Determination of the speed of the vessel traveled by the distance. Measuring the speed and distance traveled by the vessel. Record holders among ships

Determination of the ship's speed by the propeller speed mode.

To measure speed large ships use lag. On small boats, a simple lag gives big errors in determining the speed and it is not always possible to apply it. Therefore, for small vessels, it is easier to determine the speed by using tables or graphs expressing the dependence of speed on the number of rotor revolutions. To have such tables or graphs, it is necessary to determine the speed of the vessel on the measuring line for different rotations of the propeller (Fig. 59). Determination of speed is carried out in favorable weather. The yaw of the vessel on the heading shall not exceed ± 2 °.

Rice. 59. Measuring line equipment diagram

The measuring line is equipped with a leading alignment, along which the ship is heading, and four or more crossing alignments, the distances between which are accurately measured. The ship speed on the gauge line is measured with the engine running continuously. To eliminate errors in determining the speed from the influence of wind and current, two runs are made in the same engine operating mode - in one and the other direction.

The stopwatch is used to notice the moment the vessel passes the cross sections. Knowing the time t 1, t 2, t 3 and the distance between the cross sections S 1, S 2, S 3, the speed V S is calculated by the formula:

V S = S

where: V S is the ship's speed in knots;

S is the distance between cross sections in miles;

t - time of passage from point to point, sec.

During each run, it is important to maintain the correct engine speed at the correct speed. By calculating the individual speeds V 1, V 2, V 3, find the average.

After determining the speed on the measuring line, a table or graph of the dependence of the ship's speed on the number of engine revolutions is built (Fig. 60).

It is useful to determine the speed of the vessel at different draft. Then there will be several graphs and tables. For convenience, they can be depicted on one sheet of paper. Having such tables or graphs on board, it is possible to find the corresponding speed of the ship based on a given number of engine revolutions and a known draft.

Sometimes an equipped measuring line is not available nearby. However, it is always possible to select two coastal landmarks to determine the speed of the vessel, the distance between which is known accurately enough. These distances can be determined, for example, from a plan, which has both landmarks.

Leading lines can be replaced with a compass on the ship, if there is no fear that the ship will be drifted off course by wind or current, for this it is necessary to check and eliminate the influence of the running engine on the compass.

To measure speed, the vessel must be on a straight course along a safe sailing path.

Puc. 60. The plot of the dependence of the ship's speed on the engine speed

The direction of a straight line connecting objects can be determined using a compass, but it is necessary that runs can be made in a direction parallel to the line connecting objects.

In advance of approaching the first reference point, the vessel develops a certain speed and enters a measured course at a given engine speed, which during the run to the second reference point remain constant. When the first landmark is abeam, a stopwatch is started or the time is noted on the clock. The time is counted at the moment the ship passes the traverse of the second landmark. The same observations are made during the reverse run.

§ 27. Simplified method for determining the speed of the vessel.

If it is impossible, especially during navigation, to determine the speed of the vessel using one of the above methods, a different one is used, though less accurate. It is necessary to throw a temporary landmark into the water from the bow of the ship on the move - a small piece of wood and at the same time turn on the stopwatch. When the piece of wood reaches the stern cut, the stopwatch is stopped. According to the measured time and the known length of the vessel, the speed is found by the formula:

V S =,

where V S is the ship's speed in knots;

L is the length of the vessel, m;

t- transit time of an object thrown into the water, sec.

It should be borne in mind that the shorter the vessel, the greater the error.

When determining the distance traveled, it must be remembered that the movement of the vessel occurs only relative to the water, and not the ground. Wind and current are not taken into account in this case, although they constantly affect the speed of the vessel. Therefore, when conducting the laying, the distance calculated by the speed must be corrected due to drift by the current and wind. The easiest way to do this is when the course of the vessel coincides with the direction of the current and wind or is opposite to them. With side drifts, the increase or decrease in speed will be approximately proportional to the cosine of the angle between the ship's heading and the current or wind lines of action.

The main reasons for the decrease in the speed of the vessel:

1) shallow water, in which, as the speed increases, the water resistance sharply increases. Therefore, in shallow water, the speed can decrease by 10 - 15%;

2) wind and rolling. With headwinds and waves, as well as with strong tailwinds accompanied by waves, the speed decreases.

With weak tailwinds, the speed increases slightly. A decrease in speed is observed when the vessel is overloaded, heel and differential on the bow. On the wave, at the moments when the propeller leaves the water, the ship abruptly loses its speed;

3) fouling of the underwater part of the ship's hull leads to a decrease in speed by 10 - 15% compared to the speed of a ship with a clean hull.

"Determination of the speed of the vessel and the distance traveled at sea"

Distance at sea is measured in nautical miles and cable miles, therefore the distance traveled by a vessel is measured in the same units. 1 mile = 10 kbt.

The speed of a ship is expressed in miles per hour, or knots.

Knot is a unit of ship speed equal to one mile per hour. 1 node = 1 mile / hour.

The devices by which the speed of the vessel is measured and the distance traveled is determined are called lags.

Lags, depending on the principle of operation and device, are divided into

Relative (hydrodynamic, induction), measuring the speed of the vessel relative to the water

Absolute (Doppler logs, inertial and geoelectromagnetic systems), which measure the speed of the vessel relative to the ground.

