FRP Catamaran Hull Form Analysis and Operations Ernest Lam Falmouth Marine School, Killigrew Street, Falmouth, Cornwall, UK, TR11 3QS ABSTRACT This project is a 2 years project. A new 35ft FRP catamaran hull has been chosen to design. This paper will be carrying out the full process of the hull design and calculations. The result of stability shows that the catamaran might be not too stable and resistance might be increasing through water. But because of the time limitation, model is not possible to be created for experiment and study.
Parametric studies for a yacht based on
INTRODUCTION For most of the product design, the design
some other same type of yacht’s Length of All
process always follows the rules of ‘trial and
(LOA), Length of Waterline (LWL), Beam (B)
error’ which means following the steps and see if
Displacement (∆), Volume (∇) and Power (P)
the result satisfies the requirement. Designers
become useful information such as Length-Beam
generally need to repeat the process 10 times or
ratio (LB ratio), Length-Displacement ratio ( LD
even 100 times to achieve the requirement which
ratio ) and Power-Displacement ratio (PD ratio).
where ‘The design Spiral’ came from. (Larsson
(Whatley 2010)
& Eliasson, 2007) For an engine powered
Hull design is one of the most important yacht, main
operations. The reason behind it is because
operations in the design spiral are hull and decks
distinct hull forms have different parametric
design, keel and rudder design, decision of
which gives the yacht a different performances
propeller and engine, hydrostatics and stability
and stability. Designer generally set up a table
and finally evaluation. For other powered yacht
which contain section area and calculate the
such as sail powered or solar powered, more
volume for compare it with the parametric study
operations will be needed. For example, sail and
result. The first draft will be drawn after both
rig design or position and efficiency of extra
table and parametric study has identified, in
hardware. (Larsson & Eliasson, 2007)
either graph paper or Computer Aided Design
Using ‘The design Spiral’ to Design a
(CAD). Centre of Gravity and Centre of
product is impossible to operate without a target
buoyancy are required for further calculations.
or targets. Targets are mainly from parametric
(Larsson & Eliasson, 2007)
study and calculations after the information
Stability which is the intensity of Pitching,
collected from customers. (Larsson & Eliasson,
Yawing and Rolling and they are important to
2007)
find. They needed to be calculated after any
design changes of the Yacht.
đ??ˇđ?‘–đ?‘ đ?‘?đ?‘™đ?‘Žđ?‘?đ?‘’đ?‘šđ?‘’đ?‘›đ?‘Ą đ??ˇđ?‘’đ?‘›đ?‘ đ?‘–đ?‘Ąđ?‘Ś đ?‘œđ?‘“ đ?‘¤đ?‘Žđ?‘Ąđ?‘’đ?‘&#x;
đ?‘‰đ?‘œđ?‘™đ?‘˘đ?‘šđ?‘’ =
After the yacht has been designed, material is the next thing to consider. For a Fibre
Simpson’s rule
Reinforced Plastic (FRP), lamination plans are
approximant area of each curve. (McCall, 1918)
acting a big part of it. Different lamination has different properties. It is mainly depend on what
đ??´đ?‘&#x;đ?‘’đ?‘Ž =
is used to calculate
the
∆đ?‘Ľ (đ?‘Ś + 4đ?‘Ś1 + 2đ?‘Ś2 + â‹Ż + 4đ?‘Śđ?‘›âˆ’1 3 0 + đ?‘Śđ?‘› )
type of boat it is and the size of the boat. After the lamination plans has decided, the quantity of
