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Aircraft Dynamics: Modeling, Simulation, and Aerospace Engineering, Summaries of Aerospace Engineering

Middle East Technical University Aerospace Engineering

AEROSPACE ENGINEERING INTRODUCE AEROELASTICITY

Typology: Summaries

2023/2024

Uploaded on 11/23/2023

dilara-simsek 🇹🇷

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Aircraft Dynamics

Marcello R. Napolitano

AIRCRAFT

DYNAMICS

From Modeling to Simulation

A I R C R A F T D Y N A M I C S

From Modeling to Simulation

AIRCRAFT

DYNAMICS

From Modeling to Simulation

Napolitano

www.wiley.com/college/napolitano

ISBN 978-0-470-94341-0

Partial preview of the text

Download Aircraft Dynamics: Modeling, Simulation, and Aerospace Engineering and more Summaries Aerospace Engineering in PDF only on Docsity!

Aircraft Dynamics

Marcello R. Napolitano

A I R C R A F T

D Y N A M I C S

From Modeling to Simulation

A I R C R A F T

D Y N A M I C S

From Modeling to Simulation

A I R C R A F T

D Y N A M I C S

From Modeling to Simulation

Napolitano

www.wiley.com/college/napolitano

ISBN 978-0-470-94341-

“Aircraft Dynamics:

From Modeling to Simulation”

- A textbook designed to take advantage of the extensive

computational resources commonly available to today‟s students.

… The majority of the textbooks in this discipline were written before

the introduction of Matlab® and Simulink®.

- A textbook designed to help students to be able to extrapolate from

low level formulas, equations, and details to high level

comprehensive views of the main concepts.

- A textbook with emphasis on teaching students the fundamental

skills of „basic modeling‟ of aircraft aerodynamics and dynamics.

An „instructor friendly‟ textbook featuring: - An extensive variety of Student Sample Problems and Case Studies; - An extensive variety of Problems; - A number of sample Matlab ® codes; - Detailed CAD drawings and geometric data for 25 different aircraft

from different classes;

- Complete aerodynamic, geometric, and flight conditions for 10

different aircraft;

- Approx. 500 Power Point-based instructor notes with instructional

videos

Sample figure from Ch. 1 showing the sequential derivation of ALL the aircraft dynamic equations

' ' ' '

A A A T V V S

d dr CLME dV g dV F F dS dt dt d dr CAME r dV r g dV r F F dS dt dt

 

  

     

Aero Forces/Moments

Thrust Forces/Moments

Initial Conditions

X Y Z ^ ^ 

' ' r  r P  r

:  

P A T

A A T V

d V

CLME m mg F F

dt

d dr

CAME r dV M M

dt dt



 ^ ^ 

, ,

d C C C dt t X Y Z X Y Z

          X Y Z

  ^ 

P P A T

A A T V

CLME m V V mg F F

CAME r r r dV M M

 ^ ^ ^ ^ ^ ^  ^ 

X Y Z ^ ^ 

  (^)  

   

2 2

X X

Y Y

Z Z

X A T

Y A T

Z A T

XX XZ XZ ZZ YY A T

YY XX ZZ XZ A T

ZZ XZ YY XX XZ A T

m U QW RV mg F F

m V UR PW mg F F

m W PV QU mg F F

P I R I PQ I RQ I I L L

Q I PR I I P R I M M

R I P I PQ I I QR I N N

    

     

     

     

CLME & CAME

1 sin tan cos tan 0 cos sin 0 sin sec cos sec

P Q R

           (^)   (^)   (^)       (^)     (^)   (^)         ^  ^ 

' ' '

c c s c c s s s s c s c s c c c s s s s c s s c s c s c c

X U Y V Z W

                      (^)   (^)                   (^)      (^)            ^  ^ 

sin cos sin cos cos

X Y Z

g g g g g g

        

Aircraft trajectory w/r X‟Y‟Z‟

V P VP const   const

     

  (^)  

   

