AD-AOBO 465 IYDRONAUTICS INC LAUREL MO F/B 13/10TOWBOAT MANEUVERING SIMULATOR. VOLUME 111. THEORETICAL OESCRIPT-ETCtU)MAY 79 E R MILLER OT-CS-840165-A

UNCLASSIFIED 7909-1-VOL-3 USC-D-63-79 NL

I muuuuuuuuIiEEEs///ll//l///,MEN~llll

Report No. CG-D-63.-79 1

TOWBOAT MANEUVERING SIMULATOR

VOLUME III - THEORETICAL DESCRIPTION

00( I E'r

EUGENE R. MILLERj JR.E

FINAL REPORT

MAY 1979

Document is available to the public through theNational Technical Information Service,

Springfield, Virginia 22151

LA-.-.J

Prepared for

U.S. DEPARTMENT OF TRANSPORTATIONUnited States Coast Guard

Office of Research and DevelopmentWashington, D.C. 20590

30

NOTICE

S:. This document is disueminated under the sponsorship of the Departmentof Transportatlon in the interest of information exchange. The UnitedState Government assumes no liability for its contens or use thereof

The contents of this report do not necessarilv reflect the official viewor policy of the Coast Guard; and they do not constitute a standard,spcifcation, or regulation.

This report, or portions thereof may not be used for advertising orsa promotion purposes. Citation of trade names and manufacturersdoa not constitute endorsmnent or approval of such products

II

L •.

ILI

I Iii I I t i

I It

jisr

I a af~ fll, a A'

Ila % 11s1Iii -ABI n UAITnj~j

m ua voi zo om

in, T*6haicel Repo.. Decume.ti.n Peg

2. 5eGveino'. A sse,., . 3. Reqp.g so,' C60e416aN.

D-E:3-792

4 Towboat Maneuvering Simulator May 079Volume IIlyTheoretical Descriptiono e.

(~~Eugene R.- Mill1er, JrY .' 7909-1V~L9. P~M,,*A,,,t,, laO e m ime o iw- .. -P .--- so' N-.. fte N& 41rlTAAJ

Hydronautics, Inc. o--. W., -6-- %a .

Laurel, Maryland T'" DOT-CG-84Pi65-A 4

12. 5eq...n.. Aeegp None ad Ad&*$

U.S. Department of Transportation ep 878- May 079 /United States Coast Guard %,,_._ _ __IL__Office of Research and Development 'f. Agrom-- CodeWashington, 0. C. 20590 _ G-OSA-l

IS. S"016000fory "iie .....

The U. S. Coast Guard's technical representative for the work described hereinwas David A. Walden.

14. A4ba W .. .. .

N-The Towboat Maneuvering Simulator is based on the integration in time ofthe differential equations which describe the motions of the towboat and bargestring in three degrees of freedom, i.e., yaw, sway and surge.

'This volume of the simulator documentation provides a description of thebasic equations of motion included in the simulator and the relationships usedto determine external forces and moments due to a bow thruster and wind. Theseequations are completely general in nature and could be used, with the properhydrodynamic coefficients, to describe the maneuvering of vessels other thantowboats.

17. Key Wosi ' 1. Dsimh..s,. St'. m,' "

Towboat Documentation is available through theManeuvering National Technical Information Service,

Springfield, VA 22161.

19. £eewnep CI o#*$. (e " Aie .ewtl 'U. S0aiele. Cloe. (41 twe e) 21. N.. of Poo 2. Phe"

Unclassified

Pen n DOT P 1700.7 (-n) Iep mdveti of e wmelet d p e. eu"l Aed . 7 Y snd

HYDRONAUTICS, Incorporated

TABLE OF CONTENTS

Page

NOTATION -.. .............................................. i-

1. 0 INTRODUCTION ...................................... 1

2.0 14ATHEMATICAL MODEL................................. 2

3.0 EXTERNAL FORCES .................................. 13

3.1 Bow Thruster ............................... 13

3.2 Wind Forces and Moments ................... 14

3.3 Other External Forces ...................... 17

4.0 CONTROL SYSTEMS .................................. 18

REFERENCES ........................................... 19

Acceaeliou For

Juatifiti on

By--_________

* Ave11l'b111tv C A r.A all wid/or

Ds{ spec l

..........

