# Manoeuvring model of an estuary container vessel with two interacting Z-drives

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## Abstract

A 6 degrees of freedom manoeuvring model of an estuary container vessel was implemented in the inland navigation simulator Lara at Flanders Hydraulics Research (FHR). The container vessel, with dimensions 110 m × 17.5 m × 4.5 m, is equipped with two Z-drives, each one consisting of two contra rotating propellers. Both Z-drives have a 360° azimuth angle of operation during manoeuvring. The mathematical manoeuvring model was built to cover all degrees of operation. This required the execution of a significant number of captive model tests in the shallow water towing tank of FHR (in co-operation with Ghent University). Based on these tests a new mathematical manoeuvring model was built to cover all effects of operation, including the interaction effects between the two Z-drives. The new mathematical model was implemented in the simulator and both fast time and real time manoeuvring simulations have been carried out. A paper discussing the validation of the manoeuvring model has been presented during MARSIM 2015 (Vos, Delefortrie, and Van Hoydonck in Validation of the manoeuvring behaviour on an estuary vessel. MARSIM, Newcastle, 2015). The present paper discusses the details of the manoeuvring model, with emphasis on the interaction effects between the Z-drives and the influence on the hydrodynamic forces.

## Keywords

Manoeuvring Shallow water Thruster interaction## List of symbols

*a*Flow acceleration factor (−)

*a*_{H}Additional steering induction for

*Y*(−)*A*_{R}Rudder area (m

^{2})- AEP
Expanded area ratio of propeller (−)

*A*_{W}Water plane area (m

^{2})*B*Ship breadth (m)

*C*_{B}Block coefficient (−)

*C*_{D}Drag coefficient (−)

*C*_{L}Lift coefficient (−)

*C*_{T}Thrust coefficient (−)

*D*Ship depth; propeller diameter (m)

*D*Drag in drive bound axis system (N)

*D*_{DEN}Duct entry diameter (m)

*D*_{DEX}Duct exit diameter (m)

*F*Force (N)

- GM
_{(T)} Transverse metacentric height above centre of gravity (m)

- GM
_{L} Longitudinal metacentric height above centre of gravity (m)

*I*Moment of inertia (kg m

^{2})*J*Propeller advance (−)

*K*_{(*)}Roll moment [derivative of * (* represents any combination of kinematical parameter(s)

*u, v, w, p, q, r*or their derivatives)] (Nm)*K*_{T}Thrust coefficient (−)

- KM
Transverse metacentric height above keel (m)

*L*Lift in drive bound axis system (N)

*L*_{D}Duct length (m)

*L*_{OA}Ship length over all (m)

*L*_{(PP)}Ship length between perpendiculars (m)

*m*Ship’s mass (kg)

*M*_{(*)}Pitch moment [derivative of * (* represents any combination of kinematical parameter(s)

*u, v, w, p, q, r*or their derivatives)] (Nm)*N*Propeller rate (rpm, 1/s)

*N*_{(*)}Yawing moment [derivative of * (* represents any combination of kinematical parameter(s)

*u, v, w, p, q, r*or their derivatives)] (Nm)*O*Origin of coordinate system (−)

*p*Roll velocity (rad/s)

*P*Propeller pitch (m)

- PS
Port side (−)

*q*Pitch velocity (rad/s)

*r*Yaw velocity (rad/s)

- SS
Starboard side (−)

*t*Time (s)

*T*Ship draft (m)

*T*_{P}Thrust in drive bound axis system (N)

*T*_{xp}Longitudinal force in drive bound axis system (N)

*T*_{yp}Lateral force in drive bound axis system (N)

*u*Longitudinal velocity (m/s)

*v*Lateral velocity (m/s)

*w*Vertical velocity (m/s)

*w*_{R}Wake factor (steering) (−)

*w*_{T}Wake factor (thrust) (−)

*V*Global velocity in the horizontal plane (m/s)

*x*Longitudinal position (m)

*X*_{(*)}Longitudinal force [derivative of * (* represents any combination of kinematical parameter(s)

*u, v, w, p, q, r*or their derivatives)] (N)*x*_{H}Additional steering induction for

*N*(−)*y*Lateral position (m)

*Y*_{(*)}Lateral force [derivative of * (* represents any combination of kinematical parameter(s)

*u, v, w, p, q, r*or their derivatives)] (N)*z*Vertical position (m)

*Z*_{(*)}Vertical force [derivative of * (* represents any combination of kinematical parameter(s)

*u, v, w, p, q, r*or their derivatives)] (N)*z*_{H}Additional steering induction for

*K*(−)*z*_{HX}Steering induction for

*M*(m)*z*_{HZ}Steering induction for

*Z*(−)- \(\alpha\)
Effective inflow angle (°, rad)

- \(\beta\)
Drift angle (°, rad)

- \(\gamma\)
Yaw angle (°, rad)

- \(\delta\)
Azimuth angle (°, rad)

- \(\varepsilon\)
Hydrodynamic advance angle (°, rad)

- \(\Delta\)
Displacement (N)

