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 IV: Designer: Sina golshany -Longitudinal flying qualities calculations and diagrams -Lateral-directional flight dynamic calculations -Lateral-directional Flying qualities -Stabilizer trim diagrams -Roll coupling calculations and diagrams -V-n diagrams (MIL-A-8861) -Lift distribution diagrams on lift producer surface -Cost estimation -Project references
Longitudinal flying qualities Calculation Based on Dr. J. Roskam method
554
n
T2
Z g
Plong
T1
ln2 P
long
2P long
n P
long
ln2
Plong n P
long
calculations, according to MIL-F-8785C Papers: Result of calculations Condition 1-1, Air to air combat condition:
n
9.806 g
Rad
T2 10.191Sec P
LevelP Unstable Level SP III Level n SP I
555
Result of calculations Condition 2-1, Landing condition:
n
4.487
g Rad
T2 7.716Sec P
T1
Undefined 2P
LevelP Unstable Level n
SP
Leveln
SP
III I
Result of calculations Condition 2-1, Take off condition:
n
2.789
g Rad
T2 9.637Sec P
T1
Undefined 2P
LevelP Unstable Level SP III Leveln
SP
I
556
Longitudinal flying qualities Diagrams
557
102
ď Ą rad n g
Design Point
101
Level 2
558 10 1
10 0
Level 3
ď ˇ
SP n
rad
s
10 2
Level 2, Class II-L, III
Level 2, Class I, II-C, IV
Level 1, Class II-L, III
Level 1, Class I, II-C, IV
always be greater than 0.6 rad/s for Level 3 Note : For Class I,II-C, and IV airplanes, frequency shall
100 10 -1
Long. flying qualities Condition1-1
102
ď Ą rad n g
101
Design Point
Level 2
559 10 1
10 0
Level 3
ď ˇ
SP n
rad
s
10 2
Level 2, Class II-L, III
Level 2, Class I, II-C, IV
Level 1, Class II-L, III
Level 1, Class I, II-C, IV
always be greater than 0.6 rad/s for Level 3 Note : For Class I,II-C, and IV airplanes, frequency shall
100 10 -1
Long. flying qualities Condition2-1
102
ď Ą rad n g
101
560 Level 2 10 1
10 0
Level 3
ď ˇ
SP n
rad
s
10 2
Level 2, Class II-L, III
Level 2, Class I, II-C, IV
Level 1, Class II-L, III
Level 1, Class I, II-C, IV
Design Point
always be greater than 0.6 rad/s for Level 3 Note : For Class I,II-C, and IV airplanes, frequency shall
100 10 -1
Long. flying qualities Condition2-2
Lateral-directional flight dynamic calculations Based on Dr. J. Roskam Method
561
1 q U12 2 A1
B1
I XZ S I XX
S
I XZ
S
I ZZ
S
D2 s A2 s 4 B2 s 3 C2 s 2 D2 s E2
A2 U1 1 A1B1
B2 Y 1 A1B1 U1 LP N r A1 N P B1Lr
C2 U1LP N r LP N r Y LP N r A1 N P B1Lr
Y L B N
YP L N A1 NT A1 U1 L B1 N NT r
1
NT
A
D2 Y LP N r Lr N P YP L N r N Lr NT Lr
gCos1 L N A1 NT
1
562
U1 L N P N LP NT LP Yr L N P N LP NT LP
E2 gCos1 L N r N Lr NT Lr
s
C.S (s)
N D2
N s A s 3 B s 2 C s D A Y
Yr L
1 1
C.S
C.S
C Y
N L
P A1 N P B1Lr
r
B1 N
C.S
U L 1
C.S
Y L P
B1 N
C.S
C.S
N
C.S
C.S
LP N r N P Lr YP N C.S Lr L C.S N r
C.S
gCos1 L
N
D gCos1 N
s
1 A B
C.S
B Y
C.S
C.S
LP
Lr L
C.S
Nr
N
C.S s D2
563
A1
N s A s 2 B s C
A U1 L
N
C.S
B U1 N
C.S
C.S
Lr L
A1
C.S
N r Y L
L N A N A U Y N L N L
Y
C.S
1
1
T
C.S
r
C.S
N
C.S
1
T
C.S
L N C.S
s N C.S s D2 N A s 3 B s 2 C s D
C.S
B1
C.S
N P N
A U1 L B U1 L
C.S
LP
YP N L C.S NT L C.S L N C.S Y
C.S
L N P N LP
D gCos1 N L C.S NT L C.S L N C.S
564
For a complex pair of roots:
S1,2 1,21,2 J1,2 1 1,2 For real roots:
TC
1 s
Lateral – directional rudder related transfer functions: Result of calculations for condition1-1, 15 :
I XX 10216Slug ft 2 B
I ZZ 85802Slug ft 2 B
I XZ 0 B
-Polynomial form I:
s 15.7073s 4 1602.8272s 3 4499.9389s 2 637.8296s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2 182.7981s
565
-Factored form I:
s 15.7073ss 0.1352s 99.1497s 3.0288 r s 759.5145ss 0.0033s 4.0881 s 2 7.1047s 17.6399
K gain 3.489258 -Polynomial form II:
s 4219.4056s 3 9623.1644s 2 535570.7913s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s
-Factored form II:
s 4219.4056s 3 6923.1644s 2 535570.7913s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2 182.7981s
566
-Polynomial form III:
1556.7293s 3 4572.2705s 2 1058.1714s 21713.1387 s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2 182.7981s
-Factored form III :
s 1556.7293s 1.6681 s 2 4.6052s 8.3616 r s 759.5145ss 0.0033 s 2 7.1047s 17.6399
M 1 0.780 q1 212.92 lb
ft 2
W 70.40 lb 2 ft S TO I XX 10216Slug ft 2 S
