HEAVE, UNCOUPLED PITCH MOTION AND MOTION SICKNESS …

e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science

( Peer-Reviewed, Open Access, Fully Refereed International Journal )

Volume:03/Issue:10/October-2021 Impact Factor- 6.752 www.irjmets.com

www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science

[285]

HEAVE, UNCOUPLED PITCH MOTION AND MOTION SICKNESS INDEX

OF A TANKER VESSEL

Olusegun, Samuel Dare*1, Longjohn, Anthony Erekosima*2, Elakpa, Ada Augustine*3 *1,2,3Department Of Marine Engineering, Nigeria Maritime University Okerenkoko, Delta State, Nigeria.

ABSTRACT

This research work is aimed the computation of vessel Heave, uncoupled pitch vessel response and motion

sickness of a tanker vessel. Most tanker vessel are associated with motion sickness as a result of heave and

pitch motion of the vessel. Owing to this fact this research work was carried out to act as a guide of the about of

motion sickness index that is available onboard a tanker. This was achieved by the computation of the

hydrodynamics potentials of added mass, damping coefficients of each required modes of motions, their

retardation functions, the total excitation forces, which comprises of the instantaneous time varying Froud-

krylov forces, restoring and diffraction forces for each motion mode of coupled heave and pitch. Also, the

formulation of the heave and pitch response amplitude operator, the vessel motion response equation and the

motion sickness index were computed. The Runge-Kutta numerical solution was use to solved equations that

were developed and attempts were made with these solutions in testing and validating the results against those

from the commercial software (Ansys-Aqwa software). The results gotten from the validation can be said to be

impressive as an error of less than 0.001 and 0.01 were recorded for the heave and pitch response amplitude

operator respectively.

Keywords: Response Amplitude Operator; Heave; Pitch; Motion; Motion Sickness Index; Wave Frequency;

Time.

I. INTRODUCTION

The seakeeping analysis of any floating structure is a very important analysis in the design phase of offshore

structures. This has received little attention until recently in the last two centuries. Since the days of St Denis

and Pierson, ship motion has not been given considerable attention, more especially after the former’s pro-

posals of application of the principles of motion superposition. The preliminary motion prediction of vessels

before making necessary design decisions has become paramount, as the safety of the crew personnel and the

operational abilities of the facility need to perform within certain risk-free states.

Seakeeping analysis is ‘the seaworthiness’ of a vessel in calm and disturbed seaway conditions as the vessel

goes through the seaway. This analysis has had its challenges ever since the design of ships was proposed along

the design stages. The common ways of predicting seakeeping analyses were either through experiments or

some adapted designs approach of old varying results. Increasingly, experiments actually produce more

accurate results but its time consuming and a lot of resources and energies directed towards it. On the other

hand, the analytical methods and tools used in producing the same prediction has yielded a-lot closer values

with experiments which saves a lot of time and energy for the naval architects and ship project engineers in

making design decisions. All thanks to the fast-super computers we have these days. Some approaches have

been proposed for the prediction of these motions amongst which are the popular panel method, and strip

theory. The strip theory, has given some realistic results over the years in the entire circle of ship motion

computations ranging from the computations of the sectional hydrodynamics added masses and damping and

its restoring coefficients [1].

Other considerations were with regards to the domain of computations, which are further subdivided basically

into the frequency domain and time domain. While the former explored the computations of the response

amplitude operators and makes of the frequency dependency techniques, it has produced fairly accurate results

and the computation time is fairly fast. The frequency domain on the other hand has its shortcomings as it does

not cover non-linear effects and real time analysis of these floating structures. These deficiencies are made up

for much more with the time domain approach, which tries to capture the non-linear effects and gives a historic

time motion of a vessel with regards to a given time. With regards to the vessel linear dimensions, considering

the length along the longitudinal section, beam and depth, the motion of a vessel tends to express its two degree

http://www.irjmets.com/





[286]

of freedom of linear and rotational motions respectively along their linear directions of the length. Along the

longitudinal length, we have the linear and rotational motion about that axis which is the popular surge and roll

motion respectively. Also, along the beam we have the linear motion of sway and rotational motion of pitch

respectively. The popular linear heave and rotational yaw motion are along the depth of direction of the vessel.

