Dynamic Positioning in Early Design Stages

Adele Lubcke*, Stefan Kruger**Hamburg University of Technology, Hamburg, Germany, adele.luebcke@tuhh.de, krueger@tuhh.de

AbstractDynamic positioning (DP) is the capability of a vessel to automatically keep its position in open water by

counteracting the environmental forces caused by wind, waves and current. Such systems are of growing

importance. Both the accurate prediction of the limiting environmental conditions and the design of a

DP-System for specified limits save costs due to the fact that the operating time of the vessel can be

increased, anchoring becomes unnecessary and the use of expensive tugs is avoided. Typical applica-

tions of DP are offshore crane and jacking operations as well as virtual anchoring for passenger ships.

To make a precise statement about the DP capability, a calculation method has been developed by the

authors. The paper shows how the calculation of the DP capabilty is carried out by taking into consid-

eration the interaction effects between the propulsion system and the hull as well as the environmental

forces. To determine the interaction effects model tests were performed. The results are also presented

in this paper and allow a more precise statement about these effects.

Keywords: Dynamic Positioning, Ship Design, Model Tests, Offshore Engineering

1. IntroductionIn the last few years, the offshore industry has gained a growing importance to the German shipyards.

Associated with the expansion of the offshore wind-power generation, new ship types are needed to

install wind turbines in the North and Baltic Sea. In order to perform this task, it is necessary to auto-

matically keep the vessels position. Therefore, vessels have to be equipped with a dynamic positioning

(DP) system which is able to compensate external forces. Such a system has to be considered in the

early ship design stage to comply with required conditions. For this purpose, a precise prediction tool is

needed to design the propulsion system. It might be problematic that there are a lot of unknowns during

the early design stage. These inlude the environmental loads and the interaction effects between the hull

and the propulsion system. One possibility would be to perform model tests for the determination of

the unknowns. However this is a very expensive option. Alternatively, direct calculation methods and

vessels of comparison are used for a fast prediction which is needed in the very early design stage.

For calculation of the environmental loads, existing methods can be used. Only the interaction effects

between the components of the propulsion system (e.g. propeller, tunnel thruster) and the hull are then

still unknown. For ships driven by azimuth thrusters, the description of interaction effects can be found

in the literature. Dynamic positioning with conventional twin screw vessels is, though, unusual. Al-

though a similar manoeuver to DP, the berthing manoeuver of ferries, the so called crabbing manoeuver,

is common practice, it is not sufficiently studied. For a better knowledge model tests with such a config-

uration are a good opportunity to investigate the interaction effects. The paper presents these results and

1/10

is therefore focused on conventional twin screw vessels.

The computation method is implemented in the ship design environment E4, which is constantly further

developed by the Institute of Ship Design and Ship Safety and partners.

2. Calculation of the Dynamic Positioning CapabilityFor the calculation of the dynamic positioning capability the equilibrium of forces and moments between

the environmental loads and the thrust of the propulsion systems has to be solved for each direction. In

any case, it is an over-determined system of equations. The environmental loads -wind, waves and

current- are supposed to have the same direction which is shown exemplary for a conventional twin

screw configuration in figure 1. Where TPS and TS B are the thrusts of the main propeller, FR the lift of

the rudders and FB the force of bow thruster. FE and NE denote the external loads.

Fig. 1. Simplified representation of the DP-problem for a twin screw vessel (Kruger and Vorholter, 2012)

The following sections describe how to determine the environmental loads (sec. 2.1) and the interaction

effects (sec. 2.2). Using the results, the calculation of the DP capability can be carried out and is

presented afterwards (sec. 2.3).

2.1. External ForcesThe modelling of the external forces significantly determine the calculated DP capability of a vessel.

Therefore, existing and new developed calculation methods are applied to compute the wind, wave and

current forces:

• Wind forces (XW , YW , NW) are described as coefficients for each wind direction ϕ - divided into

longitudinal cW,X , transverse cW,Y and yaw cW,N - in the coordinate system of the vessel:

XW (ϕ) = 0.5 · ρL · v2W · ALat, f ront · cW,X (ϕ) (1)

YW (ϕ) = 0.5 · ρL · v2W · ALat,side · cW,Y (ϕ) (2)

NW (ϕ) = 0.5 · ρL · v2W · ALat,side · cW,N (ϕ) (3)

Where vW denotes the wind speed, ρL the density of the air, ALat,side the wind lateral area of the side

view and ALat, f ront the wind lateral area of the front view. The calculation of wind coefficients is

done by regression formulas according to Blendermann, which is common practice. Alternatively,

a database with measurements from vessels of comparison is available. A typical presentation of

the wind coefficients can be found in figure 2.

