Take off consists of several segments. In this course we will calculate only the ground roll when the aircraft is in contact with the ground. Usually take off distance includes the distance in air to clear an obstacle (35 ft or 50 ft)
Ground roll
During the ground roll on TO the plane starts from rest and accelerates to lift off speed.
Simple 1D dynamics from start of ground roll ( aircraft starts from rest)
Ground Effect Factor
The acceleration is a function of the speed. However the variation in a is fairly small from start to lift off and can be effectively estimated at 70 % of the lift off speed
(US Units only)