(MOST P 1 4Ject ~N uwc-TN-19/

V/

i i NAVAL UNDERSEA WARFARE CENTERE5 SETEMBER i 967)

_ ii

/-UNDERWATER TOWED SONAR VEHICLES,

THE VJ/SQA-13 AND THE HYDROSPACE TOWED BODIES

I SABLIT DRIVTIESDORTW

by Mi. atten A1 R. . Olive, L

San Diego, California HEP C3 Ic1

This document has boon approvedfor public relhcwe and sale; itsi

CD,

S0 02 2"

I -

0'

TABLE OF CONTENTS

Pe

1.0 Introduction

2.0 Axis System and Sign Convention 3

3.0 Equations of Motion 4

4.0 Derivative Coefficients 5

5.0 Data for the AN/SQA-13 Towed Body 8

5.1 Equations Used for Computed Coefficients 9

5.2 Scaled Drawing of AN/SQA-13 (Serial #7) Body 13

5.3 Non-Dimensional Coefficients 14

5.4 Weights and Inertias 17

6.0 Data for the Hydrospace Towed Body 18

6.1 Computation of Coefficients 19

6.2 Drawing of Hydrospace Vehicle 32

6.3 Sunmary of Values of Derivative Coefficients 33

6.4 Weights and Inertias 45

Accv2:-, For7.0 Scope -47 i- 4T

8.0 Comments Juui 47

9.0 References 48

t -I

1.0 INTRODUCTION

v 1.1 Purpose

V This memorandum presents data to be used in stability studies of two

underwater towed sonar vehicles, the AN/SQA-13, Serial #7 vehicle and the

iHydrospace vehicle. Stability derivatives, weights and inertias, and ex-

terior dimensions are presented for both of these vehicles. The stability

derivative coefficients and inertias were computed from the preliminary data

available. Sources of data are shown below, and methods of computation are

given in the text.

1.2 Background

To aid study of the characteristics of variable depth sonar systems,

the Boeing Company, Seattle, Washington, has initiated analog computer simu-

lation of towed underwater vehicles under Contract N123(953)56341A. One use

of this simulation will be to predict tow test perf5 rmance, including stabil-

ity characteristics, of vehicles to be tested at later dates. This memoran-

dum presents data to be used in formulating the analog computer representa-

tion of two of these vehicles.

1.3 Data Sources

The AN/SQA-13, Serial #7 body (built by Telephonics Corporation) was

tested by David Taylor Model Basin to determine static and dynamic body char-

acteristics. Many of the stability coefficients were measured and reported

in References 9.10 and 9.11. Methods and values used in computing the missing

coefficients are from References 9.1, 9.3, 9.6, and 9.9. Weight and inertia

information was obtained from References 9.10 and 9.11, and from the drawings

of this body (Telephonics drawings 141J1013 and l4lJl1o4).

The Serial #7 body has been previously towed at sea by the Underwater

Sound Laboratory, Hew London, Connecticut. Results of this tow testing will

be used to verify the analog computer simulation.

1L

.1i

For the. Hydrospace vehicle, no testing has been done on the present

vehicle configuration. However, Reference 9.5 presents the results of static

stability tests made by David Taylor Model Basin on a configuration that is

similar except for wing.location. Sources for the computed derivatives are

explained in the appropriate sections of this report. Data used in weight

and inertia calculations is preliminary, and was obtained from Hydrospace

personnel. The drawing of the Hydrospace body was formed from a preliminary

drawing by Hydrospace Corporation and from photographs of the vehicle.

The nomenclature used throughout this report, wherever possible, con-

forms to that shown in Reference 9.8. Reduction of the equations of motion

to small perturbation equations is consistent with Reference 9.2.

'2

' I

2.0 AXIS SYSTEM A D SIGN COINEITION

,4.

l "0

The axis system ox, oy, oz. is fixed to the body with the origin at the

center of gravity and initially oriented with the x axis parallel to the

velocity vector. Velocities u. v, and w are small perturbation velocities

measured along the ox, oy, and oz axes respectively. The forces X., Y, and Z

are positive forward, along the right vi.g, and down, respectively. Positive

roll ( ), roll rate (p0), and roll moment (K) cotrespond to right-ving-doiom

motion. Positive yaw ( ), yaw rate (rand yaw moment (N) correspond to

nose right motion. Positive pitch ( ,pitch rate ( ,and pitch moment (M)

correspond to nose-up motion.

