Inertial characteristics

The property of inertia of bodies is revealed in Newton's first law:

“Every body maintains its state of rest or uniform and rectilinear motion until external applied forces change this state.”

In other words, every body maintains its speed until forces change it.

The concept of inertia:

Any body maintains its speed unchanged in the absence of external influences in the same way. This property, which has no measure, is proposed to be called inertia 1. Different bodies change speed under the influence of forces in different ways. This property of theirs, therefore, has a measure: it is called inertia. It is inertia that is of interest when it is necessary to evaluate how the speed changes.

Inertia is a property of physical bodies, manifested in a gradual change in speed over time under the influence of forces.

Keeping the speed constant (moving as if by inertia) in real conditions is possible only when all external forces applied to the body are mutually balanced. In other cases, unbalanced external forces change the speed of the body in accordance with the measure of its inertia. The moment of inertia of a body is a measure of the inertia of a body at rotational movement. The moment of inertia of the body relative to the axis is equal to the sum of the products of the masses of all material points bodies by the squares of their distances from a given axis

The radius of inertia of a body is a comparative measure of the inertia of a given body relative to its different axes. It is measured by the square root of the ratio of the moment of inertia (relative to a given axis) to the mass of the body:

Body links like levers and pendulums

Connection points that can be considered either fulcrum points (for a lever) or plumb points (for a pendulum).

A lever is characterized by the distance between the point of application of force and the point of rotation. Levers are of the first and second kind.

A lever of the first kind or balance lever consists of only one link. An example is the attachment of the skull to the spine.

A lever of the second type is characterized by the presence of two links. Conventionally, we can distinguish between a speed lever and a force lever, depending on what predominates in their actions. The speed lever gives a gain in speed when improving work. An example is the elbow joint with a load on the palm. The lever of power gives a gain in power. An example is a foot on the toes.

Since the human body performs its movements in three-dimensional space, then its links are characterized by degrees of freedom, i.e. the ability to perform translational and rotational movements in all dimensions. If a link is fixed at one point, then it is capable of performing rotational movements and we can say that it has three degrees of freedom.

Fixing a link leads to the formation of a connection, i.e. associated movement of a fixed link with an anchoring point. Since a person’s arms and legs can perform oscillatory movements, the same formulas apply to the mechanics of their movement as for simple mechanical pendulums. Their main conclusion is that the natural frequency of oscillations does not depend on the mass of the swinging body, but depends on its length (as the length increases, the oscillation frequency decreases).

By making the frequency of steps when walking or running or strokes when swimming or rowing resonant (i.e. close to the natural frequency of vibration of the arm or leg), it is possible to minimize energy costs. With the most economical combination of frequency and length of steps or strokes, a person demonstrates a significant increase in performance. A simple example: when running, a tall athlete has a longer stride length and a lower step frequency than a shorter athlete, with the same speed of movement.

To the previously discussed kinematic measures of changes in motion (speed and acceleration), dynamic measures of changes in motion (amount of motion and kinetic torque) are added. Together with measures of the action of forces, they reflect the relationship between forces and motion. Studying them helps to understand physical basis human motor actions.

Dynamics(from the Greek dynamikós - strong, from dýnamis - strength), a section of mechanics devoted to the study of the movement of material bodies under the influence of forces applied to them. Dynamics is based on I. Newton’s three laws, from which, as consequences, all the equations and theorems necessary for solving problems of dynamics are obtained. All movements of a person and the bodies he moves under the influence of forces change in magnitude and direction of speed. To reveal the mechanism of movements (the reasons for their occurrence and the course of their changes), dynamic characteristics are studied. These include inertial characteristics (features of the moving bodies themselves), force (features of the interaction of bodies) and energy (states and changes in performance of biomechanical systems).

Inertial characteristics reveal the characteristics of the human body and the bodies it moves in their interactions. The preservation and change of speed depends on the inertial characteristics.

All physical bodies have the property of inertia (or inertia), which manifests itself in the conservation of motion, as well as in the peculiarities of its change under the influence of forces.

The concept of inertia is revealed in Newton's first law: “Every body maintains its state of rest or uniform and rectilinear motion until external applied forces force it to change this state.”

Weight is a measure of the inertia of a body during translational motion. It is measured by the ratio of the magnitude of the applied force to the acceleration it causes. Mass (m) is the amount of substance (in kilograms) contained in a body or individual link.

The mass of a body characterizes how exactly the applied force can change the movement of the body. The same force will cause a greater acceleration in a body with less mass than in a body with more mass.

Body weight - This is the force with which a body, due to its attraction to the Earth, acts on a horizontal support.