I ZZ 85802Slug ft 2 S
I XZ 0Slug ft 2 S
Y 29.3646 ft
Sec 2 567
YP 0 ft
Sec 2
Yr 0.3046 ft
Sec 2
L 380.2819s 2 LP 2.6054s 1 Lr 11.1241s 1 N 13.1552s 2 NT 0.0000s 2
N P 0.0592s 1 N r 0.3692s 1
n 4.1999 Rad D
Sec
D 0.8458 n P
Plong
lateral
Undefined Undefined
TS 299.630S 568
TR 0.245S TClateral Undefined 1
TClateral Undefined 2
TClateral Undefined 3
TClateral Undefined 4
Y 15.7073 ft r
s2
L 5.5554s 2 r
N 2.0496s 2 r
Result of calculations for aileron related transfer functions: Condition1-1: -Polynomial form I :
3203.1378s 3 8345.3320s 2 1442.7049s s a s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s
569
-Factored form I :
3203.1378ss 0.1627s 2.7681 s a s 759.5145ss 0.0033s 4.0881 s 2 7.1047s 17.6399
K gain 7.892343 -Polynomial form II:
35646.3811s 2 1216717.0963s s a s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s -Factored form II :
s 35646.3811ss 34.4330 a s 759.5145ss 0.0033s 4.0881 s 2 7.1047s 17.6399
K gain 6656.072379 -Polynomial form III:
s 3204.4229s 3 8472.5705706s 2 322.7795s 49319.3709 a s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s
570
-Factored form III:
3204.4229s 1.8412 s 2 4.4853s 8.3591 s a s 759.5145ss 0.033s 4.0881 s 2 7.1047s 17.6399 K gain 296.802490
I XX 10216Slug ft 2 I ZZ 85802Slug ft 2 s
I XZ 0Slug ft 2 s
Y 29.3646 ft YP 0 ft
Sec 2
Sec 2
Yr 0.3046 ft
S
L 380.2819s 2 LP 2.6054s 1 Lr 11.1241s 1 N 13.1552s 2 571
NT 0.0000s 2
N P 0.0592s 1 N r 0.3692s 1
n 4.2000 Rad D
Sec
D 0.8458 n
Plateral
P
lateral
Undefined
Undefined
TS 299.630s TR 0.245s TClateral Undefined 1
TClateral Undefined 2
TClateral Undefined 3
TClateral Undefined 4
Y 0.0000 ft a
s2 572
L 0.0000s 2 a
N 4.2190s 2 a
573
Lateral-directional flight dynamic calculations Based on Dr. J. Roskam Method
574
1 q U12 2 A1
B1
I XZ S I XX
S
I XZ
S
I ZZ
S
D2 s A2 s 4 B2 s 3 C2 s 2 D2 s E2
A2 U1 1 A1B1
B2 Y 1 A1B1 U1 LP N r A1 N P B1Lr
C2 U1LP N r LP N r Y LP N r A1 N P B1Lr
Y L B N
YP L N A1 NT A1 U1 L B1 N NT r
1
NT
A
D2 Y LP N r Lr N P YP L N r N Lr NT Lr
gCos1 L N A1 NT
1
575
U1 L N P N LP NT LP Yr L N P N LP NT LP
E2 gCos1 L N r N Lr NT Lr
s
C.S (s)
N D2
N s A s 3 B s 2 C s D A Y
Yr L
1 1
C.S
C.S
C Y
N L
P A1 N P B1Lr
r
B1 N
C.S
U L 1
C.S
Y L P
B1 N
C.S
C.S
N
C.S
C.S
LP N r N P Lr YP N C.S Lr L C.S N r
C.S
gCos1 L
N
D gCos1 N
s
1 A B
C.S
B Y
C.S
C.S
LP
Lr L
C.S
Nr
N
C.S s D2
576
A1
N s A s 2 B s C
A U1 L
N
C.S
B U1 N
C.S
C.S
Lr L
A1
C.S
N r Y L
L N A N A U Y N L N L
Y
C.S
1
1
T
C.S
r
C.S
N
C.S
1
T
C.S
L N C.S
s N C.S s D2 N A s 3 B s 2 C s D
C.S
B1
C.S
N P N
A U1 L B U1 L
C.S
LP
YP N L C.S NT L C.S L N C.S Y
C.S
L N P N LP
D gCos1 N L C.S NT L C.S L N C.S
577
For a complex pair of roots:
S1,2 1,21,2 J1,2 1 1,2 For real roots:
TC
1 s
Lateral – directional rudder related transfer functions: Result of calculations for condition1-1, 15 :
I XX 10216Slug ft 2 B
I ZZ 85802Slug ft 2 B
I XZ 0 B
-Polynomial form I:
s 15.7073s 4 1602.8272s 3 4499.9389s 2 637.8296s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2 182.7981s
578
-Factored form I:
s 15.7073ss 0.1352s 99.1497s 3.0288 r s 759.5145ss 0.0033s 4.0881 s 2 7.1047s 17.6399
K gain 3.489258 -Polynomial form II:
s 4219.4056s 3 9623.1644s 2 535570.7913s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s
-Factored form II:
s 4219.4056s 3 6923.1644s 2 535570.7913s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2 182.7981s
579
-Polynomial form III:
1556.7293s 3 4572.2705s 2 1058.1714s 21713.1387 s r s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2 182.7981s
-Factored form III :
s 1556.7293s 1.6681 s 2 4.6052s 8.3616 r s 759.5145ss 0.0033 s 2 7.1047s 17.6399
M 1 0.780 q1 212.92 lb
ft 2
W 70.40 lb 2 ft S TO I XX 10216Slug ft 2 S
I ZZ 85802Slug ft 2 S
I XZ 0Slug ft 2 S
Y 29.3646 ft
Sec 2 580
YP 0 ft
Sec 2
Yr 0.3046 ft
Sec 2
L 380.2819s 2 LP 2.6054s 1 Lr 11.1241s 1 N 13.1552s 2 NT 0.0000s 2
N P 0.0592s 1 N r 0.3692s 1
n 4.1999 Rad D
Sec
D 0.8458 n P
Plong
lateral
Undefined Undefined
TS 299.630S 581
TR 0.245S TClateral Undefined 1
TClateral Undefined 2
TClateral Undefined 3
TClateral Undefined 4
Y 15.7073 ft r
s2
L 5.5554s 2 r
