# Free sailing characteristics and mooring (anchoring) characteristics of propellers

Propeller characteristics refer to the relationship curve between propeller torque, power and rotational speed, that is, M=f(n), P=f(n) curves. The most commonly used are the following three typical characteristic curves:

(1) Free navigation characteristics M_{y}=f(n), P_{y}=f(n);

(2) Mooring characteristics or anchoring characteristics M_{z}=f(n), P_{z}=f(n);

(3) Inversion characteristic M_{f}=f(n).

**Free sailing characteristics**

The relationship curve between the propeller resistance torque (or power) and its rotational speed obtained when a fully loaded ship sails in still water is called the free-navigation characteristic.

The torque-speed characteristic is an approximate quadratic curve, and its expression can be written as:

M_{y}= K_{y}n^{2} (1-1)

The power-speed characteristic is an approximate cubic curve, and its expression can be written as

P_{y}= K_{y}‘n^{3} (1-2)

In the formula, M_{y} is the torque (N m); P_{y} is the power (kW); n is the rotational speed (r/min); K_{y} and K_{y}‘ are constants.

Figure 1 shows the free-navigation characteristic curve. The ship speed is approximately proportional to the propeller speed (Van). Therefore, each propeller speed on this characteristic curve corresponds to a certain ship speed. The whole characteristic curve corresponds to many different speeds.

To make the propeller run stably at a certain speed, the resistance torque of the propeller at this speed must be overcome, and there must be a corresponding prime mover torque for this purpose. For example, to run at the speed of n_{1} or n_{2}, the torque of the prime mover must be equal in magnitude and opposite in direction to the propeller resistance torque M_{y1} or M_{y2}.

**Mooring (anchoring) characteristics**

The relationship curve M_{z}=f(x) or P_{z}=(fn) of the propeller resistance torque M_{z} (or power P_{z}) and its rotational speed obtained by the fully loaded ship when the speed is equal to zero is called the mooring characteristic or throwing characteristic. When doing the test, the ship was moored, hence the name. The curve is shown in Figure 1.

The tethering characteristic expression is

M_{z}= K_{z}n^{2} (1-3)

P_{z}= K_{z}‘n^{3} (1-4)

It must be noted that in the free-navigation characteristic, each speed n of the propeller corresponds to a different speed, while in the mooring characteristic, the speed is always zero, that is, V=0. When sailing upwind in strong winds and waves, there is a lot of resistance and it is possible to approach this situation. When the propeller is started when the ship is stationary, the relationship between the propeller resistance torque and the rotational speed is a mooring characteristic. Therefore, when studying the co-working characteristics of the prime mover (or motor) and the propeller during starting, the mooring characteristics should be used.

If the ship has a dragging load (such as a tugboat), its propeller torque-speed curve is M_{t}=f(n), which is between the free-navigation characteristics and the mooring characteristics.

If the ship sails under the condition of light load or downwind, the resistance of the ship is small, and the propeller characteristics will be below the free sailing characteristics, as shown in M_{s}=f(n) in Figure 1.

Between M_{x}=f(n) and M_{s}=f(n), there are actually many similar characteristics, which vary with the ship’s load conditions and resistance conditions. When a ship is sailing in stormy weather, ship resistance can vary widely. Sometimes the propeller may also fall off, be damaged, or come out of water, etc., so that the propeller resistance moment is reduced to nearly zero. At this time, under the action of the torque of the prime mover, the propeller may even produce a “flying car” phenomenon, which makes the speed reach an unacceptable level.