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NAVI TRAINER 4000

MATHEMATICAL MODELS TECHNICAL DESCRIPTION

© Transas Marine Ltd. July, 2003

© Transas Marine Ltd. 2003

All rights reserved. The information contained herein is proprietary to Transas Marine Ltd. and shall not be duplicated in whole or in part.

The technical details contained in this manual are the best that are available at the date of issue

but are subject to change without notice. Transas Marine Ltd. pursues the policy of continuous development.

This may lead to the product described in this manual being different from the product delivered after its publication.

This document contains:

 

Introduction ................................................................................................................

3

Abstract ................................................................................................................

5

List of Symbols .....................................................................................................

5

General......................................................................................................................

13

Ship Motion Mathematical Model .......................................................................

16

The Total Mechanical Forces and Moments Components ......................

22

Ship Motion in Calm Deep Water ...........................................................................

25

Hydrodynamic Forces and Moments .................................................................

28

Inertial forces, Force of Buoyancy and Forces of Static Stability ............

29

Hull Hydrodynamic Characteristics ..........................................................

30

Steering Device Hydrodynamics..............................................................

33

Propeller Hydrodynamic Characteristics..................................................

35

Thursters ..................................................................................................

41

Engine Model With Remote Control System......................................................

41

Engine ......................................................................................................

41

Remote Control Systems .........................................................................

42

Control Driving Gear...........................................................................................

46

Steering Gear...........................................................................................

46

Tunnel Type Thruster Gear......................................................................

47

Vane Propeller Gear ................................................................................

47

Waterjet Gear...........................................................................................

48

Nozzle Gear .............................................................................................

48

Environment Mathematical Models and Resulting Aero/Hydro Forces

 

Effects .......................................................................................................................

49

Wind Forces .......................................................................................................

51

Current Forces ...................................................................................................

54

Wave Forces ......................................................................................................

56

Hydrodynamic Interaction Forces Mathematical Description.............................

59

Ship-Bottom Interaction ...........................................................................

59

Ship to Wall and Ship to Ledge Hydrodynamic Interaction Forces .........

60

Ship to Wall and Ship to Bottom Interaction Force..................................

62

Ship to Ship Interaction Force..................................................................

64

External Mechanic Forces Mathematical Models .................................................

67

Mathematical Description of Forces due to Anchor Chains, Moors and Tow

 

Lines...................................................................................................................

69

Anchor Gear Model..................................................................................

69

Mooring Gear Model ................................................................................

71

Tow-Line Forces at Hull ...........................................................................

73

Ship Collision with Other Objects.............................................................

74

Automatic Vessel Movement Control Systems ....................................................

77

Autopilot “Aist” ....................................................................................................

80

Trace Control Unit ..............................................................................................

80

NAVI-TRAINER 4000. Mathematical Models. Technical Description.

1

List Of Obligatory Maneuvers at Mathematical Model Testing...............................

81

References ........................................................................................................

85

Appendix 1 ...............................................................................................................

93

Appendix 2 ...............................................................................................................

99

2 NAVI-TRAINER 4000. Mathematical Models. Technical Description.

INTRODUCTION

This chapter contains general information on the work with the manual.

Copyright Transas Marine Ltd. 2003

Abstract

ABSTRACT

The document contains movement technical description for all the objects participating in the simulator performance, including possible mechanic and hydrodynamic influence of objects and/or environment. The technical description consists of two parts.

Part 1 contains description of conventional ships motion model, raid hardware models and environment elements.

Part 2 will contain the mathematical model description for fast mono-hull vehicle at planing and semi-planing conditions, and vehicle control systems. Part 2 is to be included into version 4.30.

LIST OF SYMBOLS

A2

AR

AWL

AX

AY

AYN

B

bcp

CB

Cm bal R CyN

Сmx BH

Сmx CHAN

Сmx R

СmxА

Сmy BOT

Сmy CHAN

Сmz BH

Сmz BOT

Сmz CHAN

Сmz IN --

Сmz R

the 2nd frame area

rudder area

waterplane area

above-water midship section area

above-water longitudinal section area

lateral area of superstructures when projected to longitudinal plane

beam midlength

rudder chord

block coefficient

non-dimensional rudder moment

non-dimensional nozzle lateral force

non-dimensional bare hull roll moment

non-dimensional roll moment due to walls influence

non-dimensional roll moment due to lateral rudder force

non-dimensional aerodynamic roll moment

non-dimensional pitch moment due to shallow waters

non-dimensional pitch moment due to walls influence

non-dimensional yaw moment on bare hull

non-dimensional yaw moment due to shallow water

non-dimensional yaw moment due to walls influence

non-dimensional hull-propeller interaction moment

non-dimensional yaw moment due to rudder

Introduction 5

List of Symbols

СmzPN

СmzА

СT

Сx 0

Сx BH

Сx BOT

Сx CHAN

Сx f0 Сx R Сx r

Сx SHIP

Сx VSP

Сx WALL

Сx WALL--1

С

Сy BH

Сy BOT

Сy CHAN

Сy IN Сy R

Сy SHIP

Сy VSP

Сy WALL

Сy WALL--1

СyPN

ССz

Сz BOT

Сz CHAN Сz R

С

СхPN

non-dimensional yaw moment due to ducted propeller non-dimensional aerodynamic yaw moment non-dimensional propeller thrust

