMMA

◆ P_0

◆ R_AIR

◆ RHO_0

◆ T_0