- \(\Delta *\)
Differential (acting on *) (−)

- \(\vartheta\)
Pitch angle (°, rad)

- \(\lambda\)
Regression coefficient (−)

- \(\rho\)
Water density (kg/m

^{3})- \(\sigma\)
Sign (± 1) (−)

- \(\tau\)
Regression coefficient (−)

- \(\varphi\)
Heel angle; phase angle (°, rad)

- \(\psi\)
Course angle (°, rad)

- \(\omega\)
Pulsation (°, rad)

## Subscripts

*D*Drag

*G*Regarding centre of gravity

*H*Regarding the hull

*i*Interaction; summation

*I*Inertia

*L*Lift

*o*Fixed coordinate system

*P*Regarding the propeller

- PS
Port side

- PT
Regarding the propeller thrust

- PTA
Oscillation amplitude regarding the propeller thrust

*R*Regarding the rudder

- SS
Starboard side

*X*In longitudinal direction

- xx
About

*x*-axis*y*In lateral direction

- yy
About

*y*-axis- zz
About

*z*-axis

## Superscripts

- (eff)
Effective

- (int)
Interaction

- .
Derivative

- \('\)
Dimensionless

- *
Apparent

## References

- 1.Vos S, Delefortrie G, Van Hoydonck W (2015) Validation of the manoeuvring behaviour on an estuary vessel. MARSIM 2015, NewcastleGoogle Scholar
- 2.Moniteur Belge (2007) Arrêté royal relatif aux bateaux de navigation intérieure qui sont aussi utilisés pour effectuer des voyages non internationaux par mer. N° 2007–1187, pp 14699–14711
**(In French)**. http://reflex.raadvst-consetat.be/reflex/pdf/Mbbs/2007/03/16/103633.pdf - 3.Truijens P, Vantorre M, van der Werff T (2006) On the design of ships for estuary service. Trans RINA Part A2 Int J Marit Eng (IJME) 148:1–15Google Scholar
- 4.Vantorre M, Vandevoorde B, De Schrijver M, Smitz H, Laforce E, Mesuere M, Heylbroeck B, Wackenier B, Claeyssens P, Van Steen J, Van Rompuy F, van der Werff T, Calluy L (2006) Risk analysis for inland vessels in estuary service. In: Proceedings 31st PIANC congress, Estoril, Portugal, p 10Google Scholar
- 5.Arrêté du 15 décembre 2014 relatif à la navigation de bateaux porteconteneurs fluviaux en mer pour la desserte de Port 2000 et des quais en Seine à Honfleur
**(In French)**Google Scholar - 6.PIANC (2013) Direct access to maritime ports by adapted inland waterway vessels. Maritime Navigation Commission & Inland Navigation Commission Expert Group, PIANC Report No. 118Google Scholar
- 7.Vantorre M, Eloot K, Delefortrie G (2012) Probabilistic regulation for inland vessels operating at sea as an alternative hinterland connection for coastal harbours. Eur J Transp Infrastruct Res 12(1):111–131Google Scholar
- 8.Nienhuis U (1982) Analysis of thruster effectivity for dynamic positioning and low speed manoeuvring, PhD Thesis, Delft University of Technology, 1982Google Scholar
- 9.Bradner P, Renilson M (1998) Interaction between two closely spaced azimuthing thrusters. J Ship Res 42(1):15–32Google Scholar
- 10.Stettler J (2004) Steady and unsteady dynamics of an azimuthing podded propulsor related to vehicle maneuvering, PhD Thesis, Massachusetts Institute of TechnologyGoogle Scholar
- 11.Islam MF, Veitch B, Liu P (2008) Experimental research on marine podded propulsor. J Nav Archit Mar Eng 4(2):57–71Google Scholar
- 12.Amini H, Steen S (2011) Experimental and theoretical analysis of propeller shaft loads in oblique inflow. J Ship Res 55:267–288CrossRefGoogle Scholar
- 13.Dang J, Laheij H (2003) Hydrodynamic aspects of steerable thrusters. Dynamic Positioning Conference, HoustonGoogle Scholar
- 14.Cozijn H, Hallmann R, Koop A (2010) Analysis of the velocities in the wake of an azimuthing thruster, using PIV measurements and CFD calculations. Dynamic Positioning Conference, HoustonGoogle Scholar
- 15.Delefortrie G, Geerts S, Vantorre M (2016). The towing tank for manoeuvres in shallow water, MASHCON 2016, HamburgGoogle Scholar
- 16.Delefortrie G, Eloot K, Lataire E, Van Hoydonck W, Vantorre M (2016) Captive model tests based 6 DOF shallow water manoeuvring model. MASHCON 2016, HamburgGoogle Scholar
- 17.Tello Ruiz M, Delefortrie G, Vantorre M, Geerts S (2012) Propulsion and steering behaviour of a ship equipped with two contra-rotating Z-drives. ICHD 2012, St-PetersburgGoogle Scholar
- 18.Veth E (2012) Personal communicationGoogle Scholar