1) The document defines key takeoff and landing airspeeds such as rotation speed, liftoff speed, obstacle clearance speed, and approach speed. 2) It also defines important distances like ground run, takeoff distance, ground roll, and landing distance. 3) The equations for calculating takeoff and landing performance are derived using concepts like conservation of energy, force summation, and drag analysis. Assumptions like constant mass and lift are made to simplify the equations.

1. Take Off and Landing
Performance

2. Definitions – TO Airspeeds
Start VRO
T
VLO
50’
VOBS
• VROT (rotation speed): Speed at rotation from ground attitude
to liftoff attitude
• VLO (liftoff speed): Speed at which aircraft leaves the ground
(1.1 VS min)
• VOBS (obstacle clearance speed): Speed at 50’ with gear
extended (1.2 VS min)

3. Definitions – TO
Airspeeds (FAA)
Start VR VLO
F 35’
V2
• VR (rotation speed): Speed at rotation from ground attitude to
liftoff attitude
• VLOF (liftoff speed): Speed at which aircraft leaves the ground
• V2 (Takeoff Safety Speed): Speed at 35’

4. Definitions – TO Airspeeds
• VREF (refusal speed): Maximum speed at which the airplane can stop within the remaining runway
length
• VCEF (critical engine failure speed): Speed at which the critical engine can fail and the airplane can
either liftoff or stop in the same distance
• V1(FAA, AKA “decision speed”): Maximum speed at which the pilot must take the first action to stop
the airplane within the accelerate-stop distance.

5. Definitions – Lnd Airspeeds
• VPA (approach speed): Speed at which the airplane clears a 50’ height above the runway (1.2 VS min)
• VTD (touchdown speed): Speed at which the airplane touches the ground (1.1 VS min)
FAA
• VREF (reference speed): Speed at which the airplane clears a 50’ height above the runway

6. Definitions – Other Airspeeds
• VMCA (Air Min Control Speed): Minimum airborne speed where the critical engine is suddenly failed
and the airplane remains in control
• VMCG (Ground Min Control Speed): Minimum speed during takeoff ground run, where the critical
engine is suddenly failed, and directional control can be maintained

7. Definitions – Distances
• Ground Run: Distance from brake release to main wheel liftoff
• Takeoff Distance: Distance from brake release to 50’ (35’, FAA) height above the
runway
}
VLO
50’
(35’, FAA)
Start
Ground Run
Takeoff Distance

8. Definitions – Distances
• Ground Roll: Distance touchdown to a full stop
• Landing Distance: Distance from a 50’ (50’, FAA) height above the runway to a full stop
{
VTD
50’
(50’, FAA)
Stop
Ground Roll
Landing Distance

9. APPROACH
 Free Body Diagram
 Apply Conservation of Energy
 Simplify Equations
Theory

10. Phases
LANDING
50 FT
TOUCHDOWN
AIR GROUND
TAKEOFF
GROUND
LIFTOFF
ROTATION
50 FT
AIR

11. TO Ground Phase – Forces
W
D
FR
L
T
FGND

12. T = Thrust (Engine Thrust Curves)
D = CD q S  CD = CDP
+ CDI
= CDP
+
L = CL q S
FR = Rolling/Bearing Friction = (W-L)
CL
2
ARe
TO Ground Phase – Forces
W
D
FR
L
T
FGND

13. TO Equation Formulation
Conservation of Energy
)
run
ground
takeoff
(
S
@
V
:
Assume
S
,
V
:
conditions
initial
Set
G
TO
0
0 0
0 


 








Dist
Forces
Work
Mgdh
MVdV
PE
KE
Work
  

 



H
V
S
Mgdh
MVdV
ds
F
TO
G
0
0
0

14. TO Equation Assumptions
  

 



H
V
S
Mgdh
MVdV
ds
F
TO
G
0
0
0
Assume constant mass and height:   2
0
2
TO
S
V
g
W
ds
F
G