Moment of inertia is a measure of the inertia of a body during rotational motion. The moment of inertia of a body relative to an axis is equal to the sum of the products of the masses of all its particles by the squares of their distances from a given axis of rotation.

From this it can be seen that the moment of inertia of a body is greater when its particles are further from the axis of rotation, which means that the angular acceleration of the body under the influence of the same moment of force is less; if the particles are closer to the axis, then the angular acceleration is greater and the moment of inertia is less. This means that if you bring the body closer to the axis, it is easier to cause angular acceleration, it is easier to accelerate the body in rotation, and it is easier to stop it. This is used when moving around an axis.

Power characteristics. It is known that the movement of a body can occur both under the influence of a driving force applied to it, and without a driving force (by inertia), when only a braking force is applied. Driving forces are not always applied; Without braking forces, there is no movement. Changes in movements occur under the influence of forces. Force is not the cause of movement, but the cause of change in movement; force characteristics reveal the connection between the action of force and a change in movement.

Strength is a measure of the mechanical effect of one body on another at a given moment in time. Numerically, it is determined by the product of the mass of the body and its acceleration caused by a given force.

Most often they talk about force and the result of its action, but this applies only to the simplest translational movement of a body. In human movements as a system of bodies, where all movements of body parts are rotational, the change in rotational motion depends not on force, but on the moment of force.

moment of force is a measure of the rotating effect of force on a body. It is determined by the product of the force and its shoulder.

The moment of a force is usually considered positive when the force causes a body to rotate counterclockwise, and negative when it rotates clockwise.

In order for a force to exert its rotating effect, it must have a shoulder. In other words, it should not pass through the axis of rotation.

Determining a force or moment of force, if the mass or moment of inertia is known, allows you to find out only the acceleration, i.e. how quickly the speed changes. We still need to find out exactly how much the speed will change. To do this, it must be known how long the force was applied. In other words, it is necessary to determine the impulse of the force (or its moment).

Impulse force - this is a measure of the impact of force on a body over a given period of time (in translational motion). He equal to the product strength and duration of its action.

Any force applied even in small fractions of a second (for example: hitting a ball) has momentum. It is the impulse of force that determines the change in speed, while force determines only acceleration.

In rotational motion, a moment of force, acting for a certain time, creates an impulse of the moment of force.

Momentum impulse - this is a measure of the impact of a moment of force relative to a given axis for a given period of time (in rotational motion).

As a result of impulse, both force and moment of force, changes in motion arise, depending on the inertial properties of the body and manifested in changes in speed (amount of motion, kinetic moment).

Quantity of movement is a measure of the translational movement of a body, characterizing its ability to be transmitted to another body in the form of mechanical movement. The momentum of a body is measured by the product of the mass of the body and its speed.

Kinetic moment (angular momentum) is a measure of the rotational motion of a body, characterizing its ability to be transmitted to another body in the form of mechanical movement. The kinetic moment is equal to the product of the moment of inertia relative to the axis of rotation and the angular velocity of the body.

A corresponding change in momentum occurs under the action of a force impulse, and under the action of a moment of force impulse, a certain change in the kinetic moment (momentum moment) occurs.

Energy characteristics. Energy (from the Greek enérgeia - action, activity), a general quantitative measure of movement and interaction of all types of matter. Energy in nature does not appear from nothing and does not disappear; it can only change from one form to another. Mechanical energy is the energy of mechanical movement and interaction of bodies of a system or their parts. Mechanical energy is equal to the sum of kinetic and potential energy mechanical system.

When a person moves, forces applied to his body along a certain path do work and change the position and speed of the parts of the body, which changes its energy. Work characterizes the process in which the energy of the system changes. Energy characterizes the state of a system that changes as a result of work. Energy characteristics show how the types of energy change during movement, and the process of energy change itself occurs.

Work of force - this is a measure of the effect of force on a body during some movement under the influence of this force. It is equal to the product of the modulus of the force and the displacement of the point of application of the force.

If the force is directed in the direction of movement (or at an acute angle to this direction), then it makes positive work, increasing the energy of body movement. When the force is directed towards the movement (or at an obtuse angle to its direction), then the work of the force is negative and the energy of movement of the body decreases.

Work of moment of force - this is a measure of the influence of a moment of force on a body along a given path (in rotational motion). It is equal to the product of the modulus of the moment of force and the angle of rotation.

The concept of work is a measure of external influences applied to a body along a certain path, causing changes in the mechanical state of the body.

Energy - this is the operating capacity of the system. Mechanical energy is determined by the speeds of movement of bodies in the system and their relative position; This means it is the energy of movement and interaction.

