0

HYDROSTATICS AND

STABILITY CALCULATION

REPORT

TRAWLER

SAINATH ATUL NASHIKKAR

12400052036

IMU-V, B.Tech 2012-2016

DESCRIPTION:

A fishing trawler (also called a dragger) is a commercial fishing vessel designed to operate fishing

trawls. Trawling is a method of fishing that involves actively dragging or pulling a trawl through the

water behind one or more trawlers. Trawls are fishing nets that are pulled along the bottom of the

sea or in mid-water at a specified depth. A trawler may also operate two or more trawl nets

simultaneously (double-rig and multi-rig).

Main particulars:

Vessel type TRAWLER

Length between perpendiculars 70m

Breadth 9.6m

Depth 6.4m

Draught 4.48m

Offset scale L-7, B- 4.8, D- 4

0

GIVEN OFFSET

Stations/Offsets 0 0.1 0.2 0.3 0.4 0.6 0.8 1 1.2 1.4 1.6

0.5 0 0.022 0.028 0.032 0.05 0.06 0.187 0.505 0.741 0.86 0.913

0.75 0 0.04 0.059 0.071 0.093 0.137 0.298 0.592 0.79 0.889 0.933

1 0 0.06 0.092 0.117 0.143 0.222 0.4 0.663 0.835 0.915 0.951

1.5 0 0.113 0.173 0.225 0.272 0.406 0.592 0.786 0.901 0.951 0.976

2 0 0.178 0.276 0.351 0.422 0.575 0.744 0.875 0.943 0.975 0.99

2.5 0 0.256 0.395 0.487 0.568 0.716 0.852 0.933 0.974 0.991 0.998

3 0 0.348 0.509 0.612 0.694 0.823 0.919 0.971 0.992 0.999 1

4 0 0.534 0.725 0.821 0.886 0.956 0.988 1 1 1 1

5 0 0.658 0.853 0.93 97 0.998 1 1 1 1 1

6 0 0.576 0.766 0.847 0.89 0.94 0.966 0.979 0.988 0.995 1

7 0 0.362 0.499 0.587 0.651 0.738 0.802 0.854 0.9 0.938 0.97

7.5 0 0.259 0.374 0.452 0.52 0.611 0.68 0.75 0.815 0.871 0.926

8 0 0.173 0.262 0.326 0.381 0.467 0.546 0.624 0.7 0.776 0.852

8.5 0 0.105 0.169 0.216 0.258 0.332 0.407 0.48 0.562 0.65 0.742

9 0 0.049 0.089 0.123 0.152 0.205 0.262 0.326 0.401 0.486 0.583

9.25 0 0.025 0.054 0.08 0.104 0.146 0.192 0.248 0.318 0.393 0.49

STERN AND BOW PROFILE

WL 0 0.1 0.2 0.3 0.4 0.6 0.8 1 1.2 1.4 1.6

STERN(x) 0.5 0.5 0.5 0.5 0.5 0.482 0.164 -0.245 -0.403 -0.466 -0.5

BOW(x) 9 9.258 9.383 9.45 9.55 9.65 9.75 9.85 9.95 10.05 10.15

SCALED OFFSET

WL1 WL2 WL3 WL4 WL5 WL6 WL7 WL8 WL9 WL10

0 0.4 0.8 1.2 1.6 2.4 3.2 4 4.8 5.6 6.4

2.16195 0 0.065229 0.083019 0.094879 0.148248 0.177898 0.554448 1.497305 2.197035 2.549866 2.707008

3.242925 0 0.192 0.2832 0.3408 0.4464 0.6576 1.4304 2.8416 3.792 4.2672 4.4784

4.3239 0 0.177898 0.272776 0.3469 0.423989 0.658221 1.185984 1.965768 2.475742 2.712938 2.819677

6.48585 0 0.33504 0.512938 0.667116 0.806469 1.203774 1.755256 2.330459 2.671429 2.819677 2.893801

8.6478 0 0.8544 1.3248 1.6848 2.0256 2.76 3.5712 4.2 4.5264 4.68 4.752

10.80975 0 0.75903 1.171159 1.443936 1.684097 2.122911 2.526146 2.766308 2.887871 2.938275 2.95903

12.9717 0 1.031806 1.509165 1.814556 2.057682 2.440162 2.724798 2.878976 2.94124 2.961995 2.96496

17.2956 0 2.5632 3.48 3.9408 4.2528 4.5888 4.7424 4.8 4.8 4.8 4.8

21.6195 0 1.950944 2.529111 2.757413 2.876011 2.95903 2.96496 2.96496 2.96496 2.96496 2.96496

