Navigation_1 / Буклеты / NT_4000_Mathematical_Models_Technical_Description_eng
.pdfList of Symbols
lN |
nozzle length |
lR |
X-coordinate of rudder lateral force |
m |
ship mass |
manch |
anchor mass |
Mbal R |
rudder stock torque |
Mx(M)ANCH |
roll torque due to anchor chain influence |
Mx(M)ROPE |
roll torque due to mooring influence |
Mx(M)SHIP |
roll torque at hulls collision |
Mx(M)WALL |
roll torque at wall collision |
MxA |
aerodynamic roll torque |
MxAP |
azimuth thruster roll torque |
MxBH |
roll torque on bare hull |
MxBOT |
roll torque due to bottom influence |
MxC |
roll torque due to current |
MxCHAN |
roll torque due to bottom and canal walls influence |
MxRIN |
roll torque on hull due to rudder force and interaction force |
MxSHIP |
roll torque due to another ship influence |
MxWAVE |
roll torque due to waves |
My(M)ANCH |
pitch torque due to anchor chain influence |
My(M)ROPE |
pitch torque due to mooring influence |
My(M)SHIP |
pitch torque due to hulls collision |
My(M)WALL |
pitch torque due to wall collision |
MyAP |
azimuth thruster pitch torque |
MyBOT |
pitch torque due to bottom influence |
MyCHAN |
pitch torque due to bottom and canal walls influence |
MyWAVE |
pitch torque due to waves |
Mz(M)ANCH |
yaw torque due to anchor chain influence |
Mz(M)ROPE |
yaw torque due to mooring influence |
Mz(M)SHIP |
yaw torque due to hulls collision |
Mz(M)WALL |
yaw torque due to wall collision |
MzA |
yaw aerodynamic torque |
MzAР |
azimuth thruster yaw torque |
MzBH |
yaw torque on bare hull |
Introduction 9
List of Symbols |
|
MzBOT |
yaw torque due to bottom influence |
MzC |
yaw torque due to current influence |
MzCHAN |
yaw torque due to canal bottom and walls |
MzP |
total propeller torque relatively to midship |
MzPN |
yaw torque due to propeller-nozzle influence |
MzRIN |
rudder yaw torque including interaction force |
MzSHIP |
yaw torque due to another ship influence |
MzTHR |
yaw torque due to the thruster |
MzWALL |
yaw torque due to wall influence |
MzWALL--1 |
yaw torque due to ledged wall influence |
MzWAVE |
yaw torque due to waves |
n |
propeller rotation frequency |
P |
propeller pitch |
QP |
propeller shaft torque |
Rn |
Reynolds number |
RVSP |
vane propeller radius at blades axis |
rmb |
buoy path radius relatively to the anchor axis |
t |
Thrust deduction fraction |
T |
draught at midship |
Vc |
current velocity |
Vlk |
relative water speed |
VA |
wind velocity |
VxA |
longitudinal wind velocity component in body axes |
VyA |
lateral wind velocity projection in body axes |
Vx, Vy, Vz |
linear velocity components in body axes |
W |
Wake scaling factor |
xR, yRP |
rudder stock co-ordinates |
Xanch |
holding anchor force |
xg, yg, zg |
ship path coordinates (at gravity center) |
xSHIP |
longitudinal distance between ships gravity centers |
ySHIP |
transverse distance between ships gravity centers |
zg |
Vertical center of gravity |
10 NAVI-TRAINER 4000. Mathematical Models. Technical Description.
List of Symbols
ZP |
number of propeller blades |
zR |
Z-coordinate of lateral force application point on rudder |
ωrelative path curvature
βVSP |
drift angle at swinging vanes |
ξCHAN |
angle between ship centre plane and channel axis’s. |
ξWALL |
angle between ship centreplane and wall |
αCHAN |
canal wall inclination |
δVSP |
vane propeller control center deflection angle |
δ AP |
azimuth thruster deflection angle |
δWJ |
waterjet deflection angle |
λR |
aspect ratio |
displacement
ρwater density
ψpitch angle
βdrift angle
θroll angle
ϕsea course angle
δrudder deflection angle
λ11, λ22, |
added masses |
λ33, λ44, |
|
λ55, λ66 |
|
χbot |
angle between ship hull centerplane and bottom |
ΣFMx, |
total mechanical force vector components |
ΣFMy, |
|
ΣFMz, |
|
ΣFx, ΣFy, total viscous force vector components |
|
ΣFz, |
|
λi |
wave length |
γi |
wave slope of surface |
ξi |
angle of wave encounter |
ΣMx(M), |
total mechanical force torque vector components |
ΣMy(M), |
|
ΣMz(M) |
|
ΣMx, ΣMy, the torque of total viscous force
ΣMz
Introduction 11
List of Symbols |
|
ρw |
air density |
ϕw |
relative wind velocity |
ϕwk |
relative wind velocity |
ωx, ωy, ωz |
Ship angular velocity components |
12 NAVI-TRAINER 4000. Mathematical Models. Technical Description.
CHAPTER 1
General
Copyright Transas Marine Ltd. 2003
List of Symbols
The set of mathematical models for a manoeuvre simulator consists of mathematical models of ships, raid hardware models and environment element models.
