Mathematical modeling of shallow water effects on ship maneuvering

Abstract

An Abkowitz-type model was extended to improve the prediction of maneuvering dynamics of inland ships in deep and shallow waters. First, additional coupled rudder and speed related hydrodynamic derivatives were added to better capture hydrodynamic forces and moments. Second, higher order drift related hydrodynamic derivatives were implemented to more reliably predict longitudinal forces. Steady RANS-based captive model tests were performed to estimate speed-dependent hydrodynamic derivatives. Unsteady captive model tests, based on applying a novel Euler equations based numerical approach, were carried out to determine acceleration-dependent zero-frequency hydrodynamic derivatives. Executed were propulsion tests, rudder tests, coupled propulsion and rudder tests, rotating arm tests, drift tests, and coupled rotating arm and drift tests, all at five water depths to draft ratios of 1.43, 1.79, 2.00, 4.00, and 8.00. Tests at the ratio 1.79 were validated against physical captive model tests, and regression analyses estimated the hydrodynamic derivatives. At each water depth, a 45 deg turning circle test, a 35/10 zigzag test, and a 45/110 evasive action test were carried out. Turning circle maneuvers were significantly influenced by shallow water. Compared to deep water, in shallow water the tactical diameter increased from 1.6L to 2.6L, and the drift angle decreased from 21 deg to about 4 deg. Compared to turning circles maneuvers, effects on the zigzag and evasive action maneuvers were relatively small in shallow water. Drift angles and yaw rates in the simulated 45 deg turning circle and a 35/5 zigzag tests agreed favorably with full-scale trials of a similar ship; however, scale effects and the slightly different hull shapes led to different speed losses.