Aircraft and Helicopter Design

7/26/2019 Aircraft and Helicopter Design

1/62

Sec t ion 9

A I R C R A F T A N D H E L IC O P T E R D E S IG N

Vehic le De f i n i t i ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2

Aerodynam ics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-7

Per f o rmance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-38

He l i cop t e r Des ign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-47

B ib l i og raphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-62


2/62

9 - 2 A I R C R A F T A N D H E L I C O P T E R D E S I G N

V e h i c l e D e f in i t io n s

G e o m e t r y

T h e f o l l o w i n g f ig u r e s a n d f o r m u l a s p r o v i d e a n i n t r o d u c t io n o n g e o m e t r i c r e-

l a ti o n s h i p s c o n c e r n i n g v e h i c l e p h y s i c a l d i m e n s i o n s . T h e s e d i m e n s i o n s a r e u s e d

t h r o u g h o u t th i s s e c t i o n .

WING

45

DEG

HORIZONTAL

TAIL

( ~ / ~)~ . I . . . . . 18F T . . . ~ '1 1 CHoRDROOT . TAILPAN24T

~ ~ _ _ ~ ] ~ ~ T?MAFCT I~ " 9 FT

C/4 SW EEP / M A ~ F ~ L ~ b . . . 1

= ~ - - \ , , , 'T~ iL;~ffM '- - ' - I- , ' I4.SFTI -

/ ~ " 18FT T IP CHORD

LEoS~EEEP " ~ /

--=~ 5.4 FT ~-

TIP CH OR D

TIP CHOR D

.=~i 4=_~.~/S VERTICALTAIL

I VERTICAL / / F " f f

COCKPIT ~ TAILARM ~ MAC / TAILSPA N /

PILOT VISION ~ 14 F A , -

T 9 FT HE f G HT

13 D E G - ' ~ 1 ~ 9 ; T 18 FT

, '

I u OVERA LLLENGTH60 FT m

I WING SPAN 4.2 FT

I I FOLDEDSPA N 33 FT ---'

I

/ VERTICAL k i I

ITAIL DIHEDRAL~ I

.?, ,O D E G ~ , ~ /

i I - - i1,

/ , ~ \~ ~ h" 4 . , WING DIHEDRAL

J ~ ~ -3 DEG

HORIZONTAL ~ ~'% ~ 40 - 45 DEG

TAIL DIHEDRAL

L " " OVER SIDE VISIONANGLE

-3 DEG ~ D I WHEELT RA CK l ~

/ 11 FT /


3/62

AIRCRAFT AND HELICOPTER DESIGN

Vehic le De f in i t ions , cont inued

9-3

Geometry Unit Wing H-Tail V-Tail

LE sweep angle deg 30.0 45.0 45.0

c/4 sweep angle deg 23.1 42.2 33.6

Reference area ft2 491.4 162 63 each

Projected span ft 42 24 9

m.a.c, ft 12.83 7 7.42

Aspect ratio AR 3.59 3.55 1.28

Taper ratio L 0.3 0.5 0.4

Thickness ratio t / c 0.05 0.04 0.03

Dihedral F - 3 deg - 3 deg 70 deg

Airfoil MOD NACA 65A MOD NACA 65A MOD NACA 65A

Tail volume V n/a 0.462 0.28

I I I

where

La = wheel base

W = wheel track

H = he ight c.g. to gro und reference

/3 = tip bac k angle

0 = tail down angle

ot = turn over angle

Gear in normal static position

Use most aft c.g. for/~, keep/~ > 0

Use most forward c.g. for ol

Use l andin g weight c.g. for 0


4/62

9 -4 A I R C R A F T A N D H E L I C O P T E R D E S I G N

V e h i c l e D e f i n i t i o n s , c o n t i n u e d

G e o m e t r y , c o n t i n u e d

The following definitions and equations apply to trapezoidal planforms, as

illustrated here.

r S ~ / m ( ~ r'I 1

_ I .

0,4

~ = b / 2 =

" ~ b

~ Y

,p,, : E \ /

r A XE ~ r _ S f C

. r ~ ,

- I

x

C o = overall length of zero-taper-ratio planform havin g same leading- and

trailing-edge sweep as subject planf orm

(~ = ratio of chordwise position of lead ing edge at tip to the root chord length

= (b/2 ) tan

A L E ( 1 / C r )

7,. 72 = span stations of bou nda ry of arbitrary increment of win g area

Am, A. = sweep angles of arbitrary chordwi se locations

rn, n = non dime nsi onal chordwise stations in terms of C

G e n e r a l

y

7 =

b / 2

~. = C , / C r

C = C r [ 1 - 7 ( 1 -

X)]

tan A = 1 tan E

XLE = (b /2)7 tan ALE

b 1 - aZ

= - tan ALE + C t = C r - -

2 1-a

A r e a

b 2 b b

S -- AR -- 2 Cr(1 + X ) ---- - ~ C o ( 1 - a ) ( 1 - X )

CoZ(1 - a)(1 - Z 2)

tan ALE

b -q l

A S = E C r [ 2 - ( 1 - ) v ) ( 7 1 - 0 2 ) ] 7 2


5/62

AIRCRAFT AND HELICOPTER DESIGN 9-5

V e h i c l e De f i n i t i o n s , c o n t i n u e d

A s p e c t R a t i o

A R - -

b 2

S

2 b 4 ( 1 - X )

Cr(l q- )~)

( 1 - - a ) ( 1 + X ) t a n A L E

C u t o u t F a c t o r

a D

t a n A T E

Cr(1 -

~) 4( 1 - )~)

- - - 1 - 1 -

t a n

A L E ( b / 2 ) t a n A L E A R ( 1 + X ) ta n A L E

S w e e p A n g l e s

1 C r 1 -

X ) 4 ( 1 - X )

t a n

A L E : - -

t a n

A T E - -

a ( b / 2 ) ( 1 - a ) A R ( 1 + X )( 1 - a )

Co(1 - X ) A R ( 1 q - ) ~ ) t a n

Ac/4 -1-

( 1 - ~ , ) 4 t a n

A c / 4

b / 2 A R ( 1 + X ) 3 + a

t a n A m = t a n A L E [ 1 - - (1 - a ) m ]

t a n A m = t a n A L E - - ~ --~ ] - ~

1

c o s A m = a n A L E , - , { 1 ) 2

~LE "[- [1 - - ( 1 - - a ) m ] 2

M e a n A e r o d y n a m i c C h o r d m .a . c . )

2 f b /2

2 ( )v2 )

e = ~ , o C 2 d y = ~ C r 1 + 1 ~ - ~

= 5 C o ( 1 - a ) +

1

4 S ~ X

2 C r x C ~ t

= -~ Cr + G Cr-7-

2

f b / 2 1 - - ( ( J / C r )

rl = S . , o C y d y - - 1 - )v - -

1

3 \ l + X /

X L E = y t a n A L E


6/62

9-6 AIRCRAFT AND HELICOPTER DESIGN

V e h i c l e D e f i n i t i o n s , c o n t i n u e d

Geom etry , continued

R o o t C h o r d

C r - -

S 4 ( b / 2 )

( b / 2 ) ( 1 + )~) A R ( 1 + )~)

C h o r d w i s e L o c a t i o n o f L e a d i n g E d g e a t T ip

C r ~ - m

AR

( 1 + ) 0 t a n A L E

4

Force-Velocity

A i r p l a n e A x i s S y s t e m

. k . ~ , . " I L r- x r , T r

W I N O ~ a - . 1 ~ - - " . - -. -- -- - I F L I G H T

'~tw

V w m

F orce M om en t L inea r Ang . o f

Ax is along abo ut ve loci ty An g. disp. A ng. vel . Inertia attack

X Fx L u q~ p Ix a

Y F y M v 0 q l y

Z F z N w g t r I z f i


7/62

A I R C R A F T A N D H E L I C O P T E R D E S I G N 9 -7

A e r od y n a m ic s

Basic Aer od y nam ic Relationships

A R = a s p e c t r a t io = b2 /S

C o = d r a g c o e f f i c i e n t = D / q S = C o o + C ol

CDi = i n d u c e d d r a g c o e f f i c i e n t = CeL/(rcARe)

C L = l i f t c o e f f i c i e n t =

L / q S

Ct

= r o l l i n g - m o m e n t c o e f f i c i e n t = r o l l i n g

m o m e n t / q b S

Cm

= p i t c h i n g - m o m e n t c o e f f i c i e n t = p i t c h i n g

m o m e n t / q c S

C n = y a w i n g - m o m e n t c o e f f i c i e n t = y a w i n g m o m e n t / q b S

Cy = s i d e - f o r c e c o e f f i c i e n t = s i d e f o rc e /qS

D = d r a g = CDqS

d = e q u i v a l e n t b o d y d i a m e t e r = ~ / 4A M A x /Y r

F R = f i n e n e s s r a t i o =

/ d

L = l i f t =

C L q S

M = M a c h n u m b e r =

V / a

P = p l a n f o r m s h a p e p a r a m e t e r = S/be

q = d y n a m i c p r e s s u r e = ( P V 2 ) =

(pa2M2)

R n = R e y n o l d s n u m b e r =

Vgp / t z

Ro = d /2

= e q u i v a l e n t b o d y r a d iu s

(t/C)RMS = r o o t - m e a n - s q u a r e t h i c k n e s s r a t io

1

i 1

[b /2

2 d y ] ~

(t/C)RMS

~-

b / 2 - r ~ r ( t /c )

V = t r u e a i r s p e e d = V e /ff 1/2

= c h o r d w i s e l o c a t i o n f r o m a p e x to C / Z ( e q u i v a l e n t t o c h o r d w i s e l o c a -

t i o n o f c e n t r o i d o f a r e a )

= - c x + y

Sjo

)LE = c h o r d w i s e l o c a t i o n o f l e a d i n g e d g e o f m . a . c .

XLE ~ X -- --

2

I = s p a n w i s e l o c a t i o n o f C ( e q u i v a l e n t t o s p a n w i s e l o c a t i o n o f c e n t r o i d o f

a r e a )

2

f b / 2

= -- cy dy

S u o

/~ = ~ - 1 ( s u p e r s o n i c ) , ~ /1 - - M 2 ( s u b s o n i c )

= c o m p l e m e n t t o w i n g s w e e p a n g l e = 9 0 d e g - -A L E

O = n o n d i m e n s i o n a l s p a n s t a t i o n =

y / ( b / 2 )

)~ = t a p e r r a t io , t i p - t o - r o o t c h o r d = C t /C r

a = a i r d e n s i t y r a t i o = P/Po

v = k i n e m a t i c v i s c o s i t y =

# / p


8/62


Sym bols

a

A MA X

a . c .

b

C

CDO

c.g.

c.p.

Cr

Ct

d

(dA/dx )AFT =

e =

g =

i

KBODY

K L E

=

S, SREF =

SEXP

T =

t =

t / c

v ~ =

X

y =

Og

Ol Lo

F =

6 =

y =

A =

ALE ~---

A T E

A H L

#

P

R

Aerody nam ics , continued

= speed of sound

= max imu m cross-sectional area

= aerodynamic center

= wing span a

= chord a

= mean aerodyna mic chord (m.a.c.)