1 1

1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 2 2 1 1 1 1

1 1 1 1

sin

cos sin

cos cos

X X

Y Y

Z Z

A T

XZ ZZ YY A T

XX ZZ XZ A T

YY XX XZ A T

m Q W R V mg F F

m U R P W mg F F

m PV Q U mg F F

PQ I R Q I I L L

PR I I P R I M M

PQ I I Q R I N N

CLME & CAME at steady state

Steady state conditions

k

Steady state conditions 1 - Rectilinear flight 2 - Level turn 3 - Symmetric pull-up

Small perturbation conditions

sin , cos 1

up wr pq p

x x x

  (^)  

   

  (^)  

1 1 1 1 1

1 1 1 1 1 1 1 1

1 1 1 1

cos

sin sin cos cos

cos sin sin cos

X X

Y Y

Z Z

A T

XX XZ XZ ZZ YY A T

m u Q w qW R v rV mg f f

m v U r uR Pw pW mg mg f f

m w Pv pV Q u U q mg mg f f

p I r I Pq Q p I R q Q r I I l l

qI P

1 1 1

1 1 1 1

XX ZZ^2 2 XZ A T

ZZ XZ YY XX XZ A T

r pR I I P p R r I m m

r I p I Pq pQ I I Q r R q I n n

Small perturbations CLME & CAME

..from steady state, wing-level, rectilinear flight conditions

  (^)  

     

1 1

1 1 1

1 1

cos

sin

cos

X X

Y Y

Z Z

A T

XX XZ A T YY A T ZZ XZ A T

m u qW mg f f

m v U r pW mg f f

m w U q mg f f

p I r I l l qI m m r I p I n n p q r







   

     

     

     

             

 U V W , , 

 P Q R , , 

 gX^ ,^ gY^ , gZ     ,^ , 

   ,^ , 

Sample figure from Ch. 3 showing the summary of the PITCHING modeling

1 1 1 1

2 2 2

A m (^) u m m m m (^) q m (^) E E m (^) iH H P P P

u c q c m q S c c c c c c c c i V V V   

  

 (^)           ^                        (^)       

cm  0 at steady-state trimmed conditions

W u

AC m L

x c c Mach

   

( ) (1 )( ) W WB^ H H

H m L CG AC L H AC CG

S d c c x x c x x S d   

  

    

( ) E H H

H m L H AC CG E

m E

S c c x x S

 

 



   



( ) i (^) H H H

H m L H AC CG

S c c x x S



   

Polhamus formula (Chapter II)

“Downwash” effect (Chapter II)

  (^)  

 

(^2 2 )

(^2 )

1 tan

AR

c

AR Mach

k Mach



  ^    

 ^  

 ^ 

4.44 AR mr cos 0.25 1

Mach

d

K K K Mach

d



  ^ ^ 

m mH c c  



H H H^ H H

H m L AC CG L H AC CG

S d

c c x x c x x

S d

  

mq m (^) q (^) W mqH

c  c  c

3 2 /

/ 3 2 0 /

tan 3

6cos

tan

6cos

q (^) W qW

c m m Mach c

AR

AR B B

c c

AR



 ^ ^  

 ^  

  ^   

2 2

B  1  Mach cos  c / 4

/ 4 0 0

cos

m (^) qW q L (^) WMach c Mach

c K c C

 (^)  

 

/ 4 3 2 / 4

/ 4

2 cos

1 tan 1

24 6 cos 8

AC W CG ACW CG

AR x x x x

C

AR

 ^  

q (^) H H H

H m L H AC CG

S

c c x x

S



    Leading Edge of wing MAC

Leading Edge of tail MAC

Wing+Body Aerodynamic Center

Tail Aerodynamic Center Aircraft CG

XAC WB

XAC H

X CG

Wing MAC

WB WB

AC AC

X X c  CG CG X X c 

H H

AC AC

X X c 

H. Tail MAC

c H

Leading Edge of wing MAC

Leading Edge of tail MAC

Wing+Body Aerodynamic Center

Tail Aerodynamic Center Aircraft CG

XAC WB

XAC H

X CG

Wing MAC

WB WB

AC AC

X X c  CG CG X X c 

H H

AC AC

X X c 

H. Tail MAC

c H

Sample figure from Ch. 4 showing the summary of the YAWING modeling

1 1 1

2 2 2

A n n n (^) p nr n (^) A A n (^) R R P P P

b p b r b n q S b c c c c c c V V V

   