LOTAW

DIRECTZOIAL STAUZLZT AND M0flIM

The t@oil~nomenclature conforms to DTm Report 1319)and IMROC RI'rt T-10 Where applicable. The pos~itive direction

Figure 1.

Symbol Ifandlocnaional Foiw Definition

2 ~Constant in quadratic fit to axialpropeller force equation XO~ f (")for each of I segments wher: Wi u 1,2,

3,41en &1a Cu t n~ u 0i appropriate

b First order coefficient in qua--atle fit to axial propeller

force equation XIP*8 -0 , - q

foi each of Ith sefimrnts, whre

I.. - 1.1,

a t Soewalaeaeauocond order o Ieficent in

quadrat rle fct t o axialforce equation X -= " (

for ~ t each ofofor each air I segints MvereI - 1,2,3*4

AD AD' - A Adiann-I

U" " Center of buoyeano

cc Center of ma of ship

U Propeller dameter

t - Steady-turnlng diameter

I'sito- Moment of inertia of ship about:x' x' .pr.Sx axle

S M.?oment of Inertia of ship about7 Y PV y axis

I '~~LMoment of Inertia of ship about

S j, uPropeller advance coeffiicentnD bsed on ship speed. '

Je . - Propeller advance coefficienta nD at steady ship command speed e

Z y' - -" Radius of gyration of ship about% k 1 6 ,,x axis

k Radius or gyration of ship about

!s I !' - Radius of Cyrataon of ship about

A 1' * 1 Charaeteristic letieth; lengthbutween Verpndiculirs Car Ccm-aerelal UhIpaI

A4 a nm Dyamic albillty lover

A. A Damping laver

v .vIf N,' Sfatr stability lever

a as mes of ship

X mqe H ydr r Sdnaue moment coamponent

W s -LU5 sou - axis (yawlnG moment)"A NA Aerodynamic A oment comont

A • NAO * Aabout 9 axis

3.

* N. N3- Yawing moment when I Or O

pro First order coe ticient used inWr N jpL'3 representing N as a function ot r

W 3 * Prlt order coefricient used InInh rq IPL'U - representing Nr as a function ot

0 (q-i)

, * i b'coefficl.nt used In representing

N *asa f•untion of

Mrjrj %~I' s .. Second order coefficient used In_r jpf s " representing Hi as a .unctlon ora.

Nt!. 1g ~. Coefricient used In representlngirier ror as a function of r

II $, iff -IP- First order coefficient used In* representing N as a function of

n" N '- First order coefficient used is

ipev representing W. as a Function or

St we's Coefficient used In representin

*IVi N asea function o

Ivir- Coefficient used In representing

Not .I! I Second order coefficient used,1 XllI jp. In representing H as a function

of v

S First order coeffic'Lent used In- 1104' jpL' representing U.1 a a untionof (4-1)

pe "Or -oFirst order coefficient used inW ~ If.'U'representing it as a function of

Or

N N O, First order coeatlfent used In, pL'J reprotenting 3r a3 a function

of (q.1) 3-

!k_ zU., j~ S "

n P'ropeller revolution ra.te

ne Propeller revolution rate atretcady cooind i. cJ

% Ordered proplllor revolution rate

a, -, . Overehoot width oi path

0 Overshoot heading angle; measuredfrom value at second execute

* N' - Steady-turning radius; mL

Fr*" rt, 0 Angular velocity component about.

U a axis relative to fluid1L'% Angular acceleration cooponent

Us about a axis relative to fluid

T TO@ Tactical diameter

IllG- I ransfr"

to aTimtl tiee YLL

t1 ' - Tim at Ith execute In an over-shoot or :,gzag maneuver

tt _0-~ Time at Initiation of a maneuver

90r of heading in a turn lf

StlO t10 "Time to reach 180-degree change

18O 1 1 of heading In a turn -

• Lnear velocity oi origin ofbody &aes relative to fluid

' ,Component 6C V In direction of

direetion the z axis

a Command speed; steady value of4U ahead speed component u for agiven propeller rpm Cor P - Or - Osign changes with propeller re-versal