N 2.0496s 2 r
Result of calculations for aileron related transfer functions: Condition1-1: -Polynomial form I :
3203.1378s 3 8345.3320s 2 1442.7049s s a s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s
582
-Factored form I :
3203.1378ss 0.1627s 2.7681 s a s 759.5145ss 0.0033s 4.0881 s 2 7.1047s 17.6399
K gain 7.892343 -Polynomial form II:
35646.3811s 2 1216717.0963s s a s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s -Factored form II :
s 35646.3811ss 34.4330 a s 759.5145ss 0.0033s 4.0881 s 2 7.1047s 17.6399
K gain 6656.072379 -Polynomial form III:
s 3204.4229s 3 8472.5705706s 2 322.7795s 49319.3709 a s 759.5145s 5 2288.5747s 4 8669.8865s 3 54742.8693s 2
182.7981s
583
-Factored form III:
3204.4229s 1.8412 s 2 4.4853s 8.3591 s a s 759.5145ss 0.033s 4.0881 s 2 7.1047s 17.6399 K gain 296.802490
I XX 10216Slug ft 2 I ZZ 85802Slug ft 2 s
I XZ 0Slug ft 2 s
Y 29.3646 ft YP 0 ft
Sec 2
Sec 2
Yr 0.3046 ft
S
L 380.2819s 2 LP 2.6054s 1 Lr 11.1241s 1 N 13.1552s 2 584
NT 0.0000s 2
N P 0.0592s 1 N r 0.3692s 1
n 4.2000 Rad D
Sec
D 0.8458 n
Plateral
P
lateral
Undefined
Undefined
TS 299.630s TR 0.245s TClateral Undefined 1
TClateral Undefined 2
TClateral Undefined 3
TClateral Undefined 4
Y 0.0000 ft a
s2 585
L 0.0000s 2 a
N 4.2190s 2 a
586
Lateral-directional flying qualities, Based on Dr. J. Roskam method
587
Magiude of D
s solved for dutch roll roots : s
s sN N s s s L s s A sL s B N s s sN s 2 A1 sLr
L
2
r
2
2
1
P
2
2
1
A1
B1
r
P
r
I XZ S I XX S I XZ S I ZZ S
s Dn jn D
D
1 D2
s re j s D
r D
s Magnitude of solved for the spiral root . S s
588
S
1 TCS
s Magnitude of solved for the roll root R s S
1 TC R
These mode cheaked against MIL F 8785C Spiral and Dutch roll mode checking:
40.7907 D
T2 207.688s S
T1
Undefined 2S
LevelS I Level I D
Leveln I D
Leveln D III
589
Roll mode performance :
Level TR I Levelt III Lateral directional transfer function for condition 2-1: Ruder related:
Polynomial form I:
9.1534s 4 525.0226s 3 1544.5327s 2 423.9859s s r s 337.5620s 5 1062.3210s 4 1204.1802s 3 3978.6915s 2 3759.1131s
Factored form I:
9.1534ss 0.2527s 54.2311s 3.3799 s r s 337.5620ss 4.4262s 0.7148 s 2 1.9940s 3.5198
K gain 0.112789
590
Polynomial form II:
s 1102.0609s 3 5913.1117s 2 88365.8752s r s 337.5620s 5 1062.3210s 4 1204.1802s 3 3978.6915s 2 3759.1131s
Factored form II:
1102.0609ss 12.0305s 6.6650 s r s 337.5620ss 4.4262s 0.7148 s 2 1.9940s 3.5198
K gain 23.507107
Polynomial form III:
s 497.0213s 3 1492.3205s 2 85.5424s 8300.3101 r s 337.5620s 5 1062.3210s 4 1204.1802s 3 3978.6915s 2
3759.1131s
591
Factored form III:
497.0213ss 4.0022 s 2 0.9996s 4.1728 s r s 337.5620ss 4.4262s 0.7148 s 2 1.9940s 3.5198 K gain 2.208050 M 1 0.308 q1 116.69 lb
W S
TO
I XX I ZZ I XZ
S
S
S
ft 2
89.81lb
ft 2
13029Slug ft 2 106547Slug ft 2 0Slug ft 2
Y 11.9374 ft Y P 0.0000 ft
s2
Y r 0.3267 ft
s
s2
592
L 163.5178s 2 LP 2.7206s 1 Lr 9.8312s 1 N 5.3987s 2 NT 0.0000s 2
N P 0.0663s 1 N r 0.3911s 1
n 1.8761Rad D
Sec
D 0.5317 n P
Plateral
lateral
Undefined
Undefined
Ts 1.399s TR 0.226s TClateral Undefined 1
TClateral Undefined 2
593
TClateral Undefined 3
TClateral Undefined 4
P
lateral
Undefined
Y 9.1534 ft r
s2
L 3.2648s 2 r
N 1.4724s 2 r
Aileron related calculations:
-Polynomial form I:
s 700.7559s 3 2413.0620s 2 539.755s a s 337.5620s 5 1062.3210s 4 1204.1802s 3 3978.6915s 2
3759.1131s
594
-Factored form I:
s 700.7559ss 0.2107s 3.6542 a s 337.5620ss 4.4262s 0.7148
s 1.9940s 3.5198 2
K gain 0.143511
-Polynomial form II:
3137.6719s 3 5557.9759s 2 131709.6604s s a s 337.5620s 5 1062.3210s 4 1204.1802s 3 3978.6915s 2 3759.1131s
-Factored form II:
s 3137.6719ss 7.4249s 5.6535 a s 337.5620ss 4.4262s 0.7148 s 2 1.9940s 3.5198
K gain 35.037429
595
-Polynomial form III:
s 701.4347s 3 2141.3239s 2 74.8475s 12526.9943 a s 337.5020s 5 1062.3210s 4 1204.1802s 3 3978.6915s 2
3759.1131s -Factored form III:
s 701.4347s 4.0328 s 2 1.0401s 4.3635 a s 337.5620ss 4.4262s 0.7148s 0.7148
s 1.9940s 3.5198 2
K gain 3.332433 M 1 0.308 q1 116.69 lb
W S
TO
ft 2
89.81lb
ft 2
I XX 13029Slug ft 2 S
I ZZ 106547Slug ft 2 S
596
I XZ 0Slug ft 2 S
