# Changes in Propeller Shaft Behavior by Fluctuating Propeller Forces during Ship Turning
## 3 Results
### Fully Laden (FL) Condition  
First, regarding the rapid port turn test as shown in Figure 10, both the amplitude of the bending moment and the bending direction changed during the turn compared with going straight ahead. The increase and the decrease in the amplitude of the port and starboard turns compared with going straight ahead within the same period appear to be directly affected by the change in the stern's wakefield due to the turn. Using Equations (7) and (8), from the amplitude of the bending moment and the bending direction as shown in Figure 10, the vertical component of the bending moment was obtained as shown in Figure 11 in the comparison with the vertical displacement while the horizontal component is shown in Figure 12. In the same manner, the results of the rapid starboard turn test are depicted in Figures 13-15. Figure 10: Bending moment during the port turn under the fully laden condition. Next, using the horizontal and vertical components shown in Figures 11 and 12 and Figures 14 and 15 as the x-axis and y-axis, respectively, the average value trajectories of the straight/port and straight/starboard turns were obtained and are shown in Figures 16 and 17, respectively. As presented in Figures 16 and 17, the trajectory plot obtained from Figures 11, 12, 14 and 15 provides another perspective to help us understand the actual shaft movement. It can be clearly seen how the fluctuating propeller forces directly have an effect on the shaft's movement while the ship is turning, and it is easy to compare it with the NCR going straight ahead case or the rapid port turn case or vice versa. It is worth noting that the moment behavior of the shaft shifts downward (counterclockwise) during the port turn compared with going straight ahead, while it shifts upward (clockwise) during the starboard turn, and the opposite trend can be seen. Figure 11: Bending moment and displacement behavior in the vertical direction during the port turn under the fully laden condition. Figure 12: Bending moment in the horizontal direction during the port turn under the fully laden condition. Figure 14: Bending moment and displacement behavior in the vertical direction during the starboard turn under the fully laden condition. Figure 13: Bending moment during the starboard turn under the fully laden condition. Figure 15: Bending moment in the horizontal direction during the starboard turn under the fully laden condition. As described above, the reason for the opposite pattern of the shaft behavior is that the formation of the wakefield is completely different at the rear of the stern tube depending on the rudder angle. These results were cross-validated with the shaft displacement values obtained from the displacement sensor during the same period as shown in Figure 18.  
Figure 16: Plot of trajectories obtained during the port 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). Stage (c): Rudder angle 12-degree: ship’s heading is gradually changing. Stage (d): Rudder angle 0-degree: NCR straight going (end). Figure 17: Plot of trajectories obtained during 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 (starboard). Stage (c): Rudder angle 12-degree: ship’s heading is gradually changing. Stage (d): Rudder angle 0-degree: NCR straight going (end). Through this, it can clearly be seen that the shaft behavior compared with going straight ahead shows a high degree of consistency in both the direction of the bending moment and the displacement value and changes to the downward direction during the port turn and to the upward direction during the starboard turn.