# Changes in Propeller Shaft Behavior by Fluctuating Propeller Forces during Ship Turning
## 3 Results
### Normal Ballast (NB) Condition  
The experiments were also performed under the normal ballast condition. Using the same signal processing procedures, the bending moment amplitudes as well as the bending directions were obtained and are shown in Figure 19 for the case of a rapid port turn and Figure 20 for the case of a rapid starboard turn. Figure 19: Bending moment during the port turn under the normal ballast condition. Figure 18: Comparison of behaviors between the port turn and the starboard turn under the fully laden condition. Stage (a): Rudder angle 0-degree: NCR straight going (begin). Stage (b): Rudder angle changes from 0 to 12-degree (port, starboard). Stage (c): Rudder angle 12-degree: ship’s heading is gradually changing. Stage (d): Rudder angle 0-degree: NCR straight going (end). The average values of the trajectories for the going straight ahead, port turn, and starboard turn cases are shown in Figures 21 and 22. In addition, as described in Section 3.1, the axis shows a similar tendency to move downward during the port turn and upward the during starboard turn. This trend was cross-validated using the shaft's vertical displacement as shown in Figure 23.  
As described in Section 3.1, the straight solid line and the straight dotted line in Figure 23 represent the average value of the shaft's bending moment and vertical displacement, respectively, obtained by rotating the shaft approximately one to two times using a turning gear. It can be observed that the shaft gradually rises as the eccentric propeller thrust gradually increases to the NCR. Figure 21: Plot of trajectories obtained during the port turn under the normal ballast condition. Stage (a): Rudder angle 0-degree: NCR straight going (begin). Stage (b): Rudder angle changes from 0 to 12-degree (port). Stage (c): Rudder angle 12-degree: ship’s heading is gradually changing. Stage (d): Rudder angle 0-degree: NCR straight going (end). Figure 20: Bending moment during the starboard turn under the normal ballast condition. In addition, compared with Figure 18, it can be observed that the average values of the static bending stress (80 kN\(\cdot\)m under the FL condition to 60 kN\(\cdot\)m under the NB condition) and the shaft's vertical displacement (0.17 mm under the FL condition to \(-\)0.2 mm under the NB condition) were changed. This is due to the effect of hull deformation according to the change in the draught, and it is the result of the deformation of the shaft line depending on it [38; 39; 40; 41]. Moreover, when taking the results together, one can observe that the shaft's vertical bending moment and displacement values show an increase during the starboard turn under both draught conditions. Figure 23: Comparison of behaviors between the port turn and the starboard turn under the normal ballast condition. Stage (a): Rudder angle 0-degree: going straight ahead at the NCR (begin). Stage (b): The rudder angle changes from 0 to 12-degree (port, starboard). Stage (c): Rudder angle 12-degree: the ship’s heading is gradually changing. Stage (d): Rudder angle 0-degree: going straight ahead at the NCR (end). Figure 22: Plot of trajectories obtained during the starboard turn under the normal ballast condition. Stage (a): Rudder angle 0-degree: NCR straight going (begin). Stage (b): Rudder angle changes from 0 to 12-degree (starboard). Stage (c): Rudder angle 12-degree: ship’s heading is gradually changing. Stage (d): Rudder angle 0-degree: NCR straight going (end). Additionally, when comparing stage (c) in Figure 18, one can also observe that the shaft continuously moves upward for a longer time under the normal ballast condition than under the fully laden condition during the starboard turn. This means that eccentric propeller thrust fluctuations directly affect the amplitude and magnitude of the vertical load applied by the vertical component to the after-stem tube bearing that supports the shaft as discussed in Section 4. Accordingly, this acts as an important observation in terms of developing safety guidelines for ship operation.