FF3 Analysis Data Item Vol. 3

ȏ Ȑ

ʹͲͲ͵ǦʹͲͲͷǡ

Sina Golshany 4/21/2005

These are computations I performed between 2003 and 2005 to evaluate an aircraft configuration I had put together when I was a sophomore in high school. My command of the English language wasn’t particularly great at the time I was putting this document together, so the dear reader will excuse occasional grammatical, composition errors and typos as well as technical errors here and there.

F-F.3 Project data unit, Volume III: Designer: Sina Golshany -Longitudinal stability derivatives -Longitudinal control derivatives -Sensivity of longitude derivatives -Lateral-directional stability derivatives -Lateral-directional control derivatives -Sensivity of lateral-directional derivatives -Stability analyses -Longitudinal flight dynamic calculations

Longitude Stability derivatives Based on Dr. J-Roskam Method

395

Longitude Stability Derivatives: -Speed related derivatives: - CD : U

CD  M1 U

CD CM

CD  tan M  C Diagram  D CM

Result of calculations for condition 1-1:

M 1  0.780 CD  0.2091 U

Result of calculations for condition 1-2:

M  0.229 CD  0.0614 U

396

- CL : U

CL  U

CL  1

M 12Cos 2  C

4W

1 M 12Cos 2  C

CL

1

4W

nW q SW

1 q  U12 2

Result of calculations for condition1-1 (  0 , n  1g ) ,Cruising:

M 1  0.780 q1  212.92 lb

ft 2

CL  0.3315 1

CL  0.1844 U

calculations for condition1-1,maneuvering: Entered parameters:

  0 n  9g 397

Results of calculations for condition 1-1, maneuvering:

C L  1.6599 U

CL  2.9838 1

Calculations for condition 1-1, light maneuvering: Entered parameter:

n  5g Results of calculation for condition 1-1, light maneuvering:

CL  0.9222 U

CL  1.6576 1

*Because of supersonic velocity of Plane in condition 1-2, there is no data available.

Result of calculations for condition 2-1:

M 1  0.308 q1  116.69 lb

ft 2

CL  0.7717 1

CL  0.0454 U

398

Result of calculations for condition 2-2:

M 1  0.228 q1  71.82 lb

ft 2

CL  1.2539 1

CL  0.0396 U

- Cm : u

Method:

X AC M1 1 M

Cm  CL u

CL  1

nW q SW

1 q  U12 2 Calculations for condition 1-1: Entered parameters:

  0 n  1g

399

X apex  27 ft W

ZW  0.1 ft S h  57.2457 ft 2 ARh  1.02

h  0.3144 C

 40 4h

X apex  46.51 ft h

Z h  0.15 ft

h  1 CL

h

Df

 4.14Rad 1  5.31 ft

Max

X AC f :

X AC

f

M  : q SW CW CL

W

400

M q CLW   36.5 0.08

n 2  W fi i 1

 X i  i

1 q  U12 2  X i   h   1  i    Xh   calculations for condition 1-1:

hMGC  6.770 ft W

CW  11.06 ft C f  13.195 ft Condition11:      X   AC f  0.0219 Condition21:      X  0 .

0218561   AC   f

401

  Condition2  2 :        X    0 .

0218562 AC f  

X AC  0 s

X AC

Nacelle

0

Result of calculations for condition 1-1:

CL

Cond .11

 0.3315

M 1  0.780 nMGC  6.770 W

X AC  0.0463 M X AC  36.77 ft w

X AC  0.2714 w

X AC

wf

 36.53 ft

X AC  50.16 ft h

X AC  1.4826 h

402

X AC  0.2637 q1  212.92 lb

ft 2

CW  11.06 ft Cm  0.0120 u

Result of calculations for condition1-1, n 7 g :

CL  2.3207 1

M 1  0.780 nMGC  6.770 ft W

X AC  0.0463 M X AC  36.77 ft W

X AC  0.2714 W

X AC

wf

 36.53 ft

X AC  50.16 ft h

X AC  1.4826 h

403

X AC  0.2637 q1  212.92 lb

ft 2

CW  11.06 ft Cm  0.0839 u

Result of calculations for condition 2-1:

CL  0.7717 1

M 1  0.308 nMGC  6.770 ft W

X AC  0.0013 M X AC  36.62 ft W

X AC  0.2573 W

X AC

 36.37 ft

X AC

 0.2355

Wf

Wf

X AC  50.34 ft h

404

X AC  1.4987 h

q1  116.69 lb

ft 2

CW  11.06 ft Cm  0.0003 u

Result of calculations for condition 2-2:

CL  1.2918 1

M 1  0.229 nMGC  6.770 ft W

X AC  0.0016 M X AC  36.61 ft W

X AC  36.61 ft W

X AC

 36.37 ft

X AC

 0.2350

Wf

Wf

X AC  50.53 ft h

405

X AC  1.4997 h

X AC  0.2584 q1  69.71lb

ft 2

CW  11.06 ft Cm  0.0005 u

-Angle of attack related derivatives: - CD : 

CD  

CL  1

2CL1 CL

 .AR.e

n.W q SW

1 q  U12 2 e  f ARW ,W 

406

Result of calculations for condition 1-1:

n  1g CL  0.3315 1

e  0.8608 CD  0.2868Rad 1 

M 1  0.780 q1  212.92 lb

ft 2

CL

 3.5237 Rad 1

CL

 3.5142Rad 1

W

Wf

 h  0.8377  CL

h

 1.4977 Rad 1

CL  3.5552Rad 1 

407

Result of calculations for condition 1-1, Maneuvering:

n  7g CL  2.3207 1

e  0.8607 CD  2.0073Rad 1 

M 1  0.780 q1  212.92 lb

ft 2

CL

 3.5237 Rad 1

CL

 3.5142Rad 1

W

Wf

 h  0.8377  CL

h

 1.4977 Rad 1

CL  3.5552Rad 1 

408

Result of calculations for condition 2-2:

CL  1.2918 1

e  0.8608 CD  0.6060 

M 1  0.308 q1  116.69 lb

ft 2

CL

 3.1785Rad 1

CL

 3.1699Rad 1

W

Wf

 h  0.7556  CL

h

 1.4132Rad 1

CL  3.2280Rad 1 

409

Result of calculations for condition 2-2:

CL  1.2918 1

e  0.8608 CD  1.0075Rad 1 

M 1  0.229 q1  69.71lb

ft 2

CL

 3.1551Rad 1

CL

 3.1466Rad 1

W

Wf

 h  0.7500  CL

h

 1.4070Rad 1

CL  3.2058Rad 1 

410

- Cm : 

CM C CL L

Cm  

CM  Static margine(S.M, X CG  X AC ) A CL Result of calculations for condition1-1:

X CG 33.7 ft  M 1  0.780 q1  212.92 lb

ft 2

X CG  0.0841 CW  11.06 ft nMGC  6.770 ft W

CL

 3.5237 Rad 1

CL

 3.5142Rad 1

W

Wf

X AC  36.77 ft W

411

X AC  36.77 ft W

X AC

 36.53 ft

X AC

 0.2495

Wf

Wf

X AC  50.16 ft h

X AC  1.4826 h

CL

h

 1.4977 Rad 1

 h  0.8377  X AC  0.2637 S.M  17.96% CL  3.5552Rad 1 

Cm  0.6386Rad 1 

Result of calculations for condition 2-1:

412

M 1  0.308 q1  116.69 lb

ft 2

X CG  0.0841 CW  11.06 ft nMGC  6.770 ft W

CL

 3.1785Rad 1

CL

 3.1699Rad 1

W

Wf

X AC  36.62 ft W

X AC  0.2573 W

X AC

 36.37 ft

X AC

 0.2355

Wf

Wf

X AC  50.34 ft h

X AC  1.4987 h

413

 1.4132Rad 1

CL

h

 h  0.7556  X AC  0.2582 S.M  17.41% CL  3.2280Rad 1 

Cm  0.5621Rad 1 

Result of calculations for condition 2-2:

M 1  0.229 q1  69.71lb

ft 2

X CG  0.2776 CW  11.06 ft nMGC  6.770 ft W

CL

W

 3.1551Rad 1

414

 3.1466Rad 1

CL

Wf

X AC  36.61 ft W

X AC  0.2569 W

X AC

 36.37 ft

X AC

 0.2350

Wf

Wf

X AC  50.35 ft h

X AC  1.4997 h

CL

h

 1.4070Rad 1

 h  0.7500  X AC  0.2584 S.M  53.60% CL  3.2058Rad 1 

Cm  1.7183Rad 1 

415

Rate of A.O.A Related derivatives:

- CD : 

CD  0.0000 

For small angels of attack he value of CD is consider 

to be zero .

