Wind Turbulence Model — Robotics/Wind

Wind Turbulence Model

Robotics / Wind

Atmospheric turbulence as band-limited white noise shaped by the Dryden or von Kármán spectra, giving the three gust velocities [u_g; v_g; w_g] and the three gust angular rates [p_g; q_g; r_g] in body axes. Two regimes run at once and the block blends them by altitude h (in feet internally):

• h ≤ 1000 ft – the intensities come from the wind speed at 20 ft (σ_w = 0.1·W₂₀, σ_u = σ_v = σ_w/(0.177 + 0.000823h)^0.4) and the scale lengths from the altitude (L_w = h, L_u = L_v = h/(0.177 + 0.000823h)^1.2); the gusts are in the mean-wind frame and are rotated into body axes by the wind direction and the DCM on the port.
• h ≥ 2000 ft – the intensity comes from the probability-of-exceedance table against altitude, the scale length is the dialog's, and the turbulence is isotropic, so it is already in body axes.
• between – linear in altitude between the two.

Ports

• Altitude – h, a scalar [1,1], in m or ft per Units.
• Airspeed – V, a scalar [1,1], in m/s, ft/s or knots per Units; it must be positive, since every filter's break frequency is V/L.
• DCM – the earth-to-body direction cosine matrix [3,3], used only in the low-altitude regime.
• Vw – the gust velocities [u_g; v_g; w_g], [3,1], in the unit the airspeed is given in.
• Omega – the gust angular rates [p_g; q_g; r_g], [3,1], in rad/s in every unit system.

Parameters

• Units – Metric (MKS) (altitude m, airspeed m/s), English (Velocity in ft/s) or English (Velocity in kts) (altitude ft). The model itself is in feet and ft/s; the gust velocities come back in the airspeed's unit.
• Specification – MIL-F-8785C, MIL-HDBK-1797 or MIL-HDBK-1797B. It selects the discrete p_g filter and nothing else.
• Model Type – the nine presets, spelled as the Aerospace dialog spells them: Continuous Von Karman (+q −r), (+q +r), (−q +r), Continuous Dryden (+q −r), (+q +r), (−q +r), Discrete Dryden (+q −r), (+q +r), (−q +r). Continuous or discrete decides the filter forms; the signs are the q and r conventions.
• Wind Speed At 6 m Altitude – W₂₀, the mean wind at 20 ft (6 m), in the airspeed's unit. It sets the low-altitude intensity.
• Wind Direction At 6 m Altitude (deg) – the mean wind's direction, degrees clockwise from north; it rotates the low-altitude gusts.
• Probability Of Exceedance Of High-Altitude Intensity – one of 2x10^-1, 10^-1, 10^-2 - Light, 10^-3 - Moderate, 10^-4, 10^-5 - Severe, 10^-6; the row of the intensity table.
• Scale Length At Medium/High Altitudes – L above 2000 ft, in m or ft per Units. 533.4 m (1750 ft) is the Dryden default, 762 m (2500 ft) the von Kármán one.
• Wingspan – b, in m or ft; it sets the angular-rate filters' break frequencies.
• Band-Limited Noise Sample Time (s) – the period the four white-noise streams are drawn at. It must be a whole multiple of the block's own sample time.
• Noise Seeds [ug vg wg pg] – four non-negative whole numbers, one per stream, seeding Simulink's generator exactly.
• Turbulence On – on or off; off publishes zeros on both ports, as disabling the filters does in Simulink.
• Integration Substeps Per Sample – how many classical Runge–Kutta substeps a CONTINUOUS preset takes per sample, a whole number ≥ 1. The default 100 is Simulink's own fixed-step ode4 at T_s/100. A discrete preset ignores it: its recursions take one step per noise period.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. Every core carries the same generator – the Park–Miller recursion is integer arithmetic that each target can hold exactly – so an exported core reproduces the same gust sequence as the simulation, sample for sample. The unit factors, the intensity table, the seeds and the filter constants are folded into the body at export time; a continuous preset's core runs its configured number of Runge–Kutta substeps per sample.

The three HDL targets are simulation-only real arithmetic, quantized only at the ports: a logarithm, a cube root and a noise whose scale spans decades have no Q16.16 form. The cores simulate correctly and are not offered as synthesizable.

Simulink bridge

Import and export, mapped to Aerospace Blockset's aerolibwind2/Dryden Wind Turbulence Model (Continuous (+q +r)): Units → units, Specification → spec, Model Type → model, Wind Speed At 6 m Altitude → W20, Wind Direction At 6 m Altitude (deg) → Wdeg, Probability Of Exceedance Of High-Altitude Intensity → TurbProb, Scale Length At Medium/High Altitudes → L_high, Wingspan → Wingspan, Band-Limited Noise Sample Time (s) → ts, Noise Seeds [ug vg wg pg] → Seed and Turbulence On → T_on – the whole dialog, every enum 1:1 and lossless. The other eight library entries (the five other Dryden variants and the three von Kármán ones) are the same masked block at a different model, and import through the bridge's alias table with that preset applied. "Sampling Time (s)" does not cross: the Simulink block defines no SampleTime parameter, measured on R2026a. Integration Substeps Per Sample does not cross either: it is an ICore-side integration choice, and the Simulink block has no counterpart for it.

Notes

• Discrete-only and stateful: the filter states of both altitude regimes, the four noise streams' generator states, the held noise and a sample counter. A continuous preset advances its states with 100 RK4 substeps per sample, which is what Simulink's ode4 at Ts/100 does.
• The output depends on the altitude, airspeed and DCM of the same instant (the intensities, the break frequencies and the rotation), so the block feeds through.
• Drawing a random number is a side effect, so the block is evaluated once per step.
• A gust sequence is reproducible: the same seeds, noise period and sample time give the same sequence in the app and in every exported core.