1. AE 440 Performance Discipline Lecture 9
Eric Loth
For AE 440 A/C Lecture

2. Some Performance Responsibilities
Define flight requirements with constraint analysis & develop discrete trajectory model for all flight segments
Determine fuel for all segments based on engine (from prop.)
Determine required thrust for mission segments
Determine minimum power/lift. for safety: engine-out, take-off, etc. (to propulsion/aero)
Calculate overall mission performance (alert sub-systems of shortcomings)
Define concept of flight operations (# of flights, airports, etc.)

3. Typical Mission Profile
Main mission flight profile definition (Jenkinson).

4. Take-Off Speed definitions (Jenkinson): VS Stalling speed
V1 Critical power failure speed (decision)
Vr Rotation speed
VLOF Lift-off speed > 1.1VS
V2 Climb speed > 1.2VS
Decision speed-speed at which distance to stop after one engine fails exactly equals the distance to continue take-off on the remaining engines

5. Ground-roll for Takeoff
Forces on the aircraft are thrust, drag, and rolling friction of the wheels-expressed as rolling friction coefficient times weight of wheels (L-Mg)

6. Transition to Climb Usually ends at best climb angle.
Equations

7. Important Forces in Climb
G = climb gradient
Geometry for performance calculation (Raymer).

8. Climb Performance Best climb rate (jet) graphical method:
Plug in for D, assumes L approx equal to W (small enough climb angle)
Graphical method for best climb (Raymer).
Best rate of climb provides max vertical velocity, best angle of climb is point of curve that is tangent with line through the origin-aircraft gains more altitude for a

9. Time and Fuel to Climb
Assume linear velocity change for each section where a = linear constant
Divide climb into smaller segment (less than 5000 ft or 1500 m)
Time to climb is change in altitude divided by rate of climb (vertical velocity). Two altitudes to determine a should be near the beginning and end of climb. Want smaller segments so fuel burned is insignificant part of total aircraft weight and can be ignored in time integration

10. Level Flight
Approx:
Aerodynamicist must provide aircraft S, CL and CD as a function of angle of attack; configurations must provide W (w/ & w/o landing gear, weapons, etc.)
Can re-write to find conditions for minimum thrust (or drag) – see Raymer Eq

11. Range Missions often specify range – not time, speed or altitude
“Breguet range equation”
“Cruise climb” maximizes range
Break mission into segments to be more accurate
Optimize altitude, speed, wing size, etc. (show this) in order to minimize weight of aircraft and of fuel needed
Equation obtained by integrating instantaneous range with respect to change in aircraft weight. Equation assumes velocity, SFC, and L/D are constant. These assumptions require that lift coefficient is held constant. As aircraft becomes lighter, dynamic pressure must be reduced for this to be true and since velocity is fixed must change density. Normally not permitted bc air traffic controllers want to keep planes at constant altitude and airspeed

12. Turn Performance Level turn geometry (Raymer).
Turn rate equals radial acceleration divided by velocity

13. Approach and Landing VTD = 1.15 VS
Obstacle height of 50 ft, Va=1.3Vs, Flare is segment where aircraft decelerates from Va to Vtd, Ground roll comprised of two segments
Approach and landing definitions (Jenkinson).

14. Ground Roll for Landing
Free-roll (no braking)
Breaking distance: where

15. Samples of Performance Results from Previous CDRs

16. Mission Requirements

17. Mission Profile

18. Instantaneous Turn for Different Load Factors

19. Landing and Takeoff Distance Trade Study

20. Range Trade Study