1. General concepts and definitions

Controllability is the ability of a vessel to move along a given trajectory, i.e. maintain a given direction of movement or change it under the influence of control devices.

The main control devices on a ship are steering controls, propulsion controls, and active control controls.

Controllability combines two properties: course stability and agility .

Course stability- this is the ability of the ship to maintain the direction of straight motion. Course stability can be automatic, when the ship is able to stay on course without operating the controls (rudders), and operational, when the ship is kept on a given course using controls.

Agility is the ability of a vessel to change the direction of movement and describe a trajectory of a given curvature.

Agility and course stability correspond to the main purpose of any control device: to turn the ship and ensure its movement in a constant direction. In addition, any control means must counteract the influence of external force factors. In accordance with this, R.Ya. Pershits introduced a definition of such an important component of controllability as obedience.

Compliance is the ability of a ship to overcome resistance to maneuvering under given external influences. In the absence of external influence, its role can be played by its own instability on the course.

Coma obedience introduced the concept sensitivity, which means the ability of the vessel to respond as quickly as possible to the action of the control, in particular to the shift of the rudder.

Propeller thrust. In order for a ship to move at a certain speed, a driving force must be applied to it to overcome the resistance to movement. The useful power required to overcome resistance is determined by the formula: Nп = R V, where R is the resistance force; V - speed of movement.

The driving force is created by a working screw, which, like any mechanism, spends part of the energy unproductively. The power expended to rotate the screw is: Nз= M n, where M is the moment of resistance to rotation of the screw; n is the screw rotation speed.

The ratio of useful power to expended power is called the propulsive coefficient of the body-propulsion complex:

h = RV/ Mn

The propulsion coefficient characterizes the vessel's energy requirement to maintain a given speed. The power of the power plant (effective power Ne) of the vessel must be greater than the power expended on rotating the propeller, since there are losses in the shaft line and gearbox:

Ne = RV/ h hв hр,

where hв, hр are the efficiency coefficients of the shafting and gearbox.

Since, with uniform linear motion, the thrust force of the propeller is equal to the resistance force, the above formula can be used to roughly estimate the thrust of the propeller in full stroke mode (Vo):

Re = Ne h hв hp / Vo,

where the propulsive coefficient is determined by the Lapp formula:

where L is the length of the vessel between perpendiculars:

n - propeller rotation speed, s -1.

The maximum propeller thrust develops in mooring mode - approximately 10% more than the propeller thrust in full speed mode.

The thrust force of the propeller when operating in reverse is approximately 70-80% of the thrust of the propeller in full speed mode.

Resistance to vessel movement

Resistance to vessel movement

Water has the properties of viscosity and weight, which cause two types of resistance when the vessel moves: viscous and wave. Viscous resistance has two components: friction and shape.
Friction resistance depends on the area and roughness of the wetted surface of the housing. The shape resistance depends on the contours of the body. Wave resistance is associated with the formation of ship waves during the interaction of the hull of a moving ship with the surrounding water.

To solve practical problems, the resistance of water to the movement of the vessel is taken to be proportional to the square of the speed:

R = kV²,

where k is a proportionality coefficient depending on the draft of the vessel and the degree of fouling of the hull.

As stated in the previous section, the drag force at full speed can be calculated using the following formula:

Ro = Ne h hв hp / Vo.

Intermediate resistance values ​​(R) for any travel speed are determined:

Inertia of the vessel and attached masses of water

Inertia of the vessel and attached masses of water

The equality of the forces of resistance of the medium to the movement of the vessel and the thrust of the propeller determines the uniform forward motion of the vessel. When changing the speed of rotation of the screw, this equality of forces is violated.
As the thrust increases, the speed of the vessel increases, and as the thrust decreases, it decreases. The change in speed occurs for a long time, until the inertia of the vessel is overcome and the propeller thrust and resistance forces are equalized again. The measure of inertia is mass. However, the inertia of a vessel moving in an aquatic environment depends not only on the mass of the vessel itself.

The hull of the vessel draws the water particles adjacent to it into motion, which consumes additional energy. As a result, in order to give the vessel some speed, longer operation of the power plant will be required.
When braking, it is necessary to extinguish not only the kinetic energy accumulated by the vessel, but also the energy of the water particles involved in the movement. This interaction of water particles with the hull is similar to an increase in the mass of the ship.
This additional mass (added mass of water) for transport ships ranges from 5 to 10% of their displacement during longitudinal movement of the vessel and approximately 80% of displacement during transverse movement.

2. Forces and moments acting on the ship as it moves

2. Forces and moments acting on the ship as it moves

When considering the movement of a vessel, a rectangular XYZ coordinate system is used, associated with the center of gravity of the vessel. Positive direction of the axes: X - to the nose; Y - towards the starboard side; Z - down.

All forces acting on the ship are divided into three groups: driving, external and reactive.

