*4.2. Actual Trajectories of the Towed Ship with Different Steering Coefficients*

In order to further investigate the influence of the steering coefficient on the actual trajectory of the towed ship, we choose different steering coefficients and lengths of towline for simulations.

When the length of towline is relatively small, such as *a* = 20 m, the actual motion trajectory of the towed ship deviates largely from the target curve, if the steering coefficient *μ* = −12 is adopted, as depicted in Figure 5a. However, for the same length of the towline, the actual trajectory of the towed ship follows very well with the target curve by using the steering coefficient *μ* = −16 in Figure 5b. When the length of the towline is relatively large, such as *a* = 40 m, we need a larger steering coefficient to obtain a satisfactory tracking performance, such as *μ* = −20, as depicted in Figure 6. As a consequence, when the length of the towline is smaller, a satisfactory trajectory tracking performance can be obtained with smaller steering coefficient, whereas, when the length of the towline is large, a larger steering coefficient must be applied to keep the tracking error of the towed ship within a smaller range.

**Figure 5.** Comparison of actual motion trajectories of the towed ship between different steering coefficients.

**Figure 6.** Comparison of actual motion trajectories of the towed ship between different steering coefficients.
