Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

## 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.

This is a preview of subscription content, log in to check access.

## Abbreviations

a :

Flow acceleration factor (−)

a H :

Additional steering induction for Y (−)

A R :

Rudder area (m2)

AEP:

Expanded area ratio of propeller (−)

A W :

Water plane area (m2)

B :

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)

GML :

Longitudinal metacentric height above centre of gravity (m)

I :

Moment of inertia (kg m2)

J :

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 :

P :

Propeller pitch (m)

PS:

Port side (−)

q :

r :

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 (−)

$$\alpha$$ :

$$\beta$$ :

$$\gamma$$ :

$$\delta$$ :

$$\varepsilon$$ :

$$\Delta$$ :

Displacement (N)

$$\Delta *$$ :

Differential (acting on *) (−)

$$\vartheta$$ :

$$\lambda$$ :

Regression coefficient (−)

$$\rho$$ :

Water density (kg/m3)

$$\sigma$$ :

Sign (± 1) (−)

$$\tau$$ :

Regression coefficient (−)

$$\varphi$$ :

Heel angle; phase angle (°, rad)

$$\psi$$ :

$$\omega$$ :

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:

y :

In lateral direction

yy:

zz:

(eff):

Effective

(int):

Interaction

.:

Derivative

$$'$$ :

Dimensionless

*:

Apparent

## References

1. 1.

Vos S, Delefortrie G, Van Hoydonck W (2015) Validation of the manoeuvring behaviour on an estuary vessel. MARSIM 2015, Newcastle

2. 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. 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) 148:1–15

4. 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 10

5. 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)

6. 6.

7. 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):111–131

8. 8.

Nienhuis U (1982) Analysis of thruster effectivity for dynamic positioning and low speed manoeuvring, PhD Thesis, Delft University of Technology, 1982

9. 9.

Bradner P, Renilson M (1998) Interaction between two closely spaced azimuthing thrusters. J Ship Res 42(1):15–32

10. 10.

Stettler J (2004) Steady and unsteady dynamics of an azimuthing podded propulsor related to vehicle maneuvering, PhD Thesis, Massachusetts Institute of Technology

11. 11.

Islam MF, Veitch B, Liu P (2008) Experimental research on marine podded propulsor. J Nav Archit Mar Eng 4(2):57–71

12. 12.

Amini H, Steen S (2011) Experimental and theoretical analysis of propeller shaft loads in oblique inflow. J Ship Res 55:267–288

13. 13.

Dang J, Laheij H (2003) Hydrodynamic aspects of steerable thrusters. Dynamic Positioning Conference, Houston

14. 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, Houston

15. 15.

Delefortrie G, Geerts S, Vantorre M (2016). The towing tank for manoeuvres in shallow water, MASHCON 2016, Hamburg

16. 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, Hamburg

17. 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-Petersburg

18. 18.

Veth E (2012) Personal communication