1. Hydrodynamic. The operation of these lags is based on measuring the difference between the static and dynamic water pressure, depending on the speed of the vessel.

2. Induction. The principle of operation is based on the use of the relationship between the speed of the vessel and the EMF induced in the water by a source of a magnetic field fixed on the bottom of the vessel.

3. Doppler. The principle of operation is based on the use of the Doppler effect, which consists in a change in the observed frequency due to the relative movement of the source of radiated energy

The movement of the vessel is also usually divided into relative with a speed V о (V l), absolute with a speed V (V а, V u) and portable V c under the influence of wind, current or their combined effect.

On ships, relative lags are mainly used, which measure the speed and distance traveled relative to the water, taking into account the wind, but not taking into account the current. Typically, lags have an error called lag correction.

Lag correction is called the systematic error, expressed as a percentage.

S -ROL

ΔL= ----------- 100%

where S- the actual (true) distance taken from the map;

ROL Is the difference in lag counts. ROL = OL 2 - OL 1.

The lag correction is often expressed in terms of the lag coefficient k l.

The lag correction and the speed of the vessel are determined after construction or repair at special landfills - measuring lines under the following conditions: sea waves no more than 3 points, wind up to 8 m / s, depth not less than 6 average precipitation.

Lag correction and vessel speed are determined on PPH, SPKh, MPKh, SMPKh in cargo and in ballast.

The results obtained are entered into the table of maneuverable elements.

If there is no current on the measuring line, 1 run is made.

In the presence of a constant flow, 2 runs are made to eliminate it, because on mutually opposite courses from formula (1) on the first run, suppose V 0 = V 1 - V T, then on the second run V 0 = V 2 - V T. The joint solution of these two equations allows you to eliminate the flow and determine the speed of the vessel relative to the water.

Accordingly, the lag correction will also be determined: calculated by formula (2) for two runs.

If a fixed-pitch propeller is installed on the ship, then during the runs notice the speed of the propeller N and make up the dependence of the speed of the ship V on it. Then the distance traveled can be determined by the formula:, where a- advance payment, i.e. the distance traveled by the vessel relative to the water in one revolution of the propeller. It is calculated by V about and the corresponding speed of rotation of the propellers N:. ...

In the sea the speed and lag correction are determined by a freely floating reference point (to exclude the current) using the radar or using high-precision observations (by satellites) with the exclusion of the current graphically or by formulas. To avoid accumulating errors, the length of one run should be at a speed of 10 knots. - 2.3 NM; 15uz. - 3.6 NM; 18 knots - 4.3 mm or; 20 knots - 4.9 NM (N. V. Averbakh, Yu. K. Baranov Determination of maneuverable elements of a sea vessel and lag corrections). Then

Tasks to be solved in calculating the numbering.

Pre-calculation of the lag count: OL i +1 = ROL + OL i, where ROL = Sl / kl.

Calculation of the distance traveled along the log: S l = V l DT.

Swimming time calculation: T = S l / V l; DT = S and / V and;

In our life, the speed of movement Vehicle measured in kilometers per hour (km / h). This is how the movement of a car, train, plane is characterized. But there is one exception to this rule. In nautical navigation, the speed of a vessel is indicated in knots. This unit of measurement is not part of the International SI system, but is traditionally allowed for use in navigation.

Measurement of speed of ships

This order has developed historically. Once upon a time, the speed of movement of the vessel was determined using a special device called sector lag... It was a board, at the end of which a line was fixed - a thin ship's cable. Throughout its length, knots were tied at regular intervals. The sailor, touching the line with his hand, counted the number of knots that passed through his hand for certain time, determining in this way the speed immediately in knots. It is important that this method did not require any additional calculations.

Nobody has been using lags of this design for a long time. Now to measure speed sea ​​vessels use devices based on the latest scientific and technical achievements in the field of hydroacoustics and hydrodynamics. Doppler-based meters are popular... There are more simple ways- with the help of special metal turntables placed in water. In this case, the speed is determined based on the number of their revolutions per unit of time.

Nautical mile

Translated into ordinary language, one knot means the speed at which a ship travels one nautical mile per hour. At first, its size was 1853.184 meters. This is exactly the length of the Earth's surface along the meridian of one arc minute. And only in 1929 the International Conference in Monaco set the length nautical mile at 1852 meters.

It must be remembered that, in addition to the nautical mile, there are others. In the past, in different states, there were several tens of different miles as units of measure for length. After the introduction of the metric system of measures, miles as a unit of measurement of distances began to rapidly lose popularity. Today, out of all the variety of land miles, only about ten remain. The most common of these is american mile... Its length is 1609.34 meters.

Not only a nautical mile is tied to the length of the earth's meridian. The old French nautical league is 5555.6 meters, which corresponds to three nautical miles. It is interesting that, in addition to the sea league, in France there was also a land league, also tied to the length of the meridian, and a postal league.

Speed ​​recalculation rules

Today, the speed of sea-going vessels is still measured in knots. In order to represent this characteristic in the form we are accustomed to, it is necessary to translate them into kilometers per hour. It can be