This document contains a hydrostatics and stability calculation report for a 70m trawler. It includes: - Main particulars of the trawler including dimensions and offsets. - Scaled offsets table providing the form coefficients at stations along the vessel. - Description of how a lines plan is developed from the offsets including drawing profiles, body plan, half-breadth plan, bilge diagonals and buttocks. - Mention that Bonjean curves will be used to calculate displacement volume and center of buoyancy for stability analysis.

1. 0
HYDROSTATICS AND
STABILITY CALCULATION
REPORT
TRAWLER
SAINATH ATUL NASHIKKAR
12400052036
IMU-V, B.Tech 2012-2016

2. 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).

3. 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

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

5. 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

6. 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

8. 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.

9. 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.

10. 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

11. 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:

12. 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.

13. 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

14. 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

15. 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.