Driving forces include created by control means: propeller thrust force, lateral rudder force, forces created by active control means.

External forces include wind pressure, sea ​​waves, currents.

Reactive forces include arising as a result of the movement of the vessel under the influence of driving and external forces. They are divided into inertial- caused by the inertia of the vessel and the attached masses of water and occurring only in the presence of accelerations. The direction of action of inertial forces is always opposite to the acting acceleration.

Non-inertial forces are caused by the viscosity of water and are hydrodynamic forces.

When analyzing the forces acting on the vessel, it is considered as a vertical wing of a symmetrical profile relative to the centerline plane (DP).

In relation to a ship, the main properties of the wing are formulated as follows:

if the ship moves linearly in a flow of water or air at a certain angle of attack, then in addition to drag forces, directed opposite to the movement, a lifting force appears, directed perpendicular to the oncoming flow. As a result, the resultant of these forces does not coincide with the direction of the flow. The magnitude of the resultant forces is proportional to the angle of attack and the square of the oncoming flow velocity;

the point of application of the resultant force is shifted along the DP from the center of the wing area towards the flow. The greater the magnitude of this displacement, the sharper the angle of attack. At angles of attack close to 90 degrees, the point of application of the resultant force coincides with center of sail(for the surface of the ship) and center of lateral resistance(for the underwater part);

in relation to the underwater part of the ship's hull: the angle of attack is the drift angle, and for the surface part - cusp angle (KA) of the apparent wind;

the center of lateral resistance usually coincides with the ship's center of gravity, and the position of the center of sail depends on the location of the superstructures.

In the absence of wind and the rudder in a straight position, the first differential equation of the ship’s motion can be represented as:

where Мх is the mass of the vessel taking into account the added mass of water.

Uniform movement: there is no acceleration, therefore the inertial force Mx dV/dt=0. Two equal and opposite forces act on the ship: water resistance and propeller thrust.

At change in propeller thrust the equality of propeller thrust forces and vessel movement resistance is violated; this causes the appearance of inertial forces, acceleration appears and the ship begins to move faster or slower. Inertial forces are directed against acceleration, i.e. prevent changes in speed.

With increasing traction force There are 3 forces acting on the ship: propeller thrust - forward, resistance force- back, the force of inertia is back.

When the traction force decreases: traction force - forward; With silt resistance- back; inertia force - forward

During the stop maneuver:Withsilt resistance- back; inertial force - forward;

When reverse:

a) before the ship stops: resistance force- back; traction force - back; the force of inertia is forward.

b) after stopping and starting to move backwards: resistance force- forward; traction force - back; the force of inertia is forward.

Note: forward - direction to the bow of the ship; back - direction towards the stern of the ship.

Forces acting on a ship when turning

Forces acting on a ship when turning

The ship turns under the influence of the shifted rudder. If you hold the rudder on board for a certain period of time, the ship will make a movement called circulation. In this case, the center of gravity of the vessel will describe a circulation curve, similar in shape to a circle.
The beginning of circulation is taken to be the moment the rudder begins to shift. Circulation is characterized by linear and angular velocities, radius of curvature and drift angle.
The circulation process is usually divided into three periods: maneuvering - continues during the time the rudder is shifted; evolutionary - begins from the moment the rudder is turned over and ends when the circulation characteristics take on steady-state values; steady - begins from the end of the second period and continues as long as the steering wheel remains in the shifted position.

The ship's rudder is considered as a vertical wing of a symmetrical profile. Therefore, when it is shifted, a lifting force arises - the lateral force of the steering wheel Рр.

Let us apply to the center of gravity of the vessel two forces equal to Pru and oppositely directed, P"ru and P""ru. These two forces are mutually compensated, i.e. they do not affect the ship's hull.

Then the following forces and moments act on the ship:

rudder drag force Ррх - reduces the speed of the vessel;

moment of force Rru R""ru - turns the ship towards the shifted rudder;

force P "ru - moves the center of gravity in the direction opposite to the turn.

Forces acting on a ship during the evolutionary period of circulation

Forces acting on a ship during the evolutionary period of circulation

The turn of the vessel under the influence of the moment of force Pru P""ru leads to the appearance of a drift angle. The ship's hull begins to act like a wing. A lifting force appears - a hydrodynamic force R. Let us apply two equal Ry and oppositely directed forces R"y R""y to the vessel's CG.

Then, in addition to the forces and moments acting in the maneuverable circulation mode, the following appear:

drag force Rx - further reduces the speed of the vessel;

moment of force Ry R"y - promotes turning; the angular speed of turning increases;

the force R""y - compensates for the force R"ru and the trajectory is bent in the direction of the turn.

Forces acting during a steady period of circulation

Forces acting during a steady period of circulation

As soon as the ship begins to move along a curved path, centrifugal force Rc appears. Each point along the length of the vessel describes its trajectory relative to the common center O.
In this case, each point has its own drift angle, the values ​​of which increase as they move towards the stern. In accordance with the properties of the wing, the point of application of the hydrodynamic force R is shifted aft beyond the center of gravity of the vessel.