= drag coefficient at zero lift

= center of gravity

= center of pressure

= root chord a

= tip chord a

= diameter

slope of aft end of configuration distribution curve

Oswal d (wing) efficiency factor

acceleration due to gravity

angle of incidence

body wave-drag factor

wing shape factor

characteristic lengtha

reference area a

exposed pl anform area

temperature

airfoil max imu m thickness at span station y

airfoil thickness ratio (parallel to axis of sy mmetry)

equivalent velocity

general chordwise location, parallel to plane of symmetrya

general spanwise location, perpendicular to plane of s ymmetrya

angle of attack, chord plane to relative wind

angle of attack for zero lift

dihedral angle

surface deflection angle

ratio of specific heats

sweep-back angle

wing leading-ed ge sweep anglea

wing trailing-edge sweep anglea

flap-hinge-line sweep angle

= coefficient of absolu te viscosity

= density

= specific gas const ant

aDefined in figure appearing on page 9-4.


9/62

A I R C R A F T A N D H E L I C O P T E R D E S I G N 9 - 9

A e r o d y n a m i c s , c o n t in u e d

S p e e d o f S o u n d v s T e m p e r a tu r e

2 0 0

1 8 0

1 6 0

1 5 0

1 4 0

1 2 0

1 0 0

8 0

4 0

2 0

0

2 0

4 0

5 0

6 0

8 0

1 0 0

- - S p e e d o f s o u n d ( a ) i n

d r y a i r

= ~

w h e r e

1 , = 1 . 4 a n d

- - T = a b s o l u t e t em p e ra t u r e in R .

/

/

/-

J

/

/ -

J i i

9 2 0 9 6 0 1 0 0 0 1 0 4 0

6p 6~o

5 ~ o

I 1 I I

1 0 8 0 1 1 2 0 t 1 6 0 1 2 0 0

7 0 0 7 5 0 8 0 0

I i i

6~o 760

S P E E D O F S O U N D

/

I

1 2 4 0 f t / s

8 5 0 m p h

i

7 5 0 k n o t s

D y n a m ic P r e s su r e (q ) v s M a ch N u m b e r

1 0 , 0 0 0

8 0 0 0 - -

6 O O O

5 0 0 0

4 0 0 0 - -

2 0 0 0

1 0 0 0

~ L, 8 0 0 - -

. a 6 0 0 - -

5 0 0

u J 4 0 0 - -

E

U )

0 ~

" ' 2 0 0

n -

o -

.

G I

///Y// I/b

@ I , ~. I _ ~ I , / i

7 X . V ~ I I ~ , I

,o o i i l , % ~ - ~ i ~ ' J i

:o '7 ;, i ~ ' j

- / i , < / z ' J / / / / ,

,o l i i l ,

2 0

/

o Y / / / / / / / / / / I / , ,

0 .1 0 .2 0 . 4 0 . 5 0 . 6 0 . 8 1 . 0 2 4. 5 6 8 1 0

M A C H N U M B E R


10/62

9 - 1 0 A I R C R A F T A N D H E L I C O P T E R D E S I G N

A er o d y n a m ics , co n tin u ed

Standard A tm osphere

S t a n d a r d a t m o s p h e r e i s a h y p o t h e t i c a l v e r t ic a l d i s tr i b u t i o n o f a t m o s p h e r i c t e m -

p e ra tu r e, p r e s s u r e , a n d d e n s i t y w h i c h , b y i n t e r n a t i o n a l o r n a t i o n a l a g r e e m e n t , i s

t a k e n t o b e t h e r e p r e s e n t a t iv e o f t h e a t m o s p h e r e f o r th e p u r p o s e o f a l ti m e t e r c a l c u -

l a t io n s , a ir cr aft d e s i g n , p e r f o r m a n c e c a l c u l a t i o n s , e t c . T h e i n t e r n a t i o n a l l y a c c e p t e d

s t an d a r d a t m o s p h e r e i s c a l l e d t h e I n t e r n a t io n a l C i v i l A v i a t i o n O r g a n i z a t i o n ( IC A O )

S t a n d a rd A t m o s p h e r e o r t h e I n t er n a t io n a l S t an d a r d A t m o s p h e r e ( I S A ) .

T e m p e r a t u r e p , p x 1 0 4 v x 1 0 4 S o- K n o t s

R K

i n .

H g s l u g l f t 3 f t 2 s

( P / P o ) ( p / p o ) a 112 q / M 2 a a o I /2

0 5 1 8 . 7 2 8 8 . 2 2 9 . 9 2 2 3 . 7 7 1 . 5 7 6 1 . 0 0 0 0 t . 0 0 0 0 1 . 0 0 0 0 1 4 8 3 6 6 1 . 3 6 6 1 . 3

1 , 0 0 0 5 1 5 .1 2 8 6 . 2 2 8 . 8 6 2 3 .0 8 1 . 6 1 4 0 . 9 6 4 4 0 . 9 7 1 1 0 . 9 8 5 4 1 4 3 0 6 5 9 . 0 6 4 9 . 4

2 , 0 0 0 5 1 1 . 6 2 8 4 .2 2 7 . 8 2 2 2 . 4 1 1 . 6 53 0 . 9 2 9 8 0 . 9 4 2 8 0 . 9 7 1 0 1 3 7 9 6 5 6 . 7 6 3 7 . 7

3 , 0 0 0 5 0 8 . 0 2 8 2 . 2 2 6 . 8 2 2 1 . 7 5 1 . 6 9 4 0 . 8 9 6 2 0 . 9 1 5 1 0 . 9 5 6 6 1 3 2 9 6 5 4 . 4 6 2 6 . 0

4 , 0 0 0 5 0 4 . 4 2 8 0 . 2 2 5 . 8 4 2 1 .1 1 1 .7 35 0 . 8 6 3 7 0 . 8 8 8 1 0 . 9 4 2 4 1 2 8 0 6 5 2 .1 6 1 4 .5

5 , 0 0 0 5 0 0 . 9 2 7 8 . 3 2 4 . 9 0 2 0 . 4 8 1 . 7 7 8 0 . 8 3 2 0 0 . 8 6 1 7 0 . 9 2 8 2 1 2 3 4 6 4 9 .8 6 0 3 . 1

6 , 0 0 0 4 9 7 . 3 2 7 6 . 3 2 3 . 9 8 1 9 .8 7 1 . 82 3 0 . 8 0 1 4 0 . 8 3 5 9 0 . 9 1 4 2 1 1 8 8 64 7 . 5 5 9 1 . 9

7 , 0 0 0 4 9 3 . 7 2 7 4 . 3 2 3 . 0 9 1 9 . 2 7 1 . 8 69 0 . 7 7 1 6 0 . 8 1 0 6 0 . 9 0 0 3 1 1 4 4 6 4 5 . 2 5 8 0 . 9

8 , 0 0 0 4 9 0 . 2 2 7 2 . 3 2 2 . 2 2 1 8 . 68 1 . 9 1 6 0 . 7 4 2 8 0 . 7 8 6 0 0 . 8 8 6 6 1 1 0 1 6 4 2 . 9 5 7 0 . 9

9 , 0 0 0 4 8 6 . 6 2 7 0 . 3 2 1 . 3 9 1 8 .1 1 1 . 96 5 0 . 7 1 4 8 0 . 7 6 2 0 0 . 8 7 2 9 1 0 6 0 6 4 0 . 5 5 5 9 .1

1 0 , 0 0 0 4 8 3 .0 2 6 8 . 3 2 0 . 5 8 1 7 .5 5 2 . 0 1 5 0 . 6 8 7 7 0 . 7 3 8 5 0 . 8 5 9 3 1 0 1 9 6 38 . 1 5 4 8 . 3

1 1 , 0 0 0 4 7 9 . 5 2 6 6 . 4 1 9 . 7 9 1 7.0 1 2 . 0 6 7 0 . 6 6 1 4 0 . 7 1 5 5 0 . 8 4 5 9 9 8 0 . 5 6 3 5 .8 5 3 7 . 8

1 2 , 0 0 0 4 7 5 . 9 2 6 4 . 4 1 9 .0 3 1 6 . 4 8 2 .1 2 1 0 . 6 3 6 0 0 . 6 9 3 2 0 . 8 3 2 6 9 4 2 . 8 6 3 3 . 4 5 2 7 . 4

1 3 , 0 0 0 4 7 2 . 3 2 6 2 . 4 1 8 . 2 9 1 5 .9 6 2 . 1 7 7 0 . 6 1 1 3 0 . 6 7 1 3 0 . 8 1 9 3 9 0 6 . 3 6 31 .1 5 1 7 . 1

1 4 , 0 0 0 4 6 8 . 8 2 6 0 . 4 1 7 . 5 8 1 5 . 4 5 2 . 2 3 4 0 . 5 8 7 5 0 . 6 5 0 0 0 . 8 0 6 3 8 7 0 . 9 6 2 8 . 7 5 0 6 . 9

1 5 , 0 0 0 4 6 5 . 2 2 5 8 . 4 1 6 . 8 9 1 4 .9 6 2 . 2 9 4 0 . 5 6 4 3 0 . 6 2 9 2 0 . 7 9 3 3 8 3 6 . 6 6 2 6 . 3 4 9 6 . 8

1 6 , 0 0 0 4 6 1 . 6 2 5 6 . 4 1 6 . 2 2 1 4 . 4 7 2 . 3 5 5 0 . 5 4 2 0 0 . 6 0 9 0 0 . 7 8 0 3 8 0 3 . 5 6 2 3 . 9 4 8 6 . 8

1 7 , 0 0 0 4 5 8 .1 2 5 4 . 5 1 5 . 5 7 1 4 .0 1 2 . 4 1 9 0 . 5 2 0 3 0 . 5 8 9 2 0 . 7 6 7 6 7 7 1 . 3 6 2 1 . 4 4 7 7 . 0

1 8 , 0 0 0 4 5 4 . 5 2 5 2 . 5 1 4 . 9 4 1 3.5 5 2 . 4 8 5 0 . 4 9 9 4 0 . 5 6 9 9 0 . 7 5 4 9 7 4 0 . 3 6 1 9 . 0 4 6 7 . 3

1 9 , 0 0 0 4 5 0 . 9 2 5 0 . 5 1 4 . 3 4 1 3 .1 0 2 . 5 5 3 0 .4 7 9 1 0 . 5 5 1 1 0 . 7 4 2 4 7 1 0 . 2 6 1 6 . 6 4 5 7 . 8

2 0 , 0 0 0 4 4 7 . 4 2 4 8 . 6 1 3 . 7 5 1 2 . 6 6 2 . 6 2 4 0 . 4 5 9 5 0 . 5 3 2 8 0 . 7 2 9 9 6 8 t . 2 6 1 4 . 1 4 4 8 . 2

2 1 , 0 0 0 4 4 3 . 8 2 4 6 . 6 1 3 . 1 8 1 2 .2 4 2 . 6 9 6 0 . 44 0 6 0 . 5 1 5 0 0 . 7 1 7 6 6 5 3. 1 6 1 1 . 7 4 3 9 .0

2 2 , 0 0 0 4 4 0 . 2 2 4 4 . 6 1 2 . 6 4 1 1 .8 3 2 . 7 7 2 0 . 4 2 2 3 0 . 4 9 7 6 0 . 7 0 5 4 6 2 6 .1 6 0 9 . 2 4 2 9 . 7

2 3 , 0 0 0 4 3 6 . 7 2 4 2 . 6 1 2 .1 1 1 1 .4 3 2 . 8 5 0 0 . 4 0 4 6 0 . 4 8 0 7 0 . 6 9 3 3 5 9 9 . 9 6 0 6 . 8 4 2 0 . 7

2 4 , 0 0 0 4 3 3 . 1 2 4 0 . 6 1 1 . 6 0 1 1 . 0 3 2 . 9 3 2 0 . 3 8 7 6 0 . 4 6 4 2 0 . 6 8 1 3 5 7 4 . 6 6 0 4 . 3 4 1 1 . 7