- CL : 

CL  2CL  hVh 

Vh

h

 X 

 h  2CL C C 



 X CG S h .

CW SW

AC h

Result of calculations for condition 2-1:

M 1  0.780 X CG  0.0063 CW  11.06 ft X AC  50.16 ft h

416

X AC  1.4826 h

CL

h

 1.4977 Rad 1

 h  0.8377  Vh  0.2507 CL

 h

 0.6290Rad 1

CL  0.6290Rad 1 

Result of calculations for condition 2-1:

M 1  0.308 X CG  0.2776 CW  11.06 ft X AC  50.34 ft h

X AC  1.4987 h

CL

h

 1.4132Rad 1

417

 h  0.7556  Vh  0.2991  0.6316Rad 1

CL

 h

CL  0.6316Rad 1 

- Cm : 

Cm  2CL  hVh 

Vh 

X

h



 X CG  h  CW

AC h

X AC  X CG . Sh CW

SW

Result of calculations for condition 1-1:

M 1  0.780 X CG  0.0063 CW  11.06 ft X AC  50.16 ft h

418

X AC  1.4826 h

CL

h

 1.4977 Rad 1

 h  0.8377  Vh  0.2507 Cm

 h

 0.9366Rad 1

Cm  0.9366Rad 1 

Result of Calculations for condition 2-1:

M 1  0.308 X CG  0.2776 CW  11.06 ft X AC  50.34 ft h

CL

h

 1.4132Rad 1

 h  0.7556 

419

Vh  0.2991 Cm

 h

 1.1346Rad 1

Cm  1.1346Rad 1 

Result of calculations for condition 2-2:

M 1  0.228 X CG  0.2776 CW  11.06 X AC  50.35 ft h

X AC  1.4997 h

CL

h

 1.4069Rad 1

 h  0.7500  Vh  0.2993 Cm

 h

 1.1225Rad 1

420

Cm  1.1225Rad 1 

Pitch-rate related derivatives: - CD : q

CD  0.0000Rad 1 q

For smal angele of attack CD isconsidertobezero. q

- CL : q

CL  CL q

qW

CL

qW



 CL

qh

ARW  2Cos C

4W

ARW B  2Cos C

  B  1 M Cos  C   4W 

 C  Lq   W | M  0

4W

2

2

   CL  q W 

   CL  W   M 0

 1 2 XW     2 C 

CLq  2CL  hVh h

h

421

X

Vh 



 X CG S h CW SW

AC h

Result of calculations for condition 1-1:

M 1  0.780 X CG  0.0063 CL

W

 3.5237 Rad 1

CW  11.06 ft X AC  50.16 ft h

X AC  1.4826 h

CL

h

 1.4977 Rad 1

Vh  0.2507 CL

 0.7509

CL

 4.1106Rad 1

qh

qW

CL  4.8616Rad 1 q

422

Result for condition 2-1:

M 1  0.308 X CG  0.2776 CL

W

 3.1785Rad 1

CW  11.06 ft X AC  50.34 ft h

X AC  1.4987 Rad 1 h

CL

h

 1.4132Rad 1

Vh  0.2991 CL

qW

 5.0377 Rad 1

CL  5.8830Rad 1 q

Result of calculations for condition 2-2:

M 1  0.308 X CG  0.2776

423

CL

W

 3.1785Rad 1

CW  11.06 ft X AC  50.34 ft h

X AC  1.4987 h

CL

h

 1.4132Rad 1

Vh  0.2991 CL CL

qh

qW

 0.8453Rad 1  5.0377 Rad 1

CL  5.8830Rad 1 q

-

Cm

q

424

Cm

  Cm  qW

qW

 ARW tan 2  C  3 4W     ARW B  6Cos C B  4    3 2   M  0  ARW tan  C   4W  3  AR  6Cos  W C  4W 

    X  2 1 X  W   ARW 2 W      2 C C   W    W     KW CL Cos C  X  W |M 0 2 AR Cos   4W   W C 4W    

C  mq

X

ARW 2 tan 2  C

4W

 24 ARW  6Cos C 4W 

KW  f ARW  Cm

qh

Vh 

Source : Airplane design VI Fig 10.40

 2CL  hVh

X

h

X

AC h

 X CG

C

1  8   

AC h

 X CG

CW

 S

h

SW

425



Result of calculations for condition 1-1:

M 1  0.780 X CG  0.2776 CW  11.06 ft X AC  50.16 ft h

X AC  1.4826 h

CL

h

 1.4977 Rad 1

Vh  0.2964 Cm Cm

qh

qw

 1.5626Rad 1  3.2065Rad 1

Cm  4.7691Rad 1 q

Result of calculations for condition 2-1:

M 1  0.308 X CG  0.0063 426

C  11.06 ft X AC  50.34 ft h

X AC  1.4987 h

CL

h

 1.4132Rad 1

Vh  0.2534 Cm Cm

qh

qw

 1.0779Rad 1  1.4540Rad 1

Cm  2.5319Rad 1 q

Result of calculations for condition 2-2:

M 1  0.229 X CG  0.2776 CW  11.06 ft X AC  50.35 ft h

X AC  1.4967 Rad 1 h

427

CL

h

 1.4070Rad 1

Vh  0.2992 Cm Cm

qh

qw

 1.4967 Rad 1  2.7656Rad 1

Cm  4.2623Rad 1 q

428

Long-Control derivatives: Based on Dr. J. Roskam method

429

Stabilizer control derivatives: - CD

e

:

CD : e

  CD

CD

e

e

  Kb e

ih

Cl

C 

l

l Theory



K b  f i ,O ,h e

Cl

C 



l Theory

e

C  



Theory

Source : Airplane designVI Fig 8.51

  Cl C  f e, C   Cl   Theory 

   Source : Airplane designVI Fig 8.15   

C  t   t    f  e ,  ,   Theory  C  c h  c h  r t  

  Cl

C  K   f  e , e Source : Airplane designVI Fig 8.13 C 

 C L  Cl

C    f  ARh , e  C 

430







Result of calculations for condition1-1,  0 :

M 1  0.780 CL

h

 4.1011Rad 1

CL  0.6887 Rad 1 ih

  0.2252 e

CD  0.1299Rad 1 ih

CD

e

 0.0292Rad 1

Result of calculations for condition2-1:

M 1  0.308 CL

h

 3.6110Rad 1

CL  0.6064Rad 1 ih

  0.3427 e

CD  0.1299Rad 1 ih

431

CD

e

 0.0392Rad 1

Result of calculations for condition2-2:

M 1  0.228 CL

h

 3.5788Rad 1

CL  0.6010Rad 1 ih

  0.3507 e

CD  0.1133Rad 1 ih

CD

e

 0.0397 Rad 1

- CL

:

CL

  CL

e

e

e

ih

 

  K b Cl e 





e

l

Theory

K b  f i ,o ,W e

K   CL .