25.9434 0 2.7648 3.6768 4.0656 4.272 4.512 4.6368 4.6992 4.7424 4.776 4.8

30.2673 0 1.073316 1.479515 1.740432 1.930189 2.18814 2.377898 2.532076 2.668464 2.781132 2.876011

32.42925 0 0.767925 1.108895 1.340162 1.541779 1.811591 2.016173 2.22372 2.416442 2.58248 2.745553

34.5912 0 0.8304 1.2576 1.5648 1.8288 2.2416 2.6208 2.9952 3.36 3.7248 4.0896

36.75315 0 0.311321 0.501078 0.640431 0.76496 0.984367 1.206739 1.423181 1.666308 1.927224 2.2

38.9151 0 0.145283 0.263881 0.36469 0.450674 0.607817 0.77682 0.966577 1.188949 1.440971 1.728572

39.99608 0 0.12 0.2592 0.384 0.4992 0.7008 0.9216 1.1904 1.5264 1.8864 2.352

SCALED OFFSETS TO LINES PLAN DRAWING (in cm)

WL1 WL2 WL3 WL4 WL5 WL6 WL7 WL8 WL9 WL10

0 0.24708 0.49416 0.74124 0.98832 1.48248 1.97664 2.4708 2.96496 3.45912 3.95328

2.16195 0 0.065229 0.083019 0.094879 0.148248 0.177898 0.554448 1.497305 2.197035 2.549866 2.707008

3.242925 0 0.118598 0.174933 0.210512 0.275741 0.4062 0.883558 1.755256 2.342318 2.635849 2.766308

4.3239 0 0.177898 0.272776 0.3469 0.423989 0.658221 1.185984 1.965768 2.475742 2.712938 2.819677

6.48585 0 0.33504 0.512938 0.667116 0.806469 1.203774 1.755256 2.330459 2.671429 2.819677 2.893801

8.6478 0 0.527763 0.818329 1.040701 1.251213 1.704852 2.20593 2.59434 2.795957 2.890836 2.93531

10.80975 0 0.75903 1.171159 1.443936 1.684097 2.122911 2.526146 2.766308 2.887871 2.938275 2.95903

12.9717 0 1.031806 1.509165 1.814556 2.057682 2.440162 2.724798 2.878976 2.94124 2.961995 2.96496

17.2956 0 1.583289 2.149596 2.434232 2.626955 2.834502 2.92938 2.96496 2.96496 2.96496 2.96496

21.6195 0 1.950944 2.529111 2.757413 2.876011 2.95903 2.96496 2.96496 2.96496 2.96496 2.96496

25.9434 0 1.707817 2.271159 2.511321 2.638814 2.787062 2.864151 2.902696 2.92938 2.950135 2.96496

30.2673 0 1.073316 1.479515 1.740432 1.930189 2.18814 2.377898 2.532076 2.668464 2.781132 2.876011

32.42925 0 0.767925 1.108895 1.340162 1.541779 1.811591 2.016173 2.22372 2.416442 2.58248 2.745553

34.5912 0 0.512938 0.77682 0.966577 1.12965 1.384636 1.618868 1.850135 2.075472 2.300809 2.526146

36.75315 0 0.311321 0.501078 0.640431 0.76496 0.984367 1.206739 1.423181 1.666308 1.927224 2.2

38.9151 0 0.145283 0.263881 0.36469 0.450674 0.607817 0.77682 0.966577 1.188949 1.440971 1.728572

39.99608 0 0.074124 0.160108 0.237197 0.308356 0.432884 0.569272 0.73531 0.942857 1.165229 1.45283

0

Lines plan:

Hull shape can be completely represented by the lines (sheer lines) plan

showing the moulded surface of a ship.

Lines plan is a set of drawings showing the form of the hull projected on three

planes perpendicular to each other. It consists of three plans: 1) a side projection

known as profile; 2) a plan showing the form of the hull at several waterlines

called half-breadth plan; 3) a plan showing the form of the hull at cross sections

called body plan. Lines plan shows the moulded surface formed by outer edges

of frames, floors and beams without the thickness of outer shell plating.

The profile plan is a projection of the ship's lines to her center line plane. It

shows the general appearance of the ship, giving the contour of the stem and

stern, the arrangement of superstructures, position of bulkheads, extent of

double bottom and position of decks. The lines which are the result of

intersecting the moulded surface of the ship by planes parallel to the centerline

are buttocks. They are called bow lines when in the fore body and buttock lines

when in the after body. Bow and buttock lines are spaced at convenient equal

intervals from the ship's centre-line. Buttocks are shown in the profile drawing

of the ship's lines. The half breadth plan is a projection of the vessel's lines on

the horizontal plane. It shows the shapes of decks and waterlines. The body plan

is a projection of the ship's lines on the midship section plane. It shows the

shapes of equidistantly spaced vertical sections of the ship. Straight lines

extending from the longitudinal middle-line plane to the frame sections of the

body plan are called diagonals or diagonal lines on the half-breadth and sheer

plans. In the body plan it is not necessary to draw both sides of the ship. The

sections in the fore body are drawn on the right-hand side, the sections in the

after body are drawn on the left.