3

H

". ~3.'0 EQUAI OrlS OF lioT Oll " .

IX m[,! + q7r - rv]

y =[m[ + ru - p]

ZZ Sa[o + pv - qu]

* ~ ~ 6 +baLV1J I)qr

2 2+~u )p .(r) + I (P)

YW ax zIN U z) + (Ig I x)P-, - Iz.) + I z(qr)

3.1 For small perturbations these equations reduc to:

ZX~m~

ZY = [.- 3+rU410

ZZ = qu0

IK= Iz - lxz9

3.2 cpaudrd Equations of lotion

x x v v $x X. I +. x , + x + x + x + 0 . + X.4 + X. fU v u 1 4 q r

ly = yu+ yV + y +y + Y + Y rl + +T.+ Y.+ y_U v q r

U v v p qZZ zu + z + +. + + + + Z.+ + Z'4+ Z'f

v v v p q r p q r

U: ,M + .v v + v +M~ + .k.4 +." K Kq+. .l} + .4+p( qz r p q r

"K+ Mv + X" + + + M. + M, + M q + r + + .4"

u v v p q r p q rU v p q r

x + N + N v+ IT. + I.u + N. + 'I + 1I + . + AN. + fl. + N. f

u v u v v p q r p q r

B'

41.0- DER~IVATIVE COEFFICIENiTS

X X x.u 1/2 p 2 U0 v 1/2 p 2 U v 1/2 p t2t

0 0 0"

Y Y yU 1/2 PZ2 UO V 1/2 pL2 U 1/2 p 2 U

00 0

u / p2 1/2 = 1/2 p2

. 1/ Z 0q 1 /2 P 3U 0 = / p 3

TP 12p3 1/2 p3 U r 1/ It =0 q /P 3

0 ~ / A 0

Z ,p Z ' q = - - - - e Z r

p 12 pAU 0 1/2 qZ3U 0 1/2% p LU 0

x. x.x.XI. u Uf .x'.= v

U 1/2 pL3 1/2 p23 ~'1/2 p L)

I.I.I

1/2 PZ3 1/2 pL 3 1/2 PZ3

Z. z. Z.=I U ZI. = 1 21 V

1/2 pt3 v 1/2 ,Z3 v 1/2p -13

A. IX. aX

Y. Y. Y

~ 12 q 1/2 1/2p r

_. ;: , . ; . .- . . .2.;... . . .: : 4 .. _... 2. i : =zz z.

z'2 -,. --P 12 p 4 q 1/2'p t4 r I12 P t4

• ' ' z2 p uo 'v 12 p3uo v1/2 ~aLo

K K K

K= t*K' = - K =

u 1/2 pZ 3t v 1/2 pZL3U 1/2plOU0 00

M M

Y, = u M'I v M'! = v

.1/2 pj3U 1/2 pt3U00 :0

N N NN'u = O N' = 2 3 N' =

1/2 p.£3*@ 1/2 PtU 1/2' 3 U

K. K. K.

ii u 1/2 2 1/2 p: L 1/2

N"' . __ __ _ _

it M. M.

Nt'. MI __._= "_. = N.1/V1 1/2 p V4 1/2 pg 4

K K KK' K' S K' rp P14 q 1/2 r 1/2

M' ,XI. a ,P r..p / jU0.12P4 1/2 4

p / p4 1/2 0 4 1/2 Pt

K. K. K.

a r

p1/2 PIS q 1/2 p S r1/2 P±5

N. N. N.1 =- = a rP l/2Ots q .1/2 P:.ts r /g

Definition Exa:-1le.6

1I

X Force along the X-axis due to a velocity perturbation (u) in X direction (ft. lbs.)

