Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010
Change in HDC by ↓ θO
M sδ Zw Z sδ Mw Zq All
+50% -50% +50%
% Change in Zigzag Parameters te
zO -3.6 15.7 17.3 -7.7 -5.6
4.4 9.4 6.6 19.1
0.3
-50% -20.8 1.3 +50%
13.6 -2.4 -50% -18.4 3.9 54.9 -50% -37.9
2.72 16.0 11.0
5.3
-50% -17.4 -19.4 -6.4 +50%
-11.4 20.5
-11.9 21.6
+50% -2.33 -2.58 0.11 -50% 2.43 +50%
-0.11 -20.0 57.1
tc
-5.6 6.5
11.5 -
12.0 -6.6 13.1
-9.5 16.6 -
1.01 1.01 -5.9 39.0
td
-5.3 6.1
11.4 -
11.4 -6.6 13.8 -
10.3 18.5 -
0.93 0.96 -6.0 41.7
Table 5 Results of sensitivity studies of HDC values for vertical plane zigzag - SUBOFF body
The change in trajectory for simultaneous variation in HDCs by ±50% for SUBOFF body is shown in Figure 8. As in Figure 7, the quickest responses correspond to 50% greater HDC values.
Change in HDC by ↓ θO
M sδ
Zw Z sδ
Zq
-10% -0.4 -0.2 -0.3 -0.2 -0.1 Mw +10% -1.4 -1.0 -0.3 -0.4 -0.4
Mq Mq Mw All
-10% +10%
-0.2 0.1 0.0 0.0 0.1 -2.4 3.0 4.2 4.1 3.9
-10% -0.2 -4.7 -4.9 -4.8 -4.6 +10%
-10.3 -8.3
-10% 9.7 9.1 +10%
10.1
1.6 -1.3 -2.9 -2.0 1.3 3.2
-10% 3.8 -1.0 -1.3 -0.4 -2.5 +10% -8.8 -10%
14.3
Table 6 Results of sensitivity studies, with small change in HDC values, for vertical plane zigzag - axisymmetric body
Change in HDC by ↓ θO
M sδ
Zw Z sδ
Mw
Figure 8 Change in trajectory simulation results for SUBOFF body due to change in HDCs by ±50%
5.4
SENSITIVITY STUDIES FOR ±10% CHANGE IN HDC VALUES
Having gained some insight into the relative importance of HDC values for both the bodies, we now consider the effect of variation in the most significant HDCs by ±10%. This is the maximum uncertainty estimated in the model testing process (Table 3), and we explore the effect of this magnitude of variation on the zigzag parameters. Results obtained by trajectory simulation using fully linear mathematical model for the axisymmetric body are given in Table 6, and for SUBOFF body in Table 7.
©2010: The Royal Institution of Naval Architects Zq All
% Change in Zigzag Parameters te
zO
+10% -0.68 -1.56 -1.16 -10% 0.90 1.82 1.27
+10% 3.32 3.92 1.16 -10% -3.25 -3.80 -1.16 +10% 3.63 -0.05 -2.74
-10% -3.77 0.09 3.06 +10% 3.08 -0.48 -2.85 -10%
-3.33 0.45 3.16
+10% -0.54 -0.59 0.00 -10% 0.54 0.60 0.00 +10% 8.88 1.21 -5.38 -10%
-8.34 tc
-4.6 0.4 1.3 0.0 2.6 -11.0 1.0 -2.4 -5.3
-1.3 3.1 6.3 +10%
% Change in values of Zigzag Parameters
zO 13.9 -10% -18.0 -12.0 te tc td
2.8 -6.9 -3.3 -4.0 -6.9 8.5 3.1 2.7
+10% 1.0 -1.9 -1.0 -0.7 -2.1 -10% +10%
-10% 12.1 11.2 +10% -1.2 -0.7
-1.6 2.4 3.6 0.0 -0.2 -0.2
-3.7 1.0 0.7 0.2 2.1 -11.0 1.6 -2.2 -4.1
td
-1.19 -1.07 1.23 1.17
2.33 2.30 -2.37 -2.27 -1.72 -1.71
1.89 1.95 -2.24 -2.46 2.46 2.72
-0.35 6.54
-0.22 -0.21 0.22 0.21 -2.81 -2.96 3.78 4.08
Table 7 Results of sensitivity studies, with small change in HDC values, for vertical plane zigzag - SUBOFF body
From Table 6 and 7, it emerges that the maximum the
change in trajectory parameters due to change in HDC values by ±10% is around 18% for the axisymmetric body and 9% for the SUBOFF body. Thus, considering an uncertainty of up to ±10% in HDC values estimated from model testing, the main parameters of the zigzag considered can be determined with a fair degree of confidence.
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