The lines plan is necessary for making all calculations and experiments,

connected with the determination of ship seaworthiness and for development of

other drawings.

Profile plan- Using the scaled offsets the lines plan is drawn. First the bow and

stern profiles are drawn. The LBP was divided into the given number of

stations.

Body plan- The body plan is drawn for these stations with stations 0 to 5(mid-

ship) on the left and stations 6 to 10 on the right. The body plan is faired if

required and accordingly the offsets are modified.

Half- breadth plan- Measuring the offsets from the body plan for different

stations at every 1m interval waterline the half-breadth plan is drawn for these

waterlines. The half- breadths may be faired if required and the offsets modified

accordingly.

Bilge diagonal- Using the offsets measured along a diagonal drawn from the

ships centreline at the draught to the bilge radius, a bilge diagonal curve is

drawn in the plan view.

Buttocks- The body plan is divided vertically at 1m interval and using the

ordinates of the intersection of these vertical lines with the different stations the

buttock lines are drawn on the profile.

In this manner the lines plan is drawn.

Sectional area and moment calculation:

Bonjean curves are used in calculating the volume of displacement and the

center of buoyancy at any waterline, or angle of trim. Most often they are used

in stability calculations, determining the capacity of the ship, or in launching

calculations.

The sectional areas are calculated at all stations for different waterlines and the

area moments are calculated by taking levers from the base. Areas are

calculated using Simpson’s Rules. These sectional areas and moments of

particular stations are plotted against vertical lines representing stations. The

curves so formed are called the Bonjean curves.

Also the sectional areas at the draught line are plotted for the various stations

and the sectional area curve is drawn. The area under this curve gives the

underwater volume at the said draught.

Sectional area curve data

The sectional area curve represents the longitudinal distribution of cross

sectional area below the DWL. The ordinates of a sectional area curve are

plotted in distance squared units. Inasmuch as the horizontal scale, or abscissa,

of Figure above represents longitudinal distances along the ship, it is clear that

the area under the curve represents the volume of water displaced by the vessel

up to the DWL, or volume of displacement. The shape of the sectional area

curve determines the relative "fullness" of the ship. The presence of parallel

middle body is manifested by that portion of the sectional area curve parallel to

the baseline of the curve. The shoulder is defined as the region of generally

greater curvature (smaller radius of curvature) where the middle body portion of

the curve joins the inward sloping portions at bow or stern.

The centroid of the vessel's sectional area curve is at the same longitudinal

location as the center of buoyancy, LCB, and the ratio of the area under the

sectional area curve to the area of a circumscribing rectangle is equal to the

prismatic coefficient, .

The SAC cuvre also shows the customary division of the underwater body into

forebody and afterbody, forward of and abaft amidships, respectively. Entrance

and run, which represent the ends of the vessel forward of and abaft the parallel

middle body, are also shown.

BONJEAN DATA(m^2)

0 t/2 t D

stn- 0 0.00

0 5.475265 21.68163

stn- 2 0.00

15.49584 52.1122 81.97224

stn- 4 0.00

32.35788 79.88245 107.4155

stn- 6 0.00

56.98247 78.99429 109.5053

stn- 8 0.00

14.04029 40.16274 64.75755

stn- 10 0.00

0 0 3.970612

HYDROSATIC PARAMETERS

The hydrostatic properties of a hull are determined by the lines and their

interpretation using rules of integration. The resulting analysis is presented in

the form of graphs, termed the "curves of form" or "displacement and other

curves." An intact stability analysis follows naturally from the hydrostatic

analysis. Hydrostatics (determination of KM) coupled with a KG value can be

used to predict initial stability. This intact stability analysis evaluates the range

of stability at both small and large angles of inclination. The responses of the

hull to static and dynamic loading situations can be inferred from the curves of

form. Their most basic use is to determine the static waterline in various loading

scenarios. A more subtle use is to determine the correct placement of the

vertical center of gravity to ensure a sea kindly roll period, stability in beam

winds, and stability in high speed turns.

Displacement in freshwater:

The displacement in freshwater is obtained by multiplying the volume of

displacement with the density of freshwater.

Displacement in freshwater = (Volume of displacement) * (Density of

freshwater)

Displacement in seawater:

The displacement in freshwater is obtained by multiplying the volume of

displacement with the density of seawater.