 (^)           (^)                    (^)       

cn 0 



n n W n B n H n V

c c c c c

    

S B l

B (^) B n N R

S l

c K K

S b

c  

 cos 1 sin 1 

V V (^) V

V^ V^ V n Y L V

d S^ X^ Z

c k c

 d S b



^     

n (^) A nA L 1 lA c K c c  (^)  

cos 1 sin 1

R (^) V

V R R n L V R R

S X Z

c c K

S b

 

   

n p n p (^) W n pV c  c  c

1 1 0

n p n p n p L W L (^) Mach W C

c c

c



  ^ 

 cos 1 sin 1   cos 1 sin 1 

V (^) V

V V V V V n p Y

X Z Z X Z

c c

b b



n r n r W nrV

c  c  c

1 0 1 0

2 2

r r W

n n nr L D L D

c c

c c c

c c

 ^ ^   ^ 

 

2 1 1 2

cos sin 2 V (^) V

V V nr Y

X Z c c b



    

Sample figure from Ch. 7 showing the solution of the linearized LONGITUDINAL equations

   

  (^)  

 

1 1

cos

sin

X X

Z Z

A T

YY A T

m u qW mg f f

m w U q mg f f

qI m m q



     

     

  

     

   

1 1 1 1 1

1 1 1 1 1 1

(^1 ) 1 1

1 1

cos 2 2

sin 2 2 2

2 2

u X u X E

u q (^) E

u T (^) u T

D D T T D L D E P P

P L L L D L L L E P P P

YY YY m m m m m P P

mu mg q S c c u^ c c u c c c V V

u c qc m w V q mg q S c c c c c c c V V V

u u I I q q S c c c c c c c V V

 

  



  

   



      (^)                            

      (^)    (^2 1 ) mT m m (^) q m (^) EE P P

c qc c c c ^  V V 

  

          X Y Z , ,   XS , YS , ZS 

U 1 (^) (^) S  V (^) P (^) 1 , W (^1) S  0

w q

 

 

1 1

, P , P

q q w V w V

   

 

     

1 1 1 1 1

1 1 1 1 1 1 1

(^1 ) 1 1

1 1

cos 2 2

sin 2 2 2

2 2

u X (^) u X E

u q (^) E

u T (^) u T T

D D T T D L D E P P

P P L L L D L L L E P P P

YY m m m m m m P P

q S u u u g c c c c c c c m V V

q S u c qc V V q g c c c c c c c m V V V

u u I q S c c c c c c c V V

 

  

 

  

    

 

                                

       (^2 1 ) m m (^) q m (^) EE P P

c qc c c c  V V 

 

       q 1   

 c S ,

 m I , YY 

 aero coef .

Longitudinal

Dimensional

Stability

Derivatives

1 1

cos

sin

u E

u T E

P u q P E

u T T q E

u g X X u X X

V g Z u Z Z Z V Z

M M u M M  M M M

 

  

 ^ 

       

      

1 1

( ) ( ) cos ( ) ( )

( ) ( ) sin ( ) ( )

( ) ( ) ( ) ( )

u E

u T E

u P q P E

u T T q E

s X X u s X s g s X s

Z u s s V Z Z s s Z V g s Z s

M M u s M s M M (^)  s s s M s M s

 

  

  

     

         

       

t  domain  s  domain

Laplace Transformation

  

       

1 1

cos ( )

sin

u E

E u

u T (^) E

u P q P E u T T q E

u s

s X X X g s

X

s

Z s V Z Z s Z V g Z

s

M

M M M s M M s s M s

s



 

  

  