As a result:

force Rtskh - reduces the speed of the ship;

Rtsu force - prevents changes in the radius of circulation;

the moment created by the hydrodynamic force Ru prevents an increase in the angular speed of rotation;

all circulation parameters tend to their steady values.

Geometrically, the circulation trajectory is characterized by:

IMO resolution A.751 (18) “Intermediate standards for the maneuverability of ships” proposed the following values ​​for newly built ships:

1) direct displacement (advance) - no more than 4.5 ship lengths;

2) tactical diameter – no more than 5 ship lengths.

Controllability of the vessel when moving in reverse

Controllability of the vessel when moving in reverse

When a vessel moves in reverse with the rudder in position, the following forces and moments act on the vessel (see figure):

lateral force of the steering wheel Rru;

the moment of forces Rru and Rru turns the ship in the direction opposite to the shifted rudder;

the hydrodynamic force Rу forms a moment that prevents a turn;

oblique throwing of water onto the rudder reduces the effective angle of the rudder by an amount equal to the drift angle and, consequently, the value of the lateral force of the rudder decreases.

The above factors determine the worse controllability of the vessel in reverse compared to forward.

Forces and moments associated with wind action

Forces and moments associated with wind action

When considering wind forces and moments, apparent wind speed is used.

In accordance with the property of the wing, when exposed to wind, an aerodynamic force A appears.

By decomposing the aerodynamic force into longitudinal and transverse components and applying two equal and oppositely directed forces Ay and A"y to the CG, we obtain:

power Ah - increases the speed of the ship;

moment of forces Ау and А "у - turns the ship to the right side;

force A""y - causes lateral movement, which leads to the appearance of a drift angle a and a hydrodynamic force R;

longitudinal component of the hydrodynamic force Rx - reduces the speed of the vessel;

the moment of forces Ry R""y, acting in the same direction with the moment of forces Ау and А"у, turns the ship even more;

the force R"y causes lateral movement opposite to the movement from the force A"y.

To keep the ship on course, it is necessary to shift the rudder to a certain angle to create a moment of lateral force of the rudder Pru, compensating for the moments of aero- and hydrodynamic forces.

A working propeller simultaneously performs translational motion with the vessel speed V relative to undisturbed water and rotational motion with angular velocity w = 2p n. Each propeller blade is treated as a separate wing.

When a water flow is thrown onto a propeller, a force is created on each blade that is proportional to the square of the flow speed and the angle of attack. Expanding this force in two directions perpendicular to each other, we obtain: the thrust force directed along the axis of rotation of the propeller and the drag force acting in the plane of the propeller disk tangentially to the circle described by the points on the propeller blade during its rotation.

Since the operating propeller is located behind the ship's hull, when it moves, the water flow flows onto the propeller blades at unequal speeds and at different angles. As a result, there is an inequality of thrust and drag forces for each blade, which leads to the appearance, in addition to the propeller thrust, of lateral forces that affect the controllability of a single-rotor vessel.

The main reasons for the appearance of lateral forces are:

a passing flow of water carried by the hull as it moves;

reaction of water to a working propeller;

uneven projection of a water jet from a working propeller onto the rudder or hull of the vessel.

Let us consider the influence of these reasons on the operation of fixed pitch propellers (FSP) and adjustable pitch propellers (CVP) of right rotation.

Impact of associated flow

In the upper part of the propeller, the speed of the associated water flow due to the shape of the body contours will be greater than in its lower part, which leads to an increase in the angle of attack of the water flow on the upper blade. This can be shown by considering the movement of a blade element located at a radius r from the axis of rotation of the propeller.

When the propeller operates, the blade element takes part in rotational motion with a linear speed equal to 2pr●n and translational motion with the vessel speed V.

The actual forward motion speed of a section of the propeller blade is reduced by the value DV of the associated flow velocity. As a result, the angle of attack increases to a value, which leads to an increase in the forces dРх and dРу.
By integrating dРх and dРу along the length of the blade, we obtain the values ​​of the thrust forces (P1) and drag forces (Q1) created by the propeller blade in the upper position. These forces will be greater than the forces P3 and Q3 created by the blade in the lower position. The inequality of the forces Q1 and Q3 causes the appearance of a lateral force DQ = Q1 - Q3, which tends to turn the stern of the ship to the left in the direction of the larger force.

Reaction of water to the propeller

Reaction of water to the propeller

The operation of the propeller is influenced by the proximity of the water surface. As a result, air leaks into the blades in the upper half of the propeller disk. In this case, the upper blades experience less water reaction force than the lower ones. As a result, a lateral reaction force of water arises, which is always directed in the direction of rotation of the propeller - in the case under consideration, to the right.

