ISA Atmosphere — Robotics/Atmosphere

ISA Atmosphere

Robotics / Atmosphere

The International Standard Atmosphere as a lapse-rate model whose ten constants are all configuration: a geopotential altitude in, and the atmosphere's temperature, speed of sound, static pressure and density out. One layer with a lapse rate up to the troposphere, an isothermal layer to the tropopause, and nothing changing above it. With hT and hS the altitude clamped into each of those two ranges:

• T = T₀ − L·hT
• θ = T·(1/T₀) and ratio = θ^g/(LR)·e^{(g/R)(h_trop−hS)/T}
• P = P₀·ratio and ρ = ρ₀·(ratio/θ)
• a = √((γR)T)

Left at its defaults it is the standard atmosphere; changed, it is any single-lapse atmosphere, which is what Aerospace Blockset offers under the second name Lapse Rate Model. A fixed seven-layer atmosphere that takes no constants at all is COESA Atmosphere.

Ports

• h – the geopotential altitude, in metres. Any size [m,n]; the block works entry by entry.
• T – the temperature, in kelvin. Same size as the input.
• a – the speed of sound, in m/s. Same size as the input.
• P – the static pressure, in pascals. Same size as the input.
• rho – the density, in kg/m³. Same size as the input.

Parameters

• Gravitational Acceleration – g, a scalar in m/s². Defaults to 9.80665.
• Ratio Of Specific Heats – γ, dimensionless. Defaults to 1.4, and it affects the speed of sound only.
• Characteristic Gas Constant – R, a scalar in J/(kg·K). Defaults to 287.0531.
• Lapse Rate – L, a scalar in K/m, and a positive value is a temperature that FALLS with altitude: T = T₀ − L·hT. Defaults to 0.0065. Exactly zero is refused – it makes the pressure exponent g/(LR) infinite, and an infinite exponent over a base that rounds to just under 1 answers zero rather than an isothermal atmosphere.
• Height Of Troposphere – h_trop, in metres, where the lapse stops. Defaults to 11000.
• Height Of Tropopause – h_strat, in metres, where the isothermal layer stops and every output holds its value. Defaults to 20000, and it must not be below the troposphere.
• Sea Level Density – ρ₀, in kg/m³. Defaults to 1.225.
• Sea Level Pressure – P₀, in pascals. Defaults to 101325.
• Sea Level Temperature – T₀, in kelvin, and it must be positive. Defaults to 288.15.
• Minimum Sea Level Altitude – h₀, in metres, a FLOOR and not an origin: the lapse is applied to the clamped altitude rather than to (h − h₀), so at h₀ = 500 the temperature is T₀ − 500L and not T₀. Defaults to 0, and it must not be above the troposphere.
• 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.

The ten constants are baked into the emitted arithmetic at export time rather than exposed as tunables, along with the four quantities derived from them – 1/T₀, g/(LR), g/R and γR. They describe which atmosphere this is, which is structure and not a knob, and deriving them once is also what keeps the ten backends from differing by an association order. All are printed at 17 significant digits.

The three hardware targets are simulation-only: a power with a fractional exponent, an exponential and a square root have no Q16.16 form, so values convert at the port boundary and the arithmetic runs in floating point. And a fixed-point port cannot carry a sea-level pressure at all – Q16.16 saturates past about 32767, while the default P₀ is 101325 – so a hardware export of this block wants either a thin-atmosphere altitude range or a smaller P₀.

Simulink bridge

Import and export, mapped to Aerospace Blockset's aerolibatmos2/Lapse Rate Model. All ten configuration values cross straight through to the parameters of the same meaning: Gravitational Acceleration → g, Ratio Of Specific Heats → gamma, Characteristic Gas Constant → R, Lapse Rate → L, Height Of Troposphere → h_trop, Height Of Tropopause → h_strat, Sea Level Density → rho0, Sea Level Pressure → P0, Sea Level Temperature → T0 and Minimum Sea Level Altitude → h0.

aerolibatmos2/ISA Atmosphere Model is the same Simulink block – identical mask, identical parameter list – differing only in whether its custom switch is on, so this one entry covers both library paths. Four parameters are always implied: custom is always on, because every constant here is configuration; useExtended always off, the extended form being a seven-layer atmosphere and therefore COESA Atmosphere's job; viscosityOut always off, since switching it on adds two more output ports and this block has four; and action always None, that parameter only choosing whether Simulink warns about an altitude outside its range. The Simulink block defines no SampleTime parameter, measured, so the rate stays on the ICore side.

Notes

• Algebraic and stateless: the outputs depend on this sample alone.
• Not linear, so the block carries no state space and model reduction correctly reports it as unmergeable.
• The altitude is GEOPOTENTIAL, not geometric, and nothing converts between the two.
• Above the tropopause nothing changes. Both clamps are saturated there, so all four outputs hold their tropopause values however high the altitude goes – which is what the reference does, and not a physical claim.
• A non-positive temperature answers zero on all four outputs. A large enough lapse rate drives T through zero, at which point the pressure's power has a negative base; VHDL's real ** asserts there rather than answering, aborting a simulation instead of producing a bad number, so all ten targets carry the same guard.
• The default ρ₀ and R are very slightly inconsistent with the perfect-gas relation, which is why this block's sea-level density is exactly 1.225 and COESA Atmosphere's is 1.2249991558877125. Both are faithful to their own reference.
• Verified against R2026a over two full parameter sets and 25 altitudes – 100 answers – agreeing to at worst 1.8×10⁻¹⁶ relative.