 
 
 ds
L
W
D
T
ds
F
Let  



  D
FR
T

15. Thrust Portion, T
Takeoff Thrust
Piston Aircraft Thrust
Curve
Thrust Variations with Speed
V

16. Takeoff Drag
WITH ROTATION
V0 VTO
CONST C
L
AERO DRAG
  












eAR
C
C
S
V
C
C
qS
qS
C
D L
D
D
D
D P
I
P


2
2
2
1
2
V
D
Thus 

17. Takeoff Rolling Friction
WITH ROTATION
V VTO
FR
 
L
W
F
Friction
Rolling
Classical R 

 

18. Takeoff Force Summation
If ΣF is linear than the average net thrust
occurs @ ~0.75 VTO for jet aircraft
FORCE
F (Thrust)
D (Aero Drag)
FR (Rolling Friction)
V
FD (Combined Drag Forces)
 
 
 


 L
W
D
T
F 

19. TO Equation Formulation
 
   



G
S
TO
AVE V
g
W
ds
L
W
D
T
0
2
2


F

  ds 
W
2g
VTO
2
0
SG

 
 AVE
TO
G
L
W
D
T
g
V
W
S





2
2

20. Landing Ground Phase
sA sG
50FT
STOP
T/D
D
FR
T
 
   




G
S
TO
AVE V
g
W
ds
L
W
D
T
0
2
2

   
  


G
S
TD
V
g
W
ds
F
0
2
2
0
2
 
 AVE
LD
G
L
W
D
T
g
V
W
S






2
2

21. Landing Ground Phase Forces
FNET FNET

22. Stopping Distance
Typical Fighter Profile
5 4 3 2 1
STOP BRK LN V RN TD
RESULT
1 Touchdown
2 Raise nose
3 Lower nose
4 Start braking
5 Stop
DRAG
FORCES
Fr (WHEELS)

23. Takeoff/Landing Air Phase
• Start again with the
work-energy equation
GROUND
LIFTOFF
ROTATION
50 FT
AIR
  

 



H
V
S
Mgdh
MVdV
ds
F
TO
G
0
0
0

24. Takeoff Air Phase
• Friction Force - Gone
• Potential Term Added
     
TO
TO
S
h
h
W
V
V
g
W
ds
D
T
A





 50
2
2
50
0
2
GROUND
LIFTOFF
ROTATION
50 FT
AIR
   
 
 AVE
TO
A
D
T
g
g
V
V
W
S




2
50
2
2
2
50

25. • Assumptions:
• Constant weight
• Constant CL
Landing Air Phase
50 FT
TOUCHDOWN
AIR GROUND
   
 
 AVE
LD
A
D
T
g
g
V
V
W
S




2
50
2
2
50
2

26. T/O Ground Roll Reduction
Weight & Velocity Effects
• Weight
• Imbedded in all parts of
equation (W, VTO, D, FR)
• VTO
• Decrease weight, increase CL,
add high lift devices
 
 AVE
TO
G
L
W
D
T
g
V
W
S





2
2
W SG
SG
VTO

27. T/O Ground Roll Reduction
Thrust Addition
B-47 Rocket Assisted Takeoff

28. T/O Ground Roll Reduction Thrust Addition
• Afterburner most common type
• Other Types
• Water Injection
• JATO or RATO
• Limited use during roll
• When to Apply?
• For a given t (fuel limit) apply at largest V
 



 dt
V
F
ds
F
Work

29. Landing Roll Reduction
Analysis
• Methods Available
• Decrease Weight
• Minimize Speed (High Lift Devices)
• Reverse Thrust
•
• Apply at max velocity (early)
• Maximize Drag (Drag Devices)
• Drag Chute
• Spoilers
• Maximize Braking
• Auto Brakes & Anti-Skid Systems
 
 AVE
LD
G
L
W
D
T
g
V
W
S






2
2
 



 dt
V
F
ds
F
Work