2/10

-3

-2

-1

0

1

2

3

4

5

0 20 40 60 80 100 120 140 160 180

fx,f

y,ya

w[k

N,k

N,k

Nm

]

phi [Deg.]

fxfy

yaw

Fig. 2. Wind forces for each wind direction

• The current forces are found in two different ways depending on the direction of the current with

regards to the vessel. The longitudinal force is interpolated by the ship resistance curve for low

velocities. This curve can be approximated using vessels of comparison or an empirical method.

The current forces in sway and yaw are calculated by using a modified slender body method (Brix,

1993). This approach is normally used for classical manoeuvring simulations, but it can easily be

adapted for the DP problem.

• The movements of a ship in waves are partially allowed. The reason for that is that there is a

difference between the first order and higher order wave forces. The first order wave forces have

a zero mean value and therefore they are not relevant for the dynamic positioning control system.

In the dynamic positioning calculation only the second order wave drift forces are considered. For

this, an approach based on strip theory is used according to Augener (Augener and Kruger, 2014).

The strip theory has been modified to include pressure and drift force computations.

For the calculation of the second order wave drift forces the input variables (significant wave height

and wave period) are given by the initial wind speed. The correlation can be found in the literature,

e.g. DNV Rules (DNV, 2013) or IMCA (IMCA, 2000).

All external forces have been compared to measurements and the calculations of these are established

methods.

2.2. Interaction EffectsIn addition to the loads depending on the environmental conditions, the propulsions systems may have

further resulting forces as a consequence of interaction effects. A typical example is the thrust reduction

as a result of transverse current in relation to the working direction of the propulsion system. This applies

to tunnel and free thrusters. Figure 3 shows the influence of current which is also considered in the DP

calculation method.

Furthermore, the induced flow of the propulsions system generates a pressure field on the hull which

can reduce or increase the thrust. The interaction effects thruster-thruster and thruster-hull are taken into

account by definition of forbidden zones to avoid such effects. Alternatively, the results of comprehensive

investigations and studies are considered, e.g. according to Lehn (Lehn, 1980).

The interaction effects of propeller-hull and tunnel thruster-hull are almost unknown. For this reason,

model tests were carried out. The results are presented and evaluated in the next section.

3/10

Fig. 3. Thruster current interactions: Tunnel thruster (left) and free thruster (right) (Brix, 1993)

2.3. Thrust AllocationIn order to calculate the dynamic positioning capability, the thrust of the propulsion system has to be

determined to compensate the external loads. For this purpose, the wind speed is varied incrementally

according to a procedure called interval bisection. So the wind force can be determined. In correlation

to the wind speed, the parameters of the sea state are specified, so that the wave forces can be calculated.

The current forces are fixed. After each calculation it is checked whether the thrusts of the propulsion

systems do not exceed the maximum values. For the calculation an optimization algorithm is used

according to Soding (Soding, 1983). A detailed description of the determination of the thrust allocation

can be found in literature (Kruger, 2012 and Viallon, 2014).

Furthermore, all single failure scenarios are calculated. The method works for all scenarios in the same

way because only the number of propulsion organs changes. A typical presentation of the results is

illustrated in figure 4, where the plot shows the limiting wind speed for each direction.

0 10 20 30 40 5090◦

135◦

180◦

-135◦

-90◦

-45◦

0◦

45◦

vw [m/s]

Failure BT 1Failure BT 2

Failure ST

Failure PS PropFailure SB Prop

Intact

Fig. 4. Dynamic positioning capability

4/10

3. The Model TestsFor the determination of the interaction effects, model tests were carried out with a conventional twin

screw vessel equipped with fixed pitch propeller, high lift rudders as well as bow and aft tunnel thrusters.

These investigations were performed as a part of the research project DYPOS which is supported by the

German Federal Ministry of Economics and Technology.

The model was fixed and global forces in longitudinal and transverse direction and the yaw moment were

measured. In figure 5 the arrangement of the model tests is shown. The red arrows illustrate the fixation

of the model. It is the model of a 340 m cruise liner. In table 1 the main dimensions of the vessel are

presented.

Fig. 5. Top view of the ship model

Table 1. Main DimensionsLenght over all 340,00 mLength between Perpendicular 297,00 mMoulded Breadth 37,00 mDesign Draft 8,32 m

The focus of the investigation is the interaction effects between the tunnel thruster and the hull as well as

the propeller and the hull. In the following, the results and conclusions of the model test are presented.

3.1. Results of the Tunnel Thruster MeasurementsThe bow thrusters were tested in two different configurations. In the first one, the model was equipped

with three and in the second one with two bow thrusters (see figure 6). The thrusters in the latter variant

have a larger diameter, but the same power. Consequently, the interaction effects between tunnel thruster

and hull can be derived from the measurements depending on the geometry of the bow thruster.

