5.1 Heaving and Pitching in Head Seas

As a first example, we will compute the heaving and pitching motions of the merchant ship that we used in Chapter 3, in regular head waves. Characteristics are given in Table 3.1 and the body plan is shown on Figure 3.8. We will make use of strip theory, using Equations (5.80) along with the results shown on Figures 5.6-5.7 to find the added mass and damping forces and moments. We will assume a speed of 10 knots, and waves with amplitude 2.0m and period 9.5s in "deep" water.

Strictly speaking, we need to consider the surge motion, also, since surge is coupled with heave and pitch. Unfortunately, though, surge forces and surge-induced forces and moments cannot be computed with the aid of strip theory. However, we can make use of the (zero-frequency) added mass and steady forces that we obtained in Chapter 3 for surge, tacitly assuming that the frequency effect is small (and ignoring the inconsistency in the orders of magnitude between the surge and heave/pitch terms). In addition, the net thrust will be assumed to be of the simple form adopted in the example in Section 7.2.3 in Chapter 3, Eq. (3.160):

(consideration of the effects of the propulsion system dynamics, described in Section 4.2 in Chapter 3, is an interesting and non-trivial problem that we will forgo here). We can use the Holtrop method (Appendix A, Chapter 3) to estimate the resistance, wake fraction and thrust deduction,...