International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com November 2015, Volume 3, Issue 11, ISSN 2349-4476
Stability Comparison On Boat Hull Using Different Materials
based on Metacenter Height
A. Srinivas *, M. Adinarayana*, S. Madhusudhana *, S. Moulali*
*Asst. Professor, Mechanical Engineering Department, SVTM College Madanapalle, India
ABSTRACT: A boats hull shape is important for a number of reason, safety, sea kindliness, load carrying capacity,
speed and efficiency in a particular speed range and operating conditions. A hull is the watertight body of a ship or boat.
The main purpose of boats is extensively used for short distance transportation, trading and fishing etc. This paper is
describes Stability comparison on boat hull using different materials based on metacenter height. In the present work,
Metacenter height and stability was calculated for a boat hull made of Four different materials like Pine Plywood, Epoxy
Glass Fiber (EGP), Kevlar, Glass Fiber Reinforced Polymers (GFRP). The composite materials are being extensively
used in varieties of engineering applications because of their superior properties over other conventional materials, the
advantages include high strength to weight ratio, high specific strength, high corrosion resistance and high fracture
toughness etc. In order to reduce the weight and to increase the performance composite materials are used for the boat
rd
hull. Theoretical calculation of metacenter height and stability for boat hull is calculated using Simpson’s
eight different boat materials.
1.
INTRODUCTION
The increasing cost and scarcity of durable
boatbuilding timbers have affected the construction
of fishing craft around the world. The developed
world has by and large witnessed the transfer from
traditional wooden boatbuilding methods to either
less conventional wood construction techniques
(e.g., plywood or wood laminates) or non-wood
materials such as fibre reinforced plastic (FRP),
steel, aluminium and ferrocement. These techniques
generally favour less labour intensive methods of
construction. Boat is generally used in sea and
ponds. However many boats are used exclusively
for sports. Boats can be made in different shapes
and sizes. They are able to float on water and move
due to various propulsion systems (engines, oars,
paddles and sails Boating is the leisurely activity of
travelling by boat, or the recreational use of a boat
whether powerboats, sailboats, or man-powered
vessels (such as rowing and paddle boats), focused
on the travel itself, as well as sports activities, such
asfishing or waterskiing. It is a popular activity, and
there are millions of boaters worldwide.
Boats are made of materials like wood, steel and
metal. There are five contributing factors that help
to keep a boat afloat and prevent it from sinking.
They are buoyancy, stability, waterproofing, air
capacity and shape.
2. PROBLEM DESCRIPTION AIM OF
PROJECT
This is extension project for Mr. A. Srinivas1 and
Mr. S. Madhusudhana. Mr. A. Srinivas find stability
1
rule for the
conditions for assuming 30m water plane. Mr. S.
Madhusudhana find stability of boat hull using
different materials. In this project we determine
stability of a boat hull by assuming 25m, 30m, 35m,
40m, 45m and 50m water planes. The objective of
the present work is to determine metacenter height
and stability of a boat hull made of four different
materials like pine plywood, Epoxy Glass Fiber
(EGP), Kevlar, Glass Fiber Reinforced Polymers
(GFRP).
The material commonly used for the
manufacturing boat is steel or wood. If steel is used
as the material then weight of the boat increases and
wood was less weight and effective corrosion
resistance
3. SPECIFICATION OF BOAT HULL and 3D
MODEL
Table1: Specification of boat hull.
S.NO PERAMETERS
VALUE (m)
1
Boat hull length
6
2
Boat hull height
2.5
3
Beam
1.2
4
Draft
25m, 30m, 35m, 40m,
45m and 50m
(Assumed)
5
Material
Aluminum, Wood and
S-Glass/Epoxy
composite.
A. Srinivas *, M. Adinarayana*, S. Madhusudhana *, S. Moulali*
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com November 2015, Volume 3, Issue 11, ISSN 2349-4476
Figure1: 3D view of Boat hull.
5. AREA BY USING SIMPSONS RULE:
5.1 Area of the water plane at 0.25 m draft
For the purpose of calculation of area of water plane
half of the water plane (wp) is considered at the
draft of 0.25m. There are six ordinates(y1, y2, y3, y4,
y5, y6) were taken and multiplied with simpson
multiplires (SM). Figure: 3.1 shows the area of the
water plane at various ordinates at 0.25m draft.