Po = s t a n d a r d p r e s s u r e a t s e a l e v e l 2 9 . 9 2 i n . H g , 1 4 . 7 0 l b / in 2 , 1 . 0 1 3 1 0 5 N / m 2 o r P a

Po = s t a n d a r d d e n s i t y a t s e a l e v e l 2 3 . 7 7 x 1 0 - 4 s l u g s / f t 3 , 1 . 2 2 5 x 1 0 3 k g / m 3

= t e m p e r a t u r e r a t i o

ct = d e n s i t y r a t i o

a = s p e e d o f s o u n d

( c o n t i n u e d )


11/62

A I R C R A F T A N D H E L I C O P T E R D E S I G N


9 - 1 1

Temperature p, p, 104 v, 104 8 tr Knots

R K in. Hg slug/ft3 ft2s

( P / P o ) ( P / P o ) c rl /2 q / M 2 a a a t/2

25,000 429.5 238.6 11.10 1 0 . 6 5 3.016 0.3711 0.4481 0.6694 550.2 601.8 402.8

26,000 426.0 236.7 1 0 . 6 3 10.28 3.103 0.3552 0.4325 0.6576 526.6 599.3 394.1

27,000 422.4 234.7 1 0 . 1 7 9.918 3.194 0.3398 0.4173 0.6460 503.8 596.8 385.5

28,000 418.8 232.7 9.725 9.567 3.287 0.3250 0.4025 0.6344 481.8 594.2 377.0

29,000 415.3 230.7 9.297 9.225 3.385 0.3107 0.3881 0.6230 460.7 591.7 368.6

30,000 411.7 228.7 8.885 8.893 3.486 0.2970 0.3741 0.6117 440.2 589.2 360.4

31,000 408.1 226.7 8.488 8.570 3.591 0.2837 0.3605 0.6005 420.6 586.6 352.3

32,000 404.6 224.8 8.106 8.255 3.700 0.2709 0.3473 0.5893 401.6 584.0 344.2

33,000 401.0 222.8 7.737 7.950 3.813 0.2586 0.3345 0.5783 383.4 581.5 336.3

34,000 397.4 220.8 7.382 7.653 3 . 9 3 1 0.2467 0.3220 0.5674 365.8 578.9 328.5

35,000 393.9 218.8 7.041 7.365 4.053 0.2353 0.3099 0.5567 348.8 576.3 320.8

36,000 390.3 216.8 6.712 7.086 4.181 0.2243 0.2981 0.5460 332.6 573.6 313.2

36,089 390.0 216.7 6.683 7.061 4.192 0.2234 0.2971 0.5450 331.2 573.4 312.5

37,000 390.0 216.7 6.397 6.759 4.380 0.2138 0.2844 0.5332 317.0 573.4 305.7

38,000 390.0 216.7 6.097 6.442 4.596 0.2038 0.2710 0.5206 302.1 573.4 298.5

39,000 390.0 216.7 5.811 6.139 4.822 0.1942 0.2583 0.5082 287.9 573.4 291.4

40,000 390.0 216.7 5.538 5.851 5.059 0.1851 0.2462 0.4962 274.4 573.4 284.5

41,000 390.0 216.7 5.278 5.577 5.308 0.1764 0.2346 0.4844 261.5 573.4 277.8

42,000 390.0 216.7 5.030 5.315 5.570 0.1681 0.2236 0.4729 249.2 573.4 271.2

43,000 390.0 216.7 4.794 5.066 5.844 0.1602 0.2131 0.4616 237.5 573.4 264.7

44,000 390.0 216.7 4.569 4.828 6.132 0.1527 0.2031 0.4507 226.4 573.4 258.4

45,000 390.0 216.7 4.355 4.601 6.434 0.1455 0.1936 0.4400 215.8 573.4 252.3

46,000 390.0 216.7 4.151 4.385 6.750 0.1387 0.1845 0.4295 205.7 573.4 246.3

47,000 390.0 216.7 3.950 4.180 7.083 0.1322 0.1758 0.4193 196.0 573.4 240.4

48,000 390.0 216.7 3.770 3.983 7.432 0.1250 0.1676 0.4094 186.8 573.4 234.7

49,000 390.0 216.7 3.593 3.797 7.797 0.1201 0.1597 0.3996 178.0 573.4 229 .1

50,000 390.0 216.7 3.425 3.618 8.181 0.1145 0.1522 0.3902 169.7 573.4 223.7

51,000 390.0 216.7 3.264 3.449 8.584 0.1091 0.1451 0.3809 161.7 573.4 218.4

52,000 390.0 216.7 3 . 1 1 1 3.287 9.007 0.1040 0.1383 0.3719 15 4 . 1 573.4 213.2

53,000 390.0 216.7 2.965 3.132 9.450 0.0991 0.1318 0.3630 146.9 573.4 208.1

54,000 390.0 216.7 2.826 2.986 9.916 0.0944 0.1256 0.3544 140.0 573.4 203.2

55,000 390.0 216.7 2.693 2.845 10.40 0.0900 0.1197 0.3460 133.4 573.4 198.4

56,000 390.0 216.7 2.567 2.712 1 0 . 9 2 0.0858 0.1141 0.3378 127.2 573.4 193.7

57,000 390.0 216.7 2.446 2.585 1 1 . 4 5 0.0818 0.1087 0.3298 121.2 573.4 189.1

58,000 390.0 216.7 2.331 2.463 12.02 0.0779 0.1036 0.3219 1 1 5 . 5 573.4 184.6

59,000 390.0 216.7 2.222 2.348 1 2 . 6 1 0.0743 0.0988 0.3143 111.0 573.4 180.2

60,000 390.0 216.7 2.118 2.238 1 3 . 2 3 0.0708 0.0941 0.3068 104.9 573.4 175.9

61,000 390.0 216.7 2.018 2.132 13.88 0.0675 0.0897 0.2995 99.98 573.4 171.7

62,000 390.0 216.7 1.924 2.032 1 4 . 5 6 0.0643 0.0855 0.2924 95.30 573.4 1 67 .7

63,000 390.0 216.7 1 . 8 3 3 1.937 15.28 0.0613 0.0815 0.2855 90.84 573.4 163.7

64,000 390.0 216.7 1.747 1.846 16.04 0.0584 0.0777 0.2787 8 6 . 6 1 573.4 1 59 .8

65,000 390.0 216.7 1 . 6 6 5 1.760 16.82 0.0557 0.0740 0.2721 82.48 573.4 156.0

Po = standard pressure at sea level 29.92 in. Hg, 14.70 lb/in 2, 1.013 x 105 N/m2 or Pa

/90 = standard densi ty at sea level 23.77 x l0 g slugs/ft3, 0.1249 kgs2/m4

= temperature ratio

~7 = density ratio

a = speed of sound


12/62



Airspeed Relationships

I A S - - i n d i c a t e d a i r sp e e d ( r e a d f r o m c o c k p i t i n s tr u m e n t a ti o n , i n c lu d e s c o c k p it -

i n s t r u m e n t e r r o r c o r r e c t i o n )

C A S - - c a l i b r a t e d a i r sp e e d ( i n d ic a te d a i r sp e e d c o r r e c te d f o r a i rs p e e d -i n st ru -

m e n t a t i o n p o s i t i o n e r r o r )

E A S - - e q u i v a l e n t a i r s p e e d ( c a l ib r a t ed a i rs p e e d c o r r e c t e d f o r c o m p r e s s i b i li t y

e f f e c t s )

T A S - - t r u e a i r s p e ed ( e q u i v a le n t a i r sp e e d c o r r ec t e d fo r c h a n g e in a t m o s p h e r i c

d e n s i t y )

E A S

T A S - -

M a c h n u m b e r :

w h e r e

Va = t rue a i r speed

a = s o n i c v e l o c i t y

y = s p e c i f i c h e a t r a t i o

g = g r a v i t a t i o n a l c o n s t a n t

R = g a s c o n s t a n t

T = a m b i e n t t e m p e r a t u r e

M - -

v o - vo/,/7 Rr

a

C h a n g e i n v e l o c i t y w i t h c h a n g e i n a i r d e n s it y , p , a t c o n s t a n t h o r s e p o w e r ,

hp:

V2 = Vl ,3 //~ ]S ( a pp rox im a t e )

V /92

C h a n g e i n v e l o c i t y w i t h c h a n g e i n h o r s e p o w e r a t c o n s t a n t a i r d e n s it y :

3/hp2 ( a p p r o x i m a t e )

V2 = V1 V hpl

T h e f o l l o w i n g a r e e q u i v a l e n t a t 1 5 , 0 0 0 f t , 3 0 C d a y :

M = 0 . 4 2 8

T A S = 2 9 0 k n

C A S = 2 1 5 k n

E A S = 2 1 3 k n


13/62

A I R C R A F T A N D H E L IC O P T E R D E S I G N 9 - 1 3

Aerod y nam ics , continued

A i r s p e e d C o n v e r s i o n C h a r t s

1.1

1.0

0.9

0 . 8

r-t

iii

CO

0,7

-r

0.6

0,5

0.4

0.3

0.2

100

= ~ ~ ~ - / /

V T ~

i

, /

/ /

150 200 250 300 350

EAS, K NOT S

400


14/62

9 - 1 4 A I R C R A F T A N D H E L IC O P T E R D E SIG N

A e r o d y n a m i c s , c o n t i n u e d

A i r s p e e d C o n v e r s i o n C h a r ts , c o n t in u e d

n"

LU

t,n

Z

.40

0

P R E S S U R E A L T I T U D E , 1 0 3F T

5 0 4 0 3 0 2 0 1 0

.50 500

~ , . . ] B Soo

/ , / I ' ~ . ~ / o O / 40 0

~20

2 0 0

' , ' o ,,.: ~ A CAS=215kt

~ ~ i B A l ti tu d e = 1 5 , 0 0 0 f t

C M = . 4 2 8

D T A S (I C A O s td . d a y )= 268 k t

| E Tam= 3 0 C I

I F T A S = 2 9 0 k t

l

10 A | j 100

1 0 0 2 0 0 3 0 0 4 0 0

C A L IB R A T E D A I R S P E E D , K N O T S

CB

I--

O

Z

v

d

W

ILl

O .

CS~

rr

W

rr


15/62

A I R C R A F T A N D H E L I C O P T E R D E S I G N 9 - 1 5

Pt-

u J

m

Z

T

J

[


P R E S S U R E A L T I T U D E , 1 0 3 F T

5 0 4 0 3 O 2 O

~.2o / / /

3 0 0 4 0 0 5 0 0 6 0 0

C A L I B R A T E D A I R S P E E D , K N O T S

0 3

I - -

O

Z

C ~

UJ

LU

O 3

n -


16/62


A e r o d y n a m ic s , c o ntin u e d

M in im um Drag

S u b s o n i c

T h e b a s ic m i n i m u m d r a g o f a n a e r o d y n a m i c v e h i c le c o n s i st s o f n o t o n l y fr ic t io n

dr ag bu t a l s o d r ag du e t o t he p res s u r e f o r ces ac t ing on t he v eh i c le .

T h e f o l lo w i n g e q u a t io n s p r e s e n t a m e t h o d o f p re d i c ti n g m i n i m u m d ra g :

M i n im u m d ra g = Com i.q S

~_,(Cfoom p )< z . . . . p )

C Om in = S -~-

COcamber -~- CDbase -~-

C Omisc

wh er e t he com po nen t s k i n - f ri c ti on coe f fi c i en ts a r e ev a l ua t ed accor d i ng t o t he f o l -

l owi ng equa t i ons .

