Flight Mechanics, Aerodynamics & Aviation Safety
Aircraft Bank Load Factor, Accelerated Stall & Turn Radius
Calculate Level Coordinated-Turn Load Factor n = 1 / COS(phi), Accelerated Stall Speed V_s_bank = V_s1g * SQRT(n), Horizontal Turn Radius V_TAS^2 / (g * TAN(phi)), and Indicated Airspeed Stall Margin.
Guard traffic-pattern base-to-final turns against SQRT(n) accelerated stall!
In a level, altitude-constant coordinated aircraft turn at bank angle phi, vertical lift L*COS(phi) must still equal aircraft weight W, forcing total wing lift to increase by Load Factor n = L / W = 1 / COS(phi_rad)—reaching exactly 2.00 g at a 60-degree bank! Because stall speed scales with the square root of load factor, Accelerated Stall Speed rises to V_s_bank = V_s(1g) * SQRT(n) (+41.4% higher at 60 deg bank!), shrinking the pilot’s safety margin below Indicated Airspeed V_IAS! Meanwhile, centripetal force L*SIN(phi) = m * V_TAS^2 / R sets Horizontal Turn Radius R = V_TAS^2 / (g * TAN(phi_rad)) (with g = 9.81 m/s^2—guarded cleanly when phi = 0 deg for straight flight)!
Verify on a Light Twin-Engine Trainer—Bank_Angle phi = 60 deg (B2), Wings_Level_1g_Stall_Speed V_s0 = 60.0 knots IAS (B3), True_Airspeed V_TAS = 98.1 m/s (B4), and Pattern_Indicated_Airspeed V_IAS = 100.0 knots (B5): Aerodynamic Load Factor is 1 / COS(60 deg) = 2.0000 g (E2); Accelerated Stall Speed jumps to 60 * SQRT(2) = 84.85 knots IAS (E3); Level Turn Radius is (98.1^2) / (9.81 * TAN(60 deg)) = 981 / 1.73205 = 566.38 m (E4); and Remaining Stall Margin above accelerated stall narrows to 100.00 - 84.85 = 15.15 knots (E5)!
| Flight Envelope Metric (60 deg Bank, Vs1g=60 kn, VTAS=98.1 m/s, VIAS=100 kn) | Formula | Verified Output |
|---|---|---|
| Coordinated Load Factor n (g) | 1 / COS(Bank_Deg * PI() / 180) | 2.0000 g (1.0000 g @ 0 deg) |
| Accelerated Stall Speed (kn) | Vs_1g * SQRT(Load_Factor_n) | 84.85 kn (60.00 kn @ 0 deg) |
| Level Turn Radius R (m) | VTAS^2 / (9.81 * TAN(Bank_Rad)) | 566.38 m (981.00 m @ 45 deg) |
| Stall Speed Margin (kn IAS) | Indicated_Airspeed - Accel_Stall | 15.15 kn |
Zero-Bank-Guarded Level Coordinated Turn Radius Formula
Validate 0 <= Bank_Deg < 85, positive V_s1g, V_TAS, and V_IAS, and guard phi = 0 deg before dividing by TAN(0)!
=LET(ph_d, B2, vs_k, B3, vt_m, B4, vi_k, B5, IF(OR(ph_d < 0, ph_d >= 85, vs_k <= 0, vt_m <= 0, vi_k <= 0), "Invalid Banked Turn Envelope", IF(ph_d = 0, "Straight Flight (Infinite Radius)", ROUND((vt_m ^ 2) / (9.81 * TAN(ph_d * PI() / 180)), 2))))45-Degree Turn Radius (TAN = 1) & Wings-Level Straight-Flight Boundary Checks
Set Bank_Angle B2 = 45 deg (TAN = 1): Turn Radius E4 equals 98.1^2 / 9.81 = 981.00 m! Set B2 = 0 deg: Load Factor E2 is 1.0000 g and E4 cleanly reports "Straight Flight (Infinite Radius)" without a #DIV/0! error!
=IF(OR(B2 < 0, B2 >= 85, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Banked Turn Envelope", ROUND(1 / COS(B2 * PI() / 180), 4))Try the example
Use the original values or change them to test your understanding.