4. THEORITICAL CALCULATIONS FOR
METACENTER HEIGHT
Simpson‟s rd rule may be used to find the areas
and volumes of irregular objects. When applied to
ships they give a good approximation of areas and
volumes. The accuracy of the answers obtained will
depend upon the spacing of the ordinates.
This rule assumes that the curve is a parabola of the
second order. A parabola of the second order is one
whose equation, reffered to co-ordinate axis, is of
the form y = a0 + a1y + a2y2, where a0, a1 and a2
are constants.
The coefficients of the ordinates are reffered to as
Simpson‟s Multiplires (SM) and they are in the
form: 1424241. There had been nine ordinates, the
multiplires would have been: 142424241.
Simpson‟s multiplier begin and end with 1.
Let the curve in Figure:2 be a parabola of the
second order. Let y1, y2, y3 and y4, represents four
ordinates equally spaced at „h‟ units apart.
Fig. 3.1 ½Area of the water plane at 0.25 m
draft.
Table 5.1. ½Area of the water plane at 0.25 m
draft.
½ Ordinate (y)
SM
½ Area Of
(m) (A)
Water plane
(B)
(m)
(A×B)
0.88
1
0.88
0.93
4
3.72
0.93
2
1.86
0.85
0.61
4
2
3.4
1.22
0
1
0
∑ = 11.08 m
Common interval (h) = 0.958 m
×h×∑
½ area of water plane =
=
= 3.538 m2
Figure:2 Parabola of the forth order.
Area of the figure = ( y1 + y2 + y3+ y4 )
Area of the water plane (∑A) = × h × ∑ × 2
=
Figure3: Schematic diagram of boat hull.
2
× 0.958 ×110.8
× 0.958 ×11.08 × 2
= 7.076 m2.
5.2. VOLUME OF WATER DISPLACED:
For the purpose of calculation of volume of
water displaced of boat hull at the draft of 0.30m for
different maerials. The volume of boat hull is taken
from Pro/E software.
A. Srinivas *, M. Adinarayana*, S. Madhusudhana *, S. Moulali*
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com November 2015, Volume 3, Issue 11, ISSN 2349-4476
5.2.1. PINE PLY WOOD :- (density = 550 kg/m3)
Weight of boat hull = volume of boat hull ×
density of boat hull material × g
= 1.077 × 550 × 9.81
= 5810.95 N
For equilibrium weight of water displaced = weight
of boat hull
Volume of water displaced = weight of water
displaced / water density
=
= 0.578 m3
5.2.1.1. BUOYANT FORCE (Bf)
Buoyant Force (Bf) = volume of water displaced × g
× density of water
= 0.578× 9.81 × 1025
= 5811.934 N
5.2.2. EPOXY GLASS FIBRE :- (density = 1500
kg/m3)
Weight of boat hull = volume of boat hull ×
density of boat hull material × g
= 1.077 × 1500 × 9.81
= 15848.05 N
For equilibrium weight of water displaced = weight
of boat hull
Volume of water displaced = weight of water
displaced /water density
=
= 1.576 m3
5.2.2.1. BUOYANT FORCE (Bf):
Buoyant Force (Bf) = volume of water displaced × g
× density of water
= 1.576 × 9.81 × 1025
= 15847.074 N
5.2.4. KEVLAR :- (density = 1350 kg/m3)
Weight of boat hull = volume of boat hull ×
density of boat hull material × g
= 1.077 × 1350 × 9.81
= 14263.25 N
For equilibrium
weight of water displaced = weight of boat hull
Volume of water displaced = weight of water
displaced /water density
3
=
= 1.418 m3
5.2.4.1. BUOYANT FORCE (Bf)
Buoyant Force (Bf) = volume of water displaced × g
× density of water
= 1.418 × 9.81 × 1025
= 14258.344 N
5.2.8. GFRP (Glass Fibre Reinforced Polymer) :(density = 1800 kg/m3)
Weight of boat hull = volume of boat hull ×
(density of boat hull material × g)
= 1.077 × 1800 × 9.81
= 19017.67N
For equilibrium weight of water displaced = weight
of boat hull
Volume of water displaced = weight of water
displaced /water density
=
= 1.89 m3
5.2.8.1. BUOYANT FORCE (Bf):
Buoyant Force (Bf) = volume of water displaced × g
× density of water
= 1.89 × 9.81 × 1025
= 19004.422 N
5.3. CENTER OF BUOYANCY:
For the purpose of calculation of center of
buoyancy at the draft of 0.25m the area of the half
of the water plane multiplied with simpson
multiplires (SM). Table 3.3 shows the center of
buoyancy at the draft of 0.25m.