When the propeller rotates, a swirling stream of water flows onto the rudder blade in its lower and upper parts at different angles of attack. In the lower part the attack strength is less than in the upper part.

As a result, a lateral force arises that tends to turn the stern to the right.

Overall screw effect: for most ships with a fixed pitch propeller and a propeller propeller, or mutually.

In this case, the associated flow is maintained. However, unlike the case discussed above, the associated flow reduces the angle of attack.

Consequently, the drag force dPy on each blade element decreases. In the upper position, this decrease is more pronounced than in the lower position, because in the lower part the speed of the passing flow is less. Therefore, the resulting drag force of the blades for the fixed propeller will be directed to the left.

The vast majority of ships have left rotation propeller propellers. For a rotary propeller, when changing the operating mode from forward to reverse, the direction of rotation is maintained, only the propeller pitch changes: the left-pitch propeller becomes a right-pitch propeller. Consequently, the resulting drag force of the blades, as well as of ships with right pitch pitch propellers, will be directed to the left.

Reaction of water to the propeller

The lateral force of the reaction of water on the propeller, as mentioned above, is always directed in the direction of rotation of the propeller: both for the fixed propeller and the rotary propeller, to the left.

The propeller jet attacks the stern of the ship.

As a result, increased hydrodynamic pressure is created and the feed will shift: for both the fixed propeller and the CV propeller - to the left.

Overall screw effect: the stern goes to the left.

The ship moves backwards, the propeller rotates backwards.

As the vessel begins to move backwards, the passing flow disappears.

Reaction of water to the propeller: to the left.

: to the left.

Overall screw effect: the stern goes to the left.

4. The influence of propellers on the controllability of a multi-rotor vessel

4. The influence of propellers on the controllability of a multi-rotor vessel

Most modern passenger ships, icebreakers, and high-speed vessels of large tonnage are equipped with two- or three-shaft power plants. The main feature of multi-rotor ships compared to single-rotor ships is their better controllability.
The propellers of twin-screw ships, as well as the side propellers of three screw-driven ships, are located symmetrically relative to the centerline plane and have the opposite direction of rotation, usually the same as the side. Let's consider the controllability of multi-rotor ships using the example of a twin-rotor ship.

When the propellers operate simultaneously forward or backward, the lateral forces caused by the associated flow, the reaction of water on the propeller and the jet from the propellers thrown onto the rudder or hull are mutually compensated, since the propellers have the opposite direction of rotation. Therefore, there is no tendency for the stern to tilt in one direction or another, as in a single-rotor vessel.

One screw goes forward, the other stops.

Using the well-known technique, apply to the CG two forces equal to the thrust force of the propeller Rl (in the figure the left side propeller is working) and oppositely directed forces, we obtain:

force P""l causes the ship to move forward;

the moment of forces Rl and R"l turns the stern towards the operating propeller;

It is known from hydrodynamics that a working propeller accelerates the flow of water flowing around the stern contours, and the hydrodynamic pressure from the side of the operating propeller drops. Due to the pressure difference, a force Pd is generated. Applying two equal Rd and oppositely directed forces P"d and P""d to the center of gravity of the vessel, we obtain: - the moment of forces Rd and P""d turns the stern towards the working propeller; force P"d - shifts the central center of the ship towards the working propeller .

Thus, the considered movement of a twin-screw ship is approximately similar to the movement of a single-screw ship with the rudder shifted.

One screw works backwards, the other stops.

Having carried out posturing and reasoning similar to the previous section, we can obtain a general conclusion that the stern of the ship tilts in the direction opposite to the propeller working backwards. It should be noted that the Rd force in the case under consideration is created due to the jet from the propeller operating backwards, thrown onto the rear part of the hull.

Turning the ship on the spot when the propellers are working against each other

Turning the ship on the spot when the propellers are working against each other

A twin-screw vessel can turn almost on the spot when the propellers operate in opposite directions (one propeller operates forward and the other operates in reverse). The rotation speed is selected in such a way that the thrust forces of the screws are the same in magnitude.
Approximate equality of forces is achieved when the machine running forward is given one step less speed than the machine running backward. For example: small forward stroke - medium backward stroke.
The turning moment is created not only due to the location of the propellers on opposite sides of the DP, but also due to the difference in water pressure at the sides of the stern valance, created by oppositely directed jets from the propellers.

The disadvantages of twin-screw ships include the reduced efficiency of the rudder located in the DP. Therefore, at low speeds, when the main part of the force generated on the steering wheel when it is shifted is created by a jet of water thrown by the propeller onto the steering wheel, the main method of control is to maneuver the machines.

Three-screw ships combine the positive maneuvering qualities of single- and twin-screw vessels and have higher maneuverability, including at low speeds. In forward motion, the middle propeller increases the efficiency of the rudder due to the propeller jet thrown onto it. In reverse, the middle propeller provides forward motion, and turns are carried out by the operation of the side propellers.