    ^ 

    ^ 

 ^ ^ ^ ^ ^ ^ ^     

U E

u s Num s

s D s

s Num s

s D s

s Num s

s D s





Transfer

Functions

3 2

Num u s A su B su C su Du

Num s A s B s C s D

Num s A s B s C

    

   

4 3 2 D s 1 ( )  A s 1  B s 1  C s 1  D s 1  E 1

Routh-Hurwitz

Stability Analysis   

4 3 2 1 1 1 1 1 1 2 2 2 2

2 SP nSP nSP 2 PH nPH nPH

D A s B s C s D s E

s   s  s   s 

1 1 1 1 1 1

u E E E

E E E

u s Num^ s u s

u s s u t L u s

s D s s

s Num s s

s s t L s

s D s s

s Num^ s s

s s t L s

s D s s







Short-Period

Approximation

u t ( )  0

 ^ 

      

1 1

( ) cos (^) ( ) ( ) sin ( ) ( ) ( )

u E E

u E

u T (^) E

u P q P E u T T q E

u s s X X X g (^) s X s Z s V Z Z s Z V g Z s M M M s M M s s M s M s



       

    

   (^)             ^      ^   ^ ^ ^ ^ ^ ^ ^             (^)                

 ^ 

      

1 1

( ) cos (^) ( ) ( ) sin ( ) ( ) ( )

u E E

u E

u T (^) E

u P q P E u T T q E

u s s X X X g (^) s X s Z s V Z Z s Z V g Z s M M M s M M s s M s M s



       

    

1 1

P P (^) E

q E

s

sV Z V s s Z

M s M s s M s M

s

 

  

   

 ^   ^   

 ^ ^ ^     

0, 0 sin 0, 0

q T

Z Z M 

 

   

q n SP P

Z M M V

  (^) 

         

q P SP q P

Z M M V

 



                 

1 1

2 q 2 2 2 q SP n SP n SP P P

Z Z M s M M s M s s V V

^   ^ ^ ^ 

                      

Short-Period Char. Equation

Sample figure from Ch. 7 showing the concept of SENSITIVITY ANALYSIS

Flight Conditions

 Alt .,^^ Mach ,^^ ^ ,^ q , 1 

Aircraft Geometry

, , , ,

, , , ,.. H

H H

H V AC

c c b b

S S S x

     

Aircraft Mass and

Inertial Properties

 m I ,^^ XX ,^ IYY^ ,^ I^ ZZ , IXZ 

Dimensionless

Stability and

Control Derivatives

, ,..,

, ,.., ,

p A R

D D D

L L L

m m m

l l l l

Y Y Y Y

n n n n

c c c

c c c c

 

  

                     

Dimensional Stability and Control Derivatives

(Tables 7.1 & 7.3)

, ,.., , , ,.., , , ,..,

, ,.., , , , ,.., , , , ,.., ,

E E E

A R A R A R

u u u

p p p

X X X Z Z Z M M M

L L L L Y Y Y Y N N N N

     

        

       

Longitudinal and

Lateral Directional

Characteristic

Equations

 D s 1 ( ),^^ D 2^ ( ) s 

Sample figure from Ch. 7 showing the key geometric parameters for SENSITIVITY ANALYSIS

Leading Edge

of wing MAC

Leading Edge

of tail MAC

  

Wing+Body

Aerodynamic

Center

Tail

Aerodynamic

Center

Aircraft CG

ACWB X

ACH

X

XCG

Wing MAC

CG CG

X

c

H H

AC AC

X

c

Tail MAC

cH

 (^) H 

AC CG

S

x  x

CRITICAL PARAMETERS

S X

VS

X

S Z

S Y

VS

Z

V

b

Vertical Arm of

Vertical Tail

Horizontal Arm of

Vertical Tail

CRITICAL PARAMETERS

V

SV

VS VS

Z X

b b

Aircraft CG

Sample figure from Ch. 9 showing the general architecture of a simulation code

Beaver dynamics and output equations

16 rb/2V

15 qc/V

14 pb/2V

13 H dot

12 H

11 ye

10 xe

9 phi

8 theta

7 psi

6 r

5 q

4 p

3 beta

2 alpha

1 V

time To Workspace In To Workspace Out To Workspace

Mux Double-click for info!