Theory C  C l

C 

Cl



h

l

Source:Airplane designVI Fig 8.51

432

Cl

C 



l Theory

C  Cl e   Source : Airplane designVI Fig 8.15 , f  C Cl   Theory  

 

 Ce  t   t   Cl  f  ,  ,   Source : Airplane designVI Fig 8.14 Theory  C  c h  c h  r t  

 

C  K   f  e , e  Source : Airplane designVI Fig 8.13 C 

 C L  C   f  ARh , e  Source : Airplane designVI Fig 8.51 C  Cl 







Result of calculations for condition 1-1,  0 :

M 1  0.780 CL

h

 4.1011Rad 1

CL  0.6887 Rad 1 ih

  0.2252 e

CL

e

 0.1551Rad 1

433

Result of calculations for condition 2-1:

M 1  0 . 308 CL CL

h

 3 . 6110 Rad  0 . 6 Rad

ih

1

1

   0 . 2252 e

CL

e

 0 . 1551 Rad

1

Result of calculations for condition 2-1:

M 1  0.308 CL

h

 4.1011Rad 1

CL  0.6887 Rad 1 ih

  0.2252 e

CL

e

 0.1551Rad 1

434

Result of calculations for condition 2-2:

M 1  0.228  3.5788Rad 1

CL

h

CL  0.6010Rad 1 ih

  0.3507 e

 0.2107 Rad 1

CL

e

- Cm

:

Cm

   Cm

e

e

e

  K b e

ih

C 

l Theory



K b  f i ,o ,h e

Cl

C 



l Theory

e

K   C L Cl .  Theory Cl  C

 

Cl



h

l

Source : Airplane designVI Fig 8.51

C  Cl e   Source : Airplane designVI Fig 8.15 , f  C Cl   Theory  

 

C  K   f  e , e  Source : Airplane designVI Fig 8.13 C 

435

 C L  Cl

C    f  ARh , e  Source : Airplane designVI Fig 8.53 C 

Result of calculations for condition 1-1:

M 1  0.780 X CG  0.8985 Vh  0.3169 CL

h

 4.1011Rad 1

Cm  1.2996Rad 1 ih

  0.2252 e

Cm

e

 0.2926Rad 1

436

Result of calculations for condition 2-1:

M 1  0.308 X CG  0.8985 Vh  0.3158 CL

h

 3.6110Rad 1

Cm  1.1404Rad 1 ih

  0.3427 e

Cm

e

 0.3908Rad 1

437

Result of calculations for condition 2-2:

M 1  0.228 X CG  0.8985 Vh  0.3158 CL

h

 3.5788Rad 1

Cm  1.1300Rad 1 ih

  0.3507 e

Cm

e

 0.3963Rad 1

438

Sensivity of the longitudinal derivatives:

439

2.5000



D rad -1 C 2.0000

1.5000

1.0000

0.5000

440 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

D

6.00

5.00

4.00

3.00

2.00

1.00

0.0000 0.00

C Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

3.6000

3.5000

 L rad -1

C 3.4000

3.3000

441 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00



5.00

4.00

3.00

2.00

1.00

3.2000 0.00

CL Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

6.0000

u L

C 5.7500

5.5000

5.2500

5.0000

4.7500

442 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

4.5000 0.00

CL U

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

-2.0000

 m rad -1

C -1.7500 -1.5000

-1.2500

-1.0000

-0.7500

443 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00



6.00

5.00

4.00

3.00

2.00

1.00

-0.5000 0.00

CM Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

-5.0000

q

m rad -1 C -4.5000

-4.0000

-3.5000

-3.0000

444 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

-2.5000 0.00

CM q

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

0.0500

u D

C

0.1000

0.1500

0.2000

445 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.2500 0.00

CD U

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

0.7000

0.6900



L rad -1 C 0.6800

0.6700

0.6600

0.6500

0.6400

0.6300

0.6200

446 n

1/T,  , 

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.6000 0.00



1/s, rad/s, -

0.6100

CL Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

6.0000

q L rad -1

C 5.7500

5.5000

5.2500

5.0000

4.7500

447 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

4.5000 0.00

CL q

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

-1.2500

-1.1250

 m rad -1

C -1.0000

-0.8750

448 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

-0.7500 0.00

CM q

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

0.0100

-0.0000

u m

C -0.0100

-0.0200

-0.0300

-0.0400

-0.0500

-0.0600

-0.0700

449 1/T,  , 

n

1/s, rad/s, -

-0.0800

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

-0.0900 0.00

CM U

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

Lateral-Directional stability derivatives Based on Dr. J-Roskam method

450

Side slip: - CY : 

CY  CY  CY 



f

 CY

V

CY

 0.00573 

CY

 2K J

w

f

S0 SW

K J  f Z w ,d f  CY

V

Source : Airplane design VI Fig 10.8

  KV CL

V



   SV 1 V     SW

 f ARV ,TE

CY

V

eff



Source : Airplane design VI Fig.10.18

eff

* TE is trailing edge surface angle of air foil.

CY

V wfh 

CY

 f bv ,2r1,bh ,l f 

V

eff 

2r1  hight of fuselage at the quarter chord point of the vertical tail.

451

calculations for condition 1-1: Entered parameters:

X  0.4074 Cr Z f  8.19 ft 2r1  5.33 ft S0  22.30 ft 2 CL

V | M  0

 2.2370Rad 1

Z f  8.19 ft Z h  0.1 X Apex  0 f

Result of calculations for condition 2-1:

M 1  0.308 ARV

eff

CL

V

 1.32  1.1844Rad 1

452

CY CY CY

 0Rad 1

W

f

V

 0.1308Rad 1  0.1552Rad 1

CY  0.2860Rad 1 

Result of calculations for condition 2-2:

M 1  0.229 ARV

eff

 1.32

CL

 1.1747 Rad 1

CY

 0Rad 1

V

CY CY

W

f

V

 0.1308Rad 1  0.1539Rad 1

CY  0.2847 Rad 1 

453

- Cl : 

454

Cl  Cl 

Cl

 Wf

 Wf

h

 Cl

C

 Cl

V

 57 .3X  Y  Z 

X  CL

Wf

 Cl   CL 

 Cl

  C l     C L 

   C

 Cl K M K f    CL  4W

   f   C , AR W , W  Source  2   C

      A 

: Airplane design VI Fig 10.20

4

KM



 f   C , AR W , W  Source 2  

: Airplane design VI Fig10.21

K f  f  AR W ,  C ,l f ,bW  Source 2W    Cl   CL 

   f AR W , W  Source  C

: Airplane designVI Fig 10.22

: Airplane designVI Fig 10.23

2

Cl  C l   Y KM  T     Cl

   C l  



  f  AR W , W ,  C  2W    



zw

Source : Airplane designVI Fig 10.24

455

M M  f  M , ARW , C Source : Airplane designVI Fig 10.25  2W   Cl

d   0.0005 ARW  f  bW  

C  l

 0.042

ZW

Zw d f bW bW

   

2

ARW

 Cl   Z   t tan  C  4W   t tan  C 4W  Cl 

 t tan  C Cl

h

    

 f ARW ,W  Source : Airplane designVI Fig 10.26 4W

 57.3X Y  Z 

X  CL

hf

  Cl    CL 

  Cl   K M k f     CL C  2

Cl  Cl    Y  KM  T    

   C l  



456



Zh

      A 

 Cl   Z   t tan  C  4 h   t tan  C 4W  Cl

 CY

V

V

    

Z vCos lv Sin bW

  Result of calculations for condition 1-1,  0  : 

M1  0.780 X AC  5.65 ft V

Z AC  4.44 ft V

ARV

eff

 1.32

CL

 1.3304Rad 1

CY

 0.1743Rad 1

V

Cl Cl

V

Wf

h

 0.0061Rad 1  0.0061Rad 1

457



Cl

 0.0047 Rad 1

V

Cl  1.6634Rad 1 

Result of calculations for condition 2-1: M 1  0.308 X AC  5.38 ft V

Z AC  4.44 ft V

ARV

eff

 1.32

CL

 1.1844Rad 1

CY

 0.1552Rad 1

Cl

 1.6396Rad 1

V

Y

Cl Cl

Wf

h

V

 0.0060Rad 1  0.0042Rad 1

Cl  1.6387 Rad 1 

458

Result of calculations for condition 2-2:

M1  0.229 X AC  5.38 ft V

Z AC  4.44 ft V

ARV

eff

 1.32

CL

 1.1747 Rad 1

CY

 0.1552Rad 1

Cl

 1.6369Rad 1

V Y

Cl Cl

Wf

h

 0.0060Rad 1  0.0042Rad 1

V

Cl  1.6387 Rad 1 

Result of calculation for condition2-2:

M 1  0.229 X AC  5.38 ft V

459

Z AC  4 .44 ft V

ARV

eff

 1 .32

CL

 1 .1747 Rad 1

CY

  0 .1539 Rad 1

V

Cl Cl Cl

V

  1 .6369 Rad 1

Wf

h

V

  0 .0060 Rad 1  0 .0042 Rad 1

Cl   1 .6387 Rad 1 

Result of calculations for condition1-1 (  30 ) : M 1  0.229 X AC  5.38 ft V

Z AC  4.44 ft V

ARV

eff

 1.32

460

CL

 1.1747 Rad 1

CY

 0.1539Rad 1

Cl

 1.6369Rad 1

V

V

Cl Cl

 wf

h

V

 0.00060Rad 1  0.0854Rad 1

Cl  1.7283Rad 1 

- Cn : 

Cn  Cn 

Cn

W

W

 Cn

f

 Cn

V

0

* For small angele of attack value of Cn

W

is consider to be

zero.



K N  f X CG ,l f , S Bs ,h1,h2 ,hMax ,W f K R  f RNf  1

461



Source : Airplane design VI Fig 10.28

RN  f

Cn

U1l f



 CY

V

V

lV Cos  ZV Sin bV

Result of calculations for condition 1-1, ( 0 ) : M 1  0.780 Re f  83.4725106 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

V

V

Cn

V

 0.0747 Rad 1

462

Cn  0.4833Rad 1 

Result of calculations for condition 1-1, ( 35 ) : Cn

 0.0692Rad 1

V

Cn  0.4888Rad 1 

Result of calculations for condition 2-1: M 1  0.308 Re f  84 106 X AC  48.22 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.1336Rad 1

CY

 0.1485Rda 1

V

V

Cn

f

 0.5156Rad 1

463

Cn

 0.0724Rad 1

V

Cn  0.4422Rad 1 

Result of calculations for condition 2-2:

M 1  0.229 Re f  66.7836 106

X AC  48.21 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.1255Rad 1

CY

 0.1474Rad 1

V

V

Cn Cn

f

V

 0.5024Rad 1  0.0729Rad 1

464

Cn  0.4295Rad 1 

-Rate of sideslip related derivatives: - CY : 

CY  2CL

V



 SV lV Cos  ZV Sin  SW bW

          t    et  Wf   57.3

   f ARW , M ,W , LEW ,bW , ZV  Source : Airplain design VI Fig10.30 

   f ARW , M ,W , LEW ,bW , ZV  Source : Airplain design VI Fig10.31 

   f ARW , M ,W , LEW ,bW , ZV  Source : Airplain design VI Fig10.32 t



Wf



 f ARW , M ,W , LEW ,bW , ZV



Source: Airplain design VI Fig10.33





Result of calculations for condition 1-1  0 : M 1  0.780 X AC  48.37 ft V

465

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.2514Rad 1

   0.0572 deg 1 

   1.1308deg 1 

   1.1308deg 1 



Wf

 0.1874

  0.1874  CY  0.0283Rad 1 





Result of calculations for condition 1-1  8 : M 1  0.780 X AC  48.37 ft V

466

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.2514Rad 1

   0.1272 deg 1 

   1.7010 deg 

   0.1012 deg 1 



Wf

 0.3208

  0.6965Rad 1  CY  0.1067 Rad 1 

Result of calculations for condition 2-1:

M 1  0.308 X AC  48.22 ft V

Z AC  7.74 ft V

467

ARV

eff

 1.43  1.1336Rad 1

CL

V

   0.0490 deg 1 

   1.0779 deg 1 

   0.0437 deg 1 



Wf

 0.1853

  0.1853  CY  0.0251Rad 1 

Result of calculations for condition 2-2:

M 1  0.229 X AC  48.21 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

468

CL

V

 1.1255Rad 1

   0.0477 deg 1 

   1.0691deg 1 

   0.0427 deg 1 

 Wf 0.1850  0.1850  CY  0.0248Rad 1 

- Cl : 

Cl  CY 



ZV Cos lV Sin bW

469

  Result of calculations for condition 1-1,  0  : 

M 1  0.780 X AC  48.37 ft V

Z AC  7.78 ft V

ARV

eff

CL

V

 1.43  1.2514Rad 1

   0.0495deg 1 



Wf

 0.1874

  0.1874 

CY  0.0283Rad 1 

Cl  0.0017 Rad 1 

470







Result of calculations for condition 1-1  8 :

M 1  0.780 X AC  48.37 ft V

Z AC  7.78 ft V

ARV

eff

CL

V

 1.43  1.2514Rad 1

   0.0495deg 1 



Wf

 0.1874

  01874 

CY  0.0283Rad 1 

Cl  0.0017 Rad 1 

471





Result of calculations for condition 1-1,  8 :

M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.2514Rad 1

   0.1272 deg 1 

   1.7010 deg 1 

   0.1012 deg 1 



Wf

 0.3208

  0.6965  CY  0.1067 Rad 1 

Cl  0.0009Rad 1 

472

Result of calculations for condition 2-1: M 1  0.308 X AC  48.22 ft V

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.1336Rad 1

   0.0490 deg 1 

   1.0779 deg 1 

   0.0437 Rad 1 



Wf

 0.1853

  0.1853  CY  0.0251Rad 1 

Cl  0.0015 

473

Result of calculations for condition 2-2: M 1  0.228 X AC  48.21 ft V

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.1254Rad 1

   0.0477 deg 1 

   1.0690 deg 1 

   0.0427 deg 1 



Wf

 0.1850

  0.1850  CY  0.0248Rad 1 

Cl  0.0015Rad 1 

474

- Cn : 

Cn  CY 



lV Cos  ZV Sin bW

Result of calculations for condition 1-1:

M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.2514Rad 1

   0.0572 deg 1 

   1.1308 deg 1 

   0.0495 deg 1 



Wf

 0.1874

  0.1874 

475

CY  0.0283Rad 1 

Cn  0.0102Rad 1 





Result of calculations for condition1-1,  8 : M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.2514Rad 1

   0.1272 deg 1 

   1.7010 deg 1 

   0.1012 deg 1 

   0.1012 deg 1 

   0.1012 deg 1 



Wf

 0.3208

476

  0.6965Rad 1  CY  0.1067 Rad 1 

Cn  0.0389Rad 1 

Result of calculations for condition 2-1: M 1  0.228 X AC  48.21 ft V

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.1336Rad 1

   0.0490 deg 1 

   1.0776 deg 1 

   0.0437 deg 1 



Wf

 0.1853

477

  0.1853  CY  0.0251Rad 1 

Cn  0.0089Rad 1 

Result of calculations for condition 2-2: M 1  0.228 X Ac  48.21 ft V

Z AC  7.74 ft V

ARV

eff

CL

V

 1.43  1.1254Rad 1

   0.0477 deg 1 

   1.0690 deg 1 

   0.0427 deg 1 



Wf

 0.1850

478

  0.1850 

CY  0.0248Rad 1 

Cn  0.0088Rad 1 

-Roll rate related derivatives: - CY : P

CY  2CY P

V

ZV Cos lV Sin  ZV  3SinW 1 4ZSinW  Cl P bW

 | 0

 Cl P K    0    K CL 0

ClP 

 Cl P   K 

    |C L  0

   

f  ARW ,  , K , C ,W  4W  





Result of calculations for condition 1-1,  0 :

M 1  0.780

479

|C L  0

X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

V

V

CY  0.0000 P





Result of calculations for condition 1-1,  8 : M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

V

V

CY  0.0253Rad 1 P

480

Result of calculations for condition 2-2: M 1  0.228 X AC  48.22 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.1254Rad 1