In broad divisions, the motion of the vessel is divided into two due to coupling effects, which are vertical and

horizontal motions. The vertical motions are heave, pitch and roll, surge and yaw make the horizontal motion.

The figure 1.1 below depicts a typical ship motion in all six degrees of motion.

Figure 1: Shows the Six Degree of Motion on Vessel

The strong, watertight construction and durability attribute of floating structures, structurally enabling it to

survive rough water was never really an issue to the old boat builders, as yatches were basically used for

leisure or a few sea activities, hence the seaworthiness was not of important factor to be looked at during

design and operational stages. Easy motions coupled with freedom from jerky and excessive rolling motion-Sea

kindliness; that quality of a floating vessel, which could ‘friendly” withstand the violent wave forces and render

them kindly to both the vessel and its crew members and operations. Other qualities such as the vessels

habitability- and space for living quarters for crew members- were not given serious concerns over the

centuries. Vessels were built based on adapted designs and sometimes with mythical beliefs and these factors

were never given concerns till there were issues on sea transportations ranging from capsizing collision

grounding to other safety related incidents such as fire.

Some inventors and scholars issued some write ups. Notably was the St Denis and Pierson papers in 1953.This

paper tries to address the issue with seakeeping and proposed that the seaworthiness of any good floating

vessel can be evaluated based on the vessel responses, the realistic seaway, the purpose of the floating

structure and strength of the vessel sea-kindliness [2]. Since the prediction of ship motion and its behavioural

abilities at sea has posed serious problems, it was only important that it got more attentions. Various

approaches were adopted ranging from the strip theories, which divide the ships’ profile views into two-

dimensional body plans and determining its hydrodynamic properties such as the added masses and damping

for the modes of freedoms. One of the popular Strip theory papers that was invented and still made relevance to

the marine ship building industry today was that proposed by Salvesen and Tucks [3]. These popular strip

methods were also combined with Conformal mapping techniques which was first adopted from the popular

Lewis 2-parameter conformal mapping techniques used for estimating ship vibration problems.

Other methods for computing the added mass and damping were also proposed amongst which are the Frank

Pulsating source theories method, which uses the high and rigorous green theorem. All of these techniques

were cumbersome to carry out by computations by hand and as even, they tend to give close approximations

with the experimental values such as those conducted by Ogilvie.






[287]

Motion Sickness Index

When a fishing boat is sailing at high speed, its longitudinal overturning moment is bigger and its restoring

moment is smaller, which results in a larger heave and pitch range of the hull and seriously affects its

navigation performance. Moreover, the severe heave and pitch motion will also produce excessive longitudinal

acceleration, which will cause seasickness and seriously reduce work efficiency. Therefore, reducing the

longitudinal motion amplitude and seasickness rate of fishing boats has become a core issue in the design of

fishing vessels. An important indicator of seaworthiness is Motion Sickness Incidence (MSI), which is the

percentage of seasickness after two hours of voyage. MSI is less than 10% for passenger ships [4]. In order to

improve the stability of longitudinal motion of fishing vessels and reduce the rate of seasickness, anti-rolling

appendages must be installed. Among them, T-wing is widely used to improve the added mass and damping of

ships as anti-rolling appendages, but as a longitudinal anti-rolling device, T-wing may increase navigation

resistance. Therefore, it is necessary to combine with the wave plate to ensure that the resistance will not

increase while the rolling is reduced.