5. Main factors influencing the controllability of the vessel

5. Main factors affecting ship controllability

Design factors.

The ratio of the length to the width of the vessel ( L/B). The greater this ratio, the worse the maneuverability of the vessel, which is associated with a relative increase in the resistance forces to the lateral movement of the vessel. Therefore, wide and short ships have better maneuverability than long and narrow ones.

Overall completeness coefficient (d). As the coefficient d increases, the agility improves, i.e. The fuller the contours of the vessel, the better its agility.

The design and location of the steering wheel. The design of the rudder (its area and relative elongation) has little effect on improving the maneuverability of the vessel. Its location has a significantly greater influence. If the rudder is located in a screw stream, then the speed of water flowing onto the rudder increases due to the additional flow speed caused by the screw stream, which provides a significant improvement in agility.

On twin-screw ships, the rudder located in the DP has relatively low efficiency. If on such vessels two rudder blades are installed behind each propeller, then agility increases sharply.

Vessel speed

The shape of the circulation and its main geometric characteristics (extension, forward displacement, reverse displacement) depend on the initial speed of the vessel. But the diameter of the established circulation at the same rudder angle remains constant and does not depend on the initial speed.

In windy conditions, controllability significantly depends on the speed of the vessel: the lower the speed, the greater the influence of the wind on controllability.

Elements of ship landing

Trim. Increasing the trim aft leads to a shift in the center of lateral resistance from the midsection towards the stern, therefore the vessel's heading stability increases and its agility deteriorates.
On the other hand, bow trim sharply worsens course stability - the ship becomes yawy, which complicates maneuvering in cramped conditions. Therefore, they try to load the ship so that it has a slight trim to the stern during the voyage.

Bank. The roll of the ship disrupts the symmetry of the flow around the hull. The area of ​​the submerged surface of the chine of the heeled side becomes greater than the corresponding area of ​​the chine of the raised side.

As a result, the ship tends to evade in the direction opposite to the roll, i.e. towards the direction of least resistance.

Draft. A change in draft leads to a change in the area of ​​lateral resistance of the submerged part of the hull and the windage area. As a result, with an increase in draft, the vessel's heading stability improves and its agility worsens, and with a decrease in draft, the opposite is true.
In addition, a decrease in draft causes an increase in the sail area, which leads to a relative increase in the influence of wind on the controllability of the vessel.

All forces acting on a ship, according to the currently accepted classification, are divided into three groups: driving, external and reactive.

Driving forces include the forces created by the controls in order to give the vessel the required linear and angular motion. Such forces include the propeller thrust, the lateral force of the rudder, the forces created by the self-propelled guns, etc.

External forces include wind pressure, sea waves, and currents. These forces, caused by external energy sources, in most cases interfere with maneuvering.

Reactive forces include forces and moments resulting from the movement of the vessel under the influence of driving and external forces. Reaction forces depend on linear and angular velocities.

By their nature, reactive forces and moments are divided into inertial and non-inertial.

Inertial forces and moments are caused by the inertia of the vessel and the attached fluid masses. These forces arise only in the presence of accelerations - linear, angular, centripetal.

The inertial force is always directed in the direction opposite to the acceleration. With uniform rectilinear motion of the vessel, inertial forces do not arise.

Non-inertial forces and their moments are caused by the viscosity of sea water, therefore, they are hydrodynamic forces and moments. When considering controllability problems, usually, as already noted, a moving coordinate system associated with the vessel with the origin at c is used. t.(tG) Positive direction of axes: X- into the nose; Y- towards the starboard side; Z - down. Positive angle reading is taken clockwise, but with reservations regarding the shift angle, drift angle and heading wind angle.

The positive direction of the rudder shift is taken to be a shift that causes clockwise circulation, i.e. shift to the starboard side (the rudder blade turns counterclockwise).

A positive drift angle is taken to be one at which the water flow comes from the port side and, therefore, creates a positive transverse hydrodynamic force on the hull. This drift angle occurs on the right circulation of the vessel.

The general case of ship motion is described by a system of three differential equations of motion: two equations of forces - along the longitudinal X and transverse Y axes and equations of moments around the vertical axis Z.

This system, in a somewhat simplified version, looks like this:

where m is the mass of the vessel

λ 11 – added masses when moving along the X axis;

λ 22 - added masses when moving along the Y axis;

V X – projection of the vessel’s speed onto the X axis;

V Y - projection of the ship's speed onto the Y axis;

ω - angular speed of the vessel;

J is the moment of inertia of the vessel relative to the Z axis;

R X – longitudinal hydrodynamic force on the body;

R Y – transverse hydrodynamic force on the body;

P E – useful force of the screw stop;

P PX – longitudinal force of water pressure on the steering wheel;

P PY – lateral force of the steering wheel;

A X – longitudinal aerodynamic force;

A Y – transverse aerodynamic force;

M R – moment of hydrodynamic force on the body;

M A – moment of aerodynamic force;

M P – moment of lateral force of the steering wheel.

