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CHAPTER 2
ANALYSIS OF LOADS
This chapter deals with the estimated critical racing configurations and the loads the catamaran is subjected to. Only the static configurations have been considered with their equivalent balance. In particular the windward sailing has been analyzed as the most critical due to the fact only one hull is immersed while the other stands out of water. The water drag is reduced in this configuration. The sail aerodynamic force and the components weight are balanced only by the fluid dynamic actions operating on the hull flowing on water (Fig. 2.1).
All forces working on the catamaran will be detailed in the following paragraphs.
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2.1 Aerodynamic sail load
The aerodynamic force has been calculated on the basis of the sail profile and geometry whose features are shown in Chart 2.1.1.
A NACA 0012 profile (Fig. 2.1.2) has been chosen. Its characteristic coefficients, with a Reynolds number Re = 700000, are detailed in Fig. 2.1.3, Fig. 2.1.4, Fig. 2.1.5, Fig.
2.1.6.
As shown in Fig.2.1.1 the aerodynamic load changes together with the roll angle. The higher is the roll angle the lower is the aerodynamic force necessary for the catamaran roll equilibrium.
Fixed a range of reasonable roll angles 10° ≤ Ψ ≥ 35° it has been taken the highest value of the aerodynamic force ( Fa= 680 N), correspondent to Ψ= 10°, to develop the
analysis and sizing the structure then.
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Fig. 2.1.2 Sail airfoil
Geometrical Property Units Value
Chord m 1,59
Surface m2 13,9
Aspect Ratio 5,44
Max thickness % 12 at 30% chord Max camber % 0 at 0% chord
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Fig. 2.1.3 Drag coefficient
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Fig. 2.1.5 Lift and drag coefficient relation
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The aerodynamic force, lift and drag have been finally calculated and their values are scheduled below (Chart 2.1.2).
Symbol Units Value
Angle of attack Α o 8
Aerodynamic Force F N 685
Lift L N 684
Drag D N 45
Lift to Drag ratio E 15
Chart 2.1.2 Aerodynamic force and components
2.2 Hull pressure load
The immersed part of the hull is subjected to water pressure and drag force. The pressure Pi is the hydrostatic pressure which balances the catamaran weight and the
aerodynamic force z-component (Fig. 2.2.1). This force component is caused by the roll momentum.
The drag force instead is composed of two components, one determined by the transversal catamaran motion (leeway), the other by the transverse waves hitting the hull during the sail (Fig. 2.2.2).
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Fi is defined as :
Fi = ∫ dS
with
S: hull wet surface
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A layout of the main forces applied to the catamaran is shown below (Fig. 2.2.3).
Fig. 2.2.3 Leeway motion
with:
La : Aerodynamic Lift
Da : Aerodynamic Drag
Dh : Hydrodynamic Drag
2.3 Components weight
The components real weight has been given by the company except for the hull, since research of its optimum weight is the aim of this thesis work.
Before starting performing the first analysis step, a below-average value of the hull weight had to be fixed. Once the points of maximum stresses and strains are calculated and checked, the hull panels will be reinforced in order to obtain a stiff and tough structure.
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Finally the skipper weight has been fixed taking into account the adult male average weight and the equipment the skipper must wear during the race.
The weights are detailed below component by component (Chart 2.3.1).
Components Weight (Kg) Hull (x2) 28 Cross-beams (x2) 3 Sail 20 Mast 12 Skipper 80 Centerboard (x2) 1 Others 3
Chart 2.3.1 Components weight
2.4 Centerboards load
The centerboard force (Fig. 2.4.1), having an effect as the leeway motion occurs, has been also considered although it affects the catamaran balance only marginally.
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with :
Fdv: centerboard force
Fdvz :centerboard force z-component
Fdvy: centerboard force y-component
2.5 Tie-rod preload.
The tie rods, whose task is to support the mast, have been preloaded.
The preload has been calculated, on the basis of their ultimate tensile strength, through a thermal gradient whose magnitude has been found by the following expression
ΔT =
with:
P = Fixed preload E = Steel young modulus A = tie rod section area
λ = 1,2*10-5 steel coefficient of thermal expansion
Thus:
