G. Leng, Flight Dynamics, Stability & Control. Lecture 1 : Introduction to Flight
Dynamics,. Stability & Control. Or appreciating the basic terms and concepts ...
Lecture 1 : Introduction to Flight Dynamics, Stability & Control Or appreciating the basic terms and concepts
G. Leng, Flight Dynamics, Stability & Control
1.0 Course Info
• • • • • •
Instructor: Office: Phone: E-mail: Consultation: Website:
Associate Professor Gerard Leng E2-02-37 6-516-6548
[email protected] M-F 12-2pm (by appt) http://dynlab.mpe.nus.edu.sg/mpelsb/
G. Leng, Flight Dynamics, Stability & Control
1.1 Course requirements • Background (Basic engineering courses ~ stage 1&2 ) – Dynamics – Calculus – Computer programming (C/C++) – Feedback & Control – Matlab (optional) • Open Book Exam (80%), CA (20%)
G. Leng, Flight Dynamics, Stability & Control
1.2 Recommended References • Robert C. Nelson, “Flight Stability and Automatic Control”, McGraw Hill, 2nd ed, 1998. • Barnes W. McCormick, “Aerodynamics, Aeronautics and Flight Mechanics”, Wiley, 2nd ed, 1995. • Bandu N. Pamadi, “Performance, Stability, Dynamics and Control of Airplanes”, AIAA, 1998 • Louis V. Schmidt, “Introduction to Aircraft Flight Dynamics”, AIAA, 1997
G. Leng, Flight Dynamics, Stability & Control
1.3 Industrial standards • FAR Part 23: Airworthiness standards: Normal, utility, acrobatic, and commuter category. • FAR Part 25: Airworthiness standards: Transport category airplanes • MIL-F-8785C: Flying qualities of piloted airplanes. (pre 1996) • MIL-STD-1797B : Flying qualities of piloted aircraft (post 1996) • MIL-F-9490D: Flight control systems, design, installation and testing of piloted aircraft, General specifications for. G. Leng, Flight Dynamics, Stability & Control
1.4 Training programme 1. Basic aerodynamic terms and concepts 2. The flight environment 3. Static longitudinal & lateral stability 4. Equations of motion 5. Dynamic stability 6. Design of flight control systems G. Leng, Flight Dynamics, Stability & Control
2.0 Basic aerodynamic terms and concepts
Mission Profile
Propulsion
Aerodynamics
Flight Dynamics & Control G. Leng, Flight Dynamics, Stability & Control
Structures
2.1 Angle of attack (AOA) and sideslip angle AOA is the angle between the direction of the airflow and the wings
aircraft longitudinal axis
airflow G. Leng, Flight Dynamics, Stability & Control
Sideslip angle is the angle between the velocity vector and the aircraft plane of symmetry velocity
By convention sideslip to the right is positive
Typically one tries to fly with zero sideslip
G. Leng, Flight Dynamics, Stability & Control
2.2 : Definition of lift & drag coefficients CL and CD Aerodynamic forces are typically expressed as L
=
1/2 V2 S CL
Similarly for the drag coefficient D = 1/2 V2 S CD G. Leng, Flight Dynamics, Stability & Control
Question : How does the lift coefficient vary with AOA ?
G. Leng, Flight Dynamics, Stability & Control
Question : How large are lift forces for a typical combat aircraft ? From Jane’s all the World’s aircraft F16C ( F100 PW engine) Weight empty
=
8 433 kg
Takeoff Weight ( 2 AAM, no tanks)
=
12 138 kg
So what’s the lift force ?
G. Leng, Flight Dynamics, Stability & Control
Question : How does combat aircraft weight vary with a typical mission ?
What about a civilian aircraft ?