The first equation of the system characterizes the movement of the vessel along the “X” axis during acceleration and braking, therefore its solution allows one to evaluate the inertial braking characteristics of the vessel. The second equation describes the patterns of lateral displacement of the vessel. The third equation, characterizing angular motion, is used to assess the controllability of ships. From this system it is clear that with uniform and rectilinear movement of the vessel, the left sides of the equations will be equal to zero, and there will be no transverse movement. Based on this, the system of equations will take the form:

P e = R X + A X + P P X

G

P PX P e A X R X

Fig.5.5. Forces acting on a ship during linear motion.

5.4 Forces arising from the operation of the propeller.

The hydromechanical interaction of the body - propeller - rudder system is very complex. A propulsion device operating near the ship's hull significantly changes its velocity field, which leads to a change in the hydrodynamic forces acting on the hull. In turn, the flow of water flowing onto the propeller receives disturbances from the hull of the moving ship. The propeller also has a significant impact on the steering wheel located behind it. As a result of the interaction of the system, the hull - propeller - rudder. A number of lateral forces arise that must be constantly taken into account and rationally used when controlling the ship’s maneuvers.

The force of a passing flow.

A hull moving in the water causes a passing flow directed in the direction the vessel is moving. The reasons for its appearance are the friction of boundary layers of water on the ship’s hull and the desire of masses of water to fill the volume displaced by the hull. Between the speed of the passing flow at the propeller location V pAnd ship speed V there is a relationship V p= V (1-ω), where ω is the associated flow coefficient. Its values ​​for different vessels can vary from 0.10 to 1.00. Thus, the influence of the housing on the propeller is reduced to a decrease in the speed of flow around the propeller.

Fig.5.6. Force of the accompanying flow

It has been experimentally established that in the upper half of the propeller disk the speed of the associated flow is greater than in the lower half. The unevenness of the velocity field of the passing flow in the propeller disk per revolution causes a change in the angle of attack and, accordingly, the thrust forces and moment on the blades passing the upper and lower positions. Thus, a blade in the upper position will have a larger angle of attack and, accordingly, greater resistance to rotation than a blade in the lower position. As a result, a lateral force arises, which, at a steady forward speed (right rotation propeller), will tilt the stern of the vessel to the left.

Force of the associated flow b manifests itself to the greatest extent at a forward steady speed, causing the stern of the vessel to tilt in the direction opposite to the rotation of the propeller.

The power of reaction.

The propeller blades passing the upper position are much closer to the surface of the water than the blades passing the lower position. As a result, air is sucked into the upper layers of water. , which significantly changes the power characteristics of the blade (thrust and moment).

The influence of the proximity of the water surface is most significant when the propeller is shallowly deepened (in transport vessels traveling in ballast, the blade in the upper position generally comes out of the water), during unsteady motion (starting from a stop), and during reverse. The difference in thrust and moment on the upper and lower blades leads to the formation of a lateral reaction force D. At steady speed and with increasing screw depth, the effect of the reaction force decreases sharply.

Fig.5.6. Action of reaction force D.

In the 1st sector, the blade, moving from position 1 to position 2, encounters water resistance, the reaction force of which will be directed first from right to left (force D 1, and then from bottom to top (force D 2); the latter does not affect the diametrical plane of the vessel, but gives vibration stern

In the 2nd sector, the blade, moving from position 2 to position 3, encounters the resistance of water, the reaction force of which is directed first from bottom to top (force D 2), and then the blade will overcome the reaction force of sufficiently dense layers of water (force D 3), directed from left to right and much greater than the strength D 1 . Consequently, the stern of the ship will deviate to the right, and the bow to the left.

, meets the resistance of water, the reaction force of which will be directed initially from left to right (force D 3), and then the blade will overcome the reaction force D 4 , directed from top to bottom. This force does not affect the center plane of the vessel, but gives vibration to the stern.

to position 1, meets the resistance of water, the reaction force of which is initially directed from top to bottom (force D 4 ), and then the blade will overcome the reaction force of less dense layers of water (force D 1), directed from right to left, significantly less than force D 3. Consequently, the stern of the ship will deviate to the right, and the bow to the left.

Reaction force D manifests itself to the greatest extent during unsteady motion, causing the stern to tilt in the direction of rotation of the propeller.

The force of the thrown jet.

As the propeller rotates, it spins the masses of water adjacent to the blades and throws them away, forming a powerful spiral flow. When the ship moves forward, this flow acts on the rudder located behind the propeller . When moving in reverse, the flow affects the stern valance of the vessel. The spiral flow generated by the screw can be represented in axial (axial) and tangential (tangential) components. The axial component, acting on the rudder located behind the propeller, significantly increases its efficiency and does not cause any lateral forces. When the vessel moves in reverse, the axial component, acting on the symmetrical contours of the stern, also does not cause any lateral forces.