U

:1 u au

I X = non-dimensional form of XI'U u

I = body length (ft)

SU = steady state velocity in X direction (ft/sec)0

p = mass density of sea water (standard) 2.0 (slug./ft3)

F

I

5.0 DATA FOR THE AN/SQA-13 TOWED BODY

I?r

8

.A EQUATIONS USED FOR CO-IUTED COEFFICIENTS

.i (a) X.(13]

(b) Y v wing wing zwing

W) wing wing 2

CLtail Stail 'ztail U

(C)~ Y. PU[(y,.) j3.

b tail

p tail tail 2 ztail U

zoodo0

(d) K b2

ie = pU2((Kp) 5

0 p wing Swing

S wing Swing (zwing

-L~tail Stall (Iztail)

+ (K'p)tail S tail 2

-Cpbody Sbody (zbody)2 EU0

(e pU2 [(,,j b2

-(Y' V)win; S Wing I zwing xv~ing

+CLatail Stal .'ztail £xtail

labody Sbody 'zbody xbody U.0

(t) K. = [Um + Ih) 1

p hx(9) N. C(M + mh)F W()

Where

n= ngl.e of attack (deg)

S = area (ft.2)

L = body length = 8.12'

b = span (ft)

U = steady state velocity in X direction (ft/sec)0

CL6 = coefficient of lift due to a change in tail surface angle

CLa = coefficient of lift due to a change in angle of attack

C = coefficient of lift due to a rotation about the X-axis

2

m = mass in ft lb sec

mn = hydrodynamic mass

Subscripts (tail, wing, body) refer to particular definitions,i.e., .S area of wia,/.

I tail = distance from C.G. to center of tail area in respectivedirection (ft)

x = distance from C.G. to center of wing area in respectiveXz wing direction (ft)

Lx body = characteristic length of body only = 7.87'

Iz body = characteristic height of body only = 3.52'

10

aQ

5.1.1 Values Used in Computed Coefficients

(a) All length, area and volume values are referenced to the drawing of

section 6.0.

(b) TEPM "VALUE REF.

a body -.015 9.1

V wing -0116c 2 9.1

(Y'.)wing .ll 9.1

CL6tail/deg" .68T 9.1

(YlI negligible ---fvbodyF v tail negligible •

(Kp )wing .26 9.1

(K'p tail .2208. 9.1

CLpbody .04 9.3(N' ~wing .2155c 9.1

CL ail /deg 1.02 upper, .938 lower 9.9

CL /deg .04 9.3

(C) K. P (m + %)lz upper tail 43.5

'-(n + Mh)lz lower tail =14.2

z upper wing

+ M)Zz lower wing' 15.0

92J1b ft

where m u=er tail = 3.49

m lower tail = 2.362 2lb secm uncperin = 1.585 '

m lower wing = 2.12

L _11

zh upper tail = ffpa 2 = 30.2

lower tail = irpa 2 = 13.9 Ref/ 9:6'h upper wing =l.-fpa 2 = 5.94 lb sec 2

mh lower wing = 1.85wpa 2 = 6-45. ft

a upper tail = 1.29

a lower tail = -. 8745

a upper wing = .4375 ft. P 5 78 Ib'eft4

a lower wing = -.4375

£z upper tail = 1.29

z lower tail = -.8745

z upper wing 2.581 ft.z lower wing -1.T49

U12

12

LUA

ci CC Lon)=' - - LLU * LQ

;:- -. - 1 -

-L to FE

C CDi= L_ -j

CD_ CD

C.3 coCC*4

CC'

C.L.

C..

co C,4LL

I-. 1-. co c

CC,

ccLi..

.') .- x-

C,:

.4S1-

c) CD)4'o CIO miI.

CC:)

Cr! c: Ci

C.C.,

elk::CN a-

____ ___ _ - -

"5.3 NOUDIMENSIONAL COEFFICIENTS

Reference: DI'MB Report 153-H-01

X' See Fig.,5.3 Y? ---- "u u u

V' ' -0.49278 '

X' Y'-- Z' -0.14268

X. -.015* Y' Z'

X' ---- Y -0.22140 z.

XZ'. -0.o686

X' ---- Y -.00175* Z'p p p

S-- Y1 Z' -0.0269P q q qX ---- y' 0.13660 z -

r r rX . --- Y' • -------.

P p P

X'. ---- •Z. 0.00483q q qX'. -Y' 0.01348 Z. -

r r

K' I N' - -

K' -0.02550 M' ---- N' " 0V V" V".

K' ---- M' -0.03724 N'w v

K'. MI.- - N'.- -

KI' -0.04250 M'. ---- N'. -0.00187V V

K'. --- M' 0.00585 NI'.

K' 0.00462* M' ---- N' 0.0081 *p pp

K' --- M' -0.04570 N'q q q

K' 0.079 M' ---- N' -0.0802r r r

K'. 0.002815* I'. N'. 0,00805*p p p

K'. ---- M'. -0.00303 N'.q q q

K'. 0.01591 M'. fI'. -0.01417r r r

Cor uted Coefficients;,assum.Ied nee1iglble for small erturbtions

I-I -

I I .r 1 . 7 1 .. I I

: ii , i i ..- .

