Takeoff Ground Roll
Approximate ground-roll distance assuming constant acceleration to lift-off speed.
Formula
Variables
Example
Doubling lift-off speed roughly quadruples the ground roll needed to reach it.
How it works
This relation estimates how much runway an aircraft needs to accelerate from rest to the speed at which it becomes airborne, assuming the average acceleration stays constant. It comes from the kinematics identity v^2 = u^2 + 2as, with initial speed u = 0 and final speed V_LO, so the distance grows with the square of takeoff speed and shrinks as acceleration increases. In practice it is a simplified model: real takeoff roll is affected by thrust changes, drag, rolling resistance, wind, slope, and runway surface conditions.
When to use it
Use this for quick performance estimates, sensitivity checks, or early-stage aircraft/mission calculations when you only know an approximate lift-off speed and average acceleration. It is especially useful for comparing how runway length changes with weight, flap setting, density altitude, or available thrust.
Worked example, step by step
Given: lift-off speed V_LO = 75 m/s and average acceleration a = 2.5 m/s² Step 1: Square the lift-off speed: V_LO² = 75² = 5625 Step 2: Multiply the denominator: 2a = 2 × 2.5 = 5 Step 3: Compute the ground roll: s = V_LO² / (2a) = 5625 / 5 = 1125 m Answer: The approximate takeoff ground roll is 1125 m.
Common mistakes to avoid
- Using the aircraft’s true airspeed in knots without converting to m/s before applying the formula
- Forgetting that the acceleration term must be the average net acceleration during the roll, not just engine thrust alone
- Reversing the relationship and dividing by V_LO² instead of by 2a
Did You Know?
Takeoff roll lengthens dramatically with weight, heat, and altitude — all of which thin the available lift and thrust.
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