The tangential component in forward motion affects the rudder blade in the upper left and lower right halves.

Due to the asymmetry of the distribution of the passing flow along the vessel's draft, and therefore the resulting peripheral velocities in the flow flowing onto the rudder, the impact of the tangential component on the lower right half of the rudder will be greater than on the upper left half. As a result, a lateral force of the projected jet C arises.

Fig.5.7. Action of force C

In the 1st sector, the blade, moving from position 1 to position 2, throws layers of water away from the vessel, and no jet thrust force is generated.

In the 2nd sector, the blade, moving from position 2 to position 3, throws layers of water onto the lower surface of the rudder, where the water density is much greater. The rudder should have a tendency to deviate to the left, but since it is installed in the center plane of the vessel, the force of the thrown the jet rushes to the entire stern of the ship and moves the stern of the ship to the left, and therefore the bow goes to the right. Let us denote this force by WITH 1 .

In the 3rd sector the blade moves from position 3 to position 4 , will throw layers of water away from the vessel, therefore, there will be no jet thrust force.

In the 4th sector the blade, moving from position 4 in position 1, it again throws layers of water, but from the other side than in the 2nd sector, and onto the upper part of the steering wheel. Let us denote this jet throwing force WITH 2 . The effect of this force will be less than the effect of the jet throwing force WITH 1 in the 2nd sector, due to the lower density of water. This leads to the following conclusion: the right rotation propeller at a steady forward speed, acting on the rudder, deflects the stern of the vessel to the left, and the bow to the right

§ 24. Forces acting on the hull of a floating vessel

The hull of a ship floating on water is subject to constant and temporary forces. Constants include static forces, such as the weight of the vessel and water pressure on the submerged part of the hull - supporting forces. Temporary forces include the forces that appear when the ship rocks on a rough water surface: the inertia forces of the ship’s masses and the resistance forces of the water.

The forces acting on a ship floating on calm water, despite the equality of their resultants, are distributed unevenly along the length of the hull. Supporting forces, as is known, are distributed along the length according to the volume of the hull immersed in water and are characterized by the shape of the formation along the frames. The weight forces are distributed along the length of the hull depending on the location of its elements, such as bulkheads, superstructures, masts, mechanisms, installations, loads, etc. In fact, it turns out that in one section along the length of the hull the weight forces prevail over the supporting forces , and on the other - vice versa.

Rice. 39. Bending of the ship's hull caused by the uneven distribution of forces acting on it. 1 - weight force curve; 2 - curve of supporting forces.

From the disproportionate distribution along the length of the body of the weight forces and supporting forces arises overall buckling ship hull (Fig. 39).

When a ship is sailing on a rough surface, supporting forces act on its hull, constantly changing their magnitude in individual sections of the length of the ship. These forces reach their maximum value when the ship moves on a course perpendicular to the direction of the wave, the length of which is equal to the length of the ship. When the top of the wave passes near the midsection, excess supporting forces are formed in the middle part of the hull with a lack of them at the extremities. In this case, the uneven distribution of support forces results in case bend(Fig. 40, a). After a short period of time, the ship moves to the bottom of the wave, while excess supporting forces move to the extremities, which causes hull deflection(Fig. 40, b).

Due to the rocking of the vessel, which occurs in waves, inertial forces act on the hull, exerting an additional impact on it, and while sailing at high speed against a large oncoming wave, when the bottom part of the bow hits the water (slamming phenomenon), additional shock or dynamic loads arise.

INERTIA-BRAKE CHARACTERISTICS OF THE VESSEL

Forces and moments acting on the ship.

System of equations of ship motion in

Horizontal plane.

Maneuvering characteristics of the vessel.

Requirements for the content of information about

Maneuvering characteristics of the vessel.

General information about inertial brakes

Vessel properties.

7. Features of reversing various types

Ship propulsion systems.

Vessel braking.

The vessel as an object of control.

A transport sea vessel moves at the boundary of two media: water and air, while experiencing hydrodynamic and aerodynamic influences.

To achieve the specified motion parameters, the vessel must be controlled. In this sense the ship is a controlled system. Each a controlled system consists of three parts: a control object, a control device and a control device (machine or human)

Control – This is such an organization of the process that ensures the achievement of a certain goal corresponding to the management task.

When a ship is sailing on the high seas, management task is in ensuring its transition from one point to another along a straight trajectory, maintaining a given course and periodically adjusting it after receiving observations. In this case the heading is a controlled coordinate, and the process of maintaining its constant value is management purpose.

