Conversion of a Second- to First-Order Linear Nomoto Model in the Light of ZigZag Manoeuvre Performance

The problem of considerable difference between the first- and second-order linear Nomoto models is undertaken, not well covered in literature so far. If the former approximates the latter (better one, of a sound hydrodynamic interpretation) for some reasons, its parameters can not be easily derived from the other one, except for some specific rare cases. For such an identification purpose, we can use a simulated zigzag response and the classic procedure proposed by Nomoto in 1960. However, the first-order model thus developed yields somehow redefined constants against the original model, which lose their normal hydrodynamic (or kinematic) sense. In other words, it is very sensitive to the manoeuvre type on input, being therein the zigzag test. Therefore, the model is allowed to be only used for simulating motions essentially similar to the input zigzag. In other words, the identification procedure works like a blind curve-fitting and the first-order model (in contrast to second-order one) is inadequate for reflecting arbitrary manoeuvres, even for mild rudder as to be within 'linear' assumptions. This study examines systematically and in detail such an incompatibility of the first order model in that it presents the conversion charts from the standpoint of 10°/10° zigzag test matching. One can receive higher or lower values for the parameters of first-order model, versus the second-order one, depending on the T3/T2 ratio of the latter model.

Artykuł zawiera systematyczne wyniki identyfikacji liniowego modelu Nomoto pierwszego rzędu na podstawie symulowanej próby wężowej różnych wariantów modelu drugiego rzędu. W toku analizy stwierdzono ogólną nieadekwatność (strukturalną) modelu pierwszego rzędu do symulacji dowolnych manewrów, w przeciwieństwie do modelu drugiego rzędu, nawet w granicach liniowości dynamiki statku. Wyniki identyfikacji silnie bowiem zależą od rozpatrywanego manewru.