Discussion on Effects of

LCB Location on

Seakeeping Analysis

2013

ENGR 473-SHIP DYNAMICS JAKE BROHAWN

SUNY MARITIME COLLEGE

pg. 1

CONTENTS

Table of Figures ............................................................................................................................... 2

Introduction .................................................................................................................................... 3

Sea Spectrum .................................................................................................................................. 5

Definition of Parameters................................................................................................................. 7

Response Amplitude Operator (RAO) ............................................................................................. 9

Parametric Investigation ............................................................................................................... 10

Pitch RAO Comparison .............................................................................................................. 10

Roll RAO Comparison ................................................................................................................ 12

Heaving RAO .............................................................................................................................. 14

Discussion on RAO’s .................................................................................................................. 16

Added Resistance .......................................................................................................................... 17

Slamming ....................................................................................................................................... 20

Bow Slamming ........................................................................................................................... 20

Stern Slamming ......................................................................................................................... 21

Motion Sickness Index .................................................................................................................. 22

Conclusion ..................................................................................................................................... 25

pg. 2

TABLE OF FIGURES

Figure 1-Maxsurf Model Hydrostatics ............................................................................................ 4

Figure 2-Sea States .......................................................................................................................... 6

Figure 3- Remote Locations ............................................................................................................ 7

Figure 4-Maxsurf Model Remote Locations ................................................................................... 8

Figure 5- Nordforsk 1987 Crieria .................................................................................................... 9

Figure 6- Pitch RAO ....................................................................................................................... 11

Figure 7-ROLL RAO ........................................................................................................................ 13

Figure 8-Heaving RAO ................................................................................................................... 15

Figure 9-Added REsistance............................................................................................................ 18

Figure 10-Polar Plot Bow Slamming.............................................................................................. 21

pg. 3

INTRODUCTION

The purpose of this report is to investigate the effects of changing the Longitudinal

Center of Buoyancy of a model in Maxsurf Motions on the seakeeping results. The base model

for the analysis has been chosen from the Maxsurf example models, see Figure 1 for its

hydrostatic properties. From there the model was parametrically transformed in Maxsurf

Modeler. In the parametric transformation all properties were left the same except for the LCB.

The LCB was shifted first 1% and 2% forward of the original position and then 1% and 2% aft of

the original. These refer to percent of the length of the waterline that the LCB was shifted. All

references are from amidships and percent of waterline length is relative to amidships a well.

This process has given us 5 Maxsurf Models with slightly different properties. The properties

are tabulated in Figure 1 and you can clearly see the differences. Further in the report each

models individual seakeeping analysis will be compared to see what the LCB change has

affected. Along with the comparison will be a discussion of several of the slamming properties

and the severity of sea sickness that can be expected on the ship.

pg. 4

FIGURE 1-MAXSURF MODEL HYDROSTATICS

Ship 1(orig) Ship 2(1%f) Ship 3 (2%f) Ship 4 (1%a) Ship 5 (2%a) Units

Displacement 5086 5086 5085 5085 5085 t

Draft Amidships 5.25 5.25 5.25 5.25 5.25 m

WL Length 100.453 100.453 100.453 100.453 100.453 m

Beam 16.495 16.495 16.494 16.494 16.495 m

Wetted Area 1904.109 1905.855 1907.273 1902.507 1900.863 m^2

Max sect. area 84.875 84.919 84.942 84.924 84.912 m^2

Waterpl. Area 1156.152 1160.579 1165.831 1151.334 1146.818 m^2

Cb 0.57 0.57 0.57 0.57 0.57

Cwp 0.698 0.7 0.704 0.695 0.692

LCB length -1.277 -0.409 0.596 -2.147 -3.035 from midships m

LCF length -3.355 -2.678 -1.88 -4.03 -4.722 from midships m

LCB % -1.271 -0.407 0.593 -2.138 -3.021 from midships % Lwl

LCF % -3.34 -2.666 -1.872 -4.012 -4.7 from midships % Lwl

KB 2.853 2.854 2.856 2.851 2.849 m

BMt 4.073 4.097 4.124 4.048 4.022 m

BML 116.763 117.253 118.021 116.303 116.03 m

GMt corrected 6.926 6.951 6.98 6.899 6.871 m

GML 119.615 120.107 120.878 119.153 118.879 m

KMt 6.926 6.951 6.98 6.899 6.871 m

KML 119.615 120.107 120.878 119.153 118.879 m

Immersion (TPc) 11.851 11.896 11.95 11.801 11.755 tonne/cm

MTc 60.673 60.921 61.302 60.431 60.294 tonne.m

pg. 5

SEA SPECTRUM

In this analysis we will be using the Bretschneider ocean wave spectrum. This wave

spectrum is defined by the equation below. Wave spectrum is used to describe irregular ocean

waves mathematically. To develop a sea spectrum from the Bretschneider formula we need

two inputs, the characteristic wave height and the average period. Both of these parameters

can be defined by a common Sea State system. This system generalizes the various conditions

of waves into different seastates as defined below.