A w co mp

C

Cfcom p =

C fwing =

Cffuselage =

C f n a c e l l e

=

C fcanopy =

C fhoriz & vert ails onepiece)

C fhoriz & vert ails hinged)

C L ....... =

C D~.mbe~

C Dbase

CDm i n

C Dmi~c

C fFP =

F R =

c o m p o n e n t w e t t e d a r ea

l if t ing s u r face expo s ed s t ream wi s e m .a .c .

c o m p o n e n t d r a g c o e f fi c ie n t

C fF p[1 + L ( t / c ) + l O 0 ( t /c ) 4 ] R e s

C f~ [1 + 1.3 /P--Ii,15 + 44/F-t~3]Rfus

CSFP Q[1 + 0.35/(F--1~)1

CfFp[1 +

1 .3 /F l~ 15 -Jr 44/F--I~3

C f ~ [ 1 + L ( t / c ) + l O 0 ( t / c ) 4 ] R t s

(1 .1 )CfFp[l +

L ( t / c ) -I- l O 0 ( t / c ) a ] R t s

CfFo X Q[1 + 1 .3 / F -R 1'5 + 4 4 / ~ 3]

0 . 7 ( A C 2 ) ( S E x p / S ) ( d o n o t u s e f o r c o n i c a l c a m b e r )

bas e d rag: a goo d es t i ma t e can be ob t a i ned b y us i ng a bas e

pr es s u re coe f f i c ien t o f Cp = - 0 . 1 . ( M o r e d e t a il e d d i sc u s s io n

o f b a s e d r a g m a y b e f o u n d in H o e r n e r ' s F l u i d D y n a m i c D r a g . )

m i n i m u m d r a g c o e f f ic i e n t

m i s ce l laneou s d r ag coe f f i c ien t

Whi te-Chr i s toph ' s f l a t -p la t e turbulent -sk in- f r i c t ion coef f i -

c i e n t b a s e d o n M a c h n u m b e r a n d R e y n o l d s n u m b e r ( in w h i c h

charac ter i st i c l ength o f l i f ting sur face equ al s exp osed m .a .c .)

f ineness r a t io

l eng t h / d i am e t e r ( f o r c l os ed bod i es o f c i r cu la r c r os s s ec ti on )

l e n g t h / ~ / ( w i d t h ) ( h e i g h t ) ( f o r c lo s e d b o d i e s o f i rr e g u la r c ro s s

s ec t i on and f o r nace l le s )

/ V/ 1 (1 ~ ) (~ )2 ( for c losed bod ies of e l l ip t i c

eng th a 1 -4-g -

c r os s s ec ti on , wh er e a = m i nor ax i s and b = m a jo r ax is )


17/62


L

m.a.c

A maxt/c

q

Q

RLS

Rfus

S

SEXP

t


= thickness location parameter

= 1.2 for (t/C)max loca ted at x > 0 .3c

= 2.0 for (t/C)max located at x < 0.3c

= mean aerodynamic chord

= sweep of lifting-surface at max im um thickness

t i c

= dynami c pressure

= interf erence factor

= 1.0 for nacelles and external stores mou nted out of the local

velocity field of the wi ng

= 1.25 for external stores mou nte d symmetri call y on the wing tip

= 1.3 for nacelles and external stores if mounte d in moderat e

proximit y of the wing

= 1.5 for nacelles and external stores mounted flush to the wing

(The same variation of the interference factor applies in the

case of a nacelle or external store stru t-mounted to or flush-

moun ted on the fuselage.)

= lifting surface factor (see Lifting Surface Correct ion graph)

---- fuselage correction factor (see Fuse lage Correct ions graph),

Refus based on length

= win g gross area

= exposed wing area

-- max im um thickness of section at exposed streamwise m.a.c.

Example

Calculatio n of uncamb ered -wi ng drag coefficient for subsoni c case.

Reference wing area, S = 1000 ft 2

Wetted area, A w = 1620 ft 2

Velocity, V = 556 ft/s = 0.54 M

Altitude, H = 22,000 ft

Mea n chord, g = 12.28 ft

Sweep at max im um thickness

t i c

= 11% at 35% chord = 24 deg

Reynolds number, R e = V ~ / v = (556)(12.28) /2.7721 10 -4 = 24.63 x 106

Thickness location parameter, L = 1.2

Lift ing surface factor, RLS = 1.13 (see Lif ting Surface Correct ion graph)

Basic skin-fr iction coefficient, CfFP = 0.00255 (see Turbulent Skin Friction

Coefficient graph)

Win g skin-f riction factor, C f = 0.0033

Wing min imu m-dr ag coefficient, Cd = 0.00535


18/62

9 -1 8 A I R C R A F T A N D H E L I C O P T E R D E S I G N


M i n i m u m D r ag , c o nt in u e d

S u b s o n i c -C o m p o n e n t C o r r e c t i o n F a c t o r s

O UT BO A R D P A N E L S I

~ - -

1 . 3 - - ' ' ' " I N B O A R D P A N E L S ~ I

1.1

- - - - -

1 . 0 ' " " ' ' . . . . I

o.9 .~_ t 1 L

0 . 8

0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0

I

O S A M A X t / c

I

I

e x a m p l e

L i f t in g s u r f a c e c o r r e c t i o n .

A p p ly r a t i o

A w e t / S r e

v a lu e f o r t h e f u s e l a g e p lu s a t t a c h e d i t e m s ( t o re s p e c t iv e

se ts o f cu rv es , dashed o r so l id ) .

1 . 1

1 . 0

0 . 9

~ o . 8

t r

0 . 7

0 . 6

0 . 5

m - . 6

I I

. . . .

5 1 0 5

7

1 . 5

4 . 0

r

2 0 2 5

R E Y N O L D S N U M B E R x 1 0 - 6

F u s e l a g e C o r r e c t i o n s .


19/62



1.0

0.9

rr

0.8

0.7

f

I

6

10

M = . 5

~ 4

~ 2

I I

20 40 50 60 100 200 400 600

REYNOLDS NUMBER x 10 -6

For Mach < 0.5.

T u r b u l e n t

Skin-Friction Coefficient

0 0 5 ~ ~ , _ M A C H ( M )

C F '

~ - , ~ N

R E Y N O L D S N U M B E R x 1 0 6

e x a m p l e

I n s u l a t e d f ia t p l a te ( W h i t e - C h r i s t o p h ) .


20/62


A e r o d y n a m ic s , c o n tin u e d

M in im um Drag , continued

S u p e r s o n i c

Wave drag.

A t s u p e r s o n i c s p e e d s , t h e p r e s s u r e d r a g is a s s o c i a t e d w i t h th e s h o c k -

w a v e p a t te r n a b o u t t he v e h i c l e a n d is c a ll e d w a v e d r a g . " A r e a - r u l e " t e c h n i q u e s a r e

g e n e r a l l y e m p l o y e d f o r d e t e rm i n i n g t h e w a v e d r a g o f a c o n fi g u r a ti o n . D u e t o t h e

l e n g t h y c a l c u l a ti o n s i n v o l v e d i n s o l v i n g t h e w a v e - d r a g e q u a t i o n , d i g i ta l c o m p u t e r s

a r e u s e d e x c l u si v e l y ; a c c u r a c y p ri m a r i l y d e p e n d s o n th e m e t h o d s e m p l o y e d f o r

g e o m e t r ic a l m a n i p u l a t io n . T h e N A S A H a r r is a r e a - r u le p r o g r a m i s u s e d e x te n s iv e l y

i n w a v e - d r a g c a l c u la t io n s .

Skin friction.

S u p e r s o n i c s k i n - f r i c t i o n d r a g i s c a l c u l a t e d f o r e a c h c o m p o n e n t

u t i l i z i n g f l a t - p l a t e s k i n - f r i c t i o n c o e f f i c i e n t s ( s e e I n s u l a t e d F l a t P l a t e g r a p h ) .

Wave drag--wing.

A s p r e v i o u s l y d i s c u s s ed , t h e c a lc u l a t io n o f w a v e d r a g f o r m o s t

c o n f i g u r a t i o n s r e q u i re s t h e r e s o u r c e s o f a d i g i ta l c o m p u t e r . A s a fi rs t a p p r o x i m a t i o n

f o r w a v e d r a g o f a n u n c a m b e r e d , u n t w i s te d , c o n v e n t i o n a l t r a p e z o i d a l w i n g w i t h

s h a r p - n o s e d a i r fo i l s e c ti o n , t h e f o l l o w i n g c a n b e u s e d .

KLE t/e)2

CD

. . . . ~.g f i ( f or f l t an ~ > 1 )

CD

. . . . ,,g =

KLEtanE t/c)2

( f o r f i t a n < 1 )

( f o r E = 9 0 d e g

--ALE)

w h e r e t h e sh a p e f a c t o r

KLE

i s s h o w n i n t h e f o l l o w i n g t a b le .

Conf igura t ion

KLE

S ing le wedg e 1

S ym met r i ca l doub l e wedge 4

Doub l e wedge with m ax imum

c/x)

thickness at

x/c

(1 -

x/c)

Biconv ex sect ion 5 .3

Streamline foil w ith

x/c

= 50 % 5 .5

Ro und-no se fo i l wi th

x/c

= 3 0 % 6 .0

Sle nde r elliptical airfoil sectio n 6.5


21/62

A I R C R A F T A N D H E L IC O P T E R D E S IG N 9 -2 1


Wave drag--body.

A f ir st a p p r o x i m a t i o n f o r a b o d y c a n b e o b t a i n e d f r o m t h e

p r e l i m i n a r y w a v e - d r a g e v a l u a t io n g r a p h h e r e f o r M = 1 .2 u s in g t h e e x p r e s s i o n :

AMAX KBODY

C D w a v e b o d y - - - -

S ~ F ~ - - ~ 2

E x a m p l e

C a l c u l a t e t h e w i n g w a v e - d r a g c o e f f ic i e n t f o r th e f o l l o w i n g c o n d i t io n s .

M a c h n u m b e r = 1 .2

A i r f o i l = 6 % t h i c k s y m m e t r i c a l d o u b l e w e d g e ( K LE = 4 . 0 )

f l = 0 . 6 6 3

= 9 0 d e g

/3 t a n E = o ~

C o . . . . . i.g = 0 . 0 2 1 7

E x a m p l e

C a l c u l a t e t h e b o d y w a v e - d r a g c o e f f i c i en t fo r th e f o l l o w i n g c o n d i t i o n s .

M a c h n u m b e r = 1 .2

F u s e l a g e = 3 f t d i a m e t e r , 3 0 f t l e n g t h ( F R = 1 0 )

d A / d x = 2 0 f t

R e f e r e n c e w i n g a r e a = 6 7 f t 2

KBODY = 1 8 ( s e e P r e l i m i n a r y W a v e - D r a g E v a l u a t i o n g r a p h )

C D . . . ~ y = 0 . 0 1 9 0

P r e l i m i n a r y W a v e -D r a g E v a l u a t io n

30

2 5

o 2 0

, , I I , ~

10

( dA

)AFT

END

A M A x K

C D w S R E F F - ' R 2

9 1 0

F IN E N E S S R A T IO F R )

32.5

3O

_)7.5

25

22.5

2O


22/62



Indu ced Dra g

S u b s o n i c

T h e d r a g d u e t o li ft , o r i n d u c e d d r a g , r e f l e c ts l i f t - p r o d u c i n g c i r c u l a t io n . P o t e n t i a l

f l o w t h e o r y s h o w s t h a t t h e r e l a t io n s h i p t o d r a g i s a f u n c t i o n o f l i ft s q u a r e d . H e n c e ,

t h e b a s i c p o l a r i s p a r a b o l i c . T h e p a r a b o l i c p o l a r i s s h i f t e d f r o m t h e o r i g i n b y

c a m b e r , w i n g i n c i d e n c e , m i n i m u m d r a g , e tc . a n d d e v i a t e s f r o m it s p a r a b o l i c s h a p e

a t h i g h e r l i f t s w h e n f l o w s e p a r a t i o n e x i s t s .

