1. FLIGHT MECHANICS BDA 20603
DR. ZAMRI BIN OMAR D
Books: Roskam, Anderson, Nelson, etc.

2. LECTURE OUTLINE Flight Mechanics is composed of: Airplane Performance
Airplane Stability and Control
What is maximum speed of airplane?
How fast can it climb to a given altitude?
How far can it fly on a given tank of fuel (Range)?
How long can it stay in the air (Endurance)?
Can the airplane land in a suitable distance?
Is airplane stable (wind, weight, etc.)?
Can airplane be controlled?

3. FLIGHT MECHANICS: LECTURE OUTLINE
Behavior of entire airplane
How fast can this airplane fly?
How far can this airplane fly on a single tank of fuel?
How long can this airplane stay in the air on a single tank of fuel?
How fast and how high can it climb?
How does it perform?

5. EXAMPLE: CONCORDE Supersonic Jetliner : The one and only.
Wing Span: 25.6m
Wing Area: m2
Length: 61.66 m
Height: 12.2 m
Useful load: kg
Empty Weight: kg
Cruise speed: Mach 2.02
Range : 7250 km
Mach 2.02=2,472 km/h
Crew: 3 (pilot, co-pilot, and flight engineer)
Capacity: 92–120 passengers (128 in high-density layout)[223]
Length: 202 ft 4 in (61.66 m)
Wingspan: 84 ft 0 in (25.6 m)
Height: 40 ft 0 in (12.2 m)
Fuselage internal length: 129 ft 0 in (39.32 m)
Fuselage width: maximum of 9 ft 5 in (2.87 m) external 8 ft 7 in (2.62 m) internal
Fuselage height: maximum of 10 ft 10 in (3.30 m) external 6 ft 5 in (1.96 m) internal)
Wing area: 3,856 ft2 (358.25 m2)
Empty weight: 173,500 lb (78,700 kg)
Useful load: 245,000 lb (111,130 kg)
Powerplant: 4 × Rolls-Royce/SNECMA Olympus 593 Mk 610 afterburning turbojets
Dry thrust: 32,000 lbf (140 kN) each
Thrust with afterburner: 38,050 lbf (169 kN) each
Maximum fuel load: 210,940 lb (95,680 kg)
Maximum taxiing weight: 412,000 lb (187,000 kg)
Performance
Maximum speed: Mach 2.04[224] (≈1,350 mph, 2,172 km/h) at cruise altitude
Cruise speed: Mach 2.02[224] (≈1,320 mph, 2,124 km/h) at cruise altitude
Range: 3,900 nmi (4,500 mi, 7,250 km)
Service ceiling: 60,000 ft (18,300 m)
Rate of climb: 5,000 ft/min (25.41 m/s)
lift-to-drag: Low speed– 3.94, Approach– 4.35, 250 kn, 10,000 ft– 9.27, Mach 0.94– 11.47, Mach 2.04– 7.14
Fuel consumption: lb/mi (13.2 kg

6. EXAMPLE: AIRBUS A380 / BOEING 747 COMPARISON
Wingspan: 79.8 m
AR: 7.53
GTOW: 560 T
Wing Loading: GTOW/b2: 87.94
Wingspan: 68.5 m
AR: 7.98
GTOW: 440 T
Wing Loading: GTOW/b2: 93.77

7. OVERALL AIRPLANE DRAG Wing or airfoil Entire Airplane
No longer concerned with aerodynamic details
Drag for complete airplane, not just wing
Wing or airfoil
Entire Airplane
Tail Surfaces
Engine Nacelles
Landing Gear

8. DRAG POLAR CD,0 is parasite drag coefficient at zero lift (aL=0)
CD,i drag coefficient due to lift (induced drag)
Oswald efficiency factor, e, includes all effects from airplane
CD,0 and e are known aerodynamics quantities of airplane
Example of Drag Polar for complete airplane