resistance coefficient

non-dimensional bare hull longitudinal aerodynamic force non-dimensional longitudinal force due to shallow waters non-dimensional longitudinal force due to walls and bottom influence frictional resistance of an equivalent plate

non-dimensional longitudinal rudder force Residuary resistance

non-dimensional longitudinal force due to other ship influence non-dimensional vane propeller thrust

non-dimensional longitudinal force due to walls influence non-dimensional longitudinal force due to ledged wall influence non-dimensional longitudinal aerodynamic force non-dimensional bare hull lateral force

non-dimensional lateral force due to shallow waters

non-dimensional lateral force due to walls and canal bottom influence non-dimensional hull-propeller interaction lateral force non-dimensional rudder lateral force

non-dimensional lateral force due to other ship influence non-dimensional vane propeller lateral force non-dimensional lateral force due to wall influence non-dimensional lateral force due to ledged wall influence non-dimensional ducted propeller lateral force non-dimensional aerodynamic lateral force non-dimensional bare hull vertical force

non-dimensional vertical force due to shallow waters

non-dimensional vertical force due to walls and canal bottom influence non-dimensional rudder vertical force

non-dimensional aerodynamic vertical force non-dimensional ducted propeller vertical force

6 NAVI-TRAINER 4000. Mathematical Models. Technical Description.

List of Symbols

HBOT

water depth

HCHAN

canal depth

eVSP

vane propeller eccentricity

DN

internal nozzle diameter

DP

propeller diameter

Fn

Froude number

Fx(M)ANCH

longitudinal force due to anchor chain influence

Fx(M)ROPE

longitudinal force due to mooring influence

Fx(M)SHIP

longitudinal force due to hulls collision

Fx(M)WALL

longitudinal force due to wall collision

FxA

longitudinal aerodynamic force

FxAР

azimuth thruster longitudinal force

FxBH

longitudinal hydrodynamic force on bare hull

FxBOT

longitudinal force due to bottom influence

FxC

longitudinal force due to current

FxCHAN

longitudinal force due to bottom and walls influence

FxP

propeller thrust

FxPN

ducted propeller thrust

FxSHIP

longitudinal force due to another ship influence

FxVSP

vane propeller longitudinal force

FxWALL

longitudinal force due to wall influence

FxWAVE

longitudinal force due to waves

FxWJ

waterjet thrust

Fy(M)ANCH

lateral force due to anchor chain influence

Fy(M)ROPE

lateral force due to mooring influence

Fy(M)SHIP

lateral force due to hulls collision

Fy(M)WALL

lateral force due to wall collision

FyA

lateral aerodynamic force

FyAР

azimuth thruster lateral force

FyBH

lateral hydrodynamic force on bare hull

FyBOT

lateral force due to bottom influence

FyC

lateral force due to current

Introduction 7

List of Symbols

FyCF

FyCHAN

FyIN

FyP

FyPN

FyR

FySHIP

FyTHR

FуVSP

FyWAVE

FyWJ

Fz (M)ANCH

Fz (M)ROPE

Fz (M)SHIP

Fz (M)WALL

Fz BOT

Fz CHAN

Fz SHIP

FzBH

Fzg

FzST

FzWAVE

g hθ

hψ

J

JVSP

Jx, Jy, Jz

KQ

KT

L

lCHN

centrifugal force

lateral force due to bottom and walls influence lateral force on hull due to rudder gear influence propeller lateral force

ducted propeller lateral force rudder lateral force

lateral force due to another ship influence thrust force

vane propeller lateral force lateral force due to waves waterjet lateral force

vertical force due to anchor chain influence vertical force due to mooring influence vertical force at hulls collision

vertical force at wall collision

vertical force due to bottom influence

vertical force due to walls and bottom influence vertical force due to another ship influence vertical hydrodynamic force on bare hull

hull weight

vertical projection of buoyancy force (in body axes) vertical force due to waves

gravitation acceleration Transverse metacentric height Longitudinal metacentric height Advance coefficient of propeller

Advance coefficient of vane propeller

moments of ship intertia torque coefficient thrust coefficient

length on waterline anchor chain length

8 NAVI-TRAINER 4000. Mathematical Models. Technical Description.

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