Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010
estimated due to various sources of error would add up. Since all
possible sources of error have not been
quantified, this estimate is not necessarily conservative (i.e., the actual error may be even greater). Since all parameters of
interest in the zigzag manoeuvre are
measured directly in the full-scale trials, simple addition of the uncertainties due to the sources of error would suffice. Thus, summing up the estimated uncertainty values for various sources of error described above, the results are given in Table 11.
Parameter Assumed Value
Overshoot pitch angle (θO)
Overshoot change of depth (zO) Time
to reach execute (te)
Time to check pitch (tc)
Time to check depth (td)
2 degrees 3 metres 6 seconds 9 seconds 19 seconds
Total
Uncertainty 1.503 1.338 0.500 0.444 0.158
Table 11 Typical uncertainty levels estimated based on various sources of bias and precision errors for one set of parameter values
In case of an UUV, if the uncertainty due to error in control force application is ignored, the total uncertainty for the case considered would reduce to 1.00 for θO , 0.67 for zO, 0.17 for te, 0.22 for tc, and 0.05 for td.
It may be noted that these estimates are only meaningful for values of parameters close to those assumed as ‘typical’. For different speeds, and certainly for different vehicles, these values would vary and accordingly the uncertainty levels would also change. In general, it is likely that for more unstable or larger bodies and / or greater
speeds (or plane deflections), the values of
parameters measured would be greater. In such a scenario, the associated uncertainties are likely to be lower.
To illustrate this aspect, the estimated total uncertainty for another set of parameters (for a case of higher speed or a more unstable vehicle or a greater control surface deflection) is shown in Table 12. The assumed values are similar to those obtained by simulation for the SUBOFF body in 15/5 zigzag (Table 1), which is a more unstable body than the axisymmetric body considered earlier.
In the uncertainty analysis described here, although some aspects pertain to manned submarines, the likely changes in case of UUVs have been mentioned. The typical manoeuvre parameter values quoted here also pertain to simulation of UUV-sized bodies. Hence the range of uncertainty reported is fairly representative of the entire gamut of underwater vehicles.
Parameter Assumed Value
Overshoot (θO)
Overshoot change depth (zO)
pitch angle of
Time to reach execute (te)
to check depth
11 degrees 26 metres 19 seconds
Time to check pitch (tc) 45 seconds Time (td)
75 seconds of parameter values (for
unstable body/ greater plane deflection) 8.
CONCLUSIONS
The process of manoeuvrability prediction of underwater vehicles is fraught with uncertainties at every stage. It is important to have an overall perspective of the subject in order to ensure that estimates at every stage are reasonably accurate, while also optimising the time and effort required in the process.
This generalised
study has considered two body geometries. A trajectory
simulation program was
developed, using which simulations have been carried out using three mathematical models. Results have been presented for a typical 15/5 vertical plane zigzag manoeuvre at 5 knots. Conclusions have been drawn regarding the effect of various choices on the values of main parameters obtained from simulating this manoeuvre.
It was seen that choice of mathematical model (linear / non-linear) can influence the zigzag trajectory parameters by 1% to 37%, with greater effect on the pitch overshoot and depth overshoot, which are measures of the depth- keeping (rather than depth-changing) ability of the underwater vehicle.
Estimation of HDC values is usually the most time- consuming aspect of manoeuvrability prediction. Based on sensitivity analysis of the effect of HDC values on vertical plane zigzag parameters, it was seen that for the axisymmetric body considered, MδS, ZδS and Mq are most significant. Variation in any one of these HDCs by ±50% causes more than 50% change in at least one of the zigzag parameters. However, for the SUBOFF body (which is more akin to a submarine form), the most significant HDCs emerge as
Z ZM , for which ws, δ , w
individual ±50% change does not cause change of zigzag parameters by more than 21%. If all significant HDCs are varied
by ±50% simultaneously, the zigzag
parameters change by up to 55% for SUBOFF and up to almost 200% for the axisymmetric body. Thus, the sensitivity of
HDCs depends not only on the Total
Uncertainty 0.276 0.159 0.158
0.089 0.040
Table 12 Typical uncertainty levels estimated for another set
higher speeds / more
A - 82
©2010: The Royal Institution of Naval Architects
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