CDi = KC2L

w h e r e C L is t o t a l li ft , i n c l u d i n g c a m b e r e f f e c t s , a n d K ---- h e p a r a b o l i c d r a g c o n -

s ta n t. F o r p l a i n w i n g s b e l o w t h e p a r a b o l i c p o l a r b r e a k l if t c o e f f ic i e n t,

1

K - - - -

7 t ( A R e )

T h e v a l u e o f e , t h e w i n g e f f i c i e n c y f a c t o r, a c c o u n t s f o r t h e n o n - e l l i p t i c i ty o f t h e li f t

d i s tr i b u ti o n ; t y p i c a l v a l u e s o f e f o r h i g h - s u b s o n i c j e t s a r e 0 . 7 5 - 0 . 8 5 . T h e h i g h e r

t h e w i n g s w e e p a n g l e , t h e l o w e r t h e e f a c t o r .

F o r w i n g s w i t h s h a r p l e a d in g e d g e s , t h e d r a g d u e t o li ft c a n b e a p p r o x i m a t e d b y

C D i ~ - 0 . 9 5 C L t a n ~ ( or = w i n g a n g l e o f a t t a c k ) .

E x a m p l e

I n d u c e d d r a g a t a li f t c o e f f i c ie n t o f 0 . 8 f o r a v e h i c l e w i t h a n e f f e c t i v e O s w a l d

e f f i c ie n c y f a c t o r e o f 0 . 8 0 a n d a n a s p e c t r a t io o f 8 .5 w i l l b e

c ~ ( 0 . 8 ) 2

CD,

J r A R e J r ( 8 .5 ) ( 0 . 8 0 ) = 0 . 0 3 0

S u p e r s o n i c

A t s u p e r s o n i c s p e e d s , t h e w a v e d r a g d u e to l if t i n c r e a s e s a s v / M - 1 a n d i s a

f u n c t i o n o f p l a n f o r m g e o m e t r y . F o r p r e l i m i n a r y d e s i g n e v a l u a ti o n , t h e f o l lo w i n g

g r a p h s p r o v i d e s u f f i ci e n t a c cu r a c y . A t s u p e r s o n i c s p e e d s , t h e p o l a rs g e n e r a l l y s h o w

n o t e n d e n c y t o d e p a r t f r o m a p a r a b o l i c s h a p e . T h u s , t h e r e i s n o c o r r e s p o n d i n g p o l a r

b r e a k a s a t s u b s o n i c s p e e d s .

E x a m p l e

F o r s t ra i g h t t a p e r e d p l a n f o r m w i t h s h a r p l e a d i n g e d g e s ,

M a c h n u m b e r = 1 . 2 W i n g a r e a , S = 6 7 f t 2

A s p e c t r a t i o = 1 .5 L e n g t h = 6 . 6 9 f t

S pa n , b ---- 1 0 . 0 2 f t Ta per r a t i o = 1 . 0

y rA R ---- 0 .6

P = S/bg. = 1 .0

/3 = 0 .663

f i ( b / 2 e ) = 0 . 4 9 7

Co, ----0 . 2 5 5 C ~


23/62

A I R C R A F T A N D H E L I C O P T E R D E S I G N 9 -2 3

A e r o d y n a m i c s , c o n tin u e d

S u p e r s o n i c D r a g D u e t o L i f t E m p i r i c a l )

Straight Tapered W ings Irregular-Shaped W ings

2 . 0 2 . 0

1 . 8 / /

"

R O UN O ~ / i

1 .6

1

'EAD~NGE D G E S / /

0 ~ # , ~

' ~ 1 ~

, ~

P 1 . 0

.8

P = ' b q '

.~.- -~ .~ _ . /

.4 ~ .4

0 .4 .8 1 .2 1 ,6 2 .0 0 .4 .8 1 .2

/ ~ ( b / 2 f ) / 3 ( b 1 2 e

/

/

/

/

1 . 6 2 . 0

Cr itica l M a ch Num ber

Subsonic drag evaluation terminates at a Mach num ber where the onset of shock

formations on a configuration causes a sudden increase in the drag l ev el --t he so-

called critical Mach number. The following graphs show simple workin g curves

for it.

Example

Find critical Mach nu mbe r for CL = 0.4.

t/c

= 0.068

CLo~,oN = 0.2

Aspect ratio = 3

Ac/4

= 45

MCRcL=0 = 0.895 (see Cri tical Mach Numb er graph)

MCRcL=o,/McRc,=o

= 0.97 (see Lift Effect on Critical Mach Nu mb er graph)

MCRcL=04 = (0.97)(0.895) = 0.868


24/62



Cr i tica l M ach Num ber , cont inued

C r i t i c a l M a c h N u m b e r C h a r t

[ C L , ~

CONVENTIONAL DE

ADVANCED DESIGN

I I I I I I I I

0.4

Acl4

1.0

.9

O

I

. _ 1

o

o .8

I

o l

e

e J

AR


25/62

AIRCRAFT AND HELICOPTER DESIGN


L i f t E f f e c t o n C r i t i c a l M a c h N u m b e r F o r C o n v e n t i o n a l A i r f o i l s )

1 . 0

o

t4

i

.9

.8

9 - 2 5

. o 2

/ / o

.0 6 .1 - -

. 0 8

1 6 1 8g ~

.4

. 1 8

.5

D r a g R i s e

F o l l o w i n g t h e c r i t i c a l M a c h n u m b e r , t h e d r a g l e v e l i n c r e a s e s a b r u p t l y . T h i s

p h e n o m e n o n i s a s s o c i a te d w i t h s t ro n g s h o c k s o c c u r r i n g o n th e w i n g o r b o d y ,

c a u s i n g f l o w s e p a r a ti o n . T o e s t i m a t e t h e d r a g r i s e i n c r e m e n t a t t h e s e c o n d i t i o n s ,

H o e r n e r , i n

Fluid Dynamic Drag,

g i v e s t h e f o l l o w i n g e m p i r i c a l r e la t io n .

A C D R ,s e = K /IO 3 )[ IO A M / c o s 1 -A L E

C R ) ] n

w h e r e

K = 0 . 3 5 f o r 6 - s e r i e s a i r f o i ls i n o p e n t u n n e l s

= 0 . 4 0 f o r a ir f o il s e c t io n s w i t h

tic ~

6 %

= 0 . 5 0 f o r th i c k e r a i r fo i ls a n d f o r 6 - s e r ie s a i r f o il s

A M = M - M CR

n = 3 /( 1 + ~-~R)


26/62



Drag Rise , continued

Example

D e t e r m i n e t h e d r a g r i s e i n c r e m e n t f o r th e f o l lo w i n g .

A M ----0 . 0 5

A s p e c t r a ti o = 3 . 0

t /c = 0 . 0 6 8 ( K = 0 . 4 0 )

ALE = 50

M c R = 0 . 8 9 5

0 .4 F 1 0 (0 .0 5) ] ,+-]/3

m foR ise - - 1 0 0 0 k c o s ( 5 ~ i

~ - 0 . 8 9 5

= 0 . 0 0 0 2 1 3 6

Aerody na m ic Cente r

T h e p r e d i c t i o n o f w i n g - a l o n e a e r o d y n a m i c c e n t e r ( a . c . ) m a y b e m a d e f r o m

c u r v e s p r e s e n t e d i n th e f o l l o w i n g g r a p h s w h i c h s h o w a .c . l o c a t io n a s a f r a ct i o n o f

t h e w i n g r o o t c h o r d . T h e s e c u r v e s a r e b a s e d o n p l a n f o r m c h a r a c t e r is t i cs o n l y a n d

a r e m o s t a p p l i c a b l e t o l o w - a s p e c t - ra t i o w i n g s . T h e c h a r a c te r i st i c s o f h i g h - a s p e c t -

r a t io w i n g s a r e p r i m a r i l y d e t e r m i n e d b y t w o - d i m e n s i o n a l s e c t io n c h a r a c te r i st i cs

o f t h e w i n g .

T h e w i n g i s t h e p r i m a r y c o m p o n e n t d e t e rm i n i n g t h e l o c a t i o n o f t h e a i r p la n e a .c .,

b u t a e r o d y n a m i c e f f e c ts o f b o d y , n a c e l le s , a n d t a il m u s t a l s o b e c o n s i d e re d . T h e s e

e f f e c t s c a n b e t a k e n i n t o a c c o u n t b y c o n s i d e r i n g e a c h c o m p o n e n t ' s i n c r e m e n t a l

l i ft w i t h i t s a s s o c i a t e d c e n t e r o f p r e s s u r e a n d u t i l i z i n g t h e e x p r e s s io n ,

CM~

a.c.--

CL~

Example

D e t e r m i n e t h e lo c a t i o n o f t h e a e r o d y n a m i c c e n t e r o f a w i n g u n d e r t h e f o l lo w i n g

c o n d i t i o n s .

M a c h n u m b e r = 1 .2 ( fl = 0 . 6 6 3 )

A LE = 4 5 d e g

A s p e c t r a t io = 2 . 0

T a p e r r a t i o ( ~.) = 0 . 2

Xac

- - 0 . 5 1 ( s ee L o c a t i o n o f W i n g A e r o d y n a m i c C e n t e r g r a p h )

Cr


27/62

A I R C R A F T A N D H E L I C O P T E R D E S IG N


Locat ion o f W ing Aerody nam ic Center

X = O

9 - 2 7

1 . 2

1 . 0

. 8

X a c

. 6

. 4

. 2

0 0

. r J

A R T a n A L E

6

5

4

3

2

1

r I - - ' I '

S U B S O N I C - . ~ ~ , - S U P E R S O N I C

| I

1 0 1 0

T a n A L E 3 (3 T a n A L E

; ~ = 0 . 2

1

/

, , ~ , ~ / A R T a n A L E

.4

S U B S O N I C -4 --= .-- S U P E R S O N I C

0 1 I =

0 T a nA L E 1 B 0 3 1 T a n A L E 0


28/62

9 -2 8 A IR C R A F T A N D H E L I C O P T E R D E S I G N


A e r o d y n a m i c C e nte r, c o n t i n u e d

Locat ion o f W ing Aerod ynam ic Center, con t inued

1 . 2

1 . 0

. 8

Xa.c~ .6

.4

.2

0 0

k = 0 . 2 5

~ ~ . ~ A R T a nA L E

S U B S O N I C - ~ - . ~ S UP E R S O N IC J

T anAL E 1 /3 0 (3 1 T a nAL E 0

B-- ~LE T~ E B-

1 . 2

1 . 0

. 8

X a C .

---C-;--r .6

. 4

.2

0 0

; k = 0 . 3 3

U N S W E P T T E

I

S U B S O N I C

l

T anALE 1 ( j

I

. .. ..AR T anALE

- - ~ 5

4

f - - 3

,..... ~ 2

1

. .= , , , . SUPERSONIC

0 1

/3 TanALE


29/62

X a c

X a . c .

c T-,

1 . 4

1 2

1 0

8

.6

.4

.2

0

2 . 0

1 , 8

1 . 6

1 . 4

1 , 2

1 . 0

. 8

A I R C R A F T A N D H E L I C O P T E R D E S I G N

A e r o d y n a m i cs , co n ti nu e d

; ~ = 0 . 5

I

S U B S O N I C . , ~

I

0 T a n A L E 1 /3

T

M..