Wetted Surface Area is the area of the
resin needed is next thing to calculate. Resin
material which touching the water or the other
type and quantity for each layer is very
way of saying it is the area under the design
important as it will change the physical
waterline. Getting the girth length of each
properties and the chemical bonding. Resin ratio
section and use the Simpson’s rule to get half of
by volume is normally about 40% on in fusion
the hull wetted surface area. For this method,
and about 50 % for other lay-up such as hand
2-4% bilge factor is needed. (Larsson & Eliasson,
lay-up etc. From the calculation, thickness,
2007)
volume and weight can also be carrying out and
đ?‘Šđ?‘’đ?‘Ąđ?‘Ąđ?‘’đ?‘‘ đ?‘ đ?‘˘đ?‘“đ?‘Žđ?‘?đ?‘’ đ??´đ?‘&#x;đ?‘’đ?‘Ž = 2 Ă— 1.02 Ă— đ??´đ?‘&#x;đ?‘’đ?‘Ž
finally the strengths like stress, strain, modulus
Stress is a measure to define the amount of force
bending moment etc. This process might need to
acting on an object. (Pilkey & Pilkey 1974)
repeat couple of times for giving the yacht the best performances and safety by not putting extra weight. (Whatley, 2010)
đ?‘†đ?‘&#x;đ?‘’đ?‘ đ?‘ =
đ??šđ?‘&#x;đ?‘œđ?‘?đ?‘’ đ??´đ?‘&#x;đ?‘’đ?‘Ž
Strain is a measure of the amount of an object is deformed when it is subjected to stress measure of stiffness. (Pilkey & Pilkey 1974)
EQUATION LB ratio represents the speed of the yacht. Yacht with higher LB ratio generally has higher
đ?‘†đ?‘Ąđ?‘&#x;đ?‘Žđ?‘–đ?‘› =
đ??¸đ?‘Ľđ?‘Ąđ?‘’đ?‘›đ?‘ đ?‘–đ?‘œđ?‘› đ?‘‚đ?‘&#x;đ?‘”đ?‘–đ?‘›đ?‘Žđ?‘™ đ?‘™đ?‘’đ?‘›đ?‘”đ?‘Ąâ„Ž
velocity if other factors are equal. It could be
Young’s module is a measure of the elastic
proof by Froude number. (Rousmaniere, 1999)
material’s stiffness. (Pilkey & Pilkey 1974)
đ??żđ??ľ đ?‘&#x;đ?‘Žđ?‘Ąđ?‘–đ?‘œ =
đ??żđ?‘Šđ??ż đ??ľ
đ?‘Œđ?‘œđ?‘˘đ?‘›đ?‘” đ?‘šđ?‘œđ?‘‘đ?‘˘đ?‘™đ?‘’đ?‘ =
đ?‘†đ?‘Ąđ?‘&#x;đ?‘’đ?‘ đ?‘ đ?‘†đ?‘Ąđ?‘&#x;đ?‘Žđ?‘–đ?‘›
LD ratio represents the potential of the hull.
Second Moment of Inertia represents the
Displacement hull has smaller ratio than racing
property of a cross-section and that can be used
hull. (Rousmaniere, 1999)
to predict the resistance of a material to bending
đ??żđ??ˇ đ?‘…đ?‘Žđ?‘Ąđ?‘–đ?‘œ =
đ??żđ?‘Šđ??ż 1 ∇3
Volume on yacht is the other form of Displacement. Using the formula of density is the way of changing around. (Munson & All 2006)
and deflection around the line lies in the cross-section area. (Pilkey, 2002) đ??źđ?‘&#x;đ?‘’đ?‘Ąđ?‘Žđ?‘›đ?‘”đ?‘™đ?‘’ =
(Beam)(Height 3 ) 12
đ??źđ??ľđ?‘’đ?‘Žđ?‘š = đ??źđ?‘&#x;đ?‘’đ?‘Ąđ?‘Žđ?‘›đ?‘”đ?‘™đ?‘’ + [(đ??´đ?‘&#x;đ?‘’đ?‘Ž)(đ??ťđ?‘’đ?‘–đ?‘”â„Žđ?‘Ą 2 )] GZ is the Horizontal length between the centre
of gravity and the centre of buoyancy. In a
đ?‘…đ?‘–đ?‘”â„Žđ?‘Ąđ?‘–đ?‘›đ?‘” đ?‘šđ?‘œđ?‘šđ?‘’đ?‘›đ?‘Ą = đ??ťđ?‘’đ?‘’đ?‘™đ?‘–đ?‘›đ?‘” đ?‘šđ?‘œđ?‘šđ?‘’đ?‘›đ?‘Ą = đ??şđ?‘? Ă— đ??ˇđ?‘–đ?‘ đ?‘?đ?‘™đ?‘Žđ?‘?đ?‘’đ?‘šđ?‘’đ?‘›đ?‘Ą
particular angle (∅), (Whatley, 2010) đ??şđ?‘? = đ??şđ?‘€ Ă— sin ∅ cos ∅
Froude Number determines the resistance of a
GM is the length between the centre of gravity
water craft moving through water. (Vaughan &
and the Metacentre, BM is the length between
O’Malley, 2005)
centre of buoyancy and Metacentre and GB is
đ??šđ?‘&#x;đ?‘œđ?‘˘đ?‘‘đ?‘’ đ?‘ đ?‘˘đ?‘šđ?‘?đ?‘’đ?‘&#x; =
