AE 1350 Lecture Notes #10. TOPICS TO BE STUDIED. Take-off and Landing Performance There is considerable variations due to pilot technique ground conditions FAR 25 regulations cover how take-off and landing distances must be computed.
We attempt to compute the ground roll as
accurately as possible.
Add an extra 20% distance to account for
transition and climb.
Transition and climb
20% of total takeoff
distance, from experience
80% of total takeoff
distance, from experience.
Let v be the aircraft speed.
dv/dt = a
where a= acceleration of the vehicle
a= (All horizontal forces acting on the aircraft) / (Mass of aircraft)
Assume “a” to be a constant.
Integrate: v = at Velocity at lift-off vLO = a tLO
Integrate again: d = 1/2 a t2 dLO = 1/2 a t2LO = v2LO/(2a)
From the previous slide, the total roll distance is
dLO = 1/2 a t2LO = v2LO/(2a)
a = Acceleration of the aircraft due to horizontal forces on it.
These forces are: Thrust, Drag, Ground Friction
Thrust far exceeds the other two factors during takeoff.
Thus, a = T/(Aircraft Mass) = T g/ (W)
Then, total roll distance is dLO = v2LO/(2a) = v2LO. W/(2Tg)
Total roll distance dLO = v2LO. W/(2Tg)
The pilot usually lifts off at 1.2 times stall velocity.
Stall velocity VStall is defined from: 1/2 r V2Stall CLmax S= W
V2Stall= W/(1/2 r CLmax S)
v2LO =(1.2 VStall)2 = 1.44 W/(1/2 r CLmax S)
Then, dLO = v2LO. W/(2Tg)= 1.44 (W)2 / (TgrS CLmax)
Include factors of safety for transition and climb:
Take-off Distance, in feet = 37.5 (W)2 / (TsS CLmax)
= 37.5 (W/S) /[(T/W)s Clmax]
where s = Density Ratio = r/rSea-Level,,W in lbs, S in square feet
There is considerable scatter in landing distances due to
use of spoiler, brakes, reverse thrust, human factors
ground conditions : wet runway , dry runway
Vapproach=VA=1.3 Vstall for civilian aircraft
Vapproach=VA=1.2 Vstall for military aircraft
Vapproach=VA=1.1 Vstall for carrier based aircraft
Total Landing Distance, in feet = 0.3 (Vapproach in knots)2
These results are empirical, because of variations in pilot technique.