Navigation / Буклеты / NT_4000_Mathematical_Models_Technical_Description_eng
.pdfReferences
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90 NAVI-TRAINER 4000. Mathematical Models. Technical Description.
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92 NAVI-TRAINER 4000. Mathematical Models. Technical Description.
APPENDIX 1
Database Information
Copyright Transas Marine Ltd. 2003
The database contains coefficients values of the conventional ships hydrodynamic characteristics.
Symbols |
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Parameters Range |
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Ship Motion In Calm Deep Water |
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Added Masses Coefficients |
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Added masses: λ11 , λ22 , λ33 , λ44 , λ55 , λ66 |
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3.5 |
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3.5 |
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Ship Hull Hydrodynamic Characteristics |
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Stern Type: V-shape, U-shape, skeg (single-screw), skeg (double-screw) |
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β |
C2 |
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Non-dimensional lateral force Cy β , |
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Non-dimensional yaw moment m1,m2 |
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Non-dimensional yaw moment at rotation |
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0.93 |
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Non-dimensional longitudinal force: CxβBH , CxωBH , CxβBHβ , CxωBHω |
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β |
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β β |
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β β |
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ω |
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ω |
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Cx BH , Cx BH , |
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0.65 |
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x BH |
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Towing resistance: |
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0.30 |
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Cxr (Fn) , Cxf 0 (Rn) . |
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A |
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0 ≤ Fn ≤ 0.3 |
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Non-dimensional lateral force: CyβBH , Cyω |
BH , CyβBHβ , Cyω |
BHω |
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≤ Rn ≤ 3 109 |
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β |
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β β |
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β |
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β β |
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ω |
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Cy BH , Cy BH , |
Cy BH |
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Non-dimensional yaw moment: Cmzβ BH , Cmzω BH , Cmzβ βBH ,
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ω |
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mz BH |
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mz BH |
mz BH |
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mz BH |
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Non-dimensional roll moment: Cmxβ |
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BH , Cmxω |
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BH , Cmxβ βBH , Cmxω ωBH , |
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C β |
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ω |
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mx BH |
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mx BH |
mx BH |
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mx BH |
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mx BH |
mx BH |
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β β |
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β |
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ω |
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β β |
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ω |
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ω |
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ω |
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Cmx BH |
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, dCmx BH , dCmx BH |
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dCmx BH |
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Appendix 1. Database Information. |
95 |
Symbols |
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Parameters Range |
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1 |
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Steering Gear Hydrodynamic Characteristics |
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Rudder types: balanced rudder, semi-balanced rudder, Shilling’s rudder, Becker’s rudder
Non-dimensional longitudinal rudder force: Cx R0 , CxδR , C δx δR .
Non-dimensional lateral rudder force: Cy0R0 |
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CyβR0 , CyωR0 , CyβRβ0 , |
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β |
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β β |
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β β |
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δ |
δ |
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ω |
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Cy R0 |
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C δy ωR ω .
Non-dimensional interaction force on hull: Cy0IN0 CyβIN0 , CyωIN0 ,
β β |
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Cy IN0 |
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CyδINω , C δy ωINω .
Non-dimensional interaction moment on hull:
β |
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β β |
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β |
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β β |
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ω |
ω |
ω |
ω |
ω |
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Cmz IN0 |
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, Cmz IN0 , Cmz IN0 |
, Cmz IN0 |
Cmz IN0 |
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Cmzβ |
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ω |
INω |
0 , Cmzβ β INω ω0 , Cmzδ |
IN0 , Cmzδ ωIN0 , C δmzω INω 0 . |
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Non-dimensional hydrodynamic moment above stock: CD0 .
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≤ |
AR / LT ≤ 0.035 |
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≤ λR ≤ 2.5 |
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−0.5 ≤ yR / DP ≤ 0.5 0 ≤ CT ≤ ∞
3.5 ≤ L / B ≤ 7.5
3.5 ≤ B /T ≤ 7.5
0.65 ≤ CB ≤ 0.83
0.30 ≤ (A2 )≤ 0.42
Propeller Hydrodynamic Characteristics
Propeller types: fixed pitch propeller, ducted fixed pitch propeller, controllable pitch propeller, ducted controllable pitch propeller, steering ducted propeller, waterjet, vane propeller.
