Turn Performance Calculator
At 100 knots and 30° of bank an aircraft turns on a radius of 467.43 m, pulling 1.15 g.
467.430358031468 m
Full answer, then cut to fewer decimals (not rounded):
- 467.430358031468 m
- 467.43035803146 m
- 467.4303580314 m
- 467.430358031 m
- 467.43035803 m
- 467.4303580 m
- 467.430358 m
- 467.43035 m
- 467.4303 m
- 467.430 m
- 467.43 m
- 467.4 m
- Load factor n = 1/cos φ
- 1.154700538
- Turn rate ω = g tan φ / V
- 6.305858178 °/s
- Time for a 360° turn
- 57.0897711 s
- Stall speed increase √n
- 1.074569932
- Bank for a standard-rate turn (3°/s)
- 15.35884675 °
Step-by-step solution
- n = 1 ÷ cos 30° = 1.154700538
- R = V² ÷ (g tan φ) = 51.44444444² ÷ (9.80665 × 0.5773502692) = 467.430358 m
- ω = g tan φ ÷ V = 0.1100579874 rad/s = 6.305858178°/s
Turn Performance Formula
R = V² / (g tan φ), ω = g tan φ / V
n = 1/cos φ; standard-rate turn 3°/s
Worked Example
A 100-knot turn at 30° of bank:
- n = 1 ÷ cos 30° = 1.154700538
- R = V² ÷ (g tan φ) = 51.44444444² ÷ (9.80665 × 0.5773502692) = 467.430358 m
- ω = g tan φ ÷ V = 0.1100579874 rad/s = 6.305858178°/s
Turn rate ω = g tan φ / V: 6.305858178 °/s · Time for a 360° turn: 57.0897711 s · Stall speed increase √n: 1.074569932 · Bank for a standard-rate turn (3°/s): 15.35884675 °
GATE tip
For the minimum turn radius or maximum turn rate, the limits are the stall (C_L,max) and the structural load factor; they meet at the manoeuvring speed.
More Airplane Performance Calculators
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Lift Equation Calculator
L = ½ ρ V² S C_L
ρ air density, V true airspeed, S wing area, C_L lift coefficient; drag uses C_D the same way
Example: A 16.2 m² wing at 60 m/s and C_L = 0.5 at sea level: Lift L = 17860.5 N.
-
Stall Speed Calculator
V_s = √(2W / (ρ S C_L,max))
in a turn V_s√n; manoeuvring speed V_A = V_s√n_max
Example: An 1100 kg aircraft with a 16.2 m² wing and C_L,max = 1.6 at sea level: Stall speed V_s = 26.0667 m/s.
-
Drag Polar Calculator
C_D = C_D0 + K C_L², K = 1/(πeAR)
(L/D)max = 1/(2√(C_D0 K)) at C_L = √(C_D0/K)
Example: C_D0 = 0.025, AR = 8, e = 0.8 at C_L = 0.5: Drag coefficient C_D = 0.037434.
-
Take-off Distance Calculator
s_LO ≈ 1.44 W² / (g ρ S C_L,max T)
lift-off at 1.2 V_s; drag and rolling friction neglected (Anderson)
Example: An 1100 kg aircraft, 16.2 m², C_L,max 1.6, 3 kN thrust at sea level: Ground roll s_LO ≈ 179.381 m.
Frequently asked questions
Why does a tighter turn need more bank?
Only the horizontal lift component L sin φ turns the aircraft, while L cos φ must still carry the weight, so R falls as tan φ rises.
What is a standard-rate turn?
3° per second, a full circle in two minutes. The bank needed grows with speed: about 15° at 100 knots.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Turn Performance Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/turn-performance-calculator/
IEEE
Scientific Converters, "Turn Performance Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/turn-performance-calculator/