Take-off Distance Calculator
An 1100 kg aircraft with 3 kN of thrust needs a ground roll of about 179.381 m at sea level, by the 1.44 W² formula.
179.380896816899 m
Full answer, then cut to fewer decimals (not rounded):
- 179.380896816899 m
- 179.38089681689 m
- 179.3808968168 m
- 179.380896816 m
- 179.38089681 m
- 179.3808968 m
- 179.380896 m
- 179.38089 m
- 179.3808 m
- 179.380 m
- 179.38 m
- 179.3 m
- In feet
- 588.5200027 ft
- Lift-off speed 1.2 V_s
- 31.28004564 m/s
- Thrust-to-weight ratio
- 0.2781044217
Step-by-step solution
- s_LO ≈ 1.44 W² ÷ (g ρ S C_L,max T) (lift-off at 1.2 V_s, drag and friction neglected)
- = 1.44 × 10787.315² ÷ (9.80665 × 1.225000018 × 16.2 × 1.6 × 3000)
- s_LO = 179.3808968 m
Take-off Distance Formula
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)
Worked Example
An 1100 kg aircraft, 16.2 m², C_L,max 1.6, 3 kN thrust at sea level:
- s_LO ≈ 1.44 W² ÷ (g ρ S C_L,max T) (lift-off at 1.2 V_s, drag and friction neglected)
- = 1.44 × 10787.315² ÷ (9.80665 × 1.225000018 × 16.2 × 1.6 × 3000)
- s_LO = 179.3808968 m
Lift-off speed 1.2 V_s: 31.28004564 m/s · Thrust-to-weight ratio: 0.2781044217
GATE tip
A headwind V_w shortens the roll by roughly (1 − V_w/V_LO)². GATE also asks about the air distance to clear a 15 m (50 ft) obstacle, added after lift-off.
More Airplane Performance Calculators
-
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.
-
Rate of Climb Calculator
R/C = (T − D)V / W
sin γ = (T − D)/W; excess power = (T − D)V
Example: 3000 N thrust and 1500 N drag at 40 m/s for an 1100 kg aircraft: Rate of climb = 5.56209 m/s.
-
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.
-
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.
Frequently asked questions
Why does weight matter so much?
Ground roll goes with W²: a heavier aircraft needs a higher lift-off speed and accelerates more slowly. Ten per cent more weight adds about 21 % to the roll.
How do altitude and temperature affect it?
Through ρ: lower density needs more true speed to lift off, so hot and high airfields lengthen the roll in proportion to 1/ρ (and further if thrust drops).
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.
Cite this page
APA
Scientific Converters. (2026, October 15). Take-off Distance Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/takeoff-distance-calculator/
IEEE
Scientific Converters, "Take-off Distance Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/takeoff-distance-calculator/