EQUATION 1 - BRETSCHNEIDER OCEAN WAVE SPECTRUM

( )

*where is frequency in rad/sec

Is the average frequency

Is the significant wave height in meters

pg. 6

WMO Sea State Code Wave Height (meters) Characteristics

0 0 Calm (glassy)

1 0 to 0.1 Calm (rippled)

2 0.1 to 0.5 Smooth (wavelets)

3 0.5 to 1.25 Slight

4 1.25 to 2.5 Moderate

5 2.5 to 4 Rough

6 4 to 6 Very rough

7 6 to 9 High

8 9 to 14 Very high

9 Over 14 Phenomenal

FIGURE 2-SEA STATES

pg. 7

The definition of each seastate includes several key characteristics besides the

significant wave height and the average period. One of them is the Zero crossing period which

can be defined as the mean time interval between the crossings of the zero point upwards or

downwards. This is a number describing the average time it takes before the wave reaches the

zero point at that seastate. Another one of the characteristics defined in the sea state is the

wind speed range. This indicates how fast the wind would be if that particular sea state was

observed. These properties can be simplified into single phrases used in everyday conversion

like Calm, Rough, or Very High.

DEFINITION OF PARAMETERS

Defining several remote locations help with the analysis of the operability criteria. These

remote locations will be used in the Maxsurf Motions program to compare severity of certain

effects of ships motions. A total of four remote locations are defined for the Maxsurf model,

Deck Wetness, Slamming at the bow, slamming at the stern, and the bridge. These locations are

defined by Figure 3 and can be seen in the picture of the model in figure 4.

Remote Location Long. Position From FP Height

Deck Wetness FWD MOST (containership) 5.5 m

Slamming BOW -15 m 5.5 m

Slamming STERN -95 m 5.5 m

Bridge -85 m 14.5 m

FIGURE 3- REMOTE LOCATIONS

pg. 8

FIGURE 4-MAXSURF MODEL REMOTE LOCATIONS

Setting up a range of headings in steps of 15 from 0 - 360 degrees ensures that we can

analyze all the different RAOs at their worst headings. For example, Rolling will be at its worst

with waves coming abeam to the ship (90 degrees) while Pitching is at its worst with seas

coming ahead (180 degrees). Comparing the RAO values plotted verse the encounter

frequency will give us insight into the changes that the LCB make to the overall ship dynamics.

The analysis will assume a value of .1 for the non-dimensional roll dampening factor.

This value is needed because the Maxsurf Motions software does not compute viscous effects,

which consist of the majority of the roll dampening. It is also important to define the criteria

we are using as the Nordforsk 1987 Seakeeping Criteria as defined below.

pg. 9

FIGURE 5- NORDFORSK 1987 CRIERIA

RESPONSE AMPLITUDE OPERATOR (RAO)

An RAO for a ship represents how the ship reacts to the given sea conditions and is used

in this experiment to compare different designs. An RAO value of 1.0 will show that the ships

motion is following the wave motion and is in unison with its pattern. As you increase the RAO

it will show that the ship will react with increased intensity to the waves its encountering.

Generally speaking at low encounter frequency pitch and heave RAO’s are close to 1.0 because

the ship follows the wave pattern approaching it, this can be thought of as a ship floating like a

cork. In contrast the RAO value at high encounter frequency approaches zero because there are

so many waves along the length of the vessel that the forces are canceled out and the ship does

not react. The RAO will see its highest value at the natural frequency of the ship.

pg. 10

PARAMETRIC INVESTIGATION

PITCH RAO COMPARISON

The pitch RAO represents the pitching induced by the ships reaction to the ocean

waves. Pitching can be considered greatest during head on seas. Heavy pitching can cause

severe bow slamming and damage to the ship as discussed later in this paper. It is Ideal to have

the lowest value for the Pitch RAO to avoid slamming.