The study of seasickness rate, [5] used a mathematical expression to define the percentage of subjects who

vomited within two hours after experimentation over 300 personnel under the name of MSI. [6]. studied

operability index of ships using seakeeping analysis and performed such method on catamaran case study

comparing to human comfort criteria. [7] studied the longitudinal motion of high-speed ferry controlled by T-

wing; [8] studied the change of motion performance and seasickness rate of trimaran with or without T-wing;

[9] studied the longitudinal motion stability of catamaran controlled by T-wing. [10] discusses the influence of

those environmental conditions on the human being that may cause motion sickness incidence. [11] with T-

wing and wave plate as anti-rolling devices, the longitudinal motion amplitude of the hull can be reduced by

36% and the MSI amplitude by 45% for 40 speed high-speed boats under 5-class sea conditions. [12] studied

the effects of roll motion on a MSI of a small boat and to access the comfort of passenger on board cruises based

on wave energy spectrum. [13]; [14] studied the improvement of MSI by ship hull form modification of the

training ship. [15] analysed the MSI of the changing factors of the ship operational environment. From the

above research, most scholars use T-wing for motion control, without considering the drag increase and wave

drift caused by T-wing while improving its motion performance. Therefore, on the basis of summarizing the

previous research results, taking a fishing boat as an example, based on the theory of regular wave and

irregular wave potential flow, the panel method is used to install T-wing and its mother type respectively. The

6DOF Response Amplitude Operators (RAO) curves, wave drift force and seasickness rate before and after

modification was compared. The results show that the motion amplitude of the ship with T-wing and flap is

obviously improved, and the seasickness rate is obviously reduced. The research method in this paper can

provide technical support for the improvement of the motion performance of the same ship.

II. METHODOLOGY

The coupled equation of heave and pitch response are given as [3].

Heave: extFnCnBnAnCnBnAM 3

535535535333333333

(1)

Pitch (2)

Computing the Heave Force,

iwetFCBAM 33333333333 (3)

But the coefficient can be found thus,

daA 3333 (4)

dbB 3333 (5)

extFnCnBnAInCnBnA 5

55555555555353353353






[288]

WgAbdgC 33 (6)

Also, the sectional coefficient can be further express as

22

00

2

332 BA

ANBMba

(7)

24

22

334 BA

bb

(8)

33ais added mass

33bis section damping

2.1 Numerical Solution

The heave and pitch motion equation 1 and 2 will be resolve using the Runge-kutta fourth order solution.

Assuming an ordinary differential equation that defines value of

⁄ in form of and , also the initial value

of , i.e.,

(9)

The formula below is used to compute next value of from the previous value . The value of n are 0, 1, 2,

3, ……………..

⁄

Where h is step height and

(10)

(11)

(12)

(13)

(14)

(15)

is the increment based on the slope at the beginning of the interval using

is the increment based on the slope at the midpoint of the interval using



is the local truncation error

2.2 Equation of Motion Sickness Index

Motion sickness is one of the important parameters that need to be investigated since they have a great effect

on the crew’s performance and also on passengers’ comfort. MSI indicates the percentage of people

experiencing vomiting when exposed to motion for a certain of time. The method uses a statistically-based,

response surface which models the laboratory observations form two landmark parametric studies on motion

induced sickness.

The MSI index (Motion Sickness Incidence) is commonly used for assessing possible occurrence of the illness

[16]:

[ (

)] (16)

where:






[289]

MSI – motion sickness incidence index;

erf – error function;

av – mean value of vertical accelerations at a selected point;

– parameter calculated from this equation:

(17)

The international standard Organization ISO [17] defines methods for estimating the percentage of people who

may have motion sickness symptoms. That standard defines the motion sickness dose value (MSDV), that may

be calculated by way of one of two methods (depending on the exposure period): – if measurements are

performed over a short exposure period:

(18)

where:

– mean value of vertical acceleration;

– time of exposure recording;

– if measurements are performed over the entire period of exposure:

√∫ ( )

(19)

where:

– vertical acceleration referred to a given frequency, accounting for the weight;

T – exposure period.