Y 11.9374 ft YP 0.0000 ft
s2
Sec
L 163.5178s 2 LP 2.7206s 1 Lr 9.8312s 1 N 5.3987s 2 NT 0.0000s 2
N P 0.0663s 1 N r 0.3911s 1
n 1.8761Rad D
Sec
D 0.5314 n P
Plateral
lateral
Undefined
Undefined
597
TS 1.399s TR 0.226s TClateral Undefined 1
TClateral Undefined 2
TClateral Undefined 3
TClateral Undefined 4
Y 0.0000 ft a
s2
L 9.2951s 2 a
N 2.077s 2 a
Roll performance checking:
LevelTR I Levelt I actual 78.52 deg
598
-Spiral and Dutch roll mode checking:
23.2607 D
T2 Undefined S
T 1 0.970s 2S
LevelS Stable Level LevelIII D
Level Level
nD
I
nD D
III
599
Lateral-Directional Transfer functions, Condition 2-2, take off: Ruder related: -Polynomial form I:
s 5.7182s 4 245.9683s 3 618.5336s 2 227.6471s r s 253.1715s 5 608.1508s 4 612.0035s 3 2810.0206s 2 1263.0411s -Factored form I:
5.7182ss 0.3256s 40.3065s 3.0337 s r s 253.1715ss 3.7444s 0.4025 s 2 1.7447s 3.3106
K gain 0.180237 -Polynomial form II:
s 516.4410s 3 2353.2514s 2 25340.3872s r s 253.1715s 5 608.1508s 4 612.0035s 3 2810.0206s 2 1263.0411s
600
-Factored form II:
516.4410ss 9.6443s 5.0877 s r s 253.1715ss 3.7444s 0.4025 s 2 1.7447s 3.3106
K gain 20.062994 -Polynomial form III:
s 232.6424s 3 574.4826s 2 25.6681s 3186.5750 r s 253.1715s 5 608.1508s 4 612.0035s 3 2810.0206s 2 1263.0411s -Factored form III:
s 232.6424ss 3.5346 s 2 1.0652s 3.8753 r s 253.1715ss 3.7444s 0.4025 s 2 1.7447s 3.3106 K gain 2.522938 M 1 0.228 q1 71.82 lb
ft 2
W 89.81lb 2 ft S TO
601
I XX 13029Slug ft 2 S
I ZZ 106548Slug ft 2 S
I XZ 0Slug ft 2 S
Y 7.3201 ft
Sec 2
YP 0.0000 ft
Sec
Yr 0.2663 ft
Sec
L 100.6856s 2 LP 2.2395s 1 Lr 8.0015s 1 N 3.1271s 2 NT 0.0000s 2
N P 0.0548s 1 N r 0.1337s 1
602
n 1.8195 Rad D
Sec
D 0.4794 n
Plateral
P
lateral
Undefined
Undefined
TS 2.485Sec TR 0.267Sec TClateral Undefined 1
TClateral Undefined 2
TClateral Undefined 3
TClateral Undefined 4
Y 5.7182 ft r
s2
L 2.0399s 2 r
N 0.9189s 2 r
603
Aileron related flying qualities:
-Polynomial form I:
s 323.0384s 4 986.3558s 2 304.0615s a s 253.1715s 5 608.1508s 4 612.0035s 3 2810.0206s 2 1263.0411s -Factored form I:
323.0384ss 0.2822s 3.3356 s a s 253.1715ss 3.7444s 0.4025 s 2 1.7447s 3.3106
K gain 0.240738
-Polynomial form II:
1446.6572s 3 2352.2805s 2 37258.1160s s a s 253.1715s 5 608.1508s 4 612.0035s 3 1810.0206s 2 1263.0411s
604
-Factored form II:
1446.6572ss 5.9526s 4.3266 s a s 253.1715ss 3.7444s 0.4025 s 2 2.7447s 3.3106
K gain 29.498735
-Polynomial form III:
323.3786s 3 812.8197s 2 23.2311s s a s 253.1715s 5 608.1508s 4 612.0035s 3 2810.0206s 2 1263.0411s
-Factored form III:
323.3786s 3.6134 s 2 1.0999s 4.0463 s a s 253.1715ss 3.7444s 0.4025 s 2 1.7447s 3.3106 K gain 3.743437
605
M 1 0.228 q1 71.82 lb
W S
TO
ft 2
89.91lb
ft 2
I XX 13029Slug ft 2 S
I ZZ 106548Slug ft 2 S
I XZ 0Slug ft 2 S
Y 7.3201 ft YP 0.0000 ft
s
Yr 0.2663 ft
s
s2
L 100.6856s 2 LP 2.2395s 1 Lr 8.0015s 1 N 3.2271s 2
606
N T 0.0000s 2
N P 0.0548s 1 N r 0.1337s 1
n 1.8195 Rad D
Sec
D 0.4794 n
Plateral
P
lateral
Undefined
Undefined
TS 2.485s T R 0.267s TClateral Undefined 1
TClateral Undefined 2
TClateral Undefined 3
TClateral Undefined 4
Y 0.0000 ft a
s2 607
L 5.7141s 2 a
N 1.2773s 2 a
Flying qualities for condition 2-2, (Take off): -Roll mode performance checking:
LevelTR I Levelt I actual 38.34 deg -Spiral Dutch roll mode checking:
16 D
T2 Undefined S
T1
1.722s 2S
LevelS Stable Level D LevelIII
608
Leveln I D
Leveln D III D
609
Lateral directional flying qualities diagram
610
0.00
-1.00
n 1/s
-2.00
-3.00
Design Point
-4.00
-5.00
-6.00
611 j
rad/s
7.00
6.00
5.00
= 6.35
4.00
3.00
2.00
1.00
-7.00 0.00
Lateral-directional spiral Dutch roll mode flying qualities Condition1-1
Stabilizer trim diagrams Based on Dr. J. Roskam method’s
612
-3.0000 -21.1
1 m
C
45.0 43.9 42.8 41.7 40.6 39.4 38.3 37.2 36.1 35.0
-2.0000 -11.7 -2.2
-1.0000
613 1 L
C
3.0000
2.5000
2.0000
1.5000
1.0000
0.5000
7.2
X = 1.75
cg
26.1
= 45.0deg
e
43.9
42.8
41.7
40.6 cg X = 1.33
45.0
39.4
38.3 35.6
37.2
36.1
35.0
16.7
deg -40.00-30.00-20.00-10.000.00 0.0000 10.00 20.0030.00 40.00 50.00 0.0000
Stabilizer trim diagram Condition1-1 cg
[deg] [deg]
e
Current Config.