Overall the Pitch RAO values between the models were different depending on the

location of the LCB. The most difference can be seen at the peak which is around and encounter

frequency of around 1.15 rads/sec. The original design is the darkest line on the graph and it is

clear to see that it is in the middle of the other four.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.2 0.7 1.2 1.7 2.2

PIT

CH

RA

O A

HEA

D S

EAS(

18

0)

ENCOUNTER FREQUENCY (RADS/SEC)

PITCH RAO

Series1

Series2

Series3

Series4

Series5

pg. 11

FIGURE 6- PITCH RAO

Zooming in on the peak we can see that the two ships with their LCB shifted aft have an

increased Pitch RAO. The two ships with the LCB shifted forward have decreased RAO values for

their Pitch RAO.

1.4

1.5

1.6

1.7

1.8

1.9

2

1 1.05 1.1 1.15 1.2 1.25

PIT

CH

RA

O A

HEA

D S

EAS(

18

0)

ENCOUNTER FREQUENCY (RADS/SEC)

PITCH RAO

Series1

Series2

Series3

Series4

Series5

pg. 12

ROLL RAO COMPARISON

The roll RAO represents the rolling induced by the ships reaction to the ocean waves. It

is non-existent in the ideal ahead seas and greatest in abeam seas. Rolling is the most reactive

ship motion because it is highly under dampened in comparison. This is due to the fact that the

beam of a ship is far smaller than the length, which is the major factor in dampening.

Overall the rolling RAO values between the different models were different depending

on the location of the LCB. The most difference can be seen at the peak which is around an

encounter frequency of .54 Rads/sec. The original design is the darkest of the lines on the graph

and it is clear to see that it is in the middle of the other four.

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

RO

LL R

AO

- B

EAM

SEA

S(9

0)

ENCOUNTER FREQUENCY(Rads/sec)

ROLLING RAO

1

2

3

4

5

pg. 13

FIGURE 7-ROLL RAO

Zooming in on the peak we can see that the two ships with their LCB shifted forward

have an increased ROLL RAO. The two ships with the LCB shifted aft can be clearly seen with

lower peak RAO values. Together it can be seen that an LCB shift of 1-2 % forward and aft of the

original design has given an increase in RAO value in the forward direction and a decrease in the

after direction.

4

4.2

4.4

4.6

4.8

5

5.2

5.4

0.45 0.5 0.55 0.6 0.65

RO

LL R

AO

- B

EAM

SEA

S(9

0)

ENCOUNTER FREQUENCY(Rads/sec)

ROLLING RAO

1

2

3

4

5

pg. 14

HEAVING RAO

The heave RAO represents the Heaving induced by the ships reaction to the ocean

waves. It is present in all wave headings. Heaving is the up and down movement of the ship due

to the waves it encounters. Because it is relevant in every heading it will be compared at 2

different headings to see differences.

The first heading analyzed is ahead seas. The RAO values for all 5 ships were effectively

unchanged by the shift in LCB in this heading. As seen in the graph below the slight differences

match the more pronounced differences in the second heading analyzed.

0

0.5

1

1.5

2

2.5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

HEA

VE

RA

O (

AH

EAD

)

ENCOUNTER FREQ (RADS/SEC)

HEAVE RAO

1

2

3

4

5

pg. 15

FIGURE 8-HEAVING RAO

For the second heading beam seas were analyzed. It can be seen that the heave RAO

values are different between the models with different LCB locations. The following graph takes

a closer look at the differences.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.5 1 1.5 2 2.5 3

HEA

VE

RA

O (

BEA

M)

Axis Title

HEAVE RAO

Series1

Series2

Series3

Series4

Series5

pg. 16

Looking at this graph it can clearly be seen that the original ship, the darkest line, is

between the other four. The two ships that had the LCB moved forward have a slightly lower

RAO value for heaving. In comparison the ships with the LCB shifted aft have a larger value for

heaving RAO then the original.

DISCUSSION ON RAO’S

The five different models had differing values for the Response Amplitude Operators for

Rolling, Pitching, and Heaving which proves that we have changed the dynamic properties of

the ship by changing the position of the LCB. These differences however slight they may be can

mean the difference in design choice to optimize comfort and safety. Also, using the peak

values you can determine the worst possible situation in any of the given directions.

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1 1.05 1.1 1.15 1.2 1.25 1.3

HEA

VE

RA

O (

BEA

M)

Axis Title

HEAVE RAO

Series1

Series2

Series3

Series4

Series5

pg. 17

The base design performed only as a reference and represented as series 1 in all graphs

can be seen as the darkest color. It is in the middle of the other four designs and holds the place

as the average ship. Design number 2, which had its LCB shifted 1% forward of design 1, is

represented by Series 2 and is the next lightest color. It performed better in Heaving and

Pitching while doing worse in rolling. Design number 3, whose LCB is shifted 2% aft of design 1,

improves on number 2 in heaving and pitching but does worse in rolling. The other two designs

represented by the lightest colors on the graph can be seen as worse in heaving and pitching

but better in rolling. Depending on what factor is important in your design you may choose any

of the designs.

The placement of the LCB of the ship affects the seakeeping performance of the ship in

several different ways. This is due to the location of mass on the ship and the shape of the

ship’s hull. The positioning of weight on the ship aids in the dampening of the reactions to the

waves the ship encounters. From the data collected it looks like the change in LCB aft improves

Heaving and Pitching but hurts Rolling. This may not be the case for further change and it must

be considered that further changing of the LCB may eventually increase these values. Thus

further analysis is needed to draw solid conclusions.

ADDED RESISTANCE

Added resistance is defined as the resistance added because of the interaction of the

ship with the waves. This affects the speed of the ship and slows the ship down in rough seas. In

this section the added resistance is compared between different headings.

pg. 18

FIGURE 9-ADDED RESISTANCE

-50

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3

AD

DED

RES

ISTA

NC

E K

N/m

2

ENCOUNTER FREQUENCY(RADS/SEC)

ADDED RESISTANCE (BEAM)

1

2

3

4

5

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3

ADDED RESISTANCE (QUARTERING)

1

2

3

4

5

pg. 19

As seen in the graphs the added resistance does change between each model along with

the change in LCB with the exception of ahead seas. In beam seas it is apparent that the 2%

shift forward in the LCB has increased the added resistances while the 2% shift aft has reduced

it. The same conclusion can be made about the added resistance in quartering seas. In ahead

seas there does not seem to be a significant change in added resistance.

0

50

100

150

200

250

300

0 0.5 1 1.5 2 2.5 3

Added Resistance(AHEAD)

Series1

Series2

Series3

Series4

Series5

pg. 20

SLAMMING

Slamming can be defined as the impact of the ship’s hull with the surface of the water. It

is usually observed when the ship is sailing into waves and the bow rises above the surface and

eventually impacts it. In this section slamming will be compared on the original model through

varying headings and sea states. The two seastates analyzed are sea state 3 and 7 which are

defined above.

BOW SLAMMING

This polar plot represents the relative vertical acceleration of the bow at various

heading and speeds. Looking at the graph it is seen that the bow acceleration is greatest at full

speed (25knts) and going straight with the waves. This is to be expected because the bow

digging into the wave straight on will provide for a situation with the maximum submerged

volume and therefore the maximum force. This force is what cause the most bow slamming

forces and it can be assumed that it will happen in ahead seas as well.

pg. 21

FIGURE 10-POLAR PLOT BOW SLAMMING

STERN SLAMMING

This polar plot represents the relative vertical acceleration of the stern at various

headings and speeds. Looking at the plot it can be determined that the stern has the most

acceleration at high speed when the waves are coming straight on to the ship. This is expected

because the maximum motion of the stern happens when the most submerged volume

happens. This happens when the ship digs into the wave and causes the maximum force in

ahead seas.

pg. 22

MOTION SICKNESS INDEX

The Maxsurf Motions software calculates a number called the Motion Sickness Index.

This number represents the percent of subjects that will vomit in the given time period. The

data were derived from test on healthy, young, male’s students who were subjected to vertical

motions for a period of up to two hours. Thus extrapolation to other demographics or longer

durations of exposure can be difficult.

pg. 23

This plot shows how the MSI at the bridge would be at various headings and speeds at

SEA STATE 4. The maximum percent of people who would vomit at full speed and the worst

heading is 14.1%. It is also seen that with waves coming from the stern there is a low

pg. 24

probability of people getting sick.

This second plot of the MSI is in SEA STATE 7. This sea state is clearly more intense as

the maximum percent is 64.2 and much more of the plot is over 25% than under. This is due to

the higher values for wave height. Also, between the two plots you can see that the severity

goes down as the encounter direction moves to the stern which indicates that ahead seas cause

significantly more discomfort than stern seas.

pg. 25

CONCLUSION

In this paper discussions on the effect of the longitudinal position of the center of

buoyancy on the seakeeping performance of a ship were proposed. Hard data was crunched

using the Maxsurf Motions and results were compared. It should be taken into consideration

that the base model was an undeveloped base provided as an example in the Motions software

and therefore may not prove to be comparable to other ships. This analysis however shows that

the LCB shift does change the seekeeping data fairly consistently over the range of models used

and this may show some validity. Finally, there is need for further analysis to provide proper

conclusions to the questions stated in the introduction but use of the data as a basis for further

investigation is acceptable.