Mux click 2x for info!

Mux

Demux

Clock

FDC Toolbox BEAVER, level 1 M.O. Rauw, October 1997

12 wwdot

11 vwdot

10 uwdot

9 ww

8 vw

7 uw

6 pz

5 n

4 deltaf

3 deltar

2 deltaa

1 deltae

xdot

y dl

uwind

uprop

uaero

Deflections of Control Surfaces

Throttle Settings

Atmospheric Turbulence (optional)

Motion Variables

Aircraft Equations of Motion

Pilot Inputs and

External Disturbance Aircraft Outputs

FDC Toolbox M.O. Rauw 1997

xdot x

yhlp

Additional outputs

Aircraft equations of motion (Beaver)

Wind forces

Gravity forces

Engine group (Beaver)

Aerodynamics group (Beaver)

(co)sines of alpha, beta, psi, theta, phi

Add + sort forces and moments

Airdata group

18 yad

17 yad

16 yad

15 yatm

14 Fwind

13 Fgrav

12 FMprop

11 FMaero

10 Cprop

9 Caero

8 yacc

7 ypow

6 yfp

5 ydl

4 yuvw

3 ybvel

2 xdot

1 x

hlpfcn

Gravity

Fwind

FMsort

BEAVER, level 2 (main level) M.O. Rauw

-K-

3 -K- uwind

2 uprop

1 uaero

Modeling of the Aerodynamic Forces and Moments

Modeling of the Propulsive Forces and Moments

Modeling of the Gravity Forces

Modeling of the Atmospheric Turbulence Forces

AIRCRAFT

EQUATIONS

OF MOTION

FDC Toolbox M.O. Rauw 1997

xdot x

yhlp

Additional outputs

Aircraft equations of motion (Beaver)

Wind forces

Gravity forces

Engine group (Beaver)

Aerodynamics group (Beaver)

(co)sines of alpha, beta, psi, theta, phi

Add + sort forces and moments

Airdata group

18 yad

17 yad

16 yad

15 yatm

14 Fwind

13 Fgrav

12 FMprop

11 FMaero

10 Cprop

9 Caero

8 yacc

7 ypow

6 yfp

5 ydl

4 yuvw

3 ybvel

2 xdot

1 x

hlpfcn

Gravity

Fwind

FMsort

BEAVER, level 2 (main level) M.O. Rauw

-K-

3 -K- uwind

2 uprop

1 uaero

Modeling of the Aerodynamic Forces and Moments

Modeling of the Propulsive Forces and Moments

Modeling of the Gravity Forces

Modeling of the Atmospheric Turbulence Forces

AIRCRAFT

EQUATIONS

OF MOTION

Sample drawing and tables from Appendix C showing aircraft data for aerodynamic modeling

“Aircraft Dynamics:

Chapter IV^ From Modeling to Simulation”

V 

LE  LE 

 

V 

LE  LE 

 

V 



Leading edge wing line

(right wing wrt. pilot)

Perpendicular to

leading edge wing line

V 



V 

Parallel to leading

edge wing line

V 

Parallel to leading

edge wing line

Perpendicular to

leading edge wing line

LEFT WING wrt. pilot RIGHT WING wrt. pilot

V 



Leading edge wing line

(right wing wrt. pilot)

Perpendicular to

leading edge wing line

V 



V 

Parallel to leading

edge wing line

V 

Parallel to leading

edge wing line

Perpendicular to

leading edge wing line

LEFT WING wrt. pilot RIGHT WING wrt. pilot

(cont.) l

c 

Conceptual Modeling of

“Aircraft Dynamics:

Chapter IV^ From Modeling to Simulation”

 

cos

V V



 

  

  

nR nL

V V  



R L

L  L

S

Negative rolling moment

3

0 WB l c 



Wing body dihedral effect

NOTE: „R‟ indicates „RIGHT‟ wrt pilot

LR  LL

S

Negative rolling moment

3

0 WB l c 



Wing body dihedral effect

NOTE: „R‟ indicates „RIGHT‟ wrt pilot

LR  LL

0 WB l III

c 



(cont.) l

c 

Conceptual Modeling of

“Aircraft Dynamics:

Chapter IV^ From Modeling to Simulation”

c 

Conceptual Modeling of (cont.)