In figure 7 the arrangement of the stern thrusters is shown which is very typical for a twin screw vessel.

At first the relation between thrust and cross force is investigated. In figure 8 and 9 the relation of thrust

of the tunnel thruster and the global cross force about the relative thrust is illustrated. In none of the

presented graphs a clear dependency on the thrust can be found. This results in an almost constant value

of the relation between thrust and cross force independent of the thrust. Furthermore, the relation is

5/10

Fig. 6. Bow thrusters in configuration 1 (left) and configuration 2 (right)

Fig. 7. Aft tunnel thrusters

higher for the bow thrusters than the stern thrusters. From this it indicates that the hull form and the

length of the thruster tunnel have a significant influence on the relation between the cross force and the

thrust.

The extreme values of the results of the stern thruster (see figure 9) are not explainable. Perhaps, the

measurements were performed too fast so that the flow was not steady.

In general, there is a significant increase of thrust at the bow thruster of at least 20%. This can be

explained by the resulting pressure fields caused by the tunnel thruster. The pressure field supports the

thrust of the tunnel thruster and an additional force is produced.

Furthermore, this resulting force of the pressure field has a point of attack which is not the same as the

thrust of the tunnel thruster. That is the reason why the resulting point of attack is investigated. This

point can be calculated using the relation between the yaw moment and the cross force multiplied with

the x-coordinate of the tunnel thruster.

In figure 10 for the bow thrusters and in figure 11 for the stern thrusters, the measurements of the point

of attack are shown. For the bow thruster an offset of 2 % is calculated. For the stern thruster it is nearly

zero. The reason for that can be found in the different hull form in range of the bow and stern thrusters.

In table 2 the results are summarized. Only the minimum values are considered to make a conservative

statement in each case. The extreme values which could not be explained are not considered.

3.2. Propeller Interaction EffectsIn the study of the main propellers (fixed pitch propellers) both directions of rotation -inward and

outward- are considered. As a result, the influence of the propeller hull interactions is found. Thus

it is possible to draw conclusions regarding the Hovgaard Effect, which is well described in literature

(Sharma, 1983) but not investigated in detail for dynamic positioning.

6/10

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

-100 -50 0 50 100

Cro

ssFo

rce

/T

hrus

tofB

owT

hrus

ter[

-]

Thrust of Bow Thruster [%]

BT 1 - Config 1BT 2 - Config 1BT 3 - Config 1

BT 1+2 - Config 1BT 1+3 - Config 1BT 2+3 - Config 1

BT 1+2+3 - Config 1

1.2

1.25

1.3

1.35

1.4

1.45

1.5

-100 -50 0 50 100

Cro

ssfo

rce

/T

hrus

tofB

owT

hrus

ter[

-]

Thrust of Bow Thruster [%]

BT 2 - Config 2BT 3 - Config 2

BT 2+3 - Config2

Fig. 8. Measurements of the non-dimensional cross force of the bow thrusters in configuration 1 (left)and configuration 2 (right)

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

-100 -50 0 50 100

Cro

ssfo

rce

/T

hrus

tofS

tern

Thr

uste

r[-]

Thrust of Stern Thruster [%]

ST 1ST 2

ST 1+2

Fig. 9. Measurements of the non-dimensional cross force of the stern thrusters

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

-100 -50 0 50 100

Yaw

Mom

ent/

(Cro

ssfo

rce·

x Thr

uste

r)[-

]

Thrust of Bow Thruster [%]

BT 1BT 2BT 3

BT 1+2BT 1+3BT 2+3

BT 1+2+3

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

-100 -50 0 50 100

Yaw

Mom

ent/

(Cro

ssfo

rce·

x Thr

uste

r)[-

]

Thrust of Bow Thruster [%]

BT 2BT 3

BT 2+3

Fig. 10. Measurements of the non-dimensional point of load attack of the bow thrusters in configuration1 (left) and configuration 2 (right)

7/10

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

-100 -50 0 50 100

Yaw

Mom

ent/

(Cro

ssfo

rce·

x Thr

uste

r)[-

]

Thrust of Stern Thruster [%]

ST 1ST 2

ST 1+2

Fig. 11. Measurements of the non-dimensional point of load attack of the stern thrusters

Table 2. Results of the tunnel thruster interaction effectsNumber of Tunnel Thruster 1 2 3

Bow amplification factor of Thrust 1.275 1.300 1.25Thruster amplification factor of point of attack 1.025 1.030 1.05Stern amplification factor of Thrust 1.025 1.010 1.000Thruster amplification factor of point of attack 1.010 1.010 1.000

Already in 1983, Sharma published investigations about the influence of the propeller direction of rota-

tion. He explained the so called Hovgaard Effect which describes a resulting cross force of a propeller

as a consequence of the propeller rotation.