_ - -

I

A R T a nA L E

6

~ 5

4

~ a

~ 2

S U P E R S O N I C

I

0 1

T a n A L E

- . T ~ - R - ~ L E ~ r

; ~ = 1 . 0

I

A R T a nA L E

~ s

/

_...~ J

3

1

- j'f

. 6 - -

J

" ' - " " ~

I

S U B S O N I C -,~ .-.m ,,- S U P E R S O N I C

, 2 I I

0 1 0 1

T a n A L E ~ /3 T a n A L E

9 - 2 9


30/62



M a x im u m L ift C o e f fi cien t (CLmax)

D e t e r m i n a t io n o f m a x i m u m l if t d e p e n d s e x c l u s i v e l y o n t h e v i s co u s p h e n o m e n a

c o n t r o l li n g t h e f l o w o v e r th e w i n g . A s w i n g i n c i d e n c e i n c r e a s e s , f lo w s e p a r a te s

f r o m t h e s u r f a ce , a n d l i ft i n g p r e s s u r e s c e a s e t o b e g e n e r at e d . T h e s e p h e n o m e n a

d e p e n d o n t h e w i n g g e o m e t r y : s w e e p , a s p e c t r a t i o , t a p e r r a t i o , t h i c k n e s s r a t i o ,

a n d a i r f o il s e c ti o n . T h e t h i c k n e s s r a t io h a s a d e c i d e d l y m a r k e d e f f e c t t h r o u g h t h e

i n f lu e n c e o f t h e l e a d i n g - e d g e r a d iu s . B e i n g a v i s c o u s p h e n o m e n o n , a s t ro n g e f f e c t

o f R e y n o l d s n u m b e r i s a p p a re n t . A s a c o n s e q u e n c e , t h e p r e c i s e d e te r m i n a t i o n

o f C L m ax f o r a n a r b i t ra r y w i n g h a s n e v e r b e e n s a t is f a c to r i ly a c c o m p l i s h e d . T h e

U S A F S ta b i li ty a n d C o n tr o l H a n d b o o k

( W A D D - T R - 6 0 - 2 6 1 : L i b . 5 7 2 1 1 ) d o e s

c o n t a in s u c h a m e t h o d . H o w e v e r , c o r r e la t i o n s i n d i ca t e e r ro r s e x c e e d i n g 2 5 % . T h i s

m e th o d w o r k s w i th s e c t i o n l i f t d a t a a n d a p p l i e s c o r r e c t i o n s f o r f i n i t e a i r p l a n e

e f fe c ts . T h e r e f o r e , p r e d i c t io n s m u s t d e p e n d o n e x i s t i n g t e s t d a t a a n d e x p e r i e n c e .

High-L i f t Devices

M a x i m u m L i f t I n c r e m e n t D u e t o F l a p s

H i g h - l if t d e v i c e s a r e d e s i g n e d f o r c e r t a in s p e c i a l iz e d f u n c t io n s . G e n e r a l l y th e y

a r e u s e d t o i n c r e a s e t h e w i n g c a m b e r o r i n s o m e o t h e r w a y t o c o n t r o l t h e f l o w

o v e r t h e w i n g , f o r e x a m p l e , t o p r e v e n t f l o w s e p a r a ti o n . W i n g f la p s in c r e a s e th e

c a m b e r a t t h e w in g t r a i l i n g e d g e , t h u s i n d u c in g a h ig h e r l i f t d u e t o i n c r e a s e d

c i r c u l a t i o n a t t h e s a m e a n g l e o f a t t a c k a s t h e p l a i n w in g . P l a in - f l a p e f f e c t i v e n e s s

c a n b e d e t e r m i n e d v e r y a c c u ra t e ly . O t h e r d e v i c e s c u s t o m a r i l y e m p l o y e d a r e s la ts ,

s lo t s, a n d s p e c i a l l e a d i n g - e d g e m o d i f i ca t i o n . E v a l u a t i o n o f t h e s e d e v i c e s d e p e n d s

o n t h e a p p l i c a t io n o f N A S A r e su l ts . B r i ti s h re p o r t A e r o 2 1 8 5 a n d N A S A T e c h n i ca l

N o t e 3 9 1 1 c o n t a i n p r e d i c ti o n c u r v e s a n d t e c h n i q u e s f o r t h e s e d e v i c e s .

A t s u p e r s o n i c s p e e d s , h ig h - l i f t d e v i c e s a r e g e n e r a l l y n o t r e q u i r e d f o r f l o w s t a -

b i li z a t io n . H o w e v e r , f l a p - t y p e c o n t r o ls m a y b e u s e d t o t r i m t h e a i r p l a n e p i tc h i n g

m o m e n t s .

T h e d e t e r m i n a t i o n o f m a x i m u m l if t i n c r e m e n t d u e t o t r a il i n g - e d g e f la p d e f le c t io n

u s es t he m e t h o d o f N A S A T N 3 9 1 1 . T h e m a x i m u m l if t i n c re m e n t i s g i v e n b y

CL.

A CL ma x = A C e max - - KcKb

Ct~

w h e r e A C e max : i n c r e m e n t o f s e c t i o n l i f t c o e f f i c i e n t d u e t o f l a p d e f l e c t i o n ( s e e

P r i n c e to n R e p o r t N o . 3 4 9 ) .


31/62



A R

c L o / C , o =

o o [ @ ) 2 c A s

+ 71- \co sA c/2]

j

w h e r e

ao

= s e c t i o n l if t -c u r v e s l o p e , p e r r a d i a n

Kb

= f la p s p a n f a c t o r ( s e e F l a p S p a n F a c t o r g r a p h )

K c = f la p c h o r d f a c t o r ( s e e F l a p C h o r d F a c t o r g r a p h )

C a r e s h o u l d b e e x e r c i s e d i n u s e o f a l l p r e d i c t i o n t e c h n i q u e s f o r A C L m ax d u e t o fl a p

d e f l e c ti o n , b e c a u s e f la p e f f e c t i v e n e s s i s m o d i f i e d t o a la r g e e x t e n t b y t h e a b i l it y o f

t h e w i n g - l e a d i n g - e d g e d e v i c e s t o m a i n t a i n a t t a c h e d f l o w .

Example

D e t e r m i n e A f L m a x d u e t o f la p d e f le c t i o n , w i t h t h e f o l l o w i n g w i n g c h a r a c t e r i s -

t i cs .

A s p e c t r a ti o = 4 . 0

S e c t i o n l if t - c u r v e s l o p e = 5 . 7 3 p e r r a d i a n

S e m i c h o r d s w e e p = 2 0 de g

T a p e r r a t io = 0 . 2

4 . 0

CL,/Ceo

= 1 = 0 . 6 1 9 7

5.73 [ ( _ ~ ) 2 [ 4 .0 , ~ 1 ~

--Y- + + ~cos(20)t j

F o r p l a in f l ap s w i t h 5 0 d e g d e f l e c ti o n , 1 6 % c h o r d ,

ACemax = 0 . 8 0 f o r a t y p i c a l p l a in f l a p

I n b o a r d s p a n , r h = 0 . 1 5

g b i

=

0 . 2 2 ( s ee F l a p S p a n F a c t o r g r a ph )

O u t b o a r d s p a n , r /o = 0 . 6 5

Kbo

= 0 . 8 0 ( s e e F l a p S p a n F a c t o r g r a p h )

K b = 0 . 8 -- 0 . 2 2 = 0 . 5 8

(otS)Ce

= 0 . 5 ( s e e F l a p C h o r d F a c t o r g r a p h )

Kc

= 1 .1 ( s e e F l a p C h o r d F a c t o r g r a p h )

CLmax = ( 0 . 8 ) ( 0 . 6 1 9 7 ) ( 1 . 1 ) ( 0 . 5 8 ) = 0 . 3 1 6 3


32/62

9 - 3 2 A I R C R A F T A N D H E L I C O P T E R D E S I G N


H i g h - L i f t D e v i c e s , c o n t i n u e d

F l a p C h o r d Fa c to r , K c

1 . 0

G

.6

.2

I

I

0

0 . 2

I

I

e x a m p l e

S

J

J

J

.4 c f /c ,6

. 8 1 . 0

2 . 0

1 . 8

K c

I

1 . 4 ~

, , 2 i - -

i

l o l

0 2 4 6 8 1 0

~ A R

I

I

example


33/62

A I R C R A F TA N D H E L IC O P T E RD E S I G N


F l ap S p a n F a c t o r , K b

9-33

1 .0=

Kb

0

0

k\\\\\x~

)

i

/

bf 1.0

I )/ 2

1.0

.8 411, X

.6 ~ 1 , 0 I

Kb / I

.4 I

I

I

I

- - I

.2 / i

I I

I

I

I

0 |

0 2 .4 .6 .8

-

' 1

/2

e x a m p l e e x a m p l e

1.0


34/62


A e r o d y n a m ic s , c o nt in u e d

High-Lift D evices, continued

E f f e c t s o f F l a p D e f l e c t i o n o n Z e r o - L i f t A n g l e o f A t t a c k

The set of Plain-Flap Effectiveness graphs may be used with the following

expression to obtain subsonic, plain-flap effectiveness. Correction factors for body

effect, partial span, and flap-leading-edge gap are shown.

AOtLo = ( 0 t ~ / 0 ~ ) C O S A H L S [ I - - ( a +

bf) l~l ]

Example

Determine At~Lo due to plain-flap deflection, with the following wing charac-

teristics.

Aspect ratio = 4.0

Sweep at flap hinge line = 10 deg

Sweep at wing leading edge = 32 deg

For inboard plain flaps with 25 deg deflection, 15% flap chord,

Flap gap ratio, GAP/(f = 0.002

Inboard span, 01 = 0.15

Outboard span, qo = 0.65

Ratio of body diameter to wing span,

2Ro/b

= 0.15

Approach Mach number = 0.1

,6 = ~ - M 2 = 0.995

Flap effectiveness = -0ot /0~ = 0.49 (see Plain-Flap Effectiveness graph)

Sweep factor:

-a = 0.039

(see Sweep factor graph)

b = 0.034

Fuselage factor:

A~Lo)wB

-- 0.93 (see Wing-body graph)

AOILo)W

Flap span factor:

S F ( P s ) / S F ( F S ) = ~ 0 - - ~1 = 0 . 6 5 - - 0 . 1 5 = 0 . 5 0

( A O t L o ) P S

- - -- 0.55 (see Flap span graph)

( A O t L o ) F S

Flap gap factor:

( A O t L ) g a p - - 0.96 (see Flap Gap graph)

( A O t L o ) s e a l e d

AotLo = (--0.49)cos(10 deg)(25)[1 - ( -0 .039 + 0.034(0.995))(25)]

x (0.93)(0.55)(0.96) ---- -6 .69 deg


35/62



Plain-F lap

E f f e c t i v e n e s s

1 . 0

_ . 7 5

. 8 ~ L ~ . , , , , , . ~ . 4 0 /

.4 ~

.2 ~ ~

C f / C

o I

0 1 2 3

A R 0 .2 .4 . 6

C f iG

Full-span effectiveness.

f

. 8 1 . 0

0 5 ~, .

04

an~ 0 3 . ~ . . . ~

b

. 0 2

- -

'

I

. 0 1 I

I

0 I

0 . 2 . 4 . 6

1 - C O S A L E

Sweep factor.

1 . 0

, , ~ . e

A

o ,

. 6

\

~ ,

\

. ~ o . 1 . 2

2 R o / b

0 W ' = = ' 1

0 . 2 . 4 . 6 . 8 1 . 0

SF (p S . )/ SF(F S )

Wing-body.

