Flight Mechanics, Structural V-n Envelope & Aircraft Design
Aircraft Wing Loading & V-n Maneuvering Corner Speed (VA)
Calculate Wing Loading W/S (N/m^2), Unaccelerated 1g Stall Speed Vs1 = SQRT((2*W/S)/(rho*CL_max)), V-n Structural Design Maneuvering Corner Speed VA = Vs1*SQRT(n_max), and Corner Dynamic Pressure.
Understand why Design Maneuvering Speed VA drops when an aircraft flies lightly loaded!
On an aircraft V-n structural flight-envelope diagram, Design Maneuvering ("Corner") Speed V_A marks the intersection of the aerodynamic positive-stall boundary (n = (0.5 * rho * V^2 * CL_max) / (W / S)) and the maximum structural limit load factor n_max: below V_A, full abrupt elevator deflection stalls the wing BEFORE airframe load reaches n_max; above V_A, full control deflection can overstress the wing! Solving for V_A gives V_A = V_s1 * SQRT(n_max) = SQRT((2 * (W / S) * n_max) / (rho * CL_max))—proving a counterintuitive safety rule tested on every pilot exam: when fuel/passenger weight W is LOWER, Wing Loading W/S drops so V_A DECREASES (flying lightly loaded requires a SLOWER turbulence penetration speed to protect the airframe)!
Verify on a Utility-Category Aircraft—Gross_Weight W = 12,250 N (B2), Wing_Planform_Area S = 10.0 m^2 (B3 -> Wing Loading W/S = 1,225.00 N/m^2 in E2), SeaLevel_Air_Density rho = 1.225 kg/m^3 (B4), Clean_Max_Lift_Coeff CL_max = 1.25 (B5), and Utility_Limit_Load_Factor n_max = 4.0 g (B6): Clean 1g Stall Speed is SQRT((2 * 1,225) / (1.225 * 1.25)) = SQRT(1,600) = 40.00 m/s (E3); Design Maneuvering Corner Speed is 40.00 * SQRT(4.0) = 80.00 m/s (E4); and Dynamic Pressure at Corner Speed is 0.5 * 1.225 * (80^2) = 3,920.00 Pa (E5)!
| V-n Envelope Metric (W=12,250 N, S=10 m^2, rho=1.225, CLmax=1.25, nmax=4.0g) | Formula | Verified Output |
|---|---|---|
| Wing Loading W/S (N/m^2) | Aircraft_Weight_N / Wing_Area_m2 | 1,225.00 N/m^2 (784 @ 7,840 N) |
| Clean 1g Stall Speed Vs1 (m/s) | SQRT((2 * (W/S)) / (rho * CL_max)) | 40.00 m/s (32.00 m/s @ Light) |
| Maneuvering Corner Speed VA | Vs1 * SQRT(Limit_Load_Factor_nmax) | 80.00 m/s (64.00 m/s @ Light) |
| Corner Dynamic Pressure q (Pa) | 0.5 * rho * VA^2 | 3,920.00 Pa |
V-n Structural Maneuvering (Corner) Speed VA Formula
Validate positive Weight, Wing_Area, Air_Density, and CL_max, plus Limit_Load_Factor n_max >= 1!
=LET(wt_n, B2, ar_s, B3, rh_a, B4, cl_m, B5, nm_x, B6, IF(OR(wt_n <= 0, ar_s <= 0, rh_a <= 0, cl_m <= 0, nm_x < 1), "Invalid V-n Envelope Input", LET(ws_l, wt_n / ar_s, vs_1, SQRT((2 * ws_l) / (rh_a * cl_m)), ROUND(vs_1 * SQRT(nm_x), 2))))Light-Weight Solo Flight VA Reduction Check (Set Weight = 7,840 N)
Reduce Aircraft_Weight B2 by 36% to 7,840 N: Wing Loading E2 drops to 784.00 N/m^2, 1g Stall Speed E3 drops 20% to 32.00 m/s, and Maneuvering Speed V_A E4 drops 20% from 80.00 m/s down to 64.00 m/s!
=IF(ISTEXT(E4), E4, ROUND(0.5 * B4 * (E4 ^ 2), 2))Try the example
Use the original values or change them to test your understanding.