The motion of all the objects is modelled including the mechanic interaction and hydrodynamic interaction between objects and environment (if necessary). The set of models can include:
About 40 models of ships equipped with diesel, steam or gas turbines, fixed or controllable pitch propellers, rudders of different type and steerable ducted propellers, thrusts and ground tackles;
Fast catamarans equipped with gas turbine, waterjets, thrusters and ground tackles;
Fast vessels equipped with diesel or gas turbine, fixed pitch propellers or waterjet, rudders of different type, thrusters, transom plates and ground tackles;
Fast boats equipped with diesel or gas turbine, fixed pitch propellers or waterjet, rudders of different type, thrusters, transom plates and ground tackles;
Towboats equipped with diesel, fixed pitch propellers or controllable pitch propellers, ducted propellers and steerable ducted propellers as well, vane or azimuth thruster, ground tackles and towing devices;
Dumb barges equipped with ground tackles.
The set of mathematical models of raid equipment and environment includes:
•Target vessels—vessels with automatically controlled movement at given path. Any ship mentioned above can be used as a target vessel;
•Automatically controlled towboats – any towboat in automatic control mode of operation;
•Mooring buoys;
•The mathematical model of “Man over board”;
•The mathematical model of wavy sea surface etc.
Part 1 of the technical description contains the description of conventional ships mathematical models and raid equipment mathematical models.
The mathematical models of fast vehicles (fast boats, catamarans, etc.) as well as their control devices will be described in Part 2 of the technical description. Part 2 will be added in version 4.30.
Chapter 1. General. |
15 |
Ship Motion Mathematical Model
SHIP MOTION MATHEMATICAL MODEL
When designing the mathematical model, a ship is considered as a controllable system. It includes the controlled object, steering gears and control systems. It provides the ship motion in the restricted water at present situation.
The diagram illustrating a vessel as a controllable system is shown on Fig. 1.
Fig. 1. Ship as Controllable System
The ship itself is the controlled object.
The steering gears are propellers, rudders, anchor and mooring systems etc. The steering gears induce the forces on ship hull. The value of forces directly depends on the control value changes. Control value is a set of the values changed by the helmsman to provide controllable ship motions.
16 NAVI-TRAINER 4000. Mathematical Models. Technical Description.
Ship Motion Mathematical Model
Ship motion can be described with or without consideration of the external forces. External forces are the forces deriving from wind, current, waves, channel geometry (the influence of water depth, walls, bottom inclination, etc.), the presence of other objects (moving or immovable).
The description of ship motion in calm infinite water is the basis of the mathematical model. The structure of the forces effecting the ship is shown on Fig. 2.
Fig. 2. Forces on Ship in Calm Deep Water
The inertia force, hydrodynamic force and hydrostatic force are the only forces defining the ship motion in calm deep water. So these forces are called “basic”.
The external forces are considered as additional values to basic forces and moments.
External forces are also divided into two groups: aerodynamic and hydrodynamic forces (the first group) and mechanical forces (the second group). The first group includes aerodynamic forces due to wind, hydrodynamic forces due to current and waves, forces due to hydrodynamic interaction with other objects, forces due to hydrodynamic influence of walls and bottom of channel, etc. The second group contains forces deriving from collision with soil, wall, other vessels, anchor chain tithing forces, etc.
Chapter 1. General. |
17 |
Ship Motion Mathematical Model
The structure of external forces is illustrated on Fig. 3.
Fig. 3. External Forces
Ship motion mathematical model is based on the set of non-linear differential equations. The set equation solutions used to define the ship motion kinematics parameters, i.e. the ship centre of gravity coordinates ( xg , yg ,zg ), the inclination angles (roll angle θ , trim
angle ψ , course angle ϕ ), and corresponding values of velocity and acceleration. Two coordinates systems are used: the fixed axes ( XgOg Zg ), a right hand orthogonal
system nominally fixed in relation to the Earth, and the body axes ( XOZ ), a right hand orthogonal system nominally fixed to the ship (see Fig. 4).
18 NAVI-TRAINER 4000. Mathematical Models. Technical Description.