I "" --I I I I I "

. . i . . . . . . . . . . .

i, , . . . .7

,, ,, .I; ,---.+ . _ --,,. .-- , i

- : ., , • .,.,

-- -

• LI

.:i'. , . . . . . . .. -~ "'-%.. - -- ;"

/___ 3_

* --________ - - - ' "-.'- -- -: .- _______, •- •:.. . .

..4 * L',_,_ _0l.,. •.• I __= I _ _

I I " • •• 15

-"L ~ ~ . ..= I """ . " """" ": I ° i _ _ ; , -

" I _.- :"

• " ":. _ _ _ _ _ _ _ _ _ i i i, _ _ _ , ! ,t : , i i , ,_ __,_,_ __I, , i i

.. ! }- : 7*... . -

-- _ _--_ _ . .... .. . . . . 0

___ -- '4. ,-

:-. . .. . . .._ __ ____= . ,- -- - • --. -

, , ' . • • * .. * ''.e- m. ' .... . ...__ _ _,_._ _

--_... -'+ H - :. 0

--'____ 5 ... 'l. .,a' i - y_ .h,.._ _ _-- -- I1 . . . I 4 •... . S

C -;, % T :' "~ .

oo o 'I c0 C) 0. 0 0

C '. ,a S ,I a a a,

oOI ,

... . ... .. pivot7

5.3.1 TRIM TAB COEFFICIENTS

6Horizontal tab = .004 :

6!1orizontal tab 6- -

where 6= tab angle

5.3.2 TRANSDUCER COEFFICIENTS d.D

14 .8.196qq

* i. =68:4: q

7.3.1 M Dtotal (" )

DI1 + D2I13 2 4

where DI = 2q2(dl)(Z - Z1) = .354 q2 b sec1 1 1 2 1 radI = £ + ( 1)=1.682 ft

.3 12

D = 2 - 12 ] d( _ 1)]= 22.313q2 lb sec

2 rad2

I4=£ + L (I2 41) 2.16 f4 •

q

=(mtransducer + Mhtran.sducer q

where khi. rt. cylinder g

2 1

Where

I = length in ft q = rotational velocity about Y-axis

D = draz force Ij = bydrodyne.ic mass

S = area in ft2 M = mass in ft lb sec 2

V = velocity g = acceleration due to gravity

r = radius of cylinder

16

5.4 WEIGHTS AND INERTIAS

TOTAL STRUCTURE TRANSDUCER FLOODWAPER

Wt. in Air (Ibs) 3800 2840 960 2000

Wt. in sea water(lbs)5000 2404 596

I 116.14 51.96 11.82 52.36

I 453-07 11.82 11T lbs ft sec 450.81 9.56

i.62 11.62

Inertia computed about the X axis through the body center line.

*Other cross products are zero by symmetry.

17

I

! 6.0 DATA FOR THE HYDROSPACE TOWED BODY

k

18

.r~~~ffr~|Y t',,-*l -

6.1 COMPaUTATION OF COEFFICIENTS

Added Mass and Inertia Derivatives

Added mass and inertia derivatives were estimated using the following

representation of the Hydrospace fish: the body was approximated by two

semi-ellipsoids-of revolution, the wing and tail surfaces were approximated

by rectangular plates as shown in the following sketch.

Linear and rotary acceleration derivatives for the body ellipsoids, and linear

acceleration derivatives for the rectanglar plates were computed using the

methods presented in Reference 6. These basic acceleration derivatives were then

combined to form the acceleration derivatives for the complete fish.

The following expressions define the basic component acceleration derivatives.

Semi-ellipsoid, linear acceleration

X. = (k1 4/3 npab2 )/2

Z. -. Y = (k 4/3 npab 2)/2

w v 2

Semi-ellipsoid, angular acceleration

M. = [k' 4/J5 npab 2 (a2 + b2)]/2,q

where a and b are long and short semi axis lengths, respectively and k., k2 and

k' are constants defined in Lamb, Hydrodynamics, Chapter 5 section 115.

