ashfordeOU Load Factor Envelope (flight-test-operations/envelope/load-factor-envelope)
Use when the task is the load factor envelope (V-n diagram) for a flight test: stall speed boundary, corner point, gust line, and placard speed cap.
Domain quick reference
- Stall speed boundary: V_s = sqrt(2 * n * W/S / (rho * CL_max)), with wing loading W/S in Pa (N/m^2), load factor n dimensionless, CL_max dimensionless, and air density rho in kg/m^3. Result in m/s EAS. Example: W/S = 6000 Pa, CL_max = 1.8, rho = 1.225 kg/m^3 at sea level, n = 1 gives about 73.8 m/s.
- Corner point (maneuvering speed VA): the stall boundary evaluated at the positive limit load factor n_lim, V_A = sqrt(2 * n_lim * W/S / (rho * CL_max)). Example: the 6000 Pa wing above with n_lim = 2.5 gives about 116.6 m/s.
- Discrete gust line (FAR 25.341 form, paraphrased): the gust load factor increment is delta_n = k_g * rho * U_de * V_eas * a / (2 * W/S) in SI units, with k_g the gust alleviation factor (typical 0.6 to 0.9), U_de the reference gust velocity in m/s EAS, V_eas in m/s EAS, and a the lift curve slope per radian. The certification formula in mixed units is delta_n = k_g * U_de * V_eas * a / (498 * W/S) with U_de in ft/s EAS, V_eas in knots EAS, and W/S in lb/ft^2; 498 is the sea level density constant. The reference gust velocity decreases with altitude (about 66 ft/s EAS at sea level to about 38 ft/s EAS at high altitude).
- Placard speed cap: the corner point must stay below the placard speeds (VNE never exceed, VMO maximum operating limit), and the gust line must stay below the positive limit load factor.
- Transport limit maneuvering load factors (FAR 25.337 / CS-25.337 context): +2.5 positive and -1.0 negative for transport category aeroplanes; the envelope is drawn between these limits.
Workflow
- Collect the wing loading W/S (Pa), the maximum lift coefficient CL_max, the air density rho (kg/m^3), and the limit load factors.
- Compute the stall speed boundary at n = 1 with stall_speed_boundary(wing_loading, cl_max, 1.0, rho).
- Derive the corner point with corner_speed(wing_loading, cl_max, limit_load_factor, rho); verify it stays below the placard speed.
- Compute the gust line increment with gust_load_factor_increment (FAR 25.341 mixed-unit form) or gust_load_factor_increment_si (SI form).
- Judge the whole envelope with envelope_verdict(corner_speed, vne, gust_increment, positive_limit, negative_limit) and gate the flight test program on the verdict.
Pitfalls
- Mixing the units of the two gust forms: gust_load_factor_increment takes ft/s EAS, knots EAS, and lb/ft^2 exactly as in the certification formula; feeding SI values into it silently scales the increment. Use gust_load_factor_increment_si for SI input.
- Using the wrong density: the corner point moves with altitude; a sea level density applied to a high altitude test point under-predicts both the stall speed and the corner point.
- Treating the corner point as fixed: VA is a function of W/S, CL_max, and rho, so it changes with weight, configuration, and altitude; the placard check must be repeated per condition.
- Forgetting the negative limit: the -1.0 negative limit bounds the inverted side of the envelope; the verdict flags any limit set that is not the transport +2.5 / -1.0 pair.
- Accepting a gust line above the maneuver line: at the design speed the 1 + delta_n gust point must stay below the positive limit load factor, otherwise the gust case sizes the structure.
- Passing zero or negative inputs; the module raises ValueError instead of returning a nonsense speed or increment.
Behavior contract (gate 3)
The stall speed boundary, corner point, gust increment, and envelope verdict logic is exercised by the gate 3 contract test: scripts/test_load_factor_envelope.py against scripts/load_factor_envelope.py (stdlib unittest, offline). Run: python3 scripts/test_load_factor_envelope.py
Compliance
- Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the V-n diagram relations and the gust increment form are common flight test methodology, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.