Table 5.2. Center of buoyancy.
Area of wp
SM
0.88
1
3.72
4
1.86
2
3.4
4
1.22
2
0
1
2
∑ = 11.08 m
Product
0.88
14.88
3.72
13.6
2.44
0
∑ = 35.52 m2
CB = ∑ (AWP ( SM ) × Z) / ∑ (product)
A. Srinivas *, M. Adinarayana*, S. Madhusudhana *, S. Moulali*
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com November 2015, Volume 3, Issue 11, ISSN 2349-4476
Where,
5.5.1. For pine ply wood:
AWP = water plane area
Z
= vertical distance b/w the base line
to water plane
CB =
= 0.08
5.4 SECOND MOMENT OF INERTIA OF
THE WATER PLANE AREA ABOUT THE
CENTERLINE:
For the purpose of calculation of second
moment of water line area about the centerline six
ordinates (y1, y2, y3, y4, y5, y6) were taken and there
cubic value was multiplied with
simpson
multiplires (SM). Table 3.8 shows the second
moment of the water line area about the centerline.
Table 5.3. Second moment of the water line area.
½
ordinate
(A)
(½
ordinate)3
(B)
SM
Product
(A
0.88
0.681
1
0.681
0.93
0.804
4
3.216
0.93
0.804
2
1.608
0.85
0.614
4
2.456
0.61
0.226
2
0.452
0
0
1
0
∑ =8.413m3
Icl = × h × ∑ (product )
= × 0.958 ×8.413
= 1.791m4
5.5. TO FIND THE DISTANCE OF “Center of
buoyancy to metacenter (BM)“ :
BM
I = Second moment of the water plane area about
the centerline
V = The volume of water displacement
4
BM =
= 3.099m
Distance of “Keel to Metacenter “with reference to
figure 3.5
KM = KB + BM
=0.08 + 3.099 =3.179 m
5.5.2. For Epoxy glass fibre:
BM =
=1.136 m
Distance of “Keel to Metacenter “with reference to
figure 3.5
KM = KB + BM
=0.08 + 1.136
=1.216 m
5.5.4. For kevlar:
BM =
= 1.263 m
Distance of “Keel to Metacenter “with reference to
figure 3.5
KM = KB + BM
=0.08 + 1.263
=1.343 m
5.5.8. For GFRP (Glass Fibre Reinforced
Polymer):
BM =
=0.948 m
Distance of “Keel to Metacenter “with reference to
figure 3.6
KM = KB + BM
=0.08 + 0.948
=1.028 m
6.
STABILITY
IN
THE
UPRIGHT
CONDITIONS:
1. If Center of gravity (G) is below
Metacenter (M), the boat in stable equilibrium.
2. If
Center of gravity (G) is above
Metacenter (M), the boat in unstable
equilibrium.
3. If Center of gravity (G) is coincide with
Metacenter (M), the boat is in neutral.
A. Srinivas *, M. Adinarayana*, S. Madhusudhana *, S. Moulali*
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com November 2015, Volume 3, Issue 11, ISSN 2349-4476
7. RESULTS
Table 7.0. Water plane height at 0.25m
S.
NO.
Materials
Centre
of
gravity
height
(m)
Metacenter
Height
(m)
1.
Pine Plywood
0.76
3.199
2.
Epoxy Glass Fiber
(EGP)
0.76
1.216
3.
Kevlar
0.76
1.343
4.
Glass Fiber
Reinforced
Polymers (GFRP)
0.76
0.948
Table 7.3. Water plane height at 0.40m
S. Materials
Centre Metacenter
of
NO.
Height
gravity
(m)
height
(m)
1.
Pine Plywood
0.76
6.441
2.