..Starting from:

n WB



 

V  V 

V  from right of the pilot



 

V  V 

V ^ from right of the pilot



V 

  0 V  from right of the pilot

Resultant of the

Lateral Side Force

in front of CG

Resultant of the

Lateral Side Force

behind CG

Moment Arm in front of CG

Moment Arm behind CG

Negative

Yawing Moment

Positive

Yawing Moment



V 

  0 V ^ from right of the pilot

Resultant of the

Lateral Side Force

in front of CG

Resultant of the

Lateral Side Force

behind CG

Moment Arm in front of CG

Moment Arm behind CG

Negative

Yawing Moment

Positive

Yawing Moment



V 

Moment Arm in front of CG

Moment Arm behind CG

Negative

Yawing Moment

Positive

Yawing Moment

n WB

c





V 

Moment Arm in front of CG

Moment Arm behind CG

Negative

Yawing Moment

Positive

Yawing Moment

n WB

c



n WB

c



For most aircraft

“Aircraft Dynamics:

Chapter IV^ From Modeling to Simulation”

c 

Conceptual Modeling of (cont.)

..next, on:

n V

c 



XS

ZS



VS

Moment arm X

Point of application of the lateral

force on the vertical tail



XS

ZS



VS

Moment arm X

Point of application of the lateral

force on the vertical tail

 XS

V 

Positive yawing moment

0 n V c 



  0

VS X

Lateral force

YS

 XS ZS

V 

Positive yawing moment

0 n V c 



  0

VS X

Lateral force

YS

ZS



XS

YS

 

 

V  V 

  0

Lateral force on

the vertical tail



XS

YS

 

 

V  V 

  0

Lateral force on

the vertical tail

n V



Aircraft Dynamics: Modeling, Simulation, and Aerospace Engineering, Summaries of Aerospace Engineering

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Aircraft Dynamics

Marcello R. Napolitano

A I R C R A F T

D Y N A M I C S

From Modeling to Simulation

A I R C R A F T

D Y N A M I C S

From Modeling to Simulation

A I R C R A F T

D Y N A M I C S

From Modeling to Simulation

Napolitano

www.wiley.com/college/napolitano

from different classes;

different aircraft;

videos

Sample figure from Ch. 1 showing the sequential derivation of ALL the aircraft dynamic equations

d V

CLME m mg F F

dt

d dr

CAME r dV M M

dt dt

 ^ ^ 

CLME m V V mg F F

CAME r r r dV M M

Aircraft trajectory w/r X‟Y‟Z‟

sin

cos sin

cos cos

m Q W R V mg F F

m U R P W mg F F

m PV Q U mg F F

PQ I R Q I I L L

PR I I P R I M M

PQ I I Q R I N N

k

sin , cos 1

up wr pq p

x x x

cos

sin sin cos cos

cos sin sin cos

m u Q w qW R v rV mg f f

m v U r uR Pw pW mg mg f f

m w Pv pV Q u U q mg mg f f

p I r I Pq Q p I R q Q r I I l l

qI P

XX ZZ^2 2 XZ A T

r pR I I P p R r I m m

r I p I Pq pQ I I Q r R q I n n

 U V W , , 

 P Q R , , 

 gX^ ,^ gY^ , gZ     ,^ , 

   ,^ , 

Sample figure from Ch. 3 showing the summary of the PITCHING modeling

1 tan

AR

c

AR Mach

k Mach

  ^    

 ^  

4.44 AR mr cos 0.25 1

d

K K K Mach

d

  ^ ^ 

S d

c c x x c x x

S d

c  c  c

tan 3

6cos

tan

6cos