Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014
C CkC C CkC
WC TFAT WDEMI TFDEMI
1
1
where β and τ = 1 for monohull [13] and [12].
Since there is no length restriction, but the displacement D is fixed, the appropriate length parameter for scaling is the cube root L*=D1/3 of the displacement. Results are presented in a non-dimensional manner as a function of the (volumetric) Froude number Fnv=U/sqrt(gL*) based on that artificial length. In fact, was it not for scale (Reynolds number) effects, all results would be universal functions of this Froude number, and displacement would be irrelevant. For example, the final minimum total drag Rt=Rv+Rw is expressed in terms of the coefficient.
Ct = Rt (1/2*ρ*U2L*2)
Which would be a function of Fnv alone where it not for the fact that the skin friction coefficient depends on Reynolds number.
Total resistance interference factor values of both hull spacing and stagger are strongly depend on the ship speed. Hence in this case, samples were taken only on the Fr= 0.47 where this Froude number is a favorable reduction in resistance and mostly operational speed of displacement catamarans. Table below shows the various total resistance interference factors at different clearance and stagger positions using Equation 7.
The table shows that the greater the hull spacing and stagger the smaller resistance interactions occurred. Other things that need to be underlined that the hull stagger R/L= 0.3 and 0.4 for S/L = 0.2 is smaller than the interactions that occur in S/L= 0.4 where this has not been answered and is still under observations.
Experimental Total Resistance Interference Factor values at Fr= 0.47
Hull Stagger
R/L=0.0 R/L=0.2 R/L=0.3 R/L=0.4
Monohull 1.000
- - -
Hull Spacing S/L= 0.2
1.041 0.983 0.910 0.849
The equation 6 IFclearance is defined as:
IF CR CR
clearance
TDH
TCAT 2 TCAT TDH
The above formula simply by writing CTDH (where CTDH is the total resistance of one demihull in isolation) instead of 2*CTDH because the number of ratio 2*R and 2*S used
©2014: The Royal Institution of Naval Architects
S/L= 0.3
1.033 - - -
S/L= 0.4
0.978 0.963 0.910 0.861
Figure 6: CT values of
Stag.Sym.Cat., S/L=0.2 CAT (6)
is to cancel each other. For the resistance itself must be written for the resistance of 2*RTDH where the total resistance must be multiplied by two demihull.
The conclusion drawn in the figures 6 and 7 show that at Fr 0.55, the stagger ratio has no influence in reduction in resistance, and at Fr> 0.55, the resistance is slightly higher. This is due to wave interference and wave breaking occurred behind the stern at higher speeds.
Figure 7: CT values of
Stag.Sym.Cat., S/L=0.4
Reply to the comment of Dr A K Dev The reference [17] proposed that the total resistance of a catamaran should be expressed by Equation 1:
Ck CF ) TCAT (1Cw (1)
Here has been introduced to take account of pressure field change around the demihull and σ takes account of the velocity augmentation between the hulls and would be calculated from an integration of local frictional resistance over the wetted surface and (1+k) is the form factor for the demihull in isolation.
For practical purposes, and σ can be combined into a viscous
interference factor γ where (1 + k) σ = (1 + γ k), whence:
CkCF (1 ) TCAT Cw (2)
Noting that for demihull in isolation, γ = 1 and τ = 1, and for a catamaran, τ can be calculated from Equation (3).
B-111
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