Hor. Tail (-) Hor. Tail (+) Stall Lines
1 m
C at X = 1.61 w c h i = 0.00 deg
-3.0000
-21.1
1 m
C
45.0 43.9 42.8 41.7 40.6 39.4 38.3 37.2 36.1 35.0
-2.0000 -11.7
-1.0000 -2.2
614 1 L
C
3.0000
2.5000
2.0000
1.5000
1.0000
0.5000
cg
X = 1.75
7.2
45.0
e
= 45.0deg
43.9
42.8
41.7
X = 1.33 40.6
cg
39.4
38.3 35.6
26.1
16.7
37.2
36.1
35.0
deg -40.00-30.00-20.00-10.000.00 0.0000 10.00 20.0030.00 40.00 50.00 0.0000
Stabilizer trim diagram Condition2-1 cg
[deg] [deg]
e
Current Config.
Hor. Tail (-) Hor. Tail (+) Stall Lines
1 m
C at X = 1.33 w c h i = 0.00 deg
-4.0000 -30.6
1 m
45.0 43.9 42.8 41.7 40.6 39.4 38.3 37.2 36.1 35.0
C -3.0000 -21.1 -11.7
-2.0000
615 1 L
C
3.0000
2.5000
2.0000
1.5000
1.0000
0.5000
cg
X = 1.75
26.1
16.7
= 45.0deg
e
43.9
42.8
41.7
cg 40.6 X = 1.33
39.4 45.0
38.335.6
37.2
36.1
35.0
deg -1.0000 -40.00-30.00-20.00-10.000.00 0.0000 10.00 20.0030.00 40.00 50.00 0.0000 -2.2 7.2
Stabilizer trim diagram Condition2-2 cg
[deg] [deg]
e
Current Config.
Hor. Tail (-) Hor. Tail (+) Stall Lines
1 m
C at X = 1.33 w c h i = 0.00 deg
Roll coupling Based on Dr. J. Roskam theory’s
616
If :
R1 Q1 0 I XZ 0 The angel of attack differential equation:
P1 C1P1 P1 M M q M M q P1 0 C1
I XX I ZZ S
S
IYY
S
Side slip deferential equation:
P1 D1P1 P1 N N r N N r P1 0 D1
IYY I XX S
S
I ZZ S
617
Differential equations are written for case of none rolling airplane:
M q M M 0 N r N N 0 n M
n N
M q M
2 M
N r N
Transfer system: As 4 Bs 3 Cs 2 Ds E 0
E|E 0
E c1P12 n 2 n 2 D1P12 4 n n P12 0
618
P1
L a a
LP
Result of calculations for condition 1-1:
n 2.5959 Rad
Sec
0.0706 n 3.6270 Rad
Sec
0.0509 P1 0.00 Rad
Sec
P1 0.40 Rad A
Sec
P1 Undefined B
619
1.0000
0.9000
n 1
/P 0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
n 1
/P
0.1000
620 1.0000
0.9000
0.8000
0.7000
0.6000
0.5000 YawDivergence
0.4000
0.3000
0.2000
0.1000
0.0000 0.0000
Roll coupling Diagram
Condition1-1
Roll Rate = 0.40 rad/s Roll Rate = 0.00 rad/s Current Configuration
Result of calculations for condition 2-1:
n 1.7239 Rad
Sec
0.0636 n 3.6270 Rad
Sec
0.0539 P1 0.89 Rad
Sec
P1 1.63 Rad
Sec
P1 4.45 Rad
Sec
A
B
621
1.0000
0.9000
n 1
/P 0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
n 1
/P
0.1000
622 1.0000
0.9000 YawDivergence
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000 0.0000
Roll coupling Diagram
Condition2-1
Roll Rate = 4.45 rad/s Roll Rate = 1.63 rad/s Roll Rate = 0.89 rad/s Current Configuration
Result of calculations for condition 2-2:
n 2.3645 Rad
Sec
0.0380 n 3.6270 Rad
Sec
0.0184 P1 0.67 P1 2.23 Rad
Sec
P1 4.46 Rad
Sec
A
B
623
1.0000
0.9000
n 1
/P 0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
n 1
/P
0.1000
624 1.0000
0.9000 YawDivergence
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000 0.0000
Roll coupling Diagram
Condition2-2
Roll Rate = 4.46 rad/s Roll Rate = 2.23 rad/s Roll Rate = 0.67 rad/s Current Configuration
V-n diagrams Based on MIL-A-8861
625
+1g stall speed:
Wgross 2.0 SW VS C N Max CN
Max
0.5
CL2 CD2 |C Max L Clean Max
Wgross 2.0 SW VS C N Max
0.5
0.5
CL2Max CD2 |C L CN Max Max V D 1.25V H n K gU deCL SW V 498Wgross
g 1.03 Kg 6.95 g 1.03
626
0.5
g
2.0Wgross SW CW CL
Derived gust velocity for design cruise speed : U de 50.0Up to 20Kft ,Then 66.67 0.000833 Altitude U de 25.0 Above50Kft Derived gust velocity for design dive speed : U de 25.0 Up to 20Kft ,Then 33.34 0.000417Altitude U de 12.5 Above50Kft Derived gust velocity for the design maximume gust intensity speed : U de 66.0Up to 20Kft , Then 84.67 0.000933Altitude U de 38.0 Above 50Kft
Result of calculations for condition1-1,W=24000lb,Alt=35000ft:
627
CN CN
Max
0.806
Max
0.848
VS 160.50Keas VS 156.46Keas VD 1500Keas VB 294.48 n 0.0080Keas 1 V VB n 0.0058Keas 1 V VC n 0.0029Keas 1 V VD n 0.0091Keas 1 V VB S
n 0.0065Keas 1 V VC S
628
n V V D
0.0033Keas 1 S
629
2000.00
eas
Speed,V keas 1500.00 1000.00
500.00
630 8.00
10.00
Load Factor
n
g
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
-8.00
0.00 -10.00
V-n Diagram, Condition 1-1: Alt 35000 ft W 24000lb
Result of calculations for condition 1-2:
0.806
CN
Max
CN
Max
0.848
VS 146.51Keas VS 142.83Keas V D 1500Keas V B 163.85Keas n 0.0085Keas 1 V VB n 0.0059Keas 1 V VC n 0.0030Keas 1 V VD n 0.0096Keas 1 V VB S
n 0.0067 Keas 1 V VC S
631
n 0.0033Keas 1 V VD S
632
2000.00
eas
Speed, V keas 1500.00 1000.00
500.00
633 8.00
10.00
Load Factor
n
g
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
-8.00
0.00 -10.00
V-n Diagram, Condition 1-2: Alt 42000 ft
W 20000lb
Result of calculations for condition 2-1:
CN CN
Max
0.806
Max
0.848
VS 181.27 Keas VS
176.71Keas
V D 1500Keas V B 341.31Keas n 0.0075Keas 1 V VB n 0.0056Keas 1 V VC n 0.0028Keas 1 V VD n 0.0083Keas 1 V VB S
n 0.0063Keas 1 V VC S
634
n 0.0031Keas 1 V VD S
635
2000.00
eas
Speed, V keas 1500.00 1000.00
500.00
636 8.00
10.00
Load Factor
n
g
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
-8.00
0.00 -10.00
V-n Diagram, Condition 2-1: Alt 5000 ft
W 30616lb
Result of calculations for condition 2-2:
0.806
CN
Max
CN
Max
0.848
VS 181.27 Keas VS 176.71Keas V D 1500Keas V B 339.10Keas n 0.0074Keas 1 V VB n 0.0056Keas 1 V VC n 0.0028Keas 1 V VD n 0.0082Keas 1 V VB S
n 0.0062Keas 1 V VC S
637
n 0.0031Keas 1 V VD S
638
2000.00
eas
Speed,V keas 1500.00 1000.00
500.00
639 8.00
10.00
Load Factor
n
g
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
-8.00
0.00 -10.00
V-n Diagram, Condition 2-2: Alt 2000 ft
W 30616lb
Lift distribution on lift producing surfaces Based on Dr. J. Roskam methods
640
100.00
90.00
Spanwise Station, % 80.00 70.00 60.00
50.00
40.00
30.00
20.00
641 1.00
0.75
0.50
0.25
0.00 0.00
1.25
Lift Coefficient
l
c
10.00
Wing lift distribution w L
C = 0.5067 Max. Airfoil Lift Total Lift Basic Lift Additional Lift
c
= 6.5500 rad-1
= 40.0 deg w|M=0 l
w C/4
AR = 3.04
w
S = 340.00 ft2
w
= 0.0 deg
w t
= 0.46
w
1
M = 0.229
100.00
90.00
Spanwise Station, % 80.00 70.00
60.00
50.00
40.00
30.00
20.00
642 6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00 0.00
6.50
Lift Coefficient
l
c
10.00
Horizontal tail lift distribution
h L
= 6.4500 rad-1 C = 4.8000 Max. Airfoil Lift Total Lift Basic Lift Additional Lift
c
h|M=0 l
= 40.0 deg
h C/4
AR = 11.14
h
S = 20.08 ft2
h
h t
= 0.0 deg
= 0.31
h
1
M = 0.229
100.00
90.00
Spanwise Station, % 80.00 70.00 60.00
50.00
40.00
30.00
20.00
643 1.25
1.00
0.75
0.50
0.25
0.00 0.00
1.50
Lift Coefficient
l
c
10.00
Vertical tail lift distribution
1
v Y
= 2.2327 rad-1 C = 1.0000 Max. Airfoil Lift Total Lift Basic Lift Additional Lift
c
v|M=0 l
= 40.0 deg
v C/4
AR = 1.99
v
S = 57.15 ft2
v
= 0.0 deg
v t
= 0.16
v
M = 0.229
Cost estimation Based on Dr. J. Roskam method’s
644
W AMPR : Alternate AMPR Weight : W AMPR log 10.1936 0.8645 log WTO W AMPR 11795 .1lb W AMPR
i 11 Wi i 1
W AMPR W wheels W ess WCool W fuelCell W els Wiae W Arm W api W apu Wtfo W whees 1268 .8lb W ess 107 .5lb WCool 0lb W fuelCell 512lb W els 452 .6lb Wiae 601lb W arm 350lb W api 254 .6lb
645
Wapu 155.6lb Wtfo 50lb W AMPR 9895.6lb Corection to alternate estimation 1899.2lb
RTDE Cost: Airframe engineering and design cost:
Caed MHRaed Re r
r
r
MHRaed 0.0396W AMPR 0.791VMax1.526 N RDTE 0.183 Fdiff FCAD r
Re r Re r 1989
CEF2005 CEF1989
Entered parameters:
W AMPR 9895.9lb VH
eas
1200Keas
N RDTE 4
646
Fdiff 1.0 FCAD 1.0 Year 2005 Re r
1989
20
US $ hr
Result of calculations:
MHRaed 3690692.7hr r
Re r 32.77
US $ hr
CEF 5.23 Caed 120.946 106US $ r
647
-Development, Support and Testing cost:
C DST 0.008325W AMPR 0.873V Max 1.89 N rdte 0.346 F diff CEF r
Entered parameters:
W AMPR 9895.9lb VH
eas
1200Keas
N RDTE 4 Fdiff 1.0 Year 2005 Results of calculations:
CEF 5.22748 CDST 142.782 106US $ r
648
-Market price of airplane:
AMP1989 Log 12.33421.0586LogWTO Result of calculation:
AMP 19.833106US $ -Engine price:
EP1989 Log 12.3044 0.8858Log TTO Result of calculation:
EP 4160927.7US $ -Flight test airplane cost:
C ft
Ce a Cman Cmat Ctool Cqc r
ar
r
Ce a Ce N e CP N P r
r
Cman MHRman Rm r
r
r
r
r
649
r
MHRman 28.984W AMPR 0.740VMax 0.543 N RDTE 0.792 Fmat CEF : r
Cmat 37.632W AMPR 0.689VMax 0.624 N RDTE 0.792 Fmat CEF r
Ctool MHRtool Rt r
r
r
MHRtool 4.0127W AMPR 0.764VMax 0.899 N RDTE 0.178 N r r
r
2005 r 1889 CEF CEF
Rt Rt r
1989
Cqc 0.13Cman r
r
Entered parameters:
Ce 4.161 r
CP 0 r
NP 0 K Avion 1 r
AMP 19.833106US $
650
0.066 F diff
N st 1 Year 2005 Rm Rt
r1989
r1989
10
US $ hr
US $ 13 hr
RDTEPhase N r 1 Result of calculations:
C man Manufacturing cost of flight test plane : r
41.757 10 6 US $ C mat Cost of material to manufacturing the flight test plane : r
27.859 10 6 US $ CEF 5.23 MHRtool Rt
r
r
3398718.2hr
21.30
US $ hr
651
C fta Cost of flight test airplane: r
219.420 106US $ MHRman 2548414.7hr r
C Avion 19.833106US $ r
Ctool tooling cost for manufacturing the flight test plane: r
72.396 106US $ Rm 16.39 r
Rt 21.30 r
US $ hr
US $ hr
Cqc Quality control cost for manufacturing flight test airplane: r
5.428106US $ Ce & a Cost of engines and avionics equipments: 71.981106US $
652
Flight test operations cost estimation:
C fto 0.001244W AMPR1.160VMax1.371N RDTE N st 1.281CEF Fdiff r
Fobs
Entered parameter:
Fobs 1.1 Result of calculations:
C fto 20.989 106US $ r
-Total RDTE Cost:
CRDTE Caed Cd r
strr
C fta Ctsf C pro C fin r
r
Ctsf Ftsf CRDTE r
C pro F pro CRDTE r
r
C fin F fin CRDTE r
r
653
r
r
Entered parameters:
Ftsf 1.00 F pro 0.000 r
F fin 0.0001 r
Result of calculations:
Ctsf 504.137 106US $ r
C pro 0$ r
C fin 0$ r
CRDTE 504.137 106US $ -Acquisition cost:
-Engineering. & Design Cost:
Caed MHRaed m
pro
Re m Caed
r
654
Re m Re m 1989 MHRaed
prog
CEF2005 CEF1989
0.0396W AMPR 0.791V Max1.526 N prg 0.183 Fdiff f CAD
Entered parameters:
Re m
1989
18
US $ hr
Result:
MHRaed
prog
Re m 29.49
12749564.8hr US $ hr
CEF 5.23 Caed Airframe engineering and design cost of program: m
255.084 106US $
655
-Airplane product program:
C apc
C e a
m
m
C int
m
C int
Fint N Pax N m
C man
m
prog
Rm
m
C mat
m
MHR man
MHR man Rm
m
m
C tool
N m C e m N e C P N P K Avion AMP
C e a
m
C man
m
prog
Rm
C man
r
m 1989
CEF2005 CEF1989
prog
C mat
r
C mat
m
C mat
prog
C mat
r
m
m
28.984W AMPR 0.740V Max 0.543 N prog 0.524 F diff
C mat
C tool
CEF1990
m
prog
C qc
CEF2005
C mat
C mat
m
m
37.632W AMPR 0.689V Max 0.624 N prog 0.792 F mat CEF
MHRtool
prog
Rt
m
C tool
656
r
m
Rt Rt m
m
CEF2005 1989 CEF 1989
Cqc 0.13Cman m
m
Entered parameters:
Rm Rt
10
m1989
m1989
12
N r 16 m
US $ hr
US $ hr
plane month
N Pax 1 Fint 1'000'000
US $ Plane
Result of calculations:
Cman Labor cost in manufacturing N m airplane: m
Cman 1411.480 106US $ m
MHRman
prog
88691564hr
657
Cmat Cost of materials while manufacturingN m plane: m
Cmat 5929.165US $ m
C Avion 19.833106US $ m
CEF 5.23 Tooling cost for manufacturing N-m Airplanes:
195.582 106US $ MHRtool
prog
Rm 16.39 m
Rt 19.66 m
13629016.3hr US $ hr
US $ hr
Cqc quality control cost for manufacturing N m airplaines m
Cqc 183.492 106US $ m
Cint Cost of airplane interior : m
658
Capc Cost of airplane program production cost : m
Capc 7745.353106US $ m
-Test operation cost:
Cf
tom
N mCOps t pft F ftoh hr
-Need to calculating operating cost: -Program cost of fuel, oil and lubricants:
C pol FOLW f
Used
FP N mission N serv N yr FD
Entered parameters:
tmis 0.75hr U ann
flt
104hr
FP 18
US $ gallon
FD 7.21
lb gallon
659
FOL 1.005 N yr 1 Nm 1 N RDTE 4 LR 0.10 105 hr 1 Result of calculations:
N missions 139
1 Year
N Serv 1 N res 0.1 N loss 0 N acq 1 CPOL Fuel and oil costs 1.722 106US $
660
Program cost of direct personnel:
CPERSDIR CCrewpt Cmpersidir CCrewpr N Ser N Crew RCr PayCrewOHRCrew N yr Cmpersoder N Serv N yrU annflt MHR flthr Rm CEF2005 Rm Rm m L 2005 ml 1989 CEF1989 Entered option and estimations:
U ann
flt
104.0hrs
N crew 15 RCr 1 Paycrew 70'000 Ccrew
Ccrew
pr
pr
US $ Year
Program cost of aircraft : 2.835106US $
661
mL
Cmpersdir Program cost of direct maintenece personnel : Cmpersdir 0.00158725106US $ CPERSIDIR Program cost of direct personnel : CPERSIDIR 2.836 106US $ Rm
ml
US $ 73.73 hr
-Consumable material cost:
CCONMAT N Serv N yrU ann MHR fthr RConmat flt
-Entered parameters:
U ann
flt
104hrs
N yr 1 N serv 1 MHR flhr 0.5h RCommat 6.50
US $ hr