c Linear velocity of current

Ue Component of cc In direction of x axis

Linear velocity of origin or bodyaxis relative to fluid

tin Component orf 11 in direction of x axis

11 PVelocity at rudder due to motionand propeller race

UA Vind velocity

V* Component ot U4 In direction of y axs

comwonent of UR 1.1 direction of y axis

" Absolute speed i1 knote

I Steady approach speed In Itnota

V9 Speed in knots at 90-dereeheading chane In a tarn

Viso Speed In kots at 180-decreeheading 41Ai ie in a twusi

V vo .1 Compoent of V In direction otthe y axis

. 1Time rate o change st v tndirection of the y axle, tLongitud.Inal body axlm; also,"the coor-11nato PC a pIlnt rela-'' "

tive to the origin of body axes

x~S -- The x coordinate ofr CB

I *%. - - Tho x coordinate or Co

K K---.---: :,capoe-A A ~ A

• ' f Aerodynamic aore componen along

it zoo , A ,coot, lmr to oft"he dlzplmce~mcot"

of CO relative to the origin ofa set o." fixed axes i

Xy - ]Ry)drodyname force conponent "

*peg, ' along x axis (longitudinal. orazaL. ore)3

,eI X -r " Second order co tlcelat usedI in representing I as a functionof r. Firat order cocLienPt."

Is ZoreZ- -X4 Coefficient used In representing

i. X as a function or Oa

a -W Second order coefficient used*p~a in repretentIng X as a function

at u in the non-p-opelled case.First order coerficient Is zero

Z Coefficient used In representing" ' X1X a8 a anotion of the product

Yr

I,, I' . Second order coefficient usedTV in rspr,.Sent ng X as a functionoa v. First order coefficient A

Is cer-

• ,- First order coefficient usedTV L In representing XW as a Cunction *

of (q-1)

r X Second order coeftcient usedP }pL'IJ' In represent mg X 3s a (unction

of sr at I * 0. First orderc',efflclont Is toeo<:-2rr~lt~lt; lllr

r-- . Second order coetflcient usedbpfU4 in representuin Xgrr as a

flunotion of tk

y * - lateral body axis also the co-

Li ordinate of a point relative to

the origin of body axes

73The T co dinate of C1

r e' 'The y coordinate of Ca

76Sys A coordinate Of the displacement

or CG relative to the oriin of aset of fixed axes

YY* -- - Hydrodynsate force cooponent alongWs y ax±s (lateral force)

YA•

Aerodynamic force component along

TpA- UAa Y &ixL

o. ye La tra I force when - - 0

Distance at port pcopeller fromP cent. ruLne

T DistAnce ot starboard propeller two.a center1JAt.

T ' First order coefficient used in.j Y pL" representing Y as a function of r

TIM- .oe% First order coaciclent used inr*. jprepresenting Tr as a function of'

r .* ( saq-uI) to t" "*7r

T T I - Coet"iclet used In representingSIre as a. function of

l* r Second order coefficient it

win Y rI U representing T As a function of r

S-- 'irat order coeficcient used niTv, 1 V Jrepresenting Y as a function of T

Y First order coefficient used InTq vq x'U representing as a function of

l- Coefficient used In representlngjpL5 Y as a function of t

'win Tj J I-.k Coefficient used In representingY as a runction o r

T cfvi Tlvje Second order coefficient used ",iI)pL ropre~entnZ Yf 3s 3 Cunctlon o V

Yv v.'q vsoi First order coeCrcictnt used in

or (R)-7

Ta a. 1oe representing4 Y as a f'uncrtion of 5P .

, ,First order coerflcient used InTom arn J'Q representing Va as a tunctlon of G

lAngle at drift

Anale Of dritt relative to fluid

p P Deflection of flankJng rudder,

63 Deflection ot steering rudder

th5a Steady rudder angle at I executaIn an overshoot or :igzag maneuver;I - 1,2,3 .. .