the length between Centre of gravity and centre of Buoyancy. (Whatley, 2010)
√đ?‘”đ?‘&#x;đ?‘Žđ?‘Łđ?‘–đ?‘Ąđ?‘Ś Ă— đ??żđ?‘Šđ??ż
Thickness of the FRP lamination can be
đ??şđ?‘€ = đ??ľđ?‘€ − đ??şđ??ľ BM has also has another relationship with Second moment of inertia and Volume. (Kemp & Young) đ??ľđ?‘€ =
đ?‘‰đ?‘’đ?‘™đ?‘œđ?‘?đ?‘–đ?‘Ąđ?‘Ś
đ??ź ∇
calculated by the following formula. (Whatley 2010) đ?‘†đ??ş đ?‘¤[ đ??š − (đ?‘†đ??şđ??š − đ?‘†đ??şđ?‘… )] đ?‘Šđ??š đ?‘‡(đ?‘šđ?‘š) = đ?‘†đ??şđ?‘… Ă— đ?‘†đ??şđ??š Ă— 1000 Ă— (1 − đ?‘˘) Where W is the Aneal density SGF is the Specific Gravity fibre (2.56)
Righting moment is restored torque of the yacht
SGR is the Specific Gravity Resin (1.15)
heeled over to its original position. (Kemp &
U is the Void content (Tupicauy 5%)
Young)
WF is the Fibre weight fraction
PROCESS Length-Displacement against Length waterline
3.50
graph 3.00
R² = 0.0563
2.50
35ft. catamaran had been chosen to design. Fig.1 and Fig.2 shows the ratio against Length
2.00
waterline of 76 FRP catamaran yachts. From the
1.50
graph,
1.00 25.00 27.00 29.00 31.00 33.00 35.00 37.00 39.00 41.00 43.00 45.00
Beam,
Length
waterline
and
Displacement has been carrying out. For designing a new full 35ft catamaran hull, the
Fig.1.Parametric study Catamaran Length-Beam
requirement are LWL = 33ft, Beam = 17.96ft,
against Length Waterline graph.
Displacement = 5123.25lb. For a single hull, LWL =- 33ft, Beam = 6.53 and
10.00
9.00
Displacement = 2561.62lb. Using the density 8.00
R² = 0.0286
formula to find out the volume which for a
7.00
single hull Volume is 1.14m3 and 2.27 m3 for a
6.00
full catamaran hull.
5.00
4.00 25.00 27.00 29.00 31.00 33.00 35.00 37.00 39.00 41.00 43.00 45.00
Fig.2.Parametric study Catamaran
Section
Area(ft2)
Area(m2)
S.M.
Product
0
0.00
0
1
0.00
1
0.65
0.0585
4
0.23
2
0.74
0.0666
2
0.13
3
1.16
0.1044
4
0.42
Fig.4 Top view of the hull design on Computer
4
1.31
0.1179
2
0.24
Aided Design (CAD)
5
1.34
0.1206
4
0.48
6
1.35
0.1215
2
0.24
7
1.21
0.1089
4
0.44
8
1.83
0.1647
2
0.33
9
1.91
0.1719
4
0.69
10
2.10
0.189
1
0.19
Sum of product
3.39
Volume
1.14
Fig.5 Side view of the hull design on CAD.
Table.1. Volume calculation using Simpson’s rules This method had repeated couple of times
Fig.6. Front view of the hull design on CAD. Fig.4, Fig.5 and Fig.6 shows the outlook of
because of its volume was the not the same as
the hull after changes and changes. The reason
requested.
of using CAD is because it is easy to correct,
2.50
more accurate and by using the hydrostatic 2.00
function to carry out the parametric of the hull.
1.50 1.00 0.50
Volume (ft3)
41.3147
Displacement (lb)
2561.62
Centre of Buoyancy
13.0032, -5.68435,
0.00
-0.272171 0
5
10
15 Wetted Surface Area
Fig.3. Area of each cross section.
111.902
(ft2)
Cross section area graph is useful because
Waterline Length(ft)
33.0003
its shows the brief shape of the hull instead of
Maximum Waterline
4.49463
just the area size of the number. After the graph
Beam(ft)
has been plotted, some of the section might need
Water Plane Area(ft2)
96.6429
to change as long as they are not in a nice
Centre of Floatation
13.4635, -5.68345,
smooth curve because the final product might have too much resistance.
