vulcan::von_karman Namespace Reference

Classes
struct	FilterState
	von Kármán filter state (higher order than Dryden) More...
struct	FilterCoeffs
	von Kármán forming filter coefficients More...

Functions
template<typename Scalar>
Scalar	psd_longitudinal (const Scalar &omega, double sigma_u, double L_u)
	von Kármán longitudinal PSD
template<typename Scalar>
Scalar	psd_lateral (const Scalar &omega, double sigma, double L)
	von Kármán lateral/vertical PSD
template<typename Scalar>
FilterState< Scalar >	init_state ()
	Initialize filter state to zero.
FilterCoeffs	compute_filter_coeffs (const wind::TurbulenceParams< double > &params, double airspeed, double dt)
	Compute von Kármán forming filter coefficients.
template<typename Scalar>
wind::GustVelocity< Scalar >	step (FilterState< Scalar > &state, const FilterCoeffs &coeffs, const Scalar &noise_u, const Scalar &noise_v, const Scalar &noise_w)
	Step the von Kármán forming filter.
FilterCoeffs	mil_spec_coeffs (double altitude, wind::TurbulenceSeverity severity, double airspeed, double dt)
	Compute all filter coefficients for MIL-spec conditions.

Variables
constexpr double	SPECTRAL_CONSTANT = 1.339
	von Kármán constant used in spectral formulation

Function Documentation

compute_filter_coeffs()

FilterCoeffs vulcan::von_karman::compute_filter_coeffs ( const wind::TurbulenceParams< double > & params, double airspeed, double dt )

inline

Compute von Kármán forming filter coefficients.

Uses a well-established rational approximation to the von Kármán spectrum. The approximation provides:

• Exact low-frequency match
• -5/6 roll-off approximated by cascade of first-order sections
• Good phase characteristics

Parameters

params	Turbulence parameters (σ and L values)
airspeed	True airspeed V [m/s]
dt	Time step [s]

Returns

Discretized filter coefficients

init_state()

template<typename Scalar>

FilterState< Scalar > vulcan::von_karman::init_state

(

)

Initialize filter state to zero.

mil_spec_coeffs()

FilterCoeffs vulcan::von_karman::mil_spec_coeffs ( double altitude, wind::TurbulenceSeverity severity, double airspeed, double dt )

inline

Compute all filter coefficients for MIL-spec conditions.

Parameters

altitude	Altitude above ground level [m]
severity	Turbulence severity level
airspeed	True airspeed [m/s]
dt	Time step [s]

Returns

FilterCoeffs ready for simulation

psd_lateral()

template<typename Scalar>

Scalar vulcan::von_karman::psd_lateral	(	const Scalar &	omega,
		double	sigma,
		double	L )

von Kármán lateral/vertical PSD

Φ_v(Ω) = σ_v² * (L_v/π) * [(1 + (8/3)(1.339·L_v·Ω)²) / (1 + (1.339·L_v·Ω)²)^(11/6)]

Template Parameters

Scalar

double or casadi::MX

Parameters

omega	Spatial frequency Ω [rad/m]
sigma	RMS turbulence intensity [m/s]
L	Scale length [m]

Returns

PSD value [m²/s²/(rad/m)]

psd_longitudinal()

template<typename Scalar>

Scalar vulcan::von_karman::psd_longitudinal	(	const Scalar &	omega,
		double	sigma_u,
		double	L_u )

von Kármán longitudinal PSD

Φ_u(Ω) = σ_u² * (2L_u/π) * [1 / (1 + (1.339·L_u·Ω)²)^(5/6)]

Note: The irrational exponent (5/6) makes this PSD impossible to realize exactly with rational transfer functions. Approximations are used.

Template Parameters

Scalar

double or casadi::MX

Parameters

omega	Spatial frequency Ω [rad/m]
sigma_u	RMS turbulence intensity [m/s]
L_u	Scale length [m]

Returns

PSD value [m²/s²/(rad/m)]

step()

template<typename Scalar>

wind::GustVelocity< Scalar > vulcan::von_karman::step	(	FilterState< Scalar > &	state,
		const FilterCoeffs &	coeffs,
		const Scalar &	noise_u,
		const Scalar &	noise_v,
		const Scalar &	noise_w )

Step the von Kármán forming filter.

Updates filter state and computes gust velocities given white noise input. Higher order than Dryden for more accurate spectral matching.

Template Parameters

Scalar

double or casadi::MX

Parameters

state	Current filter state (updated in-place)
coeffs	Pre-computed filter coefficients
noise_u	White noise input for longitudinal channel
noise_v	White noise input for lateral channel
noise_w	White noise input for vertical channel

Returns

Gust velocity (u_g, v_g, w_g)

Variable Documentation

SPECTRAL_CONSTANT

double vulcan::von_karman::SPECTRAL_CONSTANT = 1.339

inlineconstexpr

von Kármán constant used in spectral formulation