gust-loads

name	gust-loads
description	Aircraft gust loads — discrete gust (FAR 25.341), continuous turbulence (PSD/design envelope), dynamic response factor, gust load factor, dynamic amplification, gust alleviation, wing flexibility effect, structural design load cases, CS-25 requirements.
metadata	{"priority":7,"promptSignals":{"phrases":["gust loads","aircraft gust","FAR 25.341","discrete gust","continuous turbulence","gust load factor"],"minScore":3}}

Aircraft Gust Loads — Complete Skill

Gust Load Fundamentals

Gust: rapid change in ambient air velocity (vertical or lateral); induces change in angle of attack → change in lift → structural load Primary concern: vertical gust → increased lift → upward bending load on wing; occasionally downward gust Secondary: lateral gust → side force on fuselage; tail loads

Gust load factor: n_g = 1 + ΔL / W [ΔL = change in lift from gust; W = aircraft weight] For positive gust: n_g > 1 (upward load); for negative gust: n_g < 1

Discrete Gust (FAR 25.341(a))

Pratt Formula (Simple Gust)

Load increment from vertical gust: Δn = (ρ₀ × V_e × a_wing × Ude) / (2 × W/S) × K_g [ΔL/W] ρ₀ = sea level density; V_e = equivalent airspeed; a_wing = lift curve slope (per rad); Ude = design gust velocity; W/S = wing loading; K_g = gust alleviation factor

Gust alleviation factor K_g: K_g = 0.88 × μ_g / (5.3 + μ_g) μ_g = 2 × (W/S) / (ρ × c̄ × g × a_wing) [mass ratio; c̄ = mean aerodynamic chord; g = 9.81] K_g < 1: accounts for aircraft response lag (doesn't instantly respond to full gust)

Design gust velocities Ude (FAR 25.341): At V_c (design cruise): Ude = U_de_ref × F_g At V_D (design dive): Ude = 0.5 × Ude_at_Vc Reference: Ude_ref at sea level = 56 ft/s (17.1 m/s); reduces with altitude per FAR 25.341 fig

Gust load factor (final): n_max = 1 + K_g × Δn [positive gust; critical for wing upbending] n_min = 1 - K_g × Δn [negative gust; critical for wing downbending]

FAR 25.341(a)(4) discrete gust envelope: Design speed/gust combinations at: (V_B, Ude_ref); (V_C, 2/3 Ude_ref); (V_D, 1/3 Ude_ref) Plus gust loads must envelope 2.5g or -1.0g (whichever is critical)

Tuned Discrete Gust (FAR 25.341(a)(5))

1-cosine gust shape: u(t) = Ude/2 × (1 - cos(πt/T_g)) [0 ≤ t ≤ 2T_g; T_g = gust gradient distance H/V; H = 25–350 ft] Dynamic response analysis: integrate aircraft equations of motion through gust field Most critical H (gust length) selected by analysis → envelope over all H

Continuous Turbulence (FAR 25.341(b))

Power Spectral Density (PSD) Method

Turbulence model (von Karman): Φ_uu(ω) = σ_u² × L / (π) × (1 + (L × ω/V)² + 8/3 × (1.339 × L × ω/V)^(5/3))^(-1) [one-sided PSD; σ_u = turbulence intensity; L = turbulence scale length ≈ 762 m at altitude; V = airspeed]

Dryden model (simpler; also accepted): Φ_w(ω) = σ_w² × L_w / π × (1 + 3(L_w ω/V)²) / (1 + (L_w ω/V)²)²

Root Mean Square (RMS) load response: σ_response = √(∫₀^∞ |H(iω)|² × Φ_uu(ω) dω) [H(iω) = transfer function from gust input to load output] σ_load = σ_response × (W/S) / (W/S)_ref [normalised]

Design turbulence level: U_σ = limit design turbulence intensity per altitude (σ_u from FAR 25.341(b)) Sea level: σ_u ≈ 27.4 m/s (90 ft/s); decreases with altitude; varies by probability level