G. Leng, Flight Dynamics, Stability & Control
Weight variation of an Airbus A380-800 Empty
: 277,000 kg
Max Takeoff : 560,000 kg Fuel Capacity : 260,900 kg Max Payload :
84,000 kg
G. Leng, Flight Dynamics, Stability & Control
Question : How does the operational altitude and airspeed vary ? 60
kft 30
0.0
1.0
0 G. Leng, Flight Dynamics, Stability & Control
2.0
Mach
Question : So what are typical values for the lift coefficients ? F16, 1g sustained (level flight ) at 700 kts, 50 kft air density (15.2 km)
=
airspeed
=
weight (2 AAM 50% fuel)
=
10 659 kg
wing area
=
27.87 m2
Hence CL
=
W / (1/2 V2 S)
= G. Leng, Flight Dynamics, Stability & Control
Question : Is CL constant throughout flight ? Example : F16 flap schedule
G. Leng, Flight Dynamics, Stability & Control
2.3 : Describing wing shapes b : span c : mean aerodynamic chord S : surface area : aspect ratio b2/S c F16 b = 9.14 m S = 27.87 m2 =
b
G. Leng, Flight Dynamics, Stability & Control
What’s the aspect ratio for the Airbus A380-800 ? Wing span :
79.80 m
Wing area : 845.0 m²
=
G. Leng, Flight Dynamics, Stability & Control
Extreme example - Scaled Composites Model 311 Virgin Atlantic GlobalFlyer 2005 28/2 – 3/3, fastest, nonstop, unrefueled solo circumnavigation Wing span : 34.75 m Wing area : 37.16 m²
=
G. Leng, Flight Dynamics, Stability & Control
2.4 The mean aerodynamic chord The mean aerodynamic chord is defined by : b/2
c mac
2 c ( y ) dy
b / 2
S
The span-wise location of the mean aerodynamic chord is at : b/2
y mac
c( y) ydy 0
S/ 2
G. Leng, Flight Dynamics, Stability & Control
Homework : Linear taper wings x c0 Root chord c0
b Tip chord c1
c1
y
Taper ratio = c1/c0
Show 1. For the right wing c(y) = c0 [1 - 2 (1 – ) (y/b) ] 2. cmac = 2/3 c0 (1 + + 2)/(1 + ) 3. ymac = b/6 (1 + 2) / (1 + ) 4. c(ymac) = cmac G. Leng, Flight Dynamics, Stability & Control
2.5 Concept of wing loading A measure of force distribution on an aircraft Wing loading
=
Lift force Wing area
=
weight
For level flight, lift hence wing loading =
W/S
G. Leng, Flight Dynamics, Stability & Control
Question : What is the wing loading for typical combat aircraft ? Aircraft F104 MIG 21 X31 F5 Gripen Mirage III Kfir Jaguar Tornado Mirage 2000 F16 EFA Viggen Rafale F18 F14 F4 F15 MIG 25
b (m) 6.68 7.15 7.26 7.7 8 8.22 8.22 8.49 8.6 9.13 9.14 10.5 10.6 11.2 11.43 11.72 11.8 13.04 14
S (m2)
AR 18.2 23.2 21.02 15.79 28.4 34.85 34.8 24 42.3 41 27.87 50 46 47 37.2 66.3 49.26 59.3 56
2.45 2.2 2.5 3.75 1.09 1.94 1.94 3 1.75 2.03 3 2.205 2.44 2.67 3.52 2.07 2.82 2.88 3.07
W/S (N/m2) 4856 3463 2954 3989 2761 2220 4647 4263 6305 4063 3449 3332 3622 2919 3250 3847 3545 3556 4764
G. Leng, Flight Dynamics, Stability & Control
Figure 2.1
G. Leng, Flight Dynamics, Stability & Control
Moral
Large W/S
less sensitive to gust
Small W/S
better manoeuvrability
Question : Why ?
G. Leng, Flight Dynamics, Stability & Control
Wing loading : a comparison Aircraft
Mass (kg)
Wing Area (m2)
A380
560 000
845
F15
21 500
59.3
F16
9 800
27.87
GlobalFlyer
10 024
37.16
G. Leng, Flight Dynamics, Stability & Control
W/S (N/m2)
3.0 Axis System 1 : For flight dynamics and control the axis system or reference frame is fixed to the flight vehicle. 2 : The convention for flight dynamics is to place the origin at the centre of mass of the aircraft with I) The positive x axis points towards the nose II) The positive y axis points towards the right wing III) The positive z axis points downwards. NB : Aerodynamics, propulsion & structures use different conventions
G. Leng, Flight Dynamics, Stability & Control
Figure 3.1 : Axis system
G. Leng, Flight Dynamics, Stability & Control
3.1 Describing Aircraft Motion
The aircraft can rotate about the 3 axes
Term
Physical description
rotation axis
roll
wings up/down
X
pitch
nose up/down
Y
yaw
nose right/left
Z
Positive direction of rotation determined by right hand rule G. Leng, Flight Dynamics, Stability & Control
3.2 Means of controlling roll, pitch & yaw Present aircraft use control surfaces to generate the aerodynamic forces/moments for roll , pitch and yaw
G. Leng, Flight Dynamics, Stability & Control
Question : What’s downwash ? Downwash refers to the effect airflow coming off from the wing has on the tail
airflow
G. Leng, Flight Dynamics, Stability & Control
3.3 Nomenclature & symbols a e r ,,
: : : : : : :
l.m.n : p,q,r, : u,v,w :
angle of attack (AOA) sideslip angle aileron deflection elevator deflection rudder deflection air density roll, pitch and yaw angles roll, pitch & yaw moments roll, pitch and yaw angular rates velocity X,Y & Z components
G. Leng, Flight Dynamics, Stability & Control