Propellers of “B” series
thrust coefficient KT (J,P / D)
moment coefficient KQ (J, P / D)
Ducted propellers
thrust coefficient KT (J,P / D) .
moment coefficient KQ (J, P / D) .
Steering ducted propeller
Non-dimensional longitudinal force on nozzle stock: Cx0PN , Cxδ PN ,
Cxδ PNδ .
Non-dimensional lateral force on nozzle stock: Cy0PN , Cyδ PN .
Non-dimensional hydrodynamic moment about Z-axis: Cmz0 PN ,
Cmzδ PN .
Waterjet
Steering and reversing gear characteristic: KH = f (Kq) .
−∞ ≤ J ≤ ∞
0.5 |
≤ |
P / D ≤ 1.4 |
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0.4 |
≤ |
A / A0 ≤ 1.0 |
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3 ≤ |
Z ≤ |
7 |
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−∞ ≤ J |
≤ ∞ |
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0.5 |
≤ lN / DN ≤ 1.2 |
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0.5 |
≤ |
P / D ≤ 1.4 |
0.4 |
≤ |
A / A0 ≤ 1.0 |
3 ≤ |
Z ≤ 7 |
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0.5 |
≤ lN / DN ≤ 1.5 |
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0 ≤ CT |
≤ ∞ |
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0 ≤ CT ≤ ∞
0 ≤ KH ≤ 2.5
0.2 ≤ Kq ≤ 0.8
96 NAVI-TRAINER 4000. Mathematical Models. Technical Description.
Symbols |
Parameters Range |
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Vane propeller |
0 ≤ eVSP ≤ 0.75 |
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Non-dimensional longitudinal force: CxVSP . |
− 180o ≤ αVSP ≤ 180o |
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Non-dimensional lateral force: Cy VSP . |
− ∞ ≤ JVSP ≤ ∞ |
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Thrust deduction fraction: t(δ AP ) . |
AVSP / A0VSP = 0.93 |
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eVSP / DVSP = 0.63 |
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Thruster |
0 ≤ Vlq /VTHR ≤ 5.0 |
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Coefficient of ship hull influence on thrust: fxTHR . |
− 180o ≤ β ≤180o |
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Coefficient of ship hull influence on moment: fmTHR . |
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Engines with Remote Control System |
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Diesel engine types: low speed engines, medium speed engines, high speed engines |
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Partial characteristics: Qe (n,h). |
0.2 ≤ b ≤ 0.4 |
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Friction moment coefficients: A, b |
typical programs atlas |
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Air pressure moment at start: QA . |
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RCS general programs |
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General combinative diagrams |
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Environment Mathematical Models |
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Aerodynamic and Hydrodynamic forces
Ship Hull Aerodynamic Characteristics
Shape types: single superstructure with/without spirketting plate and poop, double superstructure with/without spirketting plate and poop
~k |
~k |
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Non-dimensional longitudinal force: ax i , |
bx j , |
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~k |
~k |
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≤ L / B ≤ 7.5 |
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Non-dimensional lateral force: ay i , |
by j |
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, qy k , qy k |
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~k |
~k |
0 |
1 |
2 |
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An / LH ≤ |
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Non-dimensional vertical force: az i , |
bz j |
, qz k , qz k , qz k |
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~k |
~k |
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1 |
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2 |
−0.4 ≤ xn / L ≤ 0.4 |
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Non-dimensional roll moment: amx i , bmx j , qmx k |
qmx k |
qmx k |
0.5 ≤ zn /T ≤ 2.5 |