9. 4 FORCES ACTING ON AIRPLANE
Model airplane as rigid body with four natural forces acting on it
Lift, L
Acts perpendicular to flight path (always perpendicular to relative wind)
Drag, D
Acts parallel to flight path direction (parallel to incoming relative wind)
Propulsive Thrust, T
For most airplanes propulsive thrust acts in flight path direction
May be inclined with respect to flight path angle, aT, usually small angle
Weight, W
Always acts vertically toward center of earth
Inclined at angle, q, with respect to lift direction
Apply Newton’s Second Law (F=ma) to curvilinear flight path
Force balance in direction parallel to flight path
Force balance in direction perpendicular to flight path

10. GENERAL EQUATIONS OF MOTION (6.2)
Free Body Diagram
Parallel to flight path:

11. GENERAL EQUATIONS OF MOTION (6.2)
Free Body Diagram
Parallel to flight path:
Perpendicular to flight path:

12. STATIC VS. DYNAMIC ANALYSES
Examine two forms of these equations:
Static Performance: Zero Accelerations (dV/dt = 0, V2/rc = 0)
Maximum velocity
Maximum rate of climb
Maximum range
Maximum endurance
Dynamic Performance: Accelerating Flight
Take-off and landing characteristics
Turning flight
Accelerated flight and rate of climb

13. LEVEL, UNACCELERATED FLIGHT
Equations of motion reduce to very simple expressions
Aerodynamic drag is balanced by thrust of engine
Aerodynamic lift is balanced by weight of airplane
Level means horizontal, so q = 0°
Unaccelerated flight means all accelerations = 0
For most conventional airplanes aT is small enough such that cos(aT) ~ 1

14. FORCES ON AN AIRPLANE

15. ACTUAL FORCES ON AN AIRPLANE

16. LEVEL, UNACCELERATED FLIGHT
TR is thrust required to fly at a given velocity in level, unaccelerated flight
Notice that minimum TR is when airplane is at maximum L/D
L/D is an important quantity
Airplane’s power plant must produce a net thrust which is equal to drag

17. THRUST REQUIREMENT (6.3)
TR for airplane at given altitude varies with velocity
Thrust required curve: TR vs. V∞

18. PROCEDURE: THRUST REQUIREMENT
Select a flight speed, V∞
Calculate CL
Minimum TR when airplane
flying at (L/D)max
Calculate CD
Calculate CL/CD
Calculate TR
This is how much thrust engine
must produce to fly at selected V∞

19. THRUST REQUIREMENT (6.3) Usually around 2º-8º
Thrust required, TR, varies inversely with L/D
Minimum TR when airplane is flying at L/D is a maximum
L/D is a measure of aerodynamic efficiency of an airplane
Maximum aerodynamic efficiency → Minimum TR
Recall Homework Problem #5.6, find (L/D)max for NACA 2412 airfoil
Usually around 2º-8º

20. THRUST REQUIREMENT (6.3)
Different points on TR curve correspond to different angles of attack
At b:
Small q∞
Large CL (or CL2) and a to support W
D large
At a:
Large q∞
Small CL and a
D large

21. THRUST REQUIRED VS. FLIGHT VELOCITY
Zero-Lift TR
(Parasitic Drag)
Lift-Induced TR
(Induced Drag)
Zero-Lift TR ~ V2
(Parasitic Drag)
Lift-Induced TR ~ 1/V2
(Induced Drag)

22. THRUST REQUIRED VS. FLIGHT VELOCITY
At point of minimum TR, dTR/dV∞=0
(or dTR/dq∞=0)
CD,0 = CD,i at minimum TR and maximum L/D
Zero-Lift Drag = Induced Drag at minimum TR and maximum L/D

23. MAXIMUM VELOCITY Intersection of TR curve and maximum
Maximum flight speed occurs when thrust available, TA=TR
Reduced throttle settings, TR < TA
Cannot physically achieve more thrust than TA which engine can provide
Intersection of TR
curve and maximum
TA defined maximum
flight speed of airplane

24. AIRPLANE POWER PLANTS
Consider two types of engines common in aviation today
Reciprocating piston engine with propeller
Average light-weight, general aviation aircraft
Rated in terms of POWER
Jet (Turbojet, turbofan) engine
Large commercial transports and military aircraft
Rated in terms of THRUST