Body kinetic energy - this is the energy of its mechanical movement, which determines the ability to do work. In translational motion, it is measured by half the product of the mass of the body by the square of its speed, and in rotational motion by half the product of the moment of inertia by the square of its angular velocity.

Body potential energy - that is the energy of its position, determined by the mutual relative arrangement of bodies or parts of the same body and the nature of their interaction. Potential energy in the gravity field is determined by the product of gravity and the difference between the levels of the initial and final positions above the ground (relative to which the energy is determined).

Energy as a measure of the movement of matter passes from one type to another. Thus, chemical energy in muscles is converted into mechanical energy (internal potential of elastically deformed muscles). The muscle traction force generated by the latter does work and converts potential energy into kinetic energy moving parts of the body and external bodies. The mechanical energy of external bodies (kinetic), transmitted during their action on the human body to its links, is converted into potential energy of stretched antagonist muscles, as well as into dissipated thermal energy.

In various situations, it becomes necessary to change the speed of the vessel (anchoring, mooring, sailing, etc.). This occurs by changing the operating mode of the main engine or propulsors.

After which the ship begins to move unevenly.

The path and time required to complete a maneuver associated with uneven movement are called the inertial characteristics of the vessel.

Inertial characteristics are determined by time, the distance covered by the ship during this time, and the speed at fixed intervals and include the following maneuvers:

movement of the vessel by inertia - free braking;

acceleration of the vessel to a given speed;

active braking;

slowdown.

Free braking characterizes the process of reducing the speed of the vessel under the influence of water resistance from the moment the engine stops until the vessel comes to a complete stop relative to the water. Typically, the free braking time is counted until the vessel’s controllability is lost (Fig. 1.26).

Acceleration of a ship is the process of gradually increasing the speed of movement from zero value up to a speed corresponding to the specified position of the telegraph (Fig. 1.27).

Active braking- This is braking by reversing the engine. Initially, the telegraph is set to the “Stop” position, and only after the engine speed drops by 40–50%, the telegraph handle is moved to the “Full reverse” position. The end of the maneuver is the vessel stopping relative to the water (Fig. 1.28).

The process of active braking of a vessel with a fixed pitch propeller can be divided into 3 periods:

first period (t1) - from the moment the maneuver begins until the moment the engine stops (t1 ≈ 7–8 seconds);

the second period (t2) - from the moment the engine stops until it starts in reverse;

third period (t3) - from the moment the engine starts in reverse until the vessel stops or until a steady reverse speed is acquired. The movement of the vessel in the first two periods can be considered as free braking.

In the process of movement, any vessel, especially a large-capacity one, has a significant mass and insufficiently tight adhesion to the water environment. It has the ability to stop moving rather slowly and change speed. Inertial properties are the physical relationship between mass and rate of velocity increase. They are usually determined experimentally and the results are entered into the table of the ship’s maneuverable elements. For navigation, the distance and time of inertia damping and development of maximum speed by the vessel are important; these parameters are called inertial characteristics of the vessel: braking, free coasting and acceleration.

Braking – the process of dampening the inertia of the rectilinear motion of a vessel by reversing the propulsors from forward to reverse (and vice versa). It is characterized by the length of the braking distance L t and the braking time t t. This is the distance traveled by the vessel from the moment of the “Stop” command and the propulsion reverse until the vessel comes to a complete stop and the time spent on this. Braking by the operation of propulsors “Full reverse” is called. emergency.

Coasting – the process of damping the inertia of the forward motion of a vessel under the influence of water resistance without active work movers. It is characterized by the distance L in which the vessel travels from the moment of the “Stop” command until the moment the vessel comes to a complete stop and the time spent on this.

Overclocking – the process of a ship reaching a steady speed under a given operating mode of the propulsors. It is characterized by distance L p and time upon reaching a steady speed in a given operating mode of the propulsors.

Inertial tests of the vessel are carried out according to special program Depending on the design features of the vessel, the test results are entered into the table of the maneuverable elements of the vessel. The braking characteristics are of greatest importance.

Coasting characteristics are especially important for towed vessels and convoys.

Knowledge and consideration of inertial characteristics when steering a vessel is mandatory for the navigator!

3. Controllability and circulation of the vessel, its periods and elements

The controllability of a vessel depends on the properties of the vessel: hull, steering gear, propulsors, speed, as well as external factors wind, current, waves, depth and width of the S.H. Particularly important to consider is the effect of speed, which is ambiguous. So, when the ship moves, hydrodynamic forces and moments (proportional to the square of the oncoming flow velocity) on the rudder and hull have a constant ratio, therefore the trajectory of movement is stable. But if you reduce the speed of rotation of the propeller, the steering torque will change immediately due to the weakening of the flow from the propeller, and the hydrodynamic torque on the body will remain the same, the ratio of forces and moments will be disrupted and the trajectory of movement will change.