The suction of the forward propeller creates a negative pressure area on the hull in front of the propeller.

This is shown in figure 3.2 on the left side. As a result a cross force is produced and the yaw moment

is increased significantly. On top to this pressure field, an indirect pressure field is generated depending

on the direction of rotation of the propeller. Accordingly, a negative pressure area results on skeg by an

inward and forward turning propeller (see figure 3.2, right top). If the propeller is turning outward, a

high pressure field is produced (see figure 3.2, right below).

– – –– – –

+ + ++ + +

PS ahead

SB asternCross force

PS Ahead SB Astern

Cross force

+++

PS Ahead SB astern

Cross force

---

Fig. 12. Direct suction field (left) and indirect suction field - outward turning (right top) and inwardturning (right below) (Augener and Kruger, 2013)

To quantify the influence of the propeller hull interaction, the measurements of the model test were

investigated. Therefore, the relation between the theoretical yaw moment and the measured yaw moment

is analyzed. It is shown in figure 13 for one propeller and for the push/ pull configuration for both

directions of rotation of the propeller. By sensible choice of the direction of rotation, the yaw moment

8/10

can be doubled. Otherwise the yaw moment is reduced up to 20% of the theoretical yaw moment.

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

-100 -50 0 50 100

Yaw

Mom

ent/

(Thr

usto

fPro

pelle

r·y p

rop)

[-]

Thrust of PS Propeller [-]

PS Propeller - inward turningPS Propeller - outward turning

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

-100 -50 0 50 100

Yaw

Mom

ent/

(Thr

usto

fPro

pelle

r·y p

rop)

[-]

Thrust of PS Propeller [-]

Push/Pull - inward turningPush/Pull - outward turning

Fig. 13. Yaw moment of a single propeller (left) and the propeller in push-pull configuration

The tests of the propellers in the push/-pull configuration were performed for a longitudinal force of zero.

This results in the speed ratios between the forward and backward turning propeller (see tab. 3).

Table 3. Speed Ratio of the Propeller in the Push-Pull ConfigurationRevolution PS Revolution SB Speed Ratio

[min−1] [min−1] [-]Inward -90 59.16 -0.657Turning -60 40.00 -0.667Propeller 60 -90.37 -0.664

90 -136.41 -0.660Outward -90 67.9 -0.754Turning -60 45.25 -0.754Propeller 60 -77.40 -0.775

90 -116.81 -0.770

4. Conclusion and OutlookA new method to calculate the dynamic positioning capability is developed. All kinds of external loads

are taken into account and also validated. Furthermore, the interaction effects are considered. The

interaction effects of an azimuthing thruster are given in the literature. For the interaction effects of a

conventional twin screw vessel, a study was carried out and presented. The model tests have shown that

the effects are not negligible.

In further research, the results will be used from the static calculation as the basis for the dynamic

calculation in time domain. Therefore, it is planned to describe the environmental forces in time domain,

too.

AcknowledgmentPart of this research has been funded by the German Federal Ministry of Economics and Technology.

Without this funding, our work would not have been possible.

9/10

References

Augener, P. and Kruger, S. (2014). Computation of Drift Forces for Dynamic Positioning within the Very EarlyDesign Stage of Offshore Wind Farm Installation Vessels. In Proceedings of the OMAE 2014.

Augener, P. and Kruger, S. (2013). Lecutre notes - Advanced ship design, Hamburg University of Technology.

Blendermann, W. (1996). Wind Loading of Ships - Collected Data from Wind Tunnel Tests in Uniform Flow.Bericht Nr. 574. Institut fur Schiffbau der Universitat Hamburg.

Brix, J. (1993). Manoeuvring Technical Manual. Seehafen Verlag.

Det Norske Veritas (July 2013). Dynamic Positioning Systems, Rules For Classification of Ships.

The International Marine Contractors Association (2000). Specification for DP Capability Plots, IMCA M 140.

Kruger, S. and Vorholter, H. (2012). Design Considerations of DP-Systems for Windpark Installation Vessels.In Proceedings of the IMDC 2012.

Lehn, E. (1980). Thruster Interaction Effects. The Ship Research Intitute of Norway.

Sharma, S. D. (1983). Schiffbautechnische Gesellschaft e.V., Bemerkungen uber die Steuerwirkung von Pro-pellern.

Soding, H. (1983). CHWARISMI I und II : Compiler fur technische Entwurfsaufgaben.

Viallon, M. (2014) Estimating dynamic positioning capability in early design stages. Master’s thesis, HamburgUniversity of Technology.

10/10