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~k |
0 |
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1 |
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2 |
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Non-dimensional yaw moment: amz i |
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qmz k |
qmz k |
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(where k= 0 – 2; i = 0 – 6; j = 1 – 5) are the coefficients considering the |
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relative hull and superstructures area |
kA, kAN , k1A, k1AN |
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Hull Hydrodynamic Characteristics at Even/Alternative Current |
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Non-dimensional lateral force due to local current irregularity: |
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3.5 |
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Cy (B /T ) |
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Waves Characteristics |
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Frequency and angular spectrum: sr (σ ) |
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0.2 ≤ H1 3 ≤ 8 |
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reducing coefficients: Fx(λi, ξi), Fy(λi, ξi), Fz(λi, ξi), Fmx(λi, ξi), Fmy(λi, ξi), |
0 ≤ T / λ ≤ 0.5 |
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Fmz(λi, ξi) |
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0 ≤ L / λ ≤ 7.0 |
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0 ≤ B / λ ≤ 4.0 |
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Hydrodynamic interaction in shallow waters. |
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Bottom parameters: flat bottom, inclined bottom. |
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Non-dimensional longitudinal force: CxBOT , |
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1.2 ≤ HBOT /T ≤ 20.0 |
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Non-dimensional lateral force: CyBOT , |
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0 ≤ χ ≤ 15o |
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Appendix 1. Database Information. |
97 |
Symbols |
Parameters Range |
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Non-dimensional vertical force: CmzBOT
Non-dimensional roll moment:
Non-dimensional pitch moment: CmyBOT .
Non-dimensional yaw moment: CmzBOT .
Added masses: λ11, λ22, λ66, .
Interaction coefficients due to bottom influence: WP , t
Ship to Wall Hydrodynamic Interaction
Wall parameters: flat vertical wall, ledged wall.
Non-dimensional longitudinal force: CxWALL ,
Non-dimensional lateral force: CyWALL ,
Non-dimensional yaw moment: CmzWALL .
Added masses: λ11, λ22 , λ66 .
Interaction coefficients due to bottom influence: WP , t
Hydrodynamic Interaction with Channel Walls and Bottom
Non-dimensional longitudinal force: CxCHAN ,
Non-dimensional lateral force: Cy CHAN ,
Non-dimensional yaw moment: CmzCHAN .
Added masses: λ11, λ22, λ66, .
Interaction coefficients due to bottom influence: WP , t
Ship to Ship Hydrodynamic Interaction
Non-dimensional longitudinal force: Cx SHIP .
Non-dimensional lateral force: Cy SHIP .
Non-dimensional yaw moment: Cmz SHIP .
Added masses: λ11, λ22, λ66 .
Interaction coefficients due to bottom influence: WP , t .
Anchor Gear
Anchor gear parameters: winch type, anchor type, chain gauge.
Anchor holding force coefficient: kHOLD , μ HOLD
Chain holding force coefficient: kHOLDCHN
Mooring Gear
Mooring gear parameters: winch type, rope type, knights position.
Coefficient defining rope stretch: kROPE
Fenders
Fender rigidity coefficients kS ,kVn, kVτ
0 ≤ Y0 / B ≤ 5.0
1.2 ≤ HBOT /T ≤ 5.0 − 180o ≤ ξ ≤ 180o
0 ≤ Fn ≤ 0.3
0.5 ≤ l / L ≤ ∞
0 ≤ h1 / B ≤ 1
0 ≤ h2 / B ≤ 1
1.2 ≤ HCHAN /T ≤ 5.0
1.5 ≤ BCHAN / B ≤ 5.0
0 ≤ mCHAN / B ≤ 2.0
0o ≤ α ≤ 90o
−∞ ≤ J ≤ ∞
~ |
≤ 2.0 |
− 2.0 ≤ xSHIP / L |
≤~≤
1.1ySHIP / B 5.0
0.5≤ L1 / L2 ≤ 1.5
0.5≤ V1 /V2 ≤ 1.5
holding forces atlas for different soil types
holding forces atlas for different soil types
coefficients atlas for different fender types
98 NAVI-TRAINER 4000. Mathematical Models. Technical Description.