6FLF- _' Flan"ing rudder deflection rate

a _ __ Steering rudder deflection rate

Ship propulsion ratlol "

elh~~ Toh " lhe ots of eharaeterlst2o sta-reasu 1 "edq- n r e r horzontal,plant tons I I,. o. 2

Rcadlnt or yaw anileIt|Reading angle, at I t h exece In

On overhoot or zigzag mineuver,

e,,ale from spiral maneuver

execute in an overshoot or zigzagmaneuve-' I. 2I3.

' .- Frequency of oscillation

iWo

HYDRONAUTICS, .Incorporated

1.0 INTRODUCTION

The towboat manuevering simulator is based on the integration

in time of the differential equations which describe the motions

of the towboat and barge string in three degrees of freedom, i.e.,

yaw, sway and surge. The theoretical background for these equations

are presented in Reference 1, "The Prediction of River Tow Maneu-

vering Performance," U.S. Coast Guard Report No. CG-D-32-78. This

reference presents the basic equations and a complete set of hydro-

dynamic coefficients for a representative towboat and barge train.

These coefficients were obtained by model tests.

This section of the simulator documentation provides a des-

dription of the basic equations of motion included in the simulator

and the relationships used to determine .external forces and moments

due to a bow thruster and wind. These equations are completely

general in nature and could be used, with the proper hydrodynamic

coefficients, to describe the maneuvering of vessels other than

towboats.

HYDRONAUTICS, Incorporated

-2-

2.0 MATHEMATICAL MODEL

The mathematical model for the maneuvering of a river towconsists of the coupled differential equations in three degreesof freedom (yaw, sway and surge) which describe the motions in

the X, Y plane and the complete set of hydrodynamic coefficientsand external forces which are required in order to numerically

integrate these equations. There are also auxiliary equationswhich describe the response of the steering and propulsion sys-

tem to external inputs.

A complete set of three coupled differential equations withall of the terms necessary to simulate normal maneuvers of sur-face ships are presented in Reference 2. These equations have

been used by HYDRONAUTICS, Incorporated to calculate the maneuver

trajectories for a wide range of surface ship types in deep andshallow water. These equations are based on a more complete setof equations developed by the U.S. Navy for the simulation of

submarine motions in six degrees of freedom. The equations inReference 2 differ from other sets of equations, such as those

of Reference 3 used to describe surface ship maneuvers pri-

marily in the way higher order terms are introduced. The equa-tions of Reference 3 use a Taylor expansion which results inodd functions being represented by linear and cubic terms. The

equations of Reference 2 are a square absolute representation forhigher order terms so that odd functions are represented by

linear and square terms. At large drift angles, which is a likelyoperating condition for a river tow, the forces and moments aredominated by cross flow drag which is proportional to velocity

squared. Thus, it is better to use equations in which forces andmoments are proportional to velocity squared rather than cubed.

As a result , the equations presented in Reference 2 were selected

------

HYDRONAUTICS, Incorporated

to form the basis for the equations which describe the maneuvering

of a river tow. There are a number of modifications which must

be made to these equations. These modifications and the resulting

set of equations are described in the following paragraphs.

The following equations in three degrees of freedom are re-

ferred to a right-hand prthogonal system of moving axes, fixed inthe body, with its origin normally located at the center of massof the body. The positive direction of the axes, angles, linear

velocity components, angular velocity components, forces and moments

are given in Figure 1. Unless otherwise indicated in the Notation,

the numerical values for the hydrodynamic coefficients used withthe equations are for the ship propulsion point (n - 1.0). The

equations are written in terms of the complete barge flotillia

towboat configuration. Thus the values of the coefficients embrace

the interaction effects between rudder and hull, propeller and hull,and propeller and rudder as. determined from the model tests of the

complete configuration.

An important consideration in the maneuvering of a river tow

is the effect of current which can vary significantly along thelength of the tow. As a result, it is necessary to introduce the

effect of the current velocity into the mathematical model. Theapproach adopted was to define the hydrodynamic terms in the equa-

tions based on the relative velocities and yaw rate between the

hull and the fluid rather than the inertial velocities and yaw

rate. The relative velocities and relative yaw rate can be cal-

culated by the vector addition of the inertial velocity and iner-tial yaw rate and the current velocities and current yaw rate. In

the numerical integration the procedure is to define a matrix

of current speeds (U Cj) and directions (Tcjj) at points on the

X, Y plane. Based on the location of the bow (X B, Y.) midships

... ------.

-4-

NORTH

x0

NORTH

UA WIND VELOCITY

"/- NO0RTH

Ar rc 7 c

+X

oS

+ F

J,; +Yo

FIGURE I " SIGN CONVENTION FOR RIVER TOW MANEUVERING SIMULATION

_______

HYDRONAUTICS, Incorporated

-5-

(Xa, Y.) and stern (X , , Y,) of the tow, an interpolation in the

current speed and direction matrix is carried out to obtain thecurrent speed and direction at the bow (UCB, *CB) , midships

(UCM, *CM) and stern (Ucs, *CS). The following relationships then

apply:

UCE - UCB Cos (*Cs-) VCB M UCB sin (*CB-*)

uM M U cos (* U sin (U C5 CB ' Vs UCH sinuCS W-UCS Cos (*CS-*) vCS M-UCS sin (OCS-€

U UCB + uCM+ UCS vCB + VCM + vCS=C v " C (1)

V -vrcM CB - CS

UR = U-UC V1 R V-VC r - r-rC

In this procedure the mean longitudinal and lateral current velo-

city in the body axis system is obtained from the average of the

values at the bow, midships and stern. The variation of the

lateral velocity along the tow is accounted for by the apparent

current yaw rate defined by the difference in the lateral velo-

cities at the bow and stern divided by length. This assumes the

lateral velocity varies linearly from bow to stern. If this isnot the case a more complex relationship would have to be intro-

duced.

The equations of motion formulated for a river tow are as

follows:

HYDRONAUTICS, Incorporated

U1 ~ l1 R v - UR 'sn OR U UR Cog OR

OR are tan (- a

-7-

C4

as

40

'0

+ wm

'0

++ '.

0.qdo

y4L.. -.

0N

w >

+++

+ o+

> >

+ +

0 44

+4-

w - - - -

040

4 c 94+ 4 - +

CA 1 - O

> 96

.4 4. 4r~~~a at404b-14 - I.

4 0IC

*966

0) 0

C4 k

01C4 +~ +

+~-%It

- ~o + FO 44 + -

$44 =10 +-a -3

d

> +0

4p ~at at C

at at 0

+1' + -

A. - M

HYDRONAUTICS, Incorporated

-10-

The foregoing equations of motion, as noted previously, are pat-

terned after the quasi-steady state equations of Reference 2. The

non-dimensional hydrodynamic coefficients which comprise the basic

equations are considered to be independent of speed (Froude number).

This assumption is valid since river tows always operate at low

Froude number.

These equations differ from the equations of Reference 2 in

the following details:

a. They are written in terms of the relative velocities

and yaw rate to allow the introduction of varying current as

discussed above.

b. Terms are included for steering rudders (steering rudder

angle - S.) and flanking rudder (flanking rudder angle - 8).

c. Terms are included for twin propellers which nay operate

at different RPM's and different directions of rotation. The

turning moment due to differential thrust is included in the yawing

moment, Equation (4).

d. The forces and moments generated by the rudders are basedon a velocity defined by

Up -f (dulf2 + eDnuR + fD'n)

which is a function of the relative axial velocity, uR, and pro-

peller RPM. n. The constants d, e and f depend on the sign of

ut and n. This allows a proper representation of the rudder

forces and moments at zero speed and finite ptopeller RPM.

In realistic maneuvers, river tows operate both ahead and

astern and in some cases at large drift angles. In order to pro-

perly represent the hydrodynamic forces and moments which act in

such conditions, different sets of hydrodynamic coefficients are

HYDRONAUTICS, Incorporated

-11-

used depending on the relative drift angle 0 . As will be

noted in Reference 1 in which the hydrodynamic coefficients

from the model tests are presented, most coefficients depend on

the direction of motion, i.e., ahead 2700 R 900 or astern

900 OR 1 2700. In order to obtain a better representation of

the steady sideforce and yaw moment at drift angles near 90 and

270 degrees certain coefficients have an additional v4lue when

300 < 0 S 1500 or 2100 S R S 3300.

As noted in the introduction to this section, a complete setof hydrodynamic coefficients for Equations 2, 3 and 4 for a tow-

boat and barge string are presented in Reference i. The simulator

as presently configured has the hydrodynamic coefficients as con-

stants independent of water depth. Thus, if operations in shallow

water are to be simulated, hydrodynamic coefficients applicable to

the appropriate depth should be used. As a general rule, the water

can be considered as deep if it exceeds the draft of the tow by

a factor of 2.5 or 3.

The equations of motion (i.e., equations 2, 3 and 4) are

solved stepwise in time in the computer program. In the program

the time step, DT is set equal to 1.0 seconds. For a long, re-

latively slow-moving river tow, a longer time step (2 to 4 seconds)

could be used without significantly affecting the results of most

maneuvers. The 1.0 second time step was chosen more on the basis

of the updating rate for the control display. It was considered

desirable to minimize the time delay between a control input and

the display response. A 1.0 second time step was considered rea-

sonable on this basis.

At each time step in the solution of the equations of motion,

the current velocity at the low, midship and stern of the tow is

determined. This calculation is carried out by subroutine CURT.

HYDRONAUTICS, Incorporated

-12-

In the input to the program, the current speed and direction is

specified at up to 30 lines or stations across the river. These-

may be arbitrarily spaced along the river. The river bank is

defined in the visual display by lines joining the end points of

consecutive stations. As a result, stations should be concentrated

in the area of bends or rapid changes in river width. The current

speed and direction are also likely to change rapidly in such

areas.

At each station, the current speed and direction is specified

at 8 evenly spaced points.(see Figure 13 of Volume I). Subroutine

CURT determines the current speed and direction at bow, midship

and stern by searching the stations in sequence. At each station,

the smallest distance between the vessel point and one of the 8

station points is determined. Initially this process is repeated

until the minimum distance point is found. The current defined atthe closest point is then used in calculations. After the initial

time step the search is carried out locally around the station

point found to have the minimum distance during the previous time

step. This local search technique saves significant computer time..

HYDRONAUTICS, Incorporated

-13-

3.0 EXTERNAL FORCES

3.1 Bow Thruster

The towboat maneuvering simulator contains the provisionfor a bow thruster. The forces and moments generated by the bowthruster are represented by the following relationships:

Thruster Lateral Force -

FYo - (TMAx) * (Percent Output) - THMAX * TRPM

FYO - Y force at zero forward speed

Percent output ranges from -1.0 to 1.0

The lateral forces of a tunnel type bow thruster decreases with

forward speed. Thus, the lateral force introduced into the lateral

force Equation (3) is given by:

FXP(3) - Fy - Fy (TRC(l) + TRC(2) * Cos (27 u/vj)) (5)0

for u/Vs f 0.5

- Fy ((TRC(l) - TRC(2)) + TRC(3) * (U/Vj-0.5))

for u/Vj > 0.5where

u - axial speed of vessel

Vj - thruster jet or exit velocity

vi - (F /pA)f0

p - mean density of water

A - thruster Disc Area

HYDRONAUTICS, Incorporated

-14-

Typical constants for a tunnel bow thruster based on Reference 5would be:

THKAX - 10,000 lbs

TRC(l) - 0.65

TRC(3) - 0.18

CTHV - I/PA - 0.025

Thruster YawinR Moment

Because of interaction forces with the hull the yawing momentdue to the thruster does not change with forward speed in the sameway as the lateral force. The yawing moment due to the thrusterwhich is introduced into the yawing moment equation is given by:

N Fy Xt (1 - (1 - 0.67 u/VJ)(1 -1 7) (6)YO

N - Yawing Moment due to thruster

Xt - Longitudinal location of thruster - YCSP(3)

3.2 Wind Forces and Moments

The forces and moments acting on the towboat and barges due

to wind were calculated using methods and data given in Reference

4. The forces and moment at a given time are calculated using the

instantaneous relative wind velocity.

The axial and lateral forces and yawing moment due to wind

are given by:

Xw -*PaCcvV. 2A cos 2 we -FX(2) (7)

Yw " 0aCy VG 'Ap sin2 S = FY(2) (8)

N- YWx1CP - FN(2) (9)

... .......... ... , , . _ ... .. l

VHYDRONAUTICS, Incorporated

-15-

X and Y are longitudinal and lateral forces (in ship-V coordinates) due to wind

Nw Vis yawing moment about the c.g. due to wind

Pa is air mass density

C x and C are longitudinal and lateral drag coefficients

A and A are longitudinal and lateral projections ofx P above water hull and deckhouses

V Ve is effective wind velocity = VwR

is angle measured from the ship x-axis to theeffective wind velocity vector - BW

is longitudinal position of the center ofX£CP pressure of the wind force

The effective wind velocity, including the effect of the boundarylayer at the water surface, deduced empirically in Reference 4.

is:

0.15Z ca (V )2+ v

ve \32V1 WX W7

SICa .1 u +V cos ) + (v + V sin 8w)J (10)

wherez ca is vertical center of area of the ship

V Vand V are longitudinal and lateral components of theVi Wn V effective wind velocity

u and v are components of ship velocity

V V is actual wind velocity

Bw is wind heading angle measured from ship x-axisto actual wind velocity vector

HYDRONAUTICS, Incorporated

-16-

The angle BW, is given by

ova -tan V sin

The center of pressure is determined from the longitudinal center

of area, using empirical methods and data from Reference 4 and

is: xx - L1 p 3 ± - (0.001 + 0.01 AR) (IS,'I - 90

where

L BP is ship LBP

x is longitudinal position of the center of lateralca area - XLCA

aw is the value of awe in degrees - BW

AR is hull aspect ratio, AR -2Ap /LBp - AS

Based on the data given in Reference 4 and estimated above

water hull and deckhouse shapes, the following wind force co-

efficients would apply to the towboat and barges configuration

for which hydrodynamic data are reported in Reference 1.

L BP- 745 ft

X - 58.8 ft

AR - 0.0167

C W 1.0xv

C W 1.0

A - 1520 ft2

A - 4635 ft,

ZCa a 6.2 ft

HYDRONAUTICS, Incorporated

-17-

3.3 Other External Forces

At this time no other external forces are included in the

simulator. In the future, othe. external forces such as bank

suction, interaction with passing vessels and the effects of moor-

ing lines could be included.

-I:

HYDRONAUTICS, Incorporated

-18-.

4.0 CONTROL SYSTEMS

The coatrol systems included in the towboat maneuvering

simulator include steering control for the steering and flanking

rudders, RPM control for the port and starboard propellers and thebow thruster output control. The command inputs for all of these

controls are provided thru the computer A to D input from the con-

trol station. In the simulator, the response to the control inputs

is at a constant rate. The rates used based on Reference 6 are

as follows:

Steering and Flanking Rudderd 5 deg/sec

Propeller RPM 20 RPM/sec

Thruster Output 10 percent thrust change/sec

The response to the control system inputs is considered re-presentative of a typical towboat. If required in the future, amore complex representation of the response to control inputs couldbe modeled in the simulator.

HYDRONAUTICS, Incorporated

. -19-

REFERENCES

1. Miller, E.R., Jr., "The Prediction of River Tow ManeuveringPerformance", U.S. Coast Guard Report No. CG-D-32-78, May1978.

2. Goodman, Alex, Gertler, Morton, and Kohl, Robert, "Experi-mental Techniques and Methods of Analysis Used at HYDRONAUTICSfor Surface Ship Maneuvering Predictions", HYDRONAUTICS,Incorporated Technical Report 7600-1, June 1976.

3. Mandel, P., "Ship Maneuvering and Control", Principles ofNaval Architecture, Chapter VIII, SNAME, 1967.

4. Altman, R., "Forces on Ships Moored in Protected Waters",HYDRONAUTICS, Incorporated Technidal Report 7096-1, July1971.

5. Chislett, M.S., and Bjorhkorn, 0., "Influence of Ship Speedon the Effectiveness of Lateral-Thrust Unit", Report No.HY-8; HYA, Lyngby, Denmark, April 1900.

6. Courtsal, D.P., "The Marine Business in the Central UnitedStates", Transactions SNAME, Vol. 79, 1971, pp. 542-578.

t-I