CY

 0.1474Rad 1

V

V

CY  0.0000 P

- Cl : P

Cl  Cl P

Cl

PW

PW

 Cl

  Cl P    K  

PV

  C 

C   L  Cl P  W C L

 K  .  C L  0   CL   W  C L  0

481

lP

     Cl P    0  



drag

 Cl P    K  C 

L 0

 f  ARW ,  , C ,W  4W  

C  C   l   l  K   X M   X M 0 2 2



C  C 

lP 

lP  0

2

Z  4Z  1 W Sin 12 W  Sin 2 bW  bW 

ClP drag 

C 

lP C DL CL 2 W

Cl

C 

LP C DL CLW 2

CL

2

W

 0.125CD0

W

 f  ARW , C  4W  

 

S h  bh    hS W  bW 

Ph

1  Cl 2 P

PV

Z   2 V  CY  bW  V

2

2

Cl

482

Result of Calculations for condition1-1: M 1  0.780 Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

V

Cl Cl Cl

V

PW

Ph

PV

 0.5356Rad 1  Undefined,exceed limit of 1.5     0.0024Rad 1

Cl  0.5380Rad 1 P

Result of calculations for condition 2-1: M 1  0.308 Z AC  7.74 ft V

483

AR  10 K

M 1  0.308 Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.1336Rad 1

CY

 0.1485Rad 1

V

Cl

V

 0.0021Rad 1

PV

Cl  0.5626Rad 1 P

Result of calculations for condition 2-2: M 1  0.228 Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.1254Rad 1

CY

 0.1474Rad 1

V

V

484

Cl

PW

 0.5623Rad 1

Cl  Undefined P

Cl

PV

 0.0021Rad 1

Cl  0.5644Rad 1 P

- Cn : P

Cn

PW

 Cn P  CL   CL 

  Cn P    C  0 t   t  L 

 Cn P       f  f f  f

|M

 Cn P   CL 

ARW  4Cos C   Cn P  4W   X  C L  0 ARW B  4Cos C  C L C L  0    4W M 0

M

 1  2 AR B   ARW B Cos C  tan  C  W 2 4W  4W X   2  AR  1  AR Cos  tan  C W W C  2 4 4W W    2

B  1 M  Cos C 4W 

  

2

485

     

 AR 6   ARW Cos C W  Cn P  4W      C L C  0 ARW  4Cos C   L 4W

   X   1   b

M 0

2     tan  C  tan  C    X 4W   4W X    CW ARW  12    

Cn



t Cn

 f ARW ,W 

P

 f  f   f

Cn

PV



 f ARW ,W ,i ,O ,bW f

f



Cl Cl  f 



2 bW



l Cos  ZV Sin 2 V

ZV Cos lV Sin  ZV CY

486

V





Result of calculations for condition 1-1,  0 : M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

V

V

Cn

PV

 0.0000

Cn  0.1026Rad 1 P





Result of calculations for condition 1-1,  35 : M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

487

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

Cn

 0.1026Rad 1

V

V

Cn

PW

 0.0540Rad 1

PV

Cn  0.15666Rad 1 P

Result of calculations for condition 2-1: M 1  0.308 X AC  48.22 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.1336Rad 1

CY

 0.1485Rad 1

V

V

488

Cn Cn

 0.1122Rad 1

PW

PV

 0.0000Rad 1

Cn  0.1122Rad 1 P

Result of calculations for condition 2-2: M 1  0.228 X AC  48.21 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.1254Rad 1

CY

 0.1474Rad 1

Cn

 0.1129Rad 1

V

V

Cn

PW

PV

 0.0000Rad 1

Cn  0.1129Rad 1 P

489

-Yaw rate related derivatives: - CY : r

CY  2CY

V

r

lV Cos  ZV Sin bW

  Result of calculations for condition 1-1,  0  : 

M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

V

V

C

Yr

 0.1499Rad 1

490







Result of calculations for condition 1-1,  35 : M 1  0.780 X AC  48.37 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

CL

 1.2514Rad 1

CY

 0.1640Rad 1

V

V

CY  0.1634Rad 1 r

Result of calculations for condition 2-1:

M 1  0.308 X AC  48.21 ft V

Z AC  7.74 ft V

ARV

eff

 1.43

491

CL

 1.1254Rad 1

CY

 0.1474Rad 1

V

V

CY  0.1604Rad 1 r

- Cl : r

Cl  Cl r

Cl

rW

rW

 Cl

rV

 Clr  CL  WC  L

 Cl Cl Clr r  r        f t f C  0  t  f  f  L |M

1  Clr   CL 

   C L  0  M

X

1



ARW 1 B 2



X   2B ARW  2Cos C  4W   ARW  2Cos C tan 2  C ARW  4Cos C

ARW B  2Cos C ARW B  4Cos C

4W

4W

8 4W

tan 2  C 8

4W

  B  1 M 2  Cos C  4W   492

4W

4W

 Clr   CL 

  C L  0  M 0

 Cl P   CL 

   C  0  L M 0

Clr

 0.083



Cl

t

f  ARW ,W , C  4W  

ARW Sin C

ARW  4Cos C

 Cl r   f  f   f  f 

  f

 Cl  r      Out   f f

    In

Cl Cl  f



rV

4W

 f ARW ,W 

r

Clr

Cl

4W

2 bW



l Cos  ZV Sin 2 V

ZV Cos lV Sin CY

V





Result of calculations for condition 1-1,  0 , f 35 : M 1  0.780 X AC  48.46 ft V

Z AC  10.44 ft V

493

ARV

eff

 1.44

CL

 0.8434Rad 1

CY

 0.1110Rad 1

V

Cl Cl

V

 2.2818Rad 1

rW

 0.0153Rad 1

rV

Cl  2.2971Rad 1 r





Result of calculations for condition1-1,  11 : M 1  0.780 X AC  48.46 ft V

Z AC  10.44 ft V

ARV

eff

CL

V

 1.44  0.8434Rad 1

494

CY   0.110Rad 1 V

Cl

 2.2818Rad 1

rw

Cl  0.0062Rad 1 rv

Cl  2.2880Rad 1 r

Result of calculations for condition 2-1: M 1  0.780 X AC  48.46 ft V

Z AC  10.44 ft V

ARV

eff

 1.44

CL

 0.8437 Rad 1

CY

 0.1110Rad 1

Cl

 2.2944Rad 1

V

V

Cl

rW

rV

 0.0184Rad 1

495

Cl  2.3128Rad 1 r

Result of calculations for condition2-1: M 1  0.308 X AC  48.31 ft V

Z AC  10.44 ft V

ARV

eff

 1.44

CL

 0.7445Rad 1

CY

 0.0980Rad 1

Cl

 2.0169Rad 1

V

V

Cl

rW

rV

 0.0161Rad 1

Cl  2.0330Rad 1 r

Result of calculations for condition 2-2: M 1  0.228

496

X AC  48.30 ft V

Z AC  10.44 ft V

ARV

eff

 1.44

CL

 0.7379Rad 1

CY

 0.0971Rad 1

Cl

 2.0006Rad 1

V

V

Cl

rW

rV

 0.0159Rad 1

Cl  2.0165Rad 1 r

- Cn : r

Cn  Cn r

Cn

rW

Cn

r CL 2



 Cn

rW

Cn r CL

C 2 L

W

rV

2



Cnr C D0

C D0

W

X   f  ARW ,W , C ,  4W C  

497

C D0

X   f  ARW , C ,  4W C  

Cn



Cn r

rV

2 bW

2 l Cos  Z Sin  CY    V V 2 

V





Result of calculations for condition 1-1,  0 : M 1  0.780 X AC  48.46 ft V

Z AC  10.44 ft V

ARV

eff

 1.44

CL

 0.8434Rad 1

CY

 0.1110

Cn

 0.0473Rad 1

V

V

rV

Cn  0.6403Rad 1 r





Result of calculations for condition 1-1,  11 : M 1  0.780 498

X AC  48.46 ft V

Z AC  10.44 ft V

ARV

eff

 1.44

CL

 0.8434Rad 1

CY

 0.1110Rad 1

V

V

Cn Cn

 0.5930Rad 1

rW

 0.0515Rad 1

rV

Cn  0.6445Rad 1 r

Result of calculations for condition 2-1: M 1  0.308 X AC  48.31 ft V

Z AC  10.44 ft V

ARV

eff

 1.44

499

CL

 0.7445Rad 1

CY

 0.0980Rad 1

V

Cn Cn

V

 0.6020Rad 1

rW

 0.0593Rad 1

rV

C n  0.6613Rad 1 r

Result of calculations for condition2-2: M 1  0.228 X AC  48.30 ft V

Z AC  10.44 ft V

ARV

eff

 1.44

CL

 0.7379Rad 1

CY

 0.0971Rad 1

V

Cn

V

rW

 0.2168Rad 1

500

Cn

rV

 0.0587 Rad 1

Cn  0.2755Rad 1 r

501

Lateral-Directional control derivatives Based on Dr. J. Roskam Methods

502

Result of calculations for condition 2-2: - CY

:

e

CY :Value expect to be zero for most of ailerons arangement e

CY

e

 0.0000Rad 1

- Cl

:



Cl   Cl 

e

e

Cl

 

C  



l a

Cl  

C C  Cl



l

Cl

C 



l Theory

l Theory

 C Cl a  Source : Airplane design VI 8.15  , f   C Cl  Theory  

 

 Ca  t   t    f  ,  ,   Cl  Theory  C  c W  c W  r t  

 

503

Cl K Cl    K   1 M 2 K

C 

l M  0

2

Cl

 f ia ,oa , ARW , M , C  4W  K 

   

Cl  Cl   right left   a left  a right Cl     2 2     1 2



 a   a Left  aright Cl

a





    C  

 Cl

l

left

right

Result of calculations for condition 1-1:

M 1  0.780 q1  212.92 lb Cl

a

ft 2

 0.0848Rad 1

504



Result of calculations for condition 2-1:

M 1  0.308 q1  116.69 lb Cl

a

ft 2

 0.0931Rad 1

Result of calculations for condition 2-2:

M 1  0.228 q1  71.82 lb Cl

a

ft 2

 0.0930Rad 1

- Cn

:

Cn

 K aCL Cl

a

a

W



a

K a  f i ,o , ARW ,W a

a



Source : Airplain designVI Fig 10.48

Result of calculations for condition 1-1,  0 :

M 1  0.780

505

q1  212.92 lb

ft 2

Cl

 0.0848Rad 1

Cn

 0.1550Rad 1

a

a

Result of calculations for condition 2-1:

M 1  0.308 q1  116.69 lb Cl

a

Cn

a

ft 2

 0.0931Rad 1  0.1702Rad 1

Result of calculations for condition 2-2:

M 1  0.228 q1  7.82 lb Cl

a

ft 2

 0.0930Rad 1

506

Cn

a

 0.1700Rad 1

-Rudder related control derivatives:

 i  0% r

o  84% r

 r  25 - CY

:

CY

 CL

r

r

V

K K b

 C L  Cl SV  Cl SW

C  K   f  r , r  Source : Airplain designVI Fig 8.13 C 



K b  f ir ,Or ,W

 C L  Cl



C    f  ARW , r  Source : Airplain designVI Fig 10.53 C 

 Cl  f  CCr  



507

 CY  V  C L SV Wfh    CL K K b  2    C  CY  V l S   C W  l  Veff  

CY

r

CY

V Wfh 

CY

 f bV ,2r1,bh ,l f 

Veff

Result of calculations for condition 1-1:

M 1  0.780 q1  212.9 lb ARV

eff

ft 2

 1.44

CL

 0.8434Rad 1

CY

 0.1632Rad 1

V

r

Result of calculations for condition2-1:

M 1  0.228 q1  116.69 lb

ft 2

508

 1.44

ARV

eff

CL

 0.7445Rad 1

CY

 0.2193Rad 1

V

r

Result of calculations for condition 2-2:

M 1  0.228 q1  71.82 lb

ft 2

 1.44

ARV

eff

CL

 0.7379Rad 1

CY

 0.2224Rad 1

V

r

- Cl

:

Cl



r

r

ZV Cos lV Sin CY r bW

509









Result of calculations for condition1-1,  0  :

M 1  0.780 q1  212.91lb ARV

eff

ft 2

 1.44

CL

 0.8434Rad 1

CY

 0.1632Rad 1

V

r

X AC  48.46 ft V

Z AC  10.44 ft V

 0.0243Rad 1

Cl

r







Result of calculations for condition1-1,  11 :

M 1  0.780 q1  212.92 lb ARV

eff

ft 2

 1.44

510

CL

 0.8434Rad 1

CY

 0.1632Rad 1

V

r

X AC  48.46 ft V

Z AC  10.44 ft V

 0.0066Rad 1

Cl

r

Result of calculations for condition 2-1:

M 1  0.308 q1  116.69 lb ARV

eff

ft 2

 1.44

CL

 0.8434Rad 1

CY

 0.1632Rad 1

V

r

X AC  48.46 ft V

Z AC  10.44 ft V

511

 0.0066Rad 1

Cl

r

Result of calculations for condition 2-1:

M 1  0.308 q1  116.69 lb ARV

eff

ft 2

 1.44

CL

 0.7445Rad 1

CY

 0.2193Rad 1

V

r

X AC  48.31 ft V

Z AC  10.44 ft V

Cl

r

 0.0327 Rad 1

Result of calculations for condition2-2:

M 1  0.228

512

q1  71.82 lb

ft 2

 1.44

ARV

eff

CL

 0.7379Rad 1

CY

 0.2224Rad 1

V

r

X AC  48.30 ft V

Z AC  10.44 ft V

Cl

r

 0.0332Rad 1

- Cn

:

Cn

 CY

r

r

r

lV Cos  ZV Sin bW







Result of calculations for condition1-1,  0 :

M 1  0.780 q1  212.92 lb

ft 2

513

ARV

eff

 1.44

CL

 0.8434Rad 1

CY

 0.1632Rad 1

V

r

X AC  48.46 ft V

Z AC  10.44 ft V

 0.0753Rad 1

Cn

r

Result of calculations for condition 2-1:

M 1  0.308 q1  116.69 lb ARV

eff

ft 2

 1.44

CL

 0.7445Rad 1

CY

 0.2193Rad 1

V

r

X AC  48.31 ft V

514

Z AC  10.44 ft V

 0.1206Rad 1

Cn

r

Result of calculations for condition 2-2:

M 1  0.228 q1  71.82 lb ARV

eff

ft 2

 1.44

CL

 0.7379Rad 1

CY

 0.2224Rad 1

V

r

X AC  48.30 ft V

Z AC  10.44 ft V

Cn

r

 0.1223Rad 1

515

Sensivity of lateral-directional derivatives Based on Dr. J. Roskam Theory’s

516

-0.3500

-0.3250

 y rad -1

C -0.3000

-0.2750

517 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00



5.00

4.00

3.00

2.00

1.00

-0.2500 0.00

CY Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

-1.7000

 l rad -1

C -1.6000

-1.5000

-1.4000

-1.3000

-1.2000

518 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

-1.1000 0.00

Cl  Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

-0.4000

-0.4250

 n rad -1

C -0.4500

-0.4750

519 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00



5.00

4.00

3.00

2.00

1.00

-0.5000 0.00

Cn Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

-0.1000

-0.1250

p n rad -1

C -0.1500

-0.1750

520 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

-0.2000 0.00

Cn P

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

0.2000

0.1750

r y rad -1

C 0.1500

0.1250

521 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.1000 0.00

CY r

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

2.3000

r l rad -1

C 2.2500

2.2000

2.1500

2.1000

2.0500

522 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

2.0000 0.00

Cl r

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

-0.7000

r

n rad -1 C -0.6000

-0.5000

-0.4000

-0.3000

523 1/T,  , 

n

1/s, rad/s, -

10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

-0.2000 0.00

Cn r

Sensivity Diagram Design Point Damping Ratio Frequency [rad/s] 1/T[1/s]

