Atmospheric Model

Atmospheric Model

Overview

The atmosphere determines two quantities the integrator needs: air density (through drag_coeff) and speed of sound (for Mach). lob implements the International Standard Atmosphere (ISA) with humidity corrections (McCoy pp. 166–168; Huang saturation-pressure formula). Lapse, humidity and barometric corrections are evaluated once at Build() time from the firing- site conditions, and then optionally stratified per step via ctx.k_lapse (source/constants.hpp kHydrostaticExponent/kBarometricExponent, source/lob_builder.cpp BuildDynamicDensity, source/solve_step.cpp DsDx/FastDsDx).

Inputs

Builder inputs that affect the atmosphere (source/lob_builder.cpp):

• AltitudeOfFiringSiteFt — feet, |alt| < kStratosphereAltitudeFt (65 617 ft). Outside that → kLobErrorAltitudeOfFiringSiteOOR.
• AirPressureInHg — inHg, ≥ 0. If absent, ISA sea-level 29.92 inHg propagated via the barometric formula from the site altitude.
• AltitudeOfBarometerFt — where the pressure was read; defaults to the firing-site altitude. The pressure is barometrically shifted to the firing site (source/lob_builder.cpp).
• TemperatureDegF — degrees F. If absent, kSeaLevelDegF (59 °F) at sea level lapsed to the site. If a thermometer altitude is given, AltitudeOfThermometerFt, the temperature is shifted similarly (source/lob_builder.cpp).
• RelativeHumidityPercent — 0–100, defaults to 0.

All altitudes are validated against the same ISA ceiling.

Formulas

Lapse and barometric formula (source/calc.hpp):

T(h) = max(T0 − L·h, T_min)               with L = 0.00356616 °F/ft, T_min = −69.7 °F
p(h) = p0·(1 − L·h / T_R)^e · exp(...)     e = g/(R·L), with tropopause/stratosphere branch

BarometricFormula handles the tropopause at 36 090 ft and then an isothermal exponential above it, matching the implementation.

Humidity enters via Huang's saturation-pressure formula (source/calc.hpp):

p_sat(T) = exp(A − B/(T_C+D1) − C·ln(T_C+D2))   distinct A,B,C,D1,D2 for water vs ice

and two linear corrections (McCoy p. 167–168, with h = RelativeHumidityPercent ∈ [0, 100] as a percent value, not a 0–1 fraction; 0.00378 and 0.00140 already include the percent scaling):

ρ/ρ0 = (p/p0)·(T0_R/T_R)
ρ_corr = 1 − 0.00378·h·p_sat/p0
c_corr = 1 + 0.00140·h·p_sat/p0
ρ = ρ0_ISA · (ρ/ρ0) · ρ_corr
c = c(T)·c_corr    with c(T)=49.0223·√T_R

ρ0_ISA = 0.0764742 lb/ft³, c0_ISA = 1116.45 fps. Army Standard Metro uses 0.0751265 lb/ft³ and is converted at the BC level, not here.

Output in Context

BuildEnvironment writes ctx.speed_of_sound (fps) and the intermediate Impl::air_density_lbs_per_cu_ft, which is converted to ctx.drag_coeff via CalculateCdCoefficient using the solver's ρ·π/8 relationship at BC=1 (source/lob_builder.cpp, source/calc.hpp). It also writes ctx.k_lapse ((1/R−L/g)/T_R, source/lob_builder.cpp BuildDynamicDensity) — the projected linear density lapse coefficient used per step.

Per-step stratification (source/solve_step.cpp):

u = −k_lapse·P·G          // dimensionless altitude projected onto G
ρ/ρ0 = 1 − u·(1−α·u)      // α=(e−1)/2e, e=kHydrostaticExponent
c/c0 = 1 − β·u            // β=1/2e
Cd = curve(Mach)·drag·(ρ/ρ0),  Mach=|v|/c

DsDx scales drag_coeff/speed_of_sound by ρ/ρ0/c/c0; FastDsDx uses firing-site values. LobSolve (forward) and BuildBoatright/BuildZeroAngle use Fast* fast path; LobSolveInverse uses FastSolveAngle or SolveAngle per-range gated on forward drop>100ft (elevation < −1200in, source/lob_solve.cpp kDynamicDropThreshold).

Limitations

• Per-step lapse is gated: forward solves and drop≤100ft inverse ranges stay on Fast* (firing-site density) for speed; only drop>100ft inverse ranges pay DsDx/SolveStep/SolveAngle. For the ranges lob is validated against (test/source/lob_env_test.cpp) the error is bounded by the tests' tolerances.
• Temperature is lapsed with the simple linear ISA lapse, not McCoy's exponential variant CalculateTemperatureAtAltitudeMcCoy (kept for reference only, source/calc.hpp).