Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010
Change in HDC by ↓ θO M sδ
+50%
Zw Z sδ
Zq Mw Mq Mq Mw All
% Change in values of Zigzag Parameters
zO 56.3 3.2 -25% -48.5 -26.1
te -
23.9 tc 29.1 10.5 td
-13.5 -18.0 2.2
+50% 8.0 -4.6 -2.9 -1.5 -6.5 -50.6 -45.2
-50% 3.0 1.8 -0.7 0.2 0.3 +50%
-50% 0.5 1.4 0.3 0.7 1.0
+50% -6.9 15.3 21.2 19.7 18.9 -
-50% 0.5 -26.5 +50%
-50% 78.2 +50% -50% +50%
-26.5 -50% 163.6
-38.3 -28.7 9.8 -3.1 -8.7 110.8
25.8 -8.2
197.5 -26.9 -25.9 18.3 44.2
17.6 -5.5 -5.6 -2.4 -10.7 -31.9
-6.5 7.5 -0.7 10.6 -34.9 3.9 -7.0
-17.8 -6.5 69.0 50.4
Table 4 Results of sensitivity studies of HDC values for vertical plane zigzag - axisymmetric body
td tc te z0 Theta0 -250 -150 -50 50 150 250 % Change in parameters from original values
Figure 6 Graphical representation of results of sensitivity analysis showing percentage change in zigzag parameters due to ±50% change in HDCs
Figure 6 also shows that the total change in overshoot angle (θO) could be -200% to +225%, due to the sum of the effects of variation in each HDC by ±50%. However, as seen in Table 4, for simultaneous change of all HDC values by ±50%, simulated overshoot angle (θO) values change by -32% to +164%. For overshoot change of depth (zO), around 200% increase is expected in case of simultaneous reduction in all listed HDC values by 50%, as well as in the case of the sum of changes in individual HDCs.
Mds Zwdot Zds
Zqdot Mwdot Mqdot Mq Mw
Figure 7 Change in trajectory simulation results
axisymmetric body due to change in HDCs by ±50% 5.3 SENSITIVITY STUDIES - SUBOFF BODY
These studies were repeated for the submarine-like SUBOFF body, varying all HDCs varied
for
axisymmetric body, as well as Zq, again using the linear mathematical model (Model 3). Variation of HDC values
by ±50% from model test values was considered. Results of these sensitivity studies are summarised in Table 5. Only those HDCs which had an effect of more than 2% on the zigzag parameters have been included in the Table.
The most significant HDCs for the SUBOFF body simulation emerge as ,
Z ZM . It is thus seen that ws, δ w
even for the same mathematical model, the body geometry has a significant influence on the relative importance of the HDCs.
The change in zigzag manoeuvre parameters due to HDC value variations does not exceed 21% when HDCs are varied one at a time. This is much lesser than the effect of variations in case of axisymmetric body. Even when all relevant HDCs are varied simultaneously by ±50% from original values, the variation in zigzag parameters is at most by 55% only. Although the magnitude of variation in actual terms is much greater, the percentage change is relatively less.
for
-2.9 -1.7 0.7 -0.2 -0.2 -2.1 -2.2 -0.7 -1.1 -1.3
-50% -18.2 21.8 7.2 3.9 28.5 +50%
11.1 -6.6 -20.1
-50% 68.7 55.5 -7.2 14.6 12.0 +50%
It is also seen that the parameters time to reach execute (te) and time to check pitch (tc) and depth (td) are relatively less influenced (about ±100%) by change in HDC values, as compared to the parameters θO and zO. The effect of change in trajectory of the body due to simultaneous change of ±50% in all listed HDCs is shown in Figure 7. The original response curves are in the middle, while quicker responses are for the case when HDCs were increased by 50%. Responses were delayed when all HDC values were reduced by 50%.
A - 78
©2010: The Royal Institution of Naval Architects
Parameters of zigzag manoeuvre
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