Flat plate, linear acceleration

Z. = 0- a b,4

Vhere a and b are the lengths of the short and long sides of the rectangle,

respectively, and k is evaluated in Reference 5.z

Using these relationships, the following values of elemental acceleration

derivatives were comnputed.

Elemental acceleration derivatives

Body:

X. -2.13 . = -1.22 X -.911 2

19

41~ 7;

FORWARDBODY ELLIPSOID AFT BODY ELLIPSOID

.71 x 1.31'x.3 1.31'

3.7'

VERTICAL FINIPANEL,

78' x134

REPRESENTATI Oki OF HYDROSPACE FISH USED

IN ESTIMATIUG ADDED !4ASS DERIATIVES

20

Z -20.95 Z. -595 Z. -15.0

M.B= -59.2 M. =B -3.28 m H. 559

-26.4 M. = +5.85 -32.2

• Wing:

1 Z.iww -. .86 Z. =Z. =-.93

Horizontal:

Z = -2.o4 Z. Z. = -1.02

kHT wilT1 iHT2

Vertical:

Y1 = -1.23

Coordinate locations of the centers of the flat plate areas are designated

ywl YHTI, YHT$ Zt etc-, where the subscripts wl and w2 indicate the two

wing panels, HTI, HT2 indicate the horizontal tail panels, and vt inaicates

the vertical tail panel.

Typical units for these elemental acceleration derivatives are:

X lb. sec. 2/ft.4. ,ft. 1b. sec.qMe4, lb. sec.2

21

6.1.1 Formulation of Acceleration Derivatives

Using the foregoing elemental derivatives, the complete acceleration

derivatives for the fish were computed using the following relationships.

. 13B1/2 pZ3

Y'. = (Z. + Y .3

t i, - .z.p 13 - B + vHT 2 2

M.. V (Z + Z. T)3

N.

V pyv t

z.

['* -~--.. (..Zvtoa + XB - Z.T XT/2L pLt a.

2 2o

Y.

= (M- Z---HT

' !0t =(-Z B XB - Z B X3 +Y. X )gpr

NI( y.) + z. , + y tz(t /1

22

. ....... ...... .t

Ni. = E

p

M.

-Y," X5A

i.p

>1 2.n'. = y= M.B 2 P s

4.B . -....

Zq = = (Z.u )lpZsu

3.w . 0e

" = = (y;. u)/ pjSu "

ro

Certain assumptions are incorporated in the foregoing expressions for the

derivatives. It is assumed that the derivatives X., X., Y., Y. Z., Z., K.,

K., M., "., N.6 N., X., X., Y., Z.) Zi, K, M., M., N. are zero.v U w p r q pr p r q

It is also assumed that body contributions to roll moment, side force, and

taw moment do not change with a , and that the tail surface moment length in

the X direction changes negligibly with changes in a . Effects of vertical wing0

location from the axis origin are assumed small.

23

6.1.2 Hydrodynamic Derivatives

Hydrodynamic (q dependent) stability derivatives for the Hydrospace fish

were computed using, wherever possible, the methods presented in Reference 9,

and using the basic lift, drag, and moment data presented in Reference. 5.

Reference 5 concerns a fish identical to the fish considered here except for

wing location. The changes in lift, drag and moment coefficients, total and

tail-off, due to the difference in wing location have been ignored. Down wash

angle effects and interference effects associated with the correct wing location

have been included in rotary derivative estimates.

The following pages show the equations relating the dimensional derivatives

(i.e., X . X . etc.) to the nondimensional derivatives used in conventional

aircraft analysis (i.e., Cetc.), and the methods used in calculating

each of these latter derivatives is discussed.

24

L r~~~~~zi.__ ,, , .- __________.n'i Y~l

I. Ii

Hydrodynamic (q dependent) derivatives

x ax PU S(2C).

ax s0v av

3w 2 'o xCi-U0 X

u au

0

aw

u au 2 o s(2cZ

v av

- pUo2S(Cv w 2 oztu

K K

V av 2 o t0

3 K

25

A- -ns-

am 1 )

M a, 2 .~pU o Sb(C n

xm 0

0 0

U aq &

X ax 0

r ar

x y- 0q aq

x 2y- U S(r ar 2 o r2 0

_z 0

p ap o ypU

zf _a -?I pq2S(CL b

p aq q2

26

-r ar

K i pU 2 Sb(CZ )-

qKq ag.

K= 1pU 2Sb(CZ) .r ar 20 rU

~ampap

73M 1 U 2i

q~~ qq 2 2U0

r ar

p -p2 2U

- 0

q aq

N R pUSb(Cnbrar 2 o r 2U

z L pU S(C )-

V3* 2 o0 a. 211U0 0

M.'M 1 USF' CL,v a* 2 0 o 2U

0

6e ade 21 ~

27

z dL 1 pU2(~6e 8e Z6~

6e 86e -PUO SC(C s)

y R ipU 2S( C )6r 36r 2 0 yar

K6 LK pU. Sb(CY.r

N ~ pU 2Sb(6r 36r 2 r n6r

28

6.1.3 Methods of Derivatiod of Aerodynatic Derivatives

CC z These derivatives were resolved from the lift and drag data of

Reference 5. The somewhat peculiar shape of the C vs a curvex.

arised from the component of lift resolved to the X axis, and reflects

the stall of the wing at about 180 angle of attack for the wing (with

an angle of incidence of 110) while the relatively large tail surface

remains unstalled.

Data from Reference 5 were extrapolated to obtain information for

an 110 incidence angle. The test data in Reference 5 includes data

at 00, 50, and 100 incidence.

C. Values of this coefficient were extrapolated from the data of Reference 5.

, C, Cm . These derivatives are the slopes of the Cx, C , C vs a data.

ma za zSince C and Cza are approximately constant for a large range of a,

these constants are used in computation of M' and Zw w

.CL -C ; Cm c. These damping derivatives were evaluated for

o q

0 0

wing-body and tail components using the methods of Reference 9.

CL. cCm. c The tail contribution to these derivatives, a

dowtvash-lag effect, was evaluated using the methods of Reference 9.

Wing-body contributions to these derivatves as evaluated in Reference 9

are added mass contributions, and are not included in the hydrodynamic

29

derivatives. The added mass derivatives Z'. amd Mt. constitute anV U

evaluation of these quantities by other methods. There is, incidentally,

an alarming disagreement between the added mass contributions to V.

VVand M'. as computed by the methods of Reference 9 and Reference 6.

acy acCyc = n = . These derivatives were evaluated for wing-body

U U0 0

and vertical form contributions using the methods of Reference 9.

Yn nb " Body and vertical form contributions to these derivatives werewer

derived using Reference 9. Wing contribution was ignored.

3CnCar 3 rkb Body and vertical form contribution, in accordance with Reference 9

were utilized. The wing contribution D is small in comparison with

the other contributions.

I' acCt = . Reference 9 methods were used for vertical fin and for wing

o0

contributions to this derivative.

actC = . Wing contribution, a function of CL, was evaluated using the datar no

0

from Reference 3. The vertical fin contribution, a function of CZ of

the fin was also included.

30

-

Cy. Wing-body and vertical fin contributions were computed using

0

Reference 9.

3C

C 2Wing contribution, a function of CI and vertical fin contribution

YU-)

were derived from Reference 9. .

= - 0- .Wing-body contribution was computed using the value suggested in

Reference 7. Vertical tail contribution was based on the side force

coefficient Cy and the side slip angle resulting from the rotation p.

31 -Io

6.2- Drawing of Hydrospace Vehicle

ROSE SECTION TOW POINT COINICIDES W'ITH 0.25 MAC2:1 ELLIPSE 45.0 _________i40 ~ CENiTER OF TANK3.

WING INCIDENCE 11* --. 7.~35:1 ELLIPSE NCO1

* FLATTENED ON NC01

27110 0.25 M~AC-j4.

[I IACA0015 *

39.022.0

4 .62 11.5

32

6.3. Sumarm of Values of Derivative Coefficients

6.3.1 Hon-dimensional Coefficients, Hydrospace Fish

Summary of Stability Derivatives, Force

x ( (.0845)(2) [ 4(X'aX]

x'w, ('°845)[f10(a:o)] x.,x,,x','.,Xr,

x'. = -.00675 X'., X' X' -0* U p q

Y1 = -.324V "

V . = -.o645 •, " Y- yu Y 'w Y YI* ' Y 1q

Y, = (.o275)[f .'o_' . 0 op q-&-.0-

Yr = -.0645 +.247

Y'. = -.000535[f (a )Jp f150aoSY'. = +.0126 .r

Zu (.845)(2)A 1(c)] Z'v Z'I, z, zfp Z'r,Z' =Z'. Z' 0

-.425 '

Z1= -.0722 + (.0055)(f (ao)]3o0

Z = -. 06115 -.214

Z'. -.0139q

Underlined quantities are q dependent, other quantities are added mass terms.

