# Propeller reversal characteristics

When the speed is constant, the relationship curve M_{t}=f(n) between the resistance torque and the rotational speed during the propeller reversal process is called the propeller reversal characteristic curve. The reverse characteristic curve of the propeller has a very peculiar shape, as shown in Figure 1. M_{yj} and M_{d} are the torque of the prime mover and the propeller, respectively. The positive value shown in the figure is the forward rotation speed of the propeller, and the negative value is the reverse rotation speed of the propeller.

When discussing the reversal characteristics of the propeller, the reversal of the propeller itself must be distinguished from the reverse of the ship. In order to reverse the ship, the propeller must be reversed first, and the propeller reversal time is very short, measured in s. However, the time required for the ship to reverse (for example, from full-speed forward to full-speed backward) is very long, which is calculated in minutes. Therefore, it can be considered that during a certain period of time when the ship is in reverse, the ship still continues to sail at almost full speed, although the propeller is already reversed at this time.

During reversal, there is a very specific change in the propeller drag torque due to this condition. If the propeller is reversed when the speed of the ship is zero (for example, when the ship is at berth), its reversal characteristic curve is a symmetrical curve. At this time, the reversal characteristics and the mooring characteristics will coincide as one, as shown in curve 1 in Figure 1.

If the propeller is reversed at the speed of other ships (such as when the ship is moving forward or backward), its reversal characteristic curve is a mutually asymmetrical curve, and these mutually asymmetrical curves will have such characteristics. That is, when the speed of the propeller is maintained at a positive value, negative torque will appear on their individual line segments, as shown in the BCD segment of curve 3 in Figure 1 (from full speed forward to full speed backward), and a maximum value will appear at a certain speed, such as point C.

The appearance of negative braking torque, ie, negative propeller torque, indicates that the propeller will try to maintain the original direction of rotation under the action of water pressure as the ship continues to move forward. At this time, the screw firewood no longer works as a propeller, but starts to work as a hydraulic motor.

When reversing, the magnitude of the propeller braking torque is related to the forward speed of the ship. If the forward speed of the ship was originally high, the negative braking torque of the propeller would also be high, as can be seen by comparing curves 2 and 3. Curve 2 corresponds to the ship speed V = 0.6V_{e}, and curve 3 corresponds to the full ship speed, ie V = 1.0V_{e}. V_{e} is the rated boat speed. The change of the torque of the propeller when it reverses can be analyzed by the force diagram of the propeller blade element. The details are as follows: The so-called propeller blade element is the propeller flake at the radius r. The force on the entire propeller can be understood by analyzing the force on the blade element.

A sketch of the propeller and its blade elements is drawn on Figure 2. In the figure, the hollow cylinder A is the hub; B is the blade; the shaded C is the cross-sectional schematic diagram of the blade element.

When the propeller rotates at the speed n, the circumferential linear velocity of the blade element is 2πrn, so the relative velocity of the water flow to it is also 2πrn, so it can be considered that the blade element does not move, and the water flow rushes to the blade element at a speed of 2πrn. Driven by the propeller, the ship moves at a certain speed, so the current also rushes towards the blade element from the opposite direction of the ship at a relative speed vp. Combining these two velocities as vectors, the vector W is obtained. The water flow rushes towards the leaf element at this synthetic speed, see Figure 3.

Under the impact of water flow, lift dY (direction perpendicular to W) and resistance dX (direction consistent with W) are generated on the blade element. By projecting their combined force dR to the vertical and horizontal directions, the thrust dP and the rotational force dQ can be obtained.

At point A of the reversal curve, the thrust dP is in the positive direction, pushing the ship forward. The rotational force dQ is also in the positive direction, and a resistance torque is generated to prevent the propeller from rotating. Therefore, in order to make the propeller run at the speed n, the prime mover must issue the same torque to overcome this resistance torque. In Figure 1, the schematic diagram of the direction of the propeller torque, the rotational speed and the torque of the prime mover is drawn. At point A, it is considered that M (propeller torque), M_{yd} (prime mover torque), and n (propeller speed) are all positive.

