Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010


mathematical model adopted, but also on the manoeuvre considered and the body geometry being studied.


Considering the experimental uncertainty (from model testing) as up to 10%, it emerges that


the resultant


uncertainty in zigzag parameters is approximately 18% for the axisymmetric body and 9% for the SUBOFF body. Summing up the possible uncertainties in the various stages of manoeuvrability prediction discussed, a figure of uncertainty of 11% to 55% may be suggested for the parameters of the manoeuvre considered in this study, for the axisymmetric body. For the SUBOFF body, this value would be approximately up to 45%.


However, if a variation of ±50% in the HDC values is assumed (which may be the case if prediction methods other than model tests, such as empirical or numerical methods, are used for HDC estimation), then the consequent range of


uncertainty increases to


approximately 231% for axisymmetric body and 92% for the SUBOFF body.


Uncertainty estimation for various sources of error has been discussed for full-scale sea trials, which are the ultimate benchmark for any prediction process. It is seen that the uncertainty levels in the measurement process depend on many unknown factors, and also on the values of manoeuvre parameters. Based on two typical cases, it is estimated that error magnitude of various parameters during full-scale measurements may vary from 5% to 150% for manned submarines and up to 100% in case of UUVs.


This range of uncertainty values in the measurement process appears greater than the cumulative uncertainty (11-55%) in the overall prediction process, considering 10% uncertainty in HDC values. However, in case the uncertainty in HDC values in higher (say ±50%), then the uncertainty levels of predicted zigzag parameters would be substantially greater than the uncertainty in full-scale measurements.


The quantitative results presented are for very specific cases of manoeuvre type, mathematical model, body geometry (typical of UUVs and submarines) and vehicle sizes (typical of UUVs). In addition, the following generic qualitative conclusions may be drawn:-


• The mathematical model used for trajectory simulation may contribute to a similar or even greater degree of


uncertainty in results,


compared to uncertainty due to variation in HDC values.


• The sensitivity (relative importance) of HDCs depends on the mathematical model,


the


manoeuvre considered, as well as the body geometry.


• Full-scale trials of the body performing open- loop definitive manoeuvres are the ultimate test of any manoeuvrability prediction process, but


©2010: The Royal Institution of Naval Architects 8. 9.


these trials have their own levels of uncertainty, affected by the manoeuvre performed.


• In real-life operations, uncertainties in the


prediction process are often masked by the close-loop control system action of the operator or autopilot, unless the vehicle is highly unstable.


It needs to be emphasised that predictions need to be only as accurate as can be measured and verified. The quantification of uncertainties at various stages can offer insight into margins for improvement in each of the stages of manoeuvrability prediction during design. Meaningful targets can thus be set for accuracy of each aspect of the manoeuvrability design process.


Further studies may expand the approach adopted here to other definitive manoeuvres, other bodies and other mathematical models.


9. ACKNOWLEDGEMENT


This study was undertaken as part of a project supported by the Naval Research Board (NRB) of the Defence Research & Development Organisation (DRDO), India, which is gratefully acknowledged by the authors.


10. 1.


2. 3.


4. 5. 6. 7.


REFERENCES


RAY, A., SESHADRI, V., SINGH, S.N., SEN, D.,


‘Manoeuvring Studies of Underwater


Vehicles – A Review’, Transactions of RINA, 2008.


ARENTZEN, A. and MANDEL, P., ‘Naval Architectural Aspects of Submarine Design’, SNAME Transactions, 1960.


SPENCER, J.B., ‘Stability and Control Submarines’, Journal


of of the Royal Navy


Scientific Service (JRNSS), Vol. 23, No. 3, 1967.


ABKOWITZ, M.A., Stability and Motion Control of Ocean Vehicles, MIT Press, 1969.


FOSSEN, T.I., Guidance and Control of Ocean Vehicles, John Wiley, 1994.


LEWANDOWSKI, E.M., The Dynamics of Marine Craft, World Scientific, 2004.


PRESTERO, T., ‘Verification of a Six-Degree of Freedom Simulation Model for the REMUS Autonomous Underwater Vehicle’, M.S. Thesis, Massachusetts Institute Of Technology & Woods Hole Oceanographic Institution, 2001.


NAHON, M., ‘A Simplified Dynamics Model for Autonomous Underwater Vehicles’, The Journal of Ocean Technology, Vol. 1, No. 1, 2006.


REDDY, D.N., ‘Theoretical and Experimental Studies on Motion and Control of Submerged Bodies’, M.S. Thesis, Indian Institute of Technology Kharagpur, 1996.


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