The instantaneous value of a number of coordinates determines the state of the vessel at a given moment. These coordinates are: course, speed, drift angle, lateral displacement relative to the general course and etc. They are output coordinates. In contrast, the coordinates, which are reasons for controlled movement are called input . This rudder angle and propeller speed . When choosing the values ​​of the input coordinates, the control device (autopilot, navigator) is guided by the values ​​of the output coordinates. This relationship between effect and cause is called feedback.

The considered controlled system is closed, because it operates a control device (navigator). If the control device stops functioning, then the system becomes open-loop and the behavior of the control object (vessel) will be determined by the state in which the controls are fixed (rudder angle, frequency and direction of rotation of the propeller).

In the discipline "Ship Control" the tasks of controlling a ship are studied, the movement of which occurs in close proximity to obstacles, i.e. at distances comparable to the size of the control object itself, which excludes the possibility of considering it as a point (for example, as in the “Navigation” course).

Forces and moments acting on the ship

All forces acting on the ship are usually divided into three groups: driving, external and reactive.

To the movers refers to the forces created by the controls to impart linear and angular motion to the vessel. Such forces include: propeller thrust, lateral force of the rudder, forces created by active control devices (ACS), etc.

To externalinclude wind pressure, sea waves, and currents. These forces in most cases interfere with maneuvering.

To reactiverefers to forces and moments resulting from the movement of the vessel. Reaction forces depend on the linear and angular velocities of the vessel. By their nature, reactive forces and moments are divided into inertial and non-inertial. Inertial forces and moments are caused by the inertia of the vessel and the attached fluid masses. These forces arise only when the presence of accelerations - linear, angular, centripetal. Inertial force is always directed in the direction opposite to acceleration. With uniform rectilinear motion of the vessel, inertial forces do not arise.

Non-inertial forces and their moments are caused by the viscosity of sea water, therefore, they are hydrodynamic forces and moments. When considering controllability problems, a moving coordinate system associated with the vessel with the origin at its center of gravity is used. Positive direction of the axes: X – to the nose; Y – towards the starboard side; Z – down. Positive angle reading is taken clockwise, however, with reservations regarding the shift angle, drift angle and wind heading angle.

The positive direction of the rudder shift is taken to be the shift that causes clockwise circulation, i.e. shift to the starboard side (the rudder turns counterclockwise).

A positive drift angle is taken to be one at which the water flow comes from the port side and, therefore, creates a positive transverse hydrodynamic force on the ship’s hull. This drift angle occurs on the right circulation of the vessel.

The general case of ship motion is described by a system of three differential equations: two equations of forces along the longitudinal X and transverse Y axes and an equation of moments around the vertical Z axis.

The impact of wind and current on the vessel causes the main load on the anchor chain when moored and determines the static moment of resistance on the electric motor shaft during the process of unanchoring, when the vessel is pulled to the anchor location.

When stationary, when the direction of wind and current coincide, the greatest impact of external forces on the vessel occurs, and the generalized force for screw vessels is determined by the arithmetic sum of three components

F’ = FB + F’T + F’G

where FB is the force of wind action on the surface of the vessel;

F’T – current force acting on the underwater part of the vessel;

F’G is the current force acting on the fixed propellers.

The force of wind influence on the surface part of the FB vessel depends on the wind speed and direction, the shape of the surface part of the hull, the size and location of the superstructures. The calculated value of wind force can be determined by the formula, N

FB = Kn ∙ rv ∙ Sn

where Kn = 0.5 ÷ 0.8 – coefficient of flow around the surface of the hull

рв = ρV2 / 2 – wind pressure, Pa;

ρ = 1.29 – air density, kg/m3;

V – wind speed, m/s

рв =1.29*102/2=64.5Pa

Area of ​​projection of the surface part of the vessel onto the midship section, m2:

B – vessel width, m;

H – side height, m;

T – draft, m;

b, h – width and height of ship superstructures, respectively, m.

Sn=11.6*(3.5-2.5)+11*2.5+10.5*5=91.6 m2

FB=0.5*64.5*91.6=2954.1 N

The body resistance caused by the flow is taken into account only by friction resistance, since all other types of resistance (wave, vortex) are practically absent due to the low flow speed, N

(1)

where CT = 1.4 – friction coefficient;

Scm = L∙(δ∙B + 1.7∙T)

– area of ​​the wetted surface of the vessel, m2

Here δ = 0.75 ÷ 0.85 – displacement completeness coefficient;

L, B, T – main dimensions of the vessel, m;

Scm=78*(0.84*11.6+1.7*2.5)=1055.34 m2

VT – water flow speed, m/s. (1.38 m/s)

F'T=1.4*1055.34*1.381.83=2663.7 N

(2)

where ZG is the number of propellers;

SG = 200 ÷ 300 – parameter that increases with increasing propeller disk ratio, kg/m3;

DB – outer diameter of the propeller (nozzle), m.

F’G=2*200*1.52*1.382=1713.96 N

F’=2954.1+2663.7+1713.96=7331.96 N

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