For f4, see Figure 6.3.3For fl' see Figure 6.3.6

For f8 , see Figure 6..3.5

For f15 ' see Figure 6.3.9For l' see Figure 6.3.7

For f3, see Figure 6.3.1

33

6.3.2.. fNon-dimensional Coefficients, Hydrospace Fish

Summary of Stability Derivatives - Moment.

K' = (.055)(fl(a K'u, K' , K' K' , K, u 0

K,. = (-.0o0542)[f (ao )]v15 0

K' = (.0186)(f 4(o)] -

I, x (.o186)( 5 (a)x 0* .K'§ .oo8 - .oooo 6 [S )

K-j =-.000382-.006K'. = -.000286[f (a)]r [15 (a

MIu = (_°lO)_2)[f2(__)] MI, 1', 16M, M' , M', MI M' J - 0

M' = -.0378

M'. -.0108 + .000742[f7(ao)]

M' -4.122q

M'. = -.00540

N +.o67 N', N', N', N' , N'q, N'r, N'- 0

N'. +,0134v

N = (.0186)(f 6(ao)]

N = -.216

N,. = (-.000286)f [l(ao)

NI = -,00472 1

Underlined quantities are q dependent, other quantities are mass terms.

For f,, see Figure 6.3.1 For f2, see Figure 6.3.2

For f;5) see Fisure 6.3.9 For f, see Figure 6.3.4

For f4, see Figure 6.3.3 For f6, see Figure 6.3.4

SFor f' see Figure 6.3.3

34

6.3.3 Non-dimensional Coefficients, Hydrospace Fish

Control Surface Coefficients

x 6eevator +.0845 U [f13 (%)]

Z =+.0314 uS6elevator 0o

M6elevator +0183 U0

6rudder -.0316 U0

N6rudder = +.0167 UK .0

K6rudder +.055 U [fl (a.)]t4o

Sign convention: +6e -+M

+Sr +N

35

- __ rL i

"mp

7T Z .,

,- r - ~ -.

- 777:: . := 7 -17

J-7 77TI .

V- 71

It-4 -:::7

40I__

_LA. ~~__.,

Fl _77$

7i : r.: .- .. .. .-..

K ~ I -1-71

... . .. .7

L A-1----

17 f7

-t PL_ -3 --

- -----

101

... ......-... :H 7 w1 F

Fiur 02 37 - 4.

-: 4

- -- - -

Vi

0E

... .. .. *:;-_

-: M

Fiue .. 33

11H:1

-5-.. -7F-

2..

n-4 -7j-U :=T

U ---- - F .,.77.77 -

2. ~A I L 4 ..H

Fiur 6 .43

47-

qfEi E HE

Ai - 's 4..

17... --- ---

147 7:---.

.. ... ....... .

1-17-: :7

Figr .3454

t ft t'-r -r

0

~ . 4 .. t - -*-------______

__ __ t-

H~ T_-

_

r 7=r =

. ......17

-.-

rn_

_

-.. ... ...

I

7---____

Figur 6..-

--

tat

o Li

a {-7.7r-~. 77-'-I

t-

tj 7- __ v

.... ... K T .T... ~ ....._ ._ _

::* . I-7 - - 1-. - I - - .. : 7.

f. 4

7 hi77

-.- 7j 7

C 77

Figuze 6 .74

-

I-

- n 1

---.T-*-:*"~- -

y. :t- 7 tt..

-74- 7: - ::

::.

.. ...... ... ~

.. L::: ...-.j

Figurei 6i3t8jI3

F-~ ~ ~ ~ ~~F -I- - -- - - - -- - -

c - 4 - -.. 4i

-- 7

2-: ''7:-

q- :

-774. -E:

I -7

Figure 6.. 4 ...

6.& WIGHTS PmD IETIAS, .YDROSPACE FISH

The folloing weights were used as a basis for the mass and inertia estimates:

Weight of body (without tank and electronics) in air 440 lbs.

Weight of body with tank and electronics in air 570 lbs.