25. THRUST VS. POWER
Jets Engines (turbojets, turbofans for military and commercial applications) are usually rate in Thrust
Thrust is a Force with units (N = kg m/s2)
For example, the PW is rated at 98,000 lb of thrust
Piston-Driven Engines are usually rated in terms of Power
Power is a precise term and can be expressed as:
Energy / time with units (kg m2/s2) / s = kg m2/s3 = Watts
Note that Energy is expressed in Joules = kg m2/s2
Force * Velocity with units (kg m/s2) * (m/s) = kg m2/s3 = Watts
Usually rated in terms of horsepower (1 hp = 550 ft lb/s = 746 W)
Example:
Airplane is level, unaccelerated flight at a given altitude with speed V∞
Power Required, PR=TR*V∞
[W] = [N] * [m/s]

26. AIRPLANE POWER PLANTS

27. Propeller Drive Engine
POWER AVAILABLE (6.6)
Propeller Drive Engine
Jet Engine

28. POWER REQUIRED (6.5) PR varies inversely as CL3/2/CD
Recall: TR varies inversely as CL/CD

29. POWER REQUIRED (6.5)
PR vs. V∞ qualitatively
(Resembles TR vs. V∞)

30. POWER REQUIRED (6.5) Zero-Lift PR Lift-Induced PR Zero-Lift PR ~ V3
Lift-Induced PR ~ 1/V

31. POWER REQUIRED
At point of minimum PR, dPR/dV∞=0

32. POWER REQUIRED
V∞ for minimum PR is less than V∞ for minimum TR

33. WHY DO WE CARE ABOUT THIS?
We will show that for a piston-engine propeller combination
To fly longest distance (maximum range) we fly airplane at speed corresponding to maximum L/D
To stay aloft longest (maximum endurance) we fly the airplane at minimum PR or fly at a velocity where CL3/2/CD is a maximum
Power will also provide information on maximum rate of climb and altitude

34. POWER AVAILABLE AND MAXIMUM VELOCITY (6.6)
Propeller Drive
Engine PA PR
1 hp = 550 ft lb/s = 746 W

35. POWER AVAILABLE AND MAXIMUM VELOCITY (6.6)
Jet Engine
PA = TAV∞ PR

36. ALTITUDE EFFECTS ON POWER REQUIRED AND AVAILABLE (6.7)
Recall PR = f(r∞)
Subscript ‘0’ denotes seal-level conditions

37. Vmax,ALT < Vmax,sea-level
ALTITUDE EFFECTS ON POWER REQUIRED AND AVAILABLE (6.7) Propeller-Driven Airplane
Vmax,ALT < Vmax,sea-level

38. RATE OF CLIMB (6.8) Boeing 777: Lift-Off Speed ~ 180 MPH
How fast can it climb to a cruising altitude of 30,000 ft?

39. RATE OF CLIMB (6.8)
Governing Equations:

40. RATE OF CLIMB (6.8) Rate of Climb: TV∞ is power available
Vertical velocity
Rate of Climb:
TV∞ is power available
DV∞ is level-flight power required (for small q neglect W)
TV∞- DV∞ is excess power

41. Propeller Drive Engine
RATE OF CLIMB (6.8)
Propeller Drive Engine
Jet Engine
Maximum R/C Occurs when Maximum Excess Power

42. EXAMPLE: F-15 K
Weapon launched from an F-15 fighter by a small two stage rocket, carries a heat-seeking Miniature Homing Vehicle (MHV) which destroys target by direct impact at high speed (kinetic energy weapon)
F-15 can bring ALMV under the ground track of its target, as opposed to a ground-based system, which must wait for a target satellite to overfly its launch site.

43. GLIDING FLIGHT (6.9)
To maximize range, smallest
q occurs at (L/D)max

44. EXAMPLE: HIGH ASPECT RATIO GLIDERq
To maximize range, smallest q occurs at (L/D)max
A modern sailplane may have a glide ratio as high as 60:1
So q = tan-1(1/60) ~ 1°