If the prime mover torque is reduced so that it is always smaller than the propeller resistance torque, the propeller resistance torque will have excess after offsetting the prime mover torque. Under the action of this residual torque, the propeller will decelerate, and at the same time, its resistance torque will also decrease due to the reduction of the rotational speed, and it will change according to the characteristic AB section.

When the propeller speed is low to point B, its resistance torque becomes zero, that is, the propeller rotation is not hindered. This can be seen in Figure 3b. It can be seen from the figure that the resultant force dR of dX and dY coincides with the vertical direction, its projection dP (thrust) in the vertical direction is itself, and the projection dQ (rotation force) in the horizontal direction is zero. If the prime mover torque is also zero, the propeller will run stably at this point. At this time, the rotation of the propeller is not due to the drive of the prime mover, but due to the inertia of the propeller itself.

To further reduce the propeller speed, the prime mover must give the propeller a braking torque, that is, the prime mover torque should become negative and opposite to the original direction. Under the action of the prime mover torque, the propeller decelerates and enters the BC section. In this section, although the propeller is still rotating in the original direction, its torque becomes negative, because the direction of its turning force is reversed. As shown in Figure 1, the propeller steering remains unchanged and the torque becomes negative, so this torque becomes the active torque that pushes the propeller to rotate, and the prime mover torque is the resistance torque. If M_{yd}=M_{j} at a certain speed n in the BCD segment, the propeller is in torque balance, and it is like a hydraulic turbine, which overcomes the resistance torque under the impact of the water flow and rotates continuously and stably at the speed n. Only when the absolute value of the prime mover torque is greater than the absolute value of the propeller torque, that is, |M_{yd}|>|M_{j}|, the propeller will continue to decelerate.

In the BC segment, the included angle between dR and dQ decreases as n decreases (Fig. 3b), and the included angle is 90°, while the included angle corresponding to Fig. 3c is much smaller than 90°. Therefore dQ increases as n decreases. At point C, dQ reaches the maximum value, and M_{j} also reaches the maximum value. When n further decreases, since W decreases, dR also decreases, therefore, dQ decreases, and M_{j} also decreases. In this way, a peak torque appears at point C, forming a peculiar shape of the propeller reversal characteristic.

When the speed of the propeller is reduced to zero (point D), the torque of the propeller is not equal to zero, as can be seen from Figure 3d, the torque dQ has a certain value at this time, which means that under the impact of water flow, an active torque is generated on the propeller, trying to maintain the original rotation direction. To keep the propeller stationary at this point, there must be an equal amount of drag torque from the prime mover. In order to accelerate the propeller in the opposite direction, the negative torque of the prime mover must be further increased. When the propeller accelerates in the opposite direction, the relationship between its torque and rotational speed is shown in the DE section. In this section, even if the speed is very low, the torque that the prime mover should send is quite high, otherwise it is not enough to overcome the propeller torque. Therefore, in the process of propeller reversal, the prime mover works very heavy.

If the propeller is reversed at lower ship speeds, its reversal characteristic is above that of full ship speed. For example, in Figure 1, characteristic 2 (corresponding to ship speed V=0.6V_{e}) is above characteristic 3 (corresponding to ship speed V=V_{e}, that is, full ship speed). When reversing from zero ship speed (this is reverse starting), the characteristic takes the shape of curve 1. This characteristic curve is the reverse anchoring characteristic, which is completely symmetrical with the anchoring characteristic during forward starting.

During the reverse rotation of the propeller, the speed of the boat does not actually remain constant, but decreases continuously. Therefore, the propeller torque does not change according to a certain characteristic curve, but continuously transitions from the lower characteristic curve to the upper characteristic curve, corresponding to the ship speed at each moment.

In the following discussion, we will generally ignore the friction loss of the shaft and consider the propeller power and torque as the motor power and torque.