It was .assumed that the wing and tail surfaces have a density of 10 lb per

sq. ft. of planform area, giving weights for the wing, horizontal fin and vertical

fin of 41.4 lbs, 32.0 lbs, and 19 .4 lbs, respectively. The remaining body weight-

3427.1,-L was assumed distributed uniformly over an ellipsoidal surface of length

and maximum width equal that of the body.

The volume of entrained water was assumed to be the volume of the body shell

less the volume of the tank. A better approximation than the ellipsoidal shape

was used in calculating body volume ( 15.3 cu ft). For the inertia estimates,

the mass of entrained water was assumed to have the inertia characteristics of

the ellipsoid (but solid) used in representing body shell inertia minus the

inertia characteristic of a volume of water equal to the approximate tank shape

(cycindrical with flat end and size.

The ta k and electronics weight was assumed distributed uniformaly over the

tank volume.

Inertia data is presented for an axis system with the x [xis coincident

with the body center line.

No attempt was made to rationali ze the anomaly of havi.n the center of

gravity on the body center line and at the same time having the vertical tail

and wing masses not u setriceally distributed. Instead, the cross-product of

inertia that would result from the isolated tail mass is presented.

5'.ce tainties in the weight distributions (eand other u-ncertainties arisiig

In calculation of the stability derivatives) will be resolved by precise physical

measur-.ents later in the program.

145

6.4.1 HydrosDace Fish

Weights and InertiasENiTRAINiED

TOTAL STRUCTURE WATEWATER

Weight in air (lbs.) 570

Weight in seawater (lbs.) 90

I 19.78 11.58 8.2

I -2o6.73 109.93 96.8I lb. ft. sec.2 20.96 111.16 96.A

zi'I -2 .32 -2.32 0

Inertias computed about the X axis through body CENTER LINE.

Other cross products are zero by symmetry.

I 'includes only vertical fin ,+ rudder) contribution).zx

II

I

"k6

1.0 SCOPE

Data in this report is preliminary in nature, and may be modified as

testing proceeds.

[I I8.0 COMMNTS

The dynamic damping terms IL',! .Z' and N'.(presented in Reference 9.10

and listed on Page 14 of this report) are of such sign as to give negative damp-

ing. The location of the reference point for the derivatives for the AN/SQA-13

is approximately the center of gravity, and is well aft of the tow point. This

K aft location of reference for the dynamic derivatives may account for the seem-

i jingly incorrect signs of these derivatives.

47

1 1

"9.0 REFERENCEIS

9.1 Boeing - Final Report, Development of High Speed TowinE Cables/

Underwater Toved Body - Part II (U), Vol. II of II; January 12, 1966;

The Boeing Company, Aeorspace Group, Seattle, Washington.

9.2 BuAer ReportAE-61-4, Fundaentals of Design of Piloted Aircraft

Flight Control Systems, Vol. II "Dynamics of the Airframe", Bureau

of Aeronautics.

9.3 Etkin, B; Dynamics of Flight; March, 1963.

9.4 Gertler, Morton; The Hydrodynamic Coefficients of Cable Towed Bodies.

9.5 Matthews, John T.; Subsonic Stability and Control Investigation of a

Full Scale Model Project "Position Towed Body"; David Taylor Model

Basin Aerodynamics Laboratory, Report 1339, Aero Report 960.

9.6 Patton, Kirk T.; Tables of Hydrodynanmic Mlass Factors -for Translational

Motion, ASmn's, 65-WA/UNT2.

9.7 Perkins, C. D. & Hage, R. E.; Airplane Performance Stability and Control,

I 1960.

9.8 Technical and Research Bulletin No. 1-5, Nomenclature foi Treating the

Motion of a Sub.ere da Body Through a Fluid, April 1952; Society of

Naval Architects and Marine Engineers.

9.9 USAF Stability and Control Datcon; Air Force Flight Dynamics Laborator.;

Wright-Patterson Air Force Base, Ohio.

9.10 Walton, C. 0. & Brillhart, R. . The Stability Derivatives of the

Schene 'A! Body Used -with the -:r/SQ.-13(.i-!) Variable Depth Sonar

Syem; "T!._,3 Re-zort 153-H-O. of M-ay, 1966.

9.11 Walton, C. 0. & Ra sey, J. P.; Predicted Steady Todinz Ch-racteristics

of the c het. e'A' Body and Cable Con _ -ura tions for the "3 -l)

Variable Deoth Sonar S'ste.-- (U), DT .26 Report C-2230 of June 1966.

48