662
CEF 5.22748 Result of calculations:
RConmat 10.65
US $ hr
CCONMAT Progra cost of consumable materials : CCONMAT 10.65
US $ hr
-Total operation cost:
CPERSIND Program cost of indirest personnel cot : CPERSIND 0$ CSPARES Program cost of spare: CSPARES 0$ CDEPOT Program cost of depot : CDEPOT 0$ CMISC Cost of misalliances items : CMISC 0$ 663
COPS 4.561106US $ COPS US $ 877.100 hr hr Result of test cost calculations:
t pft 50hr F ftoh 1 C fto 0.044 106US $ m
-Total manufacturing and acquisition cost:
F pro 0.1 m
F fin 0.1 m
CRDTE 504.137 106US $ N m 3000
664
Results of calculations:
C pro Manufacturing profit cost : C pro 888.942 106US $ C fin Cost to finance the manufacturing : m
C fin 8.008106US $ m
CMAN Total manufacturing cost : CMAN 8008.489 106US $ C ACQ Acquisition Cost : C ACQ 8809.338106US $ AEPAirplane estimated price per airplane: AEP 3.104 106US $ -Life cycle and disposal cost:
LCC CRDTE C ACQ COPS CDISP CDISP FDISP LCC
665
Result of calculations:
CDISP Disposal cost : CDISP 9.327 106US $ LCC 327.363106US $
666
Cost estimations, -RTDE Costs:
Caed : r
120.946 million US$
Cost of airframe engineering and design in research phase
Cdst : r
142.782 million US$
Cost of development, support and testing in research phase
AMP : 19.833 million US$ Aircraft market price EP : 4.160 million US$ Engine price Cman : r
41.757 million US$
Manufacturing cost of flight test airplanes Cmat : r
27.859 million US$
Cost of materials to manufacturing flight test planes
MHRtool : r
3398718.2 hr
Tooling man-hours for research phase Rt : r
21.30 Tooling rate for research phase C ft : ar
US$ hr
219.420 million US$
Flight test airplanes cost
667
MHRman : r
2548414.7 hr
Manufacturing man-hours for Research phase C Avion : r
19.833 million US$
Cost of avionics system in research phase Ctool : r
Tooling cost for manufacturing The flight test airplanes Rm :
72.396 million US$
r
Manufacturing rate for research phase Rt :
16.39
US$ hr
21.30
US$ hr
r
Tooling rate for research phase
Cqc
r
Quality control cost for manufacturing flight test planes
Ce & a 
r
Cost of engines and avionics Equipment in research phase CRTDE :
5.428 million US$
71.981 million US$
504.137 million US$
Total RDTE cost
668
-Acquisition costs:
MHRaed
prog
:
Man-hour of airframe engineering and design cost of program Re :
12749564.8 hr
Rate of engineering for manufacturing phase Caed :
29.49
m
m
Cost of engineering and design For manufacturing phase Cmat : m
Cost of material While manufacturing N m plane
Cman : m
Labor cost in manufacturing N m airplane
C Avion : m
Cost of avionics systems for manufacturing phase Ctool : m
Tooling cost or manufacturing N m airplane
MHRtool
prog
US$ hr
255.084 million US$
5929.165 million US$
1411.480 million US$
19.833 million US$
195.582 million US$
:
Tooling man-hour for manufacturing phase
13629016.3 hr
669
Rm : m
Rate of manufacturing in Manufacturing phase Rt :
16.39
US$ hr
Rate of tooling in manufacturing phase Cqc :
19.66
US$ hr
m
m
Quality control cost for manufacturing N m Plane
Cint : m
Cost of airplane interior Capc : m
Airplane program production cost
183.492 million US$
1.639 million US$
7745.353 million US$
670
Operating costs:
C pol :
1.722 million US$
Fuel and oil price CPERSDIR :
2.836 million US$
Program cost of direct personnel
CCrew
pr
2.835 million US$
Program cost of airplanes crew Cm : persdir
Program cost of direct maintenance personnel Rm : ml
CCONMAT
0.00158725 million US$
73.73
US$ hr
Program cost of consumable materials
49841 US$
COPS COPS hr
4.561 million US$
C fto
877.100
US$ hr
m
Cost of flight test operations during the manufacturing phase
0.044 million US$
671
Program cost:
CRDTE CPRO
504.137 million US$ 888.942 million US$
Manufacturing profit
C fin
m
Cost to finance the manufacturing
CMAN
8.008 million US$
8008.489 million US$
Total manufacturing cost
C ACQ
8809.338 million US$
Acquisition Cost
Life Cycle Cost and disposal cost:
CDISP
9.327 million US$
Disposal cost
LCC 9327.363 million US$ Life Cycle Cost
672