The controllability of the vessel is characterized by course stability and agility.

Course stability the ability of a ship to maintain a straight direction. There are: own stability– the property after the cessation of external influence, without a rudder, to come to straight motion(most ships do not have their own stability), and operational stability– the ability of a ship to maintain a given direction of movement with the help of periodic shifts of the rudder (depending on the ship, draft and trim). It is characterized by the number of required rudder shifts per unit of time to keep the ship in straight motion.

Agility – the ability of a vessel to change the direction of movement and describe a trajectory of a given curvature. Depends on the ship's controls and hull characteristics, incl. precipitation.

Stability and agility are antipodes, but both are needed and both of these properties of the vessel strive to be positive.

The process of turning a ship with the rudders shifted is called circulation , which is characterized by elements and periods.

After shifting the rudder, the ship moves for some time by inertia in the same direction; after overcoming the forces of inertia, the ship begins to move along a curved trajectory - circulation. At this time it begins to act centrifugal force C attached to Ts.T. and proportional to the mass of the vessel, the square of the forward motion speed and inversely proportional to the radius of curvature C=mv with 2/r.

Fig 10(o)

The hydrodynamic pressure is redistributed on the ship’s hull, i.e. pressure on the outer side increases.

Because water runs onto it at an angle to the DP, the point of application of these resistance forces R is located in the bow at 1/4 of the length of the ship from the stem. By applying to the CG two forces R 1 and R 2 parallel and opposite to the force R, we obtain a pair of forces R and R1 with shoulder b, creating a turning moment called. positionalMп = Rв. WITH With the appearance of the angular velocity of turn, the ship is affected by the rudder and positional moments. The influence of MP depends on the shape and size of the underwater part of the vessel and the angular speed of rotation.

Further movement (circulation) of the vessel causes an increase in hydrodynamic pressure on the hull of the vessel in the stern, creating a reactive force D with a shoulder to the CG and a moment turning the vessel in the direction opposite to the turn called. damping , thus the turning torque of the circulation consists of:

Mob = Mr + Mp – Md

Circulation – curvilinear trajectory of the center movement the gravity of the vessel at crossover okay steering body , is characterized by the maneuverability criterion by the ratio of the tactical circulation diameter to the length of the vessel Dt/L And has periods:

Maneuverable– from shifting the rudder to the beginning of the turn of the vessel, under the influence of the shifted rudder.

Evolutionary– from the beginning of the turn until the course changes by 90 degrees relative to the original one. During this period, the angular speed of turning increases, the vessel drifts in the opposite direction of the turn, and the forward motion speed decreases.

Steady circulation– after changing course by 180 degrees. from the initial one, the vessel moves along a closed trajectory with a constant diameter Dc, and a constant translational angular velocity.

Circulation elements:

Extension – the distance between the CG positions at the moment the rudder is shifted and changed to 90 degrees. course.

L1(0.6 – 1.5 Dc)

Forward offset - the distance by which the CG shifts when turning from 0 to 90 degrees. L2 (0.25-0.5Dc)

Reverse bias – distance of CG displacement in the direction opposite to the turn (0.1Dc)

Turning pole – an imaginary point on the DP or its extension around which the rotation is currently taking place.

Drift angle – the angle between the linear velocity vector Vt and the vessel’s DP.

Steady circulation diameter – the distance between the position of the CG when the course changes by 90 and 270 degrees from the original.

Tactical Circulation Diameter – the distance between the DP at a heading of 0 degrees. and heading 180 degrees.( 1.1 – 1.2 DHz)

Dt = L2 T/10Sp

Circulation depends on the characteristics and qualities of the vessel L, B, T, rudders, speed, quantity and placement of cargo, roll and trim, external factors. Data from controllability and circulation tests are entered into the table of the ship’s maneuvering elements, entered into the maneuvering characteristics form and into the pilot’s card.

The table of maneuverable elements of the vessel includes:

1. circulation elements tabular and curves

2.Tables and graphs of propulsion speed and revolutions

3. Vessel dimensions

4. Inertial characteristics in various modes

5. Table of vessel draft and subsidence

6.Evolution of “Man Overboard” anxiety

1-4 in ballast and loaded.

On the topic of this lecture, a 4-hour practical lesson No. 2.2 is conducted

Lecture No. 2.2 (2 hours). TOPIC: Influence of steering devices on the controllability of a vessel.A 2-hour session will be held on this topic. laboratory work №2.1