A further interesting development of the research would be the design of demihulls which amplify the advantages of staggered configuration. In particular, it should be considered demihulls with different hull form, optimised holding in due consideration their longitudinal positions in the wave pattern.
7. UNCERTAINTY ANALYSIS
An uncertainty analysis of the experimental towing test results was carried out in accordance with the ITTC recommended
procedures [7]. The uncertainty
assessment of the total resistance coefficient, CT, was conducted for a catamaran configuration (S/L = 0.30 and
L/1/3 = 5.075) of the model C932 and for three model speeds V = 1.892, 2.098, 2.734 m/s (corresponding to Fn = 0.331, 0.375 and 0.478).
The accuracy of a measurement indicates the closeness of agreement between an experimentally determined value of a quantity and its true value. Error is the difference between the experimentally determined value and the true value.
The total error, U, is composed of two components: a precision (random) component, P, and a bias (systematic) component, B. An error is classified as precision if it contributes to the scatter of the data; otherwise, it is a bias error. In general, the uncertainty of a quantity is a function of the value of that quantity.
The applied procedure, provided by the ITTC, estimates the uncertainty in an experimental result at a 95 per cent confidence level, meaning that the true value of the quantity is expected to be within the ±U interval about the experimentally determined value 95 times out of 100. The bias limit, BCT, of the total resistance coefficient are estimated for the individual measurements systems: hull geometry BS, (model length and wetted surface), speed BV, resistance BRx and temperature/density B. The total bias limit reduces its influence when increasing the value of the total resistance coefficient.
The precision limits are determined for single or multiple runs. In any case the precision limit is determined by the standard deviation of the total resistance coefficients calculated from multiple tests. For this reason 5 sets of tests were carried out with the model removed and reinstalled between each set of measurements. In each test at least 3 speed measurements were performed, giving in total a minimum of 15 resistance measurements for each investigated speed. This is the best way to include
random errors misalignment, trim, heel etc.
The following figures show the graphs of the variations of the total uncertainty, the bias and precision limit versus the number of tests. It is possible to note that the bias limit is constant regardless of the number of tests, while the precision and the uncertainty are decreasing if
©2007: Royal Institution of Naval Architects
the number of repetitions increases. Reducing the speed, the relative contribution of the bias limit to the total uncertainty becomes predominant, also for the single test. The total error goes from 3.5 ÷ 4.0 % of CT for the lowest speed to 1.0 ÷ 1.4 % for the highest speed.
V = 1.892 m/s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0 5 PRECISION LIMIT NUMBER OF TESTS 10 15 20 BIAS LIMIT TOTAL UNCERTAINTY
Figure 35: [C932 – L/1/3 = 4.66, S/L = 0.30, Fn = 0.331] V = 2.098 m/s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
0 5 PRECISION LIMIT 10
NUMBER OF TESTS BIAS LIMIT
15 TOTAL UNCERTAINTY
Figure 36: [C932 – L/1/3 = 4.66, S/L = 0.30, Fn = 0.375] V = 2.734 m/s
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0 5 PRECISION LIMIT in the set-up such as model
NUMBER OF TESTS BIAS LIMIT
10 15 20 TOTAL UNCERTAINTY
Figure 37: [C932 – L/1/3 = 4.66, S/L = 0.30, Fn = 0.478] 8.
REFERENCES 1.
Insel M., Molland A.F. “An Investigation into the Resistance Components of High Speed Displacement Catamarans” Transactions RINA, Vol. 134, 1992
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B-31
% OF CT
% OF CT
% OF CT
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