Table 1: Wave, Water and Vessel Parameters Input to the MATLAB

Parameters Value

Wave Height 8m

Wave Frequency 1.5

Acceleration Due to Gravity 9.8 ⁄

Density of Seawater 1025

⁄

Length of Vessel 124m

Longitudinal Centre of Buoyancy 0.98m

Exposure Time 60 min

Ships Heading 180 Degree

Ships Speed 5 ⁄

Table 1 is the wave, water and vessel parameter input to the java program. The wave parameters are wave

height, wave frequency while the water parameter is density of seawater and the vessel parameters are length

of vessel, longitudinal centre of buoyancy, exposure time, ship heading and vessel speed.

Figure 2 is the offset table of the vessel prepared in excel sheet. The offset table contain the vessel half breadth

that will be used for the computation by the program. This offset table are imported into the program by

clicking the import tab on the program. The offset table prepared in a way that the station is arrange on the first

column of the excel sheet while the draft at each waterline are arrange on the first row of the sheet. The other

row and column are made up of the half breadth of the vessel.






[290]

Figure 2: Offset Table

III. RESULTS AND DISCUSSION

Figure 3 shows the heave response amplitude operator plotted against wave frequency. The

determines the way the vessel will respond to the heave force as the wave frequency increases. The has

an immediately impact as wave frequency increases before decline. This is so because a still water vessel that

suddenly experience load is bound to move rapidly in response to the sudden load impact. The is

maximum at 0.3rad/s before a gradual decline as wave frequency increases from 0.3rad/s to 0.9rad/s when the

Heave Response amplitude operated finally fail to zero and continue at zero as wave frequency increases form

0.9rad/s to 1.5rad/s.

Figure 3: Heave Response Amplitude Operator against Wave Frequency






[291]

Figure 4 displays the plot of vessel heave motion response against time. This plot defines the reactions of the

wave impact on the vessel as time progresses. The vessel in this case slightly respond in a way that is similar to

the wave profile even though the vessel heave response is largely determined by heave response amplitude

operator. As the time increases from 0s to 0.3s, the heave motion response of the vessel increases to maximum

position at time 0.3s. Just after 0.3s, the vessel experiences a decline heave motion response downward to the

negative until it gets to maximum negative at 1.6s. There is a rapid increase of the heave motion response

toward the positive as time increases from 1.6s to 2.5s. Though it was observed that the heave motion response

of the vessel decreases in successive crest as time progresses.

Figure 4: Heave Motion Response of the Vessel Against Time

Figure 5 shows the pitch response amplitude operator plotted against wave frequency. The significant of

is that it determines the way the vessel will respond to the pitch force as the wave frequency increases.

The has an immediately impact as wave frequency increases before decline. This is so because a still

water vessel that suddenly experience load is bound to move rapidly in response to the sudden load impact.

The is maximum at 0.7rad/s before a gradual decline 1.0 as wave frequency increases from 0.7rad/s to

1.5rad/s.

Figure 5: Pitch Response Amplitude Operator against Frequency






[292]

Figure 6 displays the plot of vessel pitch motion response against time. The significant of this plot is that it

defines the reactions of the wave impact on the vessel as time progresses. The vessel in this case slightly

respond in a way that is similar to the wave profile even though the vessel pitch response is largely determined

by pitch response amplitude operator. As the time increases from 0s to 0.75s, the pitch motion response of the

vessel increases to maximum positive at time 0.75s. Just after 0.75s, the vessel experiences a decline pitch

motion response downward to the negative until it gets to maximum negative at 3.5s. There is a rapid increase

of the pitch motion response toward the positive as time increases from 3.5s to 5.5s. Though it was observed

that the pitch motion response of the vessel decreases in successive crest as time progresses. However, this is a

normal occurrence of the motion response of the vessel as the motion is expected to decay as time progresses.

Figure 6: Pitch Motion Response of the Vessel against Time

Figure 7 shows the motion sickness index MSI against exposure time. The significant of this graph is that it is

use to check the effect of vessel motion responses (in this case heave and pitch) on human. The MSI is usually

calculated in percentage and a maximum of 10% is recommended for a passenger vessel, which are usually

higher for other classes of vessel. The plot indicates that as time increases from 0min to 46min, the MSI

increases gradually and comes to maximum also from 3% to 37%. Also, as exposure time increases from 46min

to 60min, the MSI decreases from 37% to 34% and will continue if the exposure time is increase.






[293]

Figure 7: Motion Sickness Index against Exposure Time

Figure 8 presents the plot of the spectral density against wave frequencies. The significant of this plot is that it

defines the wave profile or wave energy of the region under consideration. The spectral density remains

constant at zero within bands of 0.1 to 0.3rad/s and 1.4 to 1.5rad/s. The spectral density begins to increase

rapidly at 0.3rad/s and becomes maximum at about 0.45rad/s with a magnitude of 13.0m2

rad/s. The spectral

density then decreases rapidly as the wave frequency moves from 0.45rad/s to 1.4rad/s. It remains constant at

value of approximate zero as the wave frequency move from 1.4rad/s to 1.5rad/s.

Figure 8: Wave Spectrum against Frequency






[294]

3.1 Results Validation

Figure 9 is the Heave Response Amplitude Operator result validation. The significant of this graph is that it

helps to make comparison with already existing software. The blue plot showing the line of the Java result

while the red line shown the Ansys-Aqwa result. When comparing both results it can be observed that the Java

result is maximum at about the same frequency at which that of Ansys-Aqwa. Also, the curve of the Ansys-Aqwa

is linear enough as well as that of Java. This is due to the fact that while the java was based on strip theory the

Ansys-Aqwa was based on panel theory. The Ansys-Aqwa software make use of the overall length, beam and

depth instead of the half breadth as used by the Java. The results are in great agreement as the difference

between each point of both plots is less or equal to 0.001.

Figure 9: Heave RAOs Results Validation

Figure 10 shows the Pitch Response Amplitude Operator result validation. The significant of this graph is that it

helps to make comparison between that Java results and already existing software. The blue plot showing the

line of the Java result while the red line shown the Ansys-Aqwa result. When comparing both results it can be

observed that the Java result is maximum at about the same frequency at which that of Ansys-Aqwa. Also, the

curve of the Ansys-Aqwa is higher in magnitude than that of the Java. This is due to the fact that while the Java

was based on strip theory the Ansys-Aqwa was based on panel theory. The Ansys-Aqwa software make use of

the overall length, beam and depth instead of the half breadth as used by the Java. The results are in great

agreement as the difference between each point of both plots is less or equal to 0.01.

Figure 10: Pitch RAOs Results Validation






[295]

IV. CONCLUSION

The computation of vessel response in coupled heave and pitch motion try to developed a seakeeping

prediction tool and ship motion tool to study preliminarily motioned floating vessel in time domain and

frequency. It considered the computation of the two-dimensional added mass and damping for the modes of

motions in heave, pitch and their coupling effects and the hydrodynamic properties. These hydrodynamic

properties were computed in frequency domain and for the time domain computations, they were converted to

time domain quantities using the retardation function. An Attempt was made in computing non-linear Froude-

krylov forces along with the diffraction forces and the hydrostatic pressure forces which all form the combined

excitation forces for each degree of freedom all considered along with the conversion from one coordinate

system to the other. Those modelled coupled equations were solved simultaneously by applying the Runge-

kutta numerical method of fourth order.

The vessel pitch and heave response amplitude operator were computed using Java and the results validated

with Ansys-Aqwa software. The minimal error of 0.001 for the heave response amplitude operator and 0.01 for

the pitch response amplitude operator. The motion sickness index MSI against exposure time was also

computed. The MSI results was compared with standard which state that the MSI of a passenger vessel must be

less than 10% and below 40% for other classes of vessel. The MSI was about 37% at most and 3% at least for an

exposure time of one hour.

However, this prediction tool has a lot of discrepancies and can only be used for studies and no practical works.

It was developed basically for vessels whose offsets are well defined as it cannot intuitively make up for those

offsets missing. Also, other floating structures were also not considered like floating rigs and as such cannot

even be used to study the response of such structures along static vessels as well. It also adopted the linear

strip theory approach which stipulates that the ratio of the length to the breadth should not be more than 6.

Therefore, vessels who don’t fulfil these stipulations cannot have preliminary studies carried out with this tool.

V. REFERENCES [1] Claus, D.S., Janne, F.O., Soizic, J. & Frederick, S., (2013). EFD and CFD for KCS heaving and pitching in

regular head waves. Journal of Marine Science Technology, 18(5):435–459.

[2] Maskell, S.J. & Ursell, F., (1970). The transient motion of a floating body. Journal of Fluid Mechanics,

44:303–313.

[3] Salvesen, N. T. (1970). Ship motions and sea loads. 78, 250–287.

[4] Colwell, J.L. (1994). Motion sickness habituation in the naval environment.

[5] O'Hanlon, J.F. & McCauley, M.E. (1973). Motion sickness incidence as a function of the frequency and

acceleration of vertical sinusoidal motion, DTIC Document.

[6] Tezdogan, T., Incecik, A. & Turan, O. (2014). Operability assessment of high-speed passenger ships

based on human comfort criteria. Journal of Ocean Engineering, 89, 32-52.

[7] Liu, Y.W., Zheng, F.J. & Qi Zhi, G. (2018). Control of longitudinal motion for high speed ferry. Electric

Machines and Control 22(1), 114-120.

[8] Liu, Z.L., Zheng, L.H. & Zhang, W. (2018b). Predictive Control for Longitudinal Motion of Trimaran with

T-foil. Proceedings of the 37th Chinese Control Conference, Wuhan, China. pp: 25-27.

[9] Zhang, S.T., Sun, M.X., Liang, L.H. & Jiang, J.L. (2017). A controller design using state-feedback H∞ algo-

rithm for T-foil of WPC. Journal of Ship Science and Technology 36(10), 78-82.

[10] Tomasz, C. (2012). The prediction of the Motion Sickness Incidence index at the initial design stage.

Scientific Publisher of the Maritime University of Szczecin 31(103), 45–48.

[11] Santos, M., Lopez, R. & de la Cruz, J.M. (2015). Fuzzy control of the vertical acceleration of fast ferries.

Con Eng Prac 13, 305-313.

[12] Nguyen, A.T. & Hien, L.T. (2015). Study of the effects of roll motion on transverse Stability of a small

boat. International Journal of Mechanical Engineering and Applications 3(1-3), 24-28.

[13] Han, S.J., Lee, S.C. & Ha, Y.R. (2014). A Study on the Improvement of MSI by Ship Hull Form Modification

of the Training Ship. Journal of Fisheries and Marine Science Education 26(4), 686-694.

[14] Han, S.J., Lee, S.C. & Ha, Y.R. (2014b). A Study on the Motion Sickness Incidence due to Sea State and

Location of the Training Ship Kaya. Journal of Fisheries and Marine Science Education 26(1), 126-133.






[296]

[15] Ku-Youn, K. (2012). Analysis for Motion Sickness Incidence (MSI) of the Changing Factors of the Ship

Operational Environment. Master's Thesis, Mokpo National Maritime University of Graduate School,

South Korea.

[16] Cepowski, T. (2010). Influence analysis of changes of design parameters of passenger-car ferries on

selected seakeeping qualities. Journal of Polish Maritime Research, 1(63), vol. 16, 25–33.

[17] International Standard Organization ISO (1997). Mechanical vibration and shock – Evaluation of

human exposure to whole body vibration. 2631–1.


Documents

HEAVE, UNCOUPLED PITCH MOTION AND MOTION SICKNESS …