Epoxy Glass Fiber
(EGP)
0.76
2.319
3.
Kevlar
0.76
2.702
4.
Glass Fiber
Reinforced
Polymers (GFRP)
0.76
2.058
Table 7.1. Water plane height at 0.30m
S. Materials
Centre Metacenter
of
Height
NO.
gravity
(m)
height
(m)
1.
Pine Plywood
0.76
5.263
Table 7.4. Water plane height at 0.45m
S. Materials
Centre Metacenter
of
NO.
Height
gravity
(m)
height
(m)
1.
Pine Plywood
0.76
6.637
2.
Epoxy Glass Fiber
(EGP)
0.76
1.987
2.
Epoxy Glass Fiber
(EGP)
0.76
2.537
3.
Kevlar
0.76
2.198
3.
Kevlar
0.76
2.788
4.
Glass Fiber
Reinforced
Polymers (GFRP)
0.76
1.582
4.
Glass Fiber
Reinforced
Polymers (GFRP)
0.76
2.127
Table 7.2. Water plane height at 0.35m
S.
NO.
Materials
Centre
of
gravity
height
(m)
Metacenter
Height
(m)
1.
Pine Plywood
0.76
6.455
2.
Epoxy Glass Fiber
(EGP)
0.76
2.436
3.
Kevlar
0.76
2.695
4.
Glass Fiber
Reinforced
Polymers (GFRP)
0.76
2.05
5
Table 7.5. Water plane height at 0.50m
S. Materials
Centre Metacenter
of
NO.
Height
gravity
(m)
height
(m)
1.
Pine Plywood
0.76
6.66
2.
Epoxy Glass Fiber
(EGP)
0.76
2.54
3.
Kevlar
0.76
2.806
4.
Glass Fiber
Reinforced
Polymers (GFRP)
0.76
2.144
A. Srinivas *, M. Adinarayana*, S. Madhusudhana *, S. Moulali*
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com November 2015, Volume 3, Issue 11, ISSN 2349-4476
Figure 7.0. Schematic diagram of boat hull for Pine
Plywood
Figure 7.1. Schematic diagram of boat hull for
Epoxy Glass Fiber (EGP)
8. CONCLUSION
 For stability, the center of gravity (G) is below
the metacenter (M). This condition was validated
for eight different materials are considered for this
analysis.
 By increasing height of water plane the
metacenter height increases so the stability of boat
increases similarly the height of water plane
decreases the metacenter height decreases so the
stability of boat decreases.
 From above calculations it is observed that for
Glass Fiber Reinforced Polymers (GFRP) the
metacenter height is near the center of gravity to
compare all other materials. So this material is good
stability to compare all other materials at these
levels (0.25m, 0.30m, 0.35m, 0.40m, 0.45m, 0.50m)
of water plane.
9. SCOPE FOR FUTURE WORK

The analysis can be done for different
shapes of boat hulls and the different materials of
boat hull.

CFD analysis on Flow characteristics like
drag and lift forces can be done for different boat
speeds by keeping the water and wind speed as
constant.

CFD analysis on Flow characteristics like
drag and lift forces can be done for different wind
speeds by keeping the water and boat speed as
constant.
10. BIBLIOGRAPHY
1.
Figure 7.2. Schematic diagram of boat hull for
Kevlar
2.
3.
4.
A. Srinivas “Stability and computational flow
analysis on boat hull” IJMER, Vol. 2, Issue. 5,
Sept.-Oct. 2012 pp-2975-2980 ,ISSN: 2249-6645
S. Madhusudhana. Modeling and Stability
Analysis on a Boat Hull for Different Materials
www.ijetmas.com April 2015, Volume 3 Issue 4,
ISSN 2349-4476
Gray, R. P., “Investigation of the airflow around a
sail”, Pyh. Educ. 21, 1986.
Serden GÖLPINAR. “Comparative analysis of
materials in recreational boat design: fiber
reinforced plastic boat in serial production” thesis,
iZMiR, January 2005.
Figure 7.3. Schematic diagram of boat hull for
Glass Fiber Reinforced Polymers (GFRP)
6 A. Srinivas *, M. Adinarayana*, S. Madhusudhana *, S. Moulali*