Long. Stability derivatives:

Derivative

CD

Condition1-1 0.2091 Rad 1

Condition2-1 0.0614 Rad 1

Condition2-2 -----------------

CL

0.1844 Rad 1

0.0454 Rad 1

0.0396 Rad 1

Cm

-0.0120 Rad 1

0.0003 Rad 1

0.0005 Rad 1

CD

0.2868 Rad 1

0.6060 Rad 1

1.0075 Rad 1

Cm

-0.6386 Rad 1

-0.5621 Rad 1

-1.7183 Rad 1

CD

0.0000 Rad 1

0.0000 Rad 1

0.0000 Rad 1

CL

0.6290 Rad 1

0.6387 Rad 1

0.6316 Rad 1

Cm

-0.9366 Rad 1

-1.1346 Rad 1

-1.1225 Rad 1

CD

0.0000 Rad 1

0.0000 Rad 1

0.0000 Rad 1

CL

4.8616 Rad 1

5.8830 Rad 1

5.8830 Rad 1

Cm

-4.7691 Rad 1

-2.5319 Rad 1

-4.2623 Rad 1

u

u u







  q

q q

524

Lateral-directional stability derivatives:

Derivatives:

Condition1-1 -0.3051 Rad 1

Condition2-1 -0.2860 Rad 1

Condition2-2 -0.2847 Rad 1

-1.6634 Rad 1

-1.6387 Rad 1

-1.6387 Rad 1

-0.4833 Rad 1

-0.4422 Rad 1

-0.4295 Rad 1

0.0283 Rad 1

0.0251 Rad 1

0.0248 Rad 1

0.0017 Rad 1

0.0015 Rad 1

0.0015 Rad 1

0.0102 Rad 1

0.0089 Rad 1

0.0088 Rad 1

0.0000 Rad 1

0.0000 Rad 1

0.0000 Rad 1

-0.5380 Rad 1

-0.5626 Rad 1

-0.5644 Rad 1

-0.1026 Rad 1

-0.1122 Rad 1

-0.1129 Rad 1

CY

0.01499 Rad 1

0.1616 Rad 1

0.1604 Rad 1

Cl

2.2971 Rad 1

2.3128 Rad 1

2.0330 Rad 1

-0.6403 Rad 1

-0.6613 Rad 1

-0.2755 Rad 1

CY Cl





Cn CY Cl





Cn CY Cl



 P

P

Cn

P

r

r

Cn

r

525

Long. Control derivatives:

Elevator related derivatives:

Derivatives:

Condition1-1

Condition2-1

Condition2-2

0.0292 Rad 1

0.0392 Rad 1

0.0397 Rad 1

CL

0.1551 Rad 1

0.2078 Rad 1

0.2107 Rad 1

Cm

-0.2926 Rad 1

-0.3908 Rad 1

-0.3507 Rad 1

CD

e

e e

Lateral-directional Control derivatives:

Derivatives:

Condition1-1

Condition2-1

Condition2-2

CY

0.0000

0.0000

0.0000

Cl

0.0848

0.0931

0.0930

Cn

-0.1550

-01702

-0.1700

CY

0.1632

0.2193

0.2224

Cl

0.0243

0.0327

0.0332

-0.0753

-0.1206

-0.1223

e

a a

r

r

Cn

r

526

Class II stability analyses Based on Dr. J. Roskam Method

527

- CL : 0

CL  CL 0

CL

0 Clean

CL

0Wf

0Wf Clean

 CL

0

AClean

AClean

W

0h

0W 

  0 A

Clean

 0

AClean

CL

Wf

CL

Wf

  0  iW W

   0l  W

  0W   t 

 CL

 K CW CL

0Wf Clean

0Wf Clean

0

0h

 CL

CL

0

 CL

0Wf

   

  0W   t

     0lW   t       0   lW  M  0.3

f  W , ARW , C  Source : Airplane designVI Fig 8.41 4W  

   0l   W M     0l   W  M  0.3

 t t  f  M , C ,  ,   4W  c  r  c t  

528

0  0

W

A

0

W

CL

0h

 0W CL 



W

180



CL0

W

CL

W 

 CL  h h

0   h

 iW



Sh  0 A  0 A SW



 h  0   h f  A

 h  f  hh ,b, AR,b f ,CL f  Source : Airplane design VI Fig8.70 f 0   CL

0C

 CL C C

0   C



SC  0 A  0C SW



 C 0  A

  Result of calculations for condition 1-1  0  : 

M 1  0.780

 0  3.75deg W

0

W

 3.75 deg

529



0

 3.75Rad 1

AClean

 0  3.75Rad 1 A

 0  3.14 deg h

 6.55Rad 1

CL

W 

CL

0W 

0  0.4287

CL

0Wf

CL

0Wf

CL

0h

CL

Clean

 0.4287  0.0064

0 Clean

 0.4351

CL  0.4351 0

Result of calculations for condition 2-1: M 1  0.308

 0  3.75deg W

530

0

 0.31deg

W

0

AClean

 3.75 deg

 0  0.31deg A

 0  8.38degDownwash h

 6.55Rad 1

CL

W 

CL

0W 

CL

 0.3927

0Wf Clean

CL

0Wf

CL

0h

 0.4287

 0.0360  0.0912

CL

0 Clean

 0.5190

CL  0.1272 0

0

AClean

 3.75 deg

 0  0.36 A

531

 0 h 10.62 deg CL

6.5500Rad 1 W

CL

0W 

0.4703

0.0416

CL

0Wf

CL  0.1076 0h

CL

0 Clean

 0.5362

CL  0.0660 0

- Cm : 0

Cm  Cm 0

Cm

0Wf

 CL

0Wf

 Cm

0W Clean

0h

X

CG  X ACWf

 Cm

W LE

532

 C

m0

f

 Cm0  Cm W

WTE

CL

  0 C L W

0W Clean

W

    0   0 l   0W W  W   t    0W   t 

   

   0    lW  M  t      0   lW  M  0.3

f  W , ARW ,  C  Source : Airplain design VI , Fig 8.42 4W  

   0l  t t   W   f  M ,  ,   ,   C  4   W  c  r  c t    0l   W  M  0 .3 Cm

K 2  K1 

0f

l     f 

K 2  K1   f  d f   Cm  0 M 

C 

 

   

i  n   C m0 M  2   Wf     iW  iCl f  X i   i  0W i  1 i   C m 36 .5SW CW   0 M 0 Source : Airplain designVI Fig 8.111

 f M  Source :Airplain designVI Fig 8.111

m0 M  0

533

2

Cm

0W

Cm0

t

  ARW  Cos C   Cm Cm 0r 0t 4W      2 ARW  2Cos C 4W 

  Cm  0    t  

   t 

 f  W , C , ARW  Source : Airplain designVI Fig 8.98 4  





AR CL X CG  X AC  W WTE f0 1.5 2  C    C   2   C   m C   C K P    1  Lf0 m0   W C C     C    LW  Clean    

Cm

 K

  C   2  C    K P 0.25CL0     WClean  C   C     C   K   f i ,o , ,W  Source : Airplain designVI Fig 8.107 f f C  



K P  f i ,o ,W f



f



Source : Airplain designVI Fig 8.105

Cm  f i ,O ,W f f CLW



Source:Airplain designVI Fig 8.106

534

Cf Cf 1  .  C C C C Cm

0W Clean

Cm

W LE

Cm

 Cm  C L 0

0W Clean

   Cm e le 

0W Clean

X

CG  X ACW



  S   C     X CG  X LE Cl  Wf   S C  W

 C   2  blef  0.75CL   1 0W  C   bW Clean

  f   le le

 C   C   blef   1  C  C  bW

 Cf   C    Source : Airplain designVI Fig 8.93  f  m  C    LE   

Cf   C   Source:Airplain designVI Fig 8.26  

Lift effectivenessof leading edge flap: f 

Cm

0h

 CL  h

 0h 

h





S h X AC h  X CG .  0h SW CW

 h  0   h f  A

 h f  f  hh ,bW , ARW ,b f ,CL f  Source:Airplain designVI Fig 8.70 0  

535

Wing and fuselage pitching moment coefficient at Cl  0 : Entered parameters:

Cm Cm

0W r

0W t

 0.040  0.040





Result of calculations for condition 1-1,  0 :

M 1  0.780 Cm Cm Cm

0f

0W

0Wf

 0.0016  0.0198  0.0182

Result of calculations for condition 2-1: M 1  0.308 Cm Cm

0f

0Wf

 0.0013  0.0147

536

Result of calculations for condition 2-2:

M 1  0.228 Cm Cm Cm

0f

0W

0Wf

 0.0012  0.0156  0.0144

Trailing edge flap moment coefficient at Alpha=0 Result of calculations for condition 1-1:

CL

0W 

Cm

WTE

 0.0000  0.0000

Result of calculations for condition 2-1:

CL

0W 

Cm

WTE

 0.1770  0.1181

537

Result of calculations for condition 2-2: CL

0W 

Cm

WTE

 0.2064  0.1383

-Total pitching moment coefficient at alpha=0: Result of calculations for condition 1-1: Cm Cm

0Wf

0h

 0.1205  0.0116

Cm  0.1322 0

Result of calculations for condition 2-1:

Cm Cm

0Wf

0h

 0.1608  0.1674

Cm  0.0066 0

538

Result of calculations for condition 2-2:

Cm Cm

0Wf

0h

 0.1429  0.1974

Cm  0.0545 0

-Trimmed lift coefficient:

 CL  CL  h

CL  CL

Wf

f



Cm  Cm  C1 CL 0



 CL  C2CL  C3CL f

h

CW

C2 

h

Wf

X CG  X ACWf

C1 

CL

h

S Sh  C L C C C SW SW

X CG  X AC CW

 C 

m0

h

Sh h SW

C1CLWf C3C4



C2 C3C5

539

C

SC   Sh C    S h 5 S C  SC W CL C   Cm C3C4  W  O 1 0 S C C C    2 3 5 4 W    S   Sh   h C5 C W  SW S  1C1 W   C2 C3C5    



CL

Wf

CL

h

 C 

CL

Wf

CL

C

CL

Wf

CL

C



m0



C1CL

Wf

C2

C L C2  Cm 1

C2 C1

 C  



m0

Sh h SW

0

Sh h SW

C1CLWf C3

SC C SW

CL1 C3 Cm0 C3 C1

 C 



m0

SC h SW

C1CL

Wf



C3

540

CL

Wf



CL C3 Cm 1

C3 C1

0

SC C SW

SC C SW

Result of calculations for condition 1-1:

CL  0.4316 W

CL

Wf

 0.4307

CL

f

0

CL  0.5906 h

Result of calculations for condition 2-1: CL  0.9568 W

CL

Wf

CL

 0.9547

f

 0.1770

CL  2.1438 h

541

Result of calculations for condition 2-2: CL  1.6821 W

CL

Wf

CL

 1.6784

f

 0.2109

CL  3.5583 h

542

Longitudinal Flight dynamic calculations Based on Dr. J. Roskam Method

543

Longitudinal transfer function:

1 q  U12 2 D1  A1S 4  B1S 2  D1S  E1 A1  U1  Z





B1  U1  Z  X U  X T  M q  Z  M  U1  Z q 



C1  X U  X T

U

U

M

q

U1  Z  Z  M  U1  Z q 





 M q Z  ZU X   M  gSin1  M   M T U1  Z q 







D1  gSin1 M   M T  M  X U  X T 





U



U Z  M

gCos ZU M   M U  M T

1

U



U

MT

U



 X  U1  Z q  ZU X  M q  X U  X TU 

M   M  U  Z M Z  T

1

q

q



E1  gCos1 M   M T

 M

U

MT

U



 X X 

U

Z

U

 XT

U



 Z M U  M T

M

544

  M T

U



  gSin

1

U S  NU   C.S S  D1 NU  AU S 3  BU S 2  CU S  DU AU  X 

BU   X  CU  X  Z

C.S

M

U1  Z 

C.S

C.S

C.S

U Z M 1

M



q  Z  M 

q Z  M  gSin1 

U1  Z q  Z C.S X  

M

  M T

U  Z  1

q

 M  gCos1  X  M q  M  C.S X  M q 

C.S

X  U1  Z q U1  Z gCos1

DU  X 

C.S

M   M  gSin  Z T

1

C.S

M  gCos1  M 

Z gCos1  X  gSin1  s  N    C.S s  D1 N   A S 2  B S  C A  Z

C.S

B  X 

C.S

U1  Z 

M   M 

C.S

Z

U1  Z M  M TU 

U M  

545

C.S

M

C.S

Z X

 s 

 C.S S 



U



 X TU  X  ZU



N D1

N  A S 3  B S 2  C S  D A  Z

C.S

M X

B  X 

C.S

ZU  Z

C  X 

C.S

U  Z M

Z

C.S

M

U

1

C.S

q

q

U

Long



U



 M TU gCos1  M 

1 S

calculations for condition 1-1:

IYY  76078.67 Slug

 XT

U



 M U  Z   C.S

1

q



 M T  M q ZU 

S1,2   1,21,2  1,2 1 1,2 TC

U

ft 2

546

C.S

X

U





 X TU gSin1  ZU gCos1

Result of Transfer function calculations for condition1-1:

M 1  0.780 n  0.87 g q1  212.92 lb W

S Steady State

ft 2

 82.14 lb

ft 2

X U  0.0722S 1 X T  0.2064S 1 U

X   3.9763 ft

s2

ZU  0.0928S 1 Z  312.0758 ft Z  0.3778 ft

s

Z q  2.9201 ft

s

s2

547

M U  0.0026 1 MT  0 1 U

ft.S

ft.S

M   6.7385S  2 M T  0S  2 

M   0.0720S 1 M q  0.3664S 1

n

SP

 2.6175 Rad

Sec

 SP  0.1625 n

Plong

P

long

 0.0998 Rad

Sec

 0.6815

n  Undefined 3

 3  Undefined TClong  Undefined 1

548

TClong  Undefined 2

TClong  Undefined 3

TClong  Undefined 4

M i  0S  2 h

Result of Transfer function calculations for condition2-1: IYY  83220.9763Slug. ft 2 B

M 1  0.308 n  1g q1  116.69 lb

W S 

Steady State

ft 2  89.81lb

ft 2

X U  0.0639S 1 X T  0.2349S 1 U

X   6.9162 ft

S2

ZU  0.1965S 1 549

Z  144.2712 ft

S2

Z  0.4367 ft

S

Z q  4.0227 ft

S

M U  0.0031 1

ft.S

MT  0 1 U

ft.S

M   2.9117S  2 M T  0S  2 

M   0.0983S 1 M q  0.2193S 1 M T  0S 1 

M   0.0983S 1 M q  0.2193S 1

n

SP

 0.1898 Rad

Sec

550

 SP  0.2170 n

 0.1898 Rad

Plong

P

long

Sec

 0.4733

n  Undefined 3

 3  Undefined TC Long  Undefined 1

TC Long  Undefined 2

Result of Transfer function calculations for condition2-2:

M 1  0.228 n  0.62 g q1  71.82 lb

W S 

ft 2

Steady State

 89.81lb

ft 2

X U  0.0696S 1 X T  0.1930S 1 U

551

X   6.0576 ft

S2

ZU  0.1614S 1 Z  89.6894 ft

S2

Z  0.3533 ft

S

Z q  3.3040 ft

S

M U  0.0026 1

ft.S

M T  0.0000 1 U

ft.S

M   5.5907S 1 M T  0S 1 

M   0.0798S 1 M q  0.1799S 1

n

SP

 2.3565 Rad

Sec

 SP  0.1340

552

n

Plong

P

long

 0.1704 Rad

Sec

 0.4221

Xi  0 Zi  0 h

Mi  0 h

553