. 3

k

~ o q l I _~

e ' ,

0

. 0 2 . 0 4 . 0 6

G A P I ~ f

Flap span. Flap gap.


36/62



High-Lift Devices, continued

I n d u c e d D r a g d u e t o F l a p s D e p l o y e d

S u b s o n i c .

T r a i l i n g - e d g e f l a p s o n a w i n g g i v e i t a c a m b e r f o r i m p r o v i n g l i f t .

E l e v o n s i n a s i m i l a r m a n n e r c a m b e r th e w i n g , a l t h o u g h t h e y a r e u t i li z e d f o r c o n t r o l

a t c r u i s e l i ft v a l u e s . D r a g d u e t o l if t r a t io c a n b e e x p r e s s e d a s f o l lo w s .

C D i ~ ( l _ _ F ) ( O l ~ O l L o $ ) 2 ( ~ - - O l L ~

- - - - + F

C oi8 = 0 \ Ol -- OlLo -- OILo .]

w h e r e F = s i n A c / 4 ( 0 . 2 9 5 + 0 . 0 6 6 c t - 0 . 0 0 1 6 5 o t 2 ) .

T h e f o l l o w i n g g r a p h s h o w s w o r k i n g p l o t s o f t h e s e re l a t io n s h i p s . Z e r o - l i ft a n g l e

o f a t t a c k w i t h f la p s d e f l e c te d i s o b t a i n e d f r o m t h e p r e c e d i n g s e c t io n .

S u p e r s o n i c . A t t h e s u p e r s o n i c s p e e d s , f l a p s a s s u c h a r e n o t l i k e l y t o b e u s e d .

H o w e v e r , e l e v o n s s t il l a r e r e q u i r e d o n t a i ll e s s c o n f i g u r a t i o n s f o r p i tc h c o n t r o l . T h e

s u b s o n i c d a t a l i st e d a b o v e m a y b e u s e d .

E x a m p l e

F i n d i n d u c e d - d r a g r a t i o f o r f la p s d e p l o y e d f o r t h e f o l l o w i n g w i n g c h a r a c t e ri s ti c s :

an g l e o f a t t ack a t z e ro l i f t C~Loo f - - 6 d e g a n d q u a r t e r- c h o r d s w e e p Ac /4 :

2 6

deg .

F o r a p l a i n f l a p w i t h 2 5 d e g d e f l e c t io n , a n d w i t h a n g l e o f a tt a c k a t z e r o - l if t w i t h

f la p s d e f le c t e d aL o ~ o f - 1 0 d e g , th e i n d u c e d - d r a g r a t i o a t 1 0 d e g a n g l e o f a t t a c k

w i l l b e a s f o l l o w s .

F

- -

- - 0 . 7 9 ( s e e D r a g - D u e - t o - L i f t R a ti o w i th F l a p D e f le c t io n g r a p h )

s i n A c / 4

CDi~

Coi8 = 0

- O t L o ~ _ 1 0 - ( - 1 0 ) _ 1 . 2 5

o t - O tLo 1 0 - ( - 6 )

F = ( 0 . 7 9 ) s i n ( 2 6 de g ) = 0 . 3 4 6 3

- - - - 1 .4 54 ( se e D r a g -D u e - to - L if t R a ti o w i th F la p D e f l e c t i o n g ra ph )


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A e r o d y n a m ic s , c o n tin u e d

Drag-D ue- to -L i ft Rat io w i th F lap D ef lect ion

2.5 ~--

2.0 ,///~.6'

I I I / / . o

. 5

.~. . . . . # / / / /

~'~ )

~ j

1 . 0 - I

j ,

F

I

1 . 0 - . - . - , . . ~ I

0 .5 . 8 ~ I

j ~ ,

~ 0 I

I

I

I

0 I

0 0.5 ot--


38/62


39/62

A I R C R A F T A N D H E L I C O P T E R D E S IG N 9 - 3 9

gstall

VTD

A V

W

%

Y

/z

/ZBRK

P

Per fo rm an ce, co n t in ued

= ( 2 W / S p C L m a x ) U2 = s t al l s p e e d

= A V stan = l a n d i n g v e l o c i t y

= v e l o c i ty i n c r e m e n t

= w e i g h t

= f u e l f l o w

= f l i g h t - p a t h a n g l e

= c o e f f i c i e n t o f r o l l in g f r i c t io n

= c o e f f i c i e n t o f b r a k i n g f r i c ti o n

= a i r d e n s i t y a t a n a l ti t u d e

= r a t e o f t u r n

T a k e o f f

T a k e o f f - d i s t a n c e c a l c u l a t i o n s t r e a t g r o u n d r o l l a n d t h e d i s t a n c e t o c l e a r a n o b -

s ta c le . O b s t a c l e r e q u i r e m e n t s d i f f e r f o r c o m m e r c i a l ( 3 5 f t) a n d m i l i t a r y ( 5 0 f t)

a i r c ra f t .

T a k e o f f G r o u n d R o l l

Sgnd ~-

w/s

g p ( C D - - # C L )

6 1 1 - A 2 ( C D - I Z C L )

T h e s ta l l m a r g i n A t y p i c a l l y is 1 .2 .

T o t a l T a k e o f f D i s t a n c e

STO = (Sgnd) ( Fpl )

T h e f a c t o r t o c l e a r a n o b s t a c l e d e p e n d s g r e a t l y o n a v a i l a b l e e x c e s s t h r u s t , f l i g h t

p a t h, a n d p i l o t te c h n i q u e . T h e f o l l o w i n g t y p i c a l f a c t o r s c h a r a c t e ri z e p l a n f o r m s i n

a b i l it y t o c l e a r a 5 0 - f t o b s t a c l e .

Plan for m Fpl

S t ra igh t w ing 1 .15

S wep t w ing 1 .36

D el ta w ing 1 .58


40/62


P e r fo r m a n c e , c o n t in u e d

Takeoff, continu ed

T o t a l T a k e o f f D i s t a n c e , c o n t i n u e d

Exam ple

T a k e o f f d i s t a n c e f o r a s t r a i g h t - w i n g a i r c r a f t w i t h t h e f o l l o w i n g c h a r a c t e r i s ti c s :

W = 2 2 ,0 96 lb Sgna = 1 2 55 f t A -----1 . 2

S = 2 6 2 f t2 CLmax = 1 .8 STO = 1 44 4 f t

C c = 0 . 4 6 F = 1 9 , 2 9 0 p = 0 . 0 0 2 3 7 6 9 l b - s2 - f t 4

C o = 0 . 3 5 3 8 / z = 0 . 0 2 5

T a k e o f f F u e l A l l o w a n c e

F o r b r a k e r e l e a s e t o i n i t i a l c l i m b s p e e d ,

W t

Vl

F u e l - - g ( ~ - - - D 1 )

_ ( W f ' ~ ) W f '

w h e r e

W 1 ---- w e i g h t a t s t a r t o f c l i m b

Vl ----- n i t i a l c l im b spe e d , f t / s

g = 3 2 . 1 7 4 f t /s 2

F1 ---- m a x i m u m p o w e r t h r u s t a t i n i t i a l c l i m b s p e e d

D 1 = d r a g a t 1 - g f li g h t c o n d i t i o n , in i t i a l c l i m b s p e e d

Wfo = m a x i m u m p o w e r f ue l f lo w a t b r a k e re l e a se , lb / s

Wf,

= m a x i m u m p o w e r f u el f l o w at i n i t ia l c l i m b s p e e d , l b /s

Clim b

T i m e , f u e l , a n d d i s t a n c e t o c l i m b f r o m o n e a l t i t u d e ( h i ) t o a n o t h e r ( h 2 ) c a n

b e c a l c u l a t e d i n i n c r e m e n t s a n d t h e n s u m m e d . B y u s i n g t h i s t e c h n i q u e , s p e c i f ic

c l im b s p e e d s c h e d u l e s - - i . e . , c o n s ta n t M a c h n u m b e r c l i m b a n d m a x i m u m r a t e o f

c l i m b - - - c a n b e d e p i c t e d .

R a t e o f C l i m b

F o r s m a l l a n g le s , th e r a t e o f c l i m b c a n b e d e t e r m i n e d f r o m

/

/ C : (F - D ) V W 1 - - .

g T

w h e r e V / g d V / d h i s t h e c o r r e c t i o n t e r m f o r f l ig h t a c c e l e r a t io n .


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Per fo r m ance, con tinu ed

T h e f o l l o w i n g t a b l e g iv e s a c c e l e r a t i o n c o r r e c t i o n s f o r ty p i c a l f l ig h t p r o c e d u r e s .

V dV

Altitude, fl Pr oc ed ur e g ' d--h-

36 ,089 Cons tan t CA S 0.566 8 M 2

o r le ss C o n s ta n t M a c h - 0 . 1 3 3 2 M 2

O v e r C o n s ta n t C A S 0.7 M 2

36 ,0 8 9 Cons t an t M ach Zero

F o r l o w s u b s o n i c c l i m b s p e e d s , t h e a c c e l e r a t i o n t e r m i s u s u a l l y n e g l e c t e d .

R/ C = F - D)V /W

F l i g h t - P a t h G r a d i e n t

T im e t o C l i m b

D i s t a n c e t o C l i m b

F u e l t o C l i m b

S u m i n c r e m e n t s f o r to ta l.

y = sin-X ( - ~ )

A t =

2 ( h 2 - - h i )

(R / C) l -Iv (R /C )2

As-- V At)

A F u e l =

W f A t )


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P e r fo r m a n c e , c o n t in u e d

Accelerat ion

T h e t i m e , f u e l , a n d d i s t a n c e f o r a c c e l e r a t i o n a t a c o n s t a n t a l t i t u d e f r o m o n e

s p e e d t o a n o th e r c a n b e c a l c u l at e d i n in c r e m e n t s a n d t h e n s u m m e d u p . B y u s i n g

t h is t e c h n iq u e , s p e c i fi c f u n c ti o n s c a n b e s i m u l a t e d ( e . g. , e n g i n e p o w e r s p o o l - u p ) .

T i m e - t o - A c c e l e r a t e I n c r e m e n t

A t - - - -

A V

g

D i s t a n c e - t o - A c c e l e r a t e I n c r e m e n t

A S = V ( A T )

F u e l - t o - A c c e l e r a t e I n c r e m e n t

A F u e l =

W f ( A t )

S u m i n c r e m e n t s t o y i e l d to t a l t i m e , f u e l, a n d d i s t a n c e t o a c c e le r a t e .

Cruise

T h e b a s i c c ru i s e d i s t a n c e c a n b e d e t e r m i n e d b y u s i n g t h e B r e g u e t r a n g e e q u a t i o n

f o r j e t a i r c r a f t , a s f o l l o w s .

C r u i s e R a n g e

R = L / D ( V / S F C ) f i~ (W o /W ~ )

w h e r e s u b s c r i p ts " 0 " a n d " 1 " s t an d f o r in i ti a l a n d fi n al w e i g h t , r e sp e c t iv e l y .

C r u i s e F u e l

Fu el = W0 - W, =

W f ( e R /k -

1 )

w h e r e k , t h e r a n g e c o n s t a n t , e q u a l s

L / D ( V / S F C ) .

D a s h R a n g e

F o r f li g h t a t c o n s t a n t M a c h n u m b e r a n d c o n s t a n t a l t it u d e , t h e fo l l o w i n g e q u a t i o n

g i v e s d a s h r a n g e .

R = (F u e l )


43/62


Per fo rm an ce, co n t in u ed

F o r l a r g e e x c u r s i o n s o f w e i g h t , s p e e d , a n d a l t i tu d e d u r i n g c r u i s e , i t i s r e c o m -

m e n d e d t h a t t h e r a n g e c a l c u la t io n s b e d i v i d e d i n to in c r e m e n t s a n d s u m m e d u p f o r

t he t o t a l.

Example

F i n d c r u i s e d i s t a n c e f o r a n a i r c r a f t w i t h t h e f o l l o w i n g c h a r a c t e r i s ti c s .

W 0 = 1 5 , 8 0 0 lb

W 1 = 1 4 , 6 0 0 l b

V = 2 6 8 k n

S F C = 1 . 2 6 l b / h /l b

L / D

= 9 . 7

R = 9 . 7 ( 2 6 8 / 1 . 2 6 ) ~ ( 1 5 , 8 0 0 / 1 4 , 6 0 0 ) = 1 6 3 n m i le

C r u i s e S p e e d s

C r u i s e - s p e e d s c h e d u l e s f o r s u b s o n i c f li g ht c a n b e d e t e r m i n e d b y t h e f o l l o w i n g

e x p r e s s i o n s .

O p t im u m M a c h N u m b e r M D D ), O p t im u m -A l t i t u d e C r u i s e

F i r s t c a l c u l a t e t h e p r e s s u r e a t a l ti t u d e .

W

P =

0.7(MZoo)(CLoo)S

T h e n e n t e r v a l u e f r o m C r u i s e -A l t i tu d e D e t e r m i n a t i o n g r a p h f o r c r u is e a l ti tu d e .

O p t i m u m M a c h N u m b e r , C o n s t a n t -A l t i t u d e C r u i s e

O p t i m u m o c cu rs a t m a x i m u m

M ( L / D ) .

f , s f

=

0 . - V c o n

C o n s t a n t M a c h N u m b e r , O p t im u m -A l t i t u d e C r u i s e

D e r i v e o p t i m u m a l t i t u d e , a s a b o v e , e x c e p t M o o a n d CLoo are r e p l a c e d w i t h

v a l u e s f o r t h e s p e c i f ie d c r u i s e c o n d i t i o n s .


44/62

9 -4 4 A IRCRAFT AND HELICOPTER DESIGN

P e r f o r m a n c e , c o n t in u e d

C r u i se , c o n t in u e d

C r u i s e - A l t i t u d e D e t e r m i n a t i o n

I -

LL

E ,

t.u

a

i -

_J

, ' ] ' L i m i t /

7 0 0 - S ea-Level Std

l< 5 0 0 5 , ~ ~ S td D ay

If) I ~ ~ T. C). Lim it

o

4 0 0

3 0 O

/ ~ / , ~ / / . , , ~ " 1 5,0 00 ' S td

2 0 0 ~ . . ~ / / . . , ~ " " 2 0 , O 0 0 ' S t d

l O O . 5 , o o o s t .

\ 30 ,000 ' Std

O 0 2 6 0 ' 6 ( ) 0 ' I 0 ( )0 ' 1 4 ' 0 0 ' 1 8 ' 0 0 ' 2 2 ' 0 0

E n g i n e S h a f t H o r s e p o w e r

Typ ica l engine fue l f low charac ter is t ics . ( Source :

Helicopter Pe rform ance, Stabili ty, a nd

Control,

page 2 76, f igure 4 .3 , by R . W . Prouty . Cop yrig ht (~) 1995, K rieg er Publish ing

Com pany , M alaba r , FL . Rep roduced w i th pe rmiss ion o f Kr iege r. )


59/62


Helicopter Design, continued

Bas ic F l i gh t L o a d i n g C o n d i t i o n s

C r i ti c al f li g h t l o a d i n g c o n d i t i o n s n o r m a l l y c o n s i d e r e d i n t h e d e s i g n o f a p u r e

h e l i c o p t e r a r e d e f i n e d a s fo l l o w s .

M a x i m u m s p e e d ( d e s ig n l im i t s p e e d V u )

S y m m e t r i c a l d i v e a n d p u l l o u t a t d e s i g n l i m i t s p e e d VDL a n d a t 0 . 6 VH, a p p r o x -

i m a t e l y th e s p e e d o f m a x i m u m l o a d f a c to r c ap a b i l it y

V e r ti ca l t a k e o f f ( j u m p t a k e o f f )

Ro l l i n g p u l l o u t

Y a w ( p e d a l k i c k s )

A u t o r o t a ti o n a l m a n e u v e r s

3.0

r.~ 2.5

2.0

1.5

1 . 0

Level Flight

0.5

0

- - 0 .5

4 .0

3.5

/

-40 --20 0 20 40 60 80 100 ~20 140 160 180 200

T r u e A i r s p e e d ( V) , k no t s

A typical design V - N diagram. (Source: Hel icopter Aerod yna m ics (Rotor & W ing In-

ternational) , b y R . W .

Prouty. Co pyright

(~) 1995 , PJS Pub l ica t ions . Rep rodu ced w i th

permiss ion from Raym ond W. Prou ty . )

T h e s e , a n d o t h e r l im i t s , a re n o r m a l l y s e t b y t h e c u s t o m e r o r c e r ti f y i n g a u t h o r i t y

a n d a r e d e p i c t e d i n t h e v e l o c i t y - l o a d ( V - N ) d i a g r a m . O t h e r p a r a m e t e r s u s u al ly

d e f i n e d i n t h e V - N d i a g r a m a re n e v e r - t o - e x c e e d v e l o c i t y (V N E) a n d m a x i m u m

r e a r w a r d v e l o c i t y ( V A v r ) . T h e d e s i g n s t r u c t u r a l e n v e l o p e m u s t s a t i s f y t h e V - N

d i a g r a m l i m i t s.


60/62


H e l i c o p t e r D e s ig n , c o n t i n u e d

P e r f or m a n c e , c o n t in u e d

R o t o r Thrus t Cap ab i l it ies

T h e m a x i m u m r o t o r t h r u st c a p a b i li t ie s a re s h o w n b e l o w .

0 . 18

0 . 1 6

0 . 1 4

E

0 . 1 2

0 . 1 0

0 . 08

0 . 0 6

0 . 0 4

0 . 0 2

0 0 . 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0 . 5 0

L o w D ra g

H ig h D ra g

T ip s p e e d ra t io , / J

Source:

Helicopter Performance, Stability, and Control,

page 345, f igure 5.2 , by R. W.

Prouty. Copyright (~ 1 995 , Krieger Publishing Com pany, M alabar, FL. Reproduced with

permission of Krieger.)

R o t o r t h r u st c a p a b i l i t y

C v R o t o r t h ru s t

D e n s i t y o f a i r x b l a d e a re a x ( t ip s p e e d ) 2

"

a n d t i p s p e e d r a ti o

F o r w a r d s p e e d o f h e l i co p t e r

T i p s p e e d


61/62


Helicopter Design, continued

One- Hou r He l icopte r Des ign Process

R e q u i r e m e n t s

A s a n i l lu s t r a ti o n o f th e p r o c e d u r e , i t i s h e l p f u l t o u s e a s p e c i fi c e x a m p l e . T h i s

w i l l b e a s m a l l b a t t l e f i e l d t r a n s p o r t h e l i c o p t e r d e s i g n e d t o m e e t t h e f o l l o w i n g

p e r f o r m a n c e r e q u i r e m e n t s .

P a y l o a d : fi v e f u l l y - e q u i p p e d t r o o p s @ 2 2 8 lb = 1 7 6 0 lb

C r e w : tw o p e o p l e @ 2 0 0 l b = 4 0 0 lb

M a x i m u m s p e e d a t s e a l ev e l : 2 0 0 k n a t t h e 3 0 - m i n r a ti n g

C r u i s e s p e e d a t s e a l ev e l : a t l e a st 1 7 5 k n a t t h e m a x i m u m c o n t i n u o u s e n g i n e

r a t i n g

R a n g e : 3 0 0 n m i l e a t c o n t i n u o u s e n g i n e r a ti n g w i th 3 0 - m i n f u e l r e s e rv e

V e r ti ca l r a t e - o f- c l im b : 4 5 0 f t / m i n @ 4 0 0 0 f t, 9 5 F , w i t h 9 5 % o f 3 0 - m i n r a t in g

E n g i n e s : tw o w i t h s e a l ev e l m a x i m u m c o n t i n u o u s r a ti n g o f 6 5 0 h p e a c h , 3 0 - m i n

r a ti n g o f 8 0 0 h p e a c h .

I n i t i a l G r o s s W e ig h t E s t i m a t i n g

E s t i m a t e t h e f u e l r e q u i re d t o d o t h e m i s s io n . A s s u m e a s p ec i fi c fu e l c o n s u m p t i o n

o f 0 . 5 lb p e r h p - h . F o r c r u i s e a t c o n t i n u o u s e n g i n e r a t i n g a n d 1 7 5 k n f o r 3 0 0 n

m i l e , th is g i v e s 4 4 0 l b i n c l u d in g r e s e rv e . W h e n a d d e d t o t h e p a y l o a d a n d t h e c r e w

w e i g h t , t h e r e s u l t a n t " u s e f u l l o a d " is 3 6 0 0 lb .

E s t i m a t e t h e g r o s s w e i g h t u s i n g t h e H i s to r i c T r e n d o f U s e f u l L o a d t o G r o s s

W e i g h t c u rv e . T w o l in e s a r e s h o w n o n t h e cu r v e , o n e f o r c o m m e r c i a l h e l i c o p t e rs

a n d a s li g h tl y l o w e r o n e f o r c o m b a t h e l ic o p t e rs , w h i c h a r e p e n a l i z e d b y t h e n e -

c e s s it y t o c a r r y t h in g s s u c h a s r e d u n d a n t c o m p o n e n t s , a r m o r p r o t e c ti o n , a n d s e lf -

s e a l in g f u e l t a n k s. F o r a d e s i g n o f t h e 1 9 9 0 ' s , t h e r a ti o f o r th e c o m b a t h e l i c o p t e r

h a s b e e n c h o s e n a s 0 . 5 , w h i c h m e a n s t h a t t h e e x a m p l e h e l i c o p t e r s h o u l d h a v e a

g r o s s w e i g h t o f a b o u t 7 2 0 0 lb .

C h e c k o n M a x im u m F o r w a r d S p e e d

E s t i m a t e t h e d r a g c h a r a c t e r i s ti c s b y u s i n g t h e s t at is t ic a l t r e n d f o r e q u i v a l e n t

p l a t e a r e a a s s h o w n i n t h e S t a t i s t i c a l T r e n d f o r E q u i v a l e n t F l a t P l a t e A r e a c u r v e ,

w h i c h i s b a s e d o n a n u m b e r o f e x is t in g h e l i c o p te r s . C h o o s i n g t o u se t h e l in e l a b e l e d

" A v e r a g e D r a g , " t h e h e l i c o p t e r w i ll h a v e a n e q u i v a l e n t f l at p l a t e a r e a o f 1 6 ft 2 . T h e

m a x i m u m s p e e d c a n b e e s t im a t e d b y a s s u m i n g t h a t 7 0 % o f t h e i n st a ll e d p o w e r is

b e i n g u s e d t o o v e r c o m e p a r as it e d r a g a t h i g h s p e e d u s i n g t h e f o l lo w i n g e q u a t i o n .

[ 3 0 - m i n r a ti ng o f b o t h e n g i n e s ~ 1/3

M a x S p e e d = 4 1 1 . . . . . | ,

\ e q u i v a l e n t f l at p l a t e a r e a )


62/62


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Aircraft and Helicopter Design

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