0 Draft(ft)
0.81
CB
0.33
CP
0.60
Table.2. The parametric of a side of the catamaran hull. Volume (ft3)
80.16
Displacement (lb)
5234.25
Centre of Buoyancy
13.0032,
0,
Angle
GZ(m)
RM (kg m)
0
0
0
10
0.467908
1113.247848
20
0.381889
908.5929544
-0.272171 Wetted Surface Area
223.804
(ft2) Waterline Length(ft)
33.0003
30
-0.15622
-371.6868758
Maximum Waterline
15.86
40
-0.50939
-1211.950448
50
-0.25953
-617.4635992
60
0.297578
707.9988104
Beam(ft) Water Plane Area(ft2)
193.286
Centre of Floatation
13.4635,
Table.5. GZ length and righting moment with
0
different angle.
0 Draft(ft)
Fig,7, and Table.5. show that the hull has
0.81
the stability range at between 0 and about 26
Table.3. The parametric of the full catamaran
degree and stable upside down at between about
hull
26 and about 56 degree. It has a minimum GZ of
Table 2 and table 3 shows the parametric of both
-0.5 at 40 degree and maximum GZ of 0.47 at 10
single hull and the full catamaran hull. They are
degree.
useful for stability calculations.
Displacement (kg)
Density Resign:
2379.204545
Fibre (g/m )
Beam(m)
1.99
CSM
600
LOA(m)
10.67073171
WR
600
80.16
CSM
600
7.007646468
WR
600
15
CSM
600
1.731707317
WR
600
Ir (m )
103.9795999
CSM
600
BM (m)
1.297150697
WR
600
GB (m)
0.2721
CSM
600
GM (m)
1.025050697
WR
600
Table.4. Second moment of Inertia and and GM
CSM
600
calculation
WR
600
CSM
600
0.4
WR
600
0.2
CSM
600
WR
600
CSM
600
WR
600
CSM
600
3
Volume(m ) ITDM 2
Area(m ) Height (m) 4
0.6
0 -0.2 0
20
40
60
-0.4
80
T
Fibre
Resin
WF 2
fibre
(mm) Weight(kg) weight(kg)
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
1:1
1:1
1:1
1:1
1:1
1:1
1:1
1:1
1:1
-0.6 Fig.7. The GZ-angle curve of the catamaran
WR
600
CSM
600
WR
600
CSM
600
1:1
0.50 0.80
16.18
16.18
questions and general information for deck, US:
2.5 : 1 0.29 1.62
16.18
40.44
Bureau of Reconstruction and Repair
0.50 0.80
16.18
16.18
2.5 : 1 0.29 1.62
16.18
40.44
Munson, B.R., Young, D.F. and Okiishi, T.H.
Total 28.19
372.05
663.22
(2006). Fundamentals of fluid mechanics. 5th edn.
1035.26
John Wiley & Sons, Inc
1:1
Table. 6 The lamination of Catamaran hull and calculation of total thickness and weight. Table 6 shows the total thickness and
Pilkey, W.D. (2002) Analysis and Design of Elastic Beams. John Wiley & Sons, Inc
weight of the FRP lamination of each layer. It also carries out how much resin to use. Total
Pilkey,
W.D.
and
thickness of the hull is 28.19mm with the weight
Mechanics of solids
Pilkey,
O.H.
(1974)
of 1085.26kg. CONCLUSION For the whole process of designing the
Rousmaniere, J. (1999) The Annapolis Book of Seamanship, New York
catamaran take a lot of time especially for the outlook design. The limitation of time cause the
Vaughan, C.L., O’Melley, M.J. (2005) Froude
catamaran did not have chances to improve and
and the contribution of naval architecture to our
study by experiment. Although the process is
understanding of bipedal locomotion
followed, some of the information seems hugely different compare to normal. If time is available,
Whatley, A. (2010) Lesson with Alex Whatley,
experiment would be the idea of getting the
March
stability right and performances might also able to carry out. The further design, improvement and experiment will be on progress. ACKNOWLEDGEMENTS Special thanks to Alex Whatley and Mash Derrick from Falmouth Marine School for assistance on calculation and CAD works. REFERENCES Kemp and Young, ship stability
Larsson, L and Eliasson, R. E. (2007) The Principles Of Yacht Design. 3rd edn. London: Adlard Coles Nautical
McCall, P (1918) The naval artificer's manual: (The naval artificer's handbook revised) text,