FAR 25.341(b) envelope: Limit load: A̅_limit = A̅_mean + C × A̅_σ [where A̅ = load measure; C = probability level constant] At 10⁻⁷ probability per flight hour (1 per 10 million hours)

Dynamic Amplification Factor (DAF)

Static equivalent gust load → too conservative for flexible aircraft: Dynamic response of wing adds phase shift → actual structural load differs from static DAF = dynamic peak load / static equivalent peak load For stiffer aircraft: DAF ≈ 1.0–1.1; flexible aircraft (high aspect ratio): DAF can be 0.7–1.3 (can be lower or higher)

Modal superposition for dynamic response: Include first 5–10 structural modes; each mode's response: R_i(t) = ∫ h_i(t-τ) × F_gust(τ) dτ [h_i = impulse response of mode i; F_gust = generalized force]

Gust Load Alleviation (GLA)

Purpose: reduce wing root bending moment from gusts → lighter structure GLA system: accelerometers detect gust → deploy ailerons/spoilers → counteract lift change Effectiveness: 10–30% WRBM (wing root bending moment) reduction → structural weight savings 3–8%

Control law: δ_GLA(t) = K × nz(t) + K_rate × ṅz(t) [δ = aileron deflection; nz = normal acceleration; K = control gain] Bandwidth: 10–20 Hz required for GLA; structural modes must be damped (> 0.02 critical damping)

Load alleviation limit: At positive gust: ailerons deflect up (reduce lift) + spoilers deploy At negative gust: ailerons deflect down (increase lift)

Flutter margin with GLA: Adding control surfaces and sensors may affect flutter → must demonstrate flutter clearance per FAR 25.629 with GLA active and failed

Wing Flexibility Effect

Flexible vs. rigid wing gust response: Rigid wing: responds instantly; conservative Flexible wing: structural deformation reduces effective angle of attack → "washes out" gust effect Gust load alleviation from flexibility: Δa_eff = Δa_rigid × (1 - ε_dihedral_wash_out) ∂ε/∂α (wash-out coefficient): 0.1–0.3 for typical wings → gust load reduction 10–30%

Aeroelastic correction to gust load: n_aeroelastic = n_rigid × (1 - ε/(1 + ε)) × K_flex K_flex < 1 for flexible wings → beneficial; reduces structural design load

V-n Diagram with Gust

V-n envelope (maneuver + gust combined): Maneuver: n_max = +2.5 to +3.8g (FAR 25.337); n_min = -1.0g Gust: adds diagonal lines from 1g at low speed to gust load factor at V_B, V_C, V_D Combined envelope: outermost boundary; structural design loads

Gust loads at V_B (design gust speed): V_B = V_S1 × √(n_B_gust) → selected to minimize combined maneuver + gust envelope area

Standards

Standard	Scope
FAR 25.341	Gust and turbulence loads — transport category
CS-25 Book 1, AMC 25.341	European equivalent (EASA)
MIL-A-8861	Aircraft load requirements (military)
MIL-HDBK-1797	Flying qualities of piloted aircraft
EUROCAE ED-14G (RTCA DO-160)	Environmental test — turbulence

Output

Provide: aircraft type and mass W [kg], wing loading W/S [kg/m²], design cruise speed V_C [KEAS] and dive speed V_D [KEAS], lift curve slope a [per rad], mass ratio μ_g, gust alleviation factor K_g, design gust velocity Ude [m/s] at V_C and V_D (FAR 25.341), gust load factor n_g+ (positive) and n_g- (negative), wing root bending moment from gust [kN·m], dynamic amplification factor DAF (if flexible), GLA system effectiveness [% WRBM reduction] (if applicable), governing load case (gust vs. maneuver), and applicable standard (FAR 25.341, CS-25, MIL-A-8861).