Displacement in seawater = (Volume of displacement) * (Density of seawater)

Longitudinal Centre of Buoyancy (LCB) about AP:

The longitudinal centre of buoyancy is calculated by integrating the sectional

areas at different waterlines and taking moments about the aft perpendicular

(AP). The moment calculated is divided by the volume of displacement up to

that waterline to get the LCB at that particular waterline.

waterplane area (Awp):

The offset values at a particular waterline for different stations are integrated to

give waterplane area.

Longitudinal Center of floatation (LCF) about AP:

The LCF is calculated by integrating the offset values at a particular waterline

for different stations and taking first moments about the aft perpendicular (AP).

The moment calculated is divided by the waterplane area at that waterline to

give longitudinal center of floatation.

Longitudinal moment of inertia about LCF:

The longitudinal moment of inertia is calculated by taking second moment of

area with reference to a particular axis such as AP and shifted to LCF using

parallel axes theorem.

Transverse moment of inertia:

The transverse moment of inertia about the centerline is calculated by

integrating the cube of the offset value.

Vertical centre of buoyancy (VCB):

The longitudinal centre of buoyancy is calculated by integrating the waterplane

areas at different waterlines and taking moments about the keel. The moment

calculated is divided by the volume of displacement up to that waterline to get

the VCB at that particular waterline.

Transverse metacentric radius (BMT):

The transverse metacentric radius at a particular waterline is obtained by

dividing the transverse moment of inertia at that waterline with volume of

displacement at that waterline.

BMT = (IT/V)

Longitudinal metacentric radius (BML):

The longitudinal metacentric radius at a particular waterline is obtained by

dividing the longitudinal moment of inertia at that waterline with volume of

displacement at that waterline.

BML = (IL/V)

Tonnes per centimeter immersion in freshwater (TPC):

The TPC for any draft is the mass which must be loaded or discharged to

change a ship’s mean draft by one centimeter.

TPC = (Water-plane area * Density of water )/100

Mid-ship section area (Am):

The mid-ship section area is obtained from the bonjean data.

Water plane area coefficient (Cw):

The water – plane area coefficient is the ratio of the water – plane area to the

area of the rectangle having the same length and breadth.

Cw = (Area of water – plane area)/(L * B)

Block coefficient (Cb):

The block coefficient of a ship at any particular draft is the ratio of the volume

of displacement at that draft to the volume of a rectangular block having the

same overall length, breadth, and depth.

Cb = (Volume of displacement)/(L * B * draft)

Midship coefficient (CM):

The midships coefficient to any draft is the ratio of the transverse area of the

midship section (Am) to a rectangle having the same breadth and depths.

Cm = (Midship area)/ (B * d)

Prismatic coefficient (CP):

The prismatic coefficient of a ship at any draft is the ratio of the volume of

displacement at that draft to the volume of a prism having the same length as

the ship and the same cross – sectional area as the ship’s midships area.

Prismatic coefficient (CP) = (Volume of ship)/(L * Am)

= Cb/CM

Vertical prismatic coefficient (CVP):

The vertical prismatic coefficient is calculated using the formula

CVP = Cb/CWP

Transverse metacentric height (KMT):

The transverse metacentric height is given by

KMT = KB + BMT

Longitudinal metacentric height (KML):

The longitudinal metacentric height is calculated using the formula

KML = KB + BML

Moment to change trim by one cm (MCT1cm):

The MCT 1cm is the moment required to change trim by 1 cm and may be

calculated by using the formula :

MCT 1cm = (W* GML)/(100*L)

The vessel’s displacement in freshwater is known. GML is assumed equal to

BML. The MCT 1cm for different waterlines is calculated.

Longitudinal moment of inertia about midship :

The value of longitudinal moment of inertia about LCF has been calculated

already. By applying parallel axes theorem, the longitudinal moment of inertia

about midship is calculated.

HYDROSTATIC PARTICULAR

wl-0m wl-t/2 wl-t wl-D

V 790.43 1820.36 2704.98

WPA 0.00 400.23 547.47 599.04

LCB 0.00 34.52 36.60 36.72 } aft of

FP LCF 0.00 35.73 38.58 37.64

KB 0.62 1.19 2.37 3.39

TPC 0.00 4.00 5.47 5.99

ILCF 0.00 83249.39 168157.16 399203.84

IT 0.00 2044.51 3439.90 4068.40

BMT 0.00 2.59 1.89 1.50

BML 105.32 92.38 147.58

MCT 1189.28 2402.25 5702.91

KML 0.62 106.51 94.75 150.97

KMT 0.62 3.77 4.26 4.90

0

CONCLUSION

This preliminary ship design project enabled me to understand all the aspects of ship drawing namely lines plan , half breath plan

and body plan. Summarized , it can be stated that different types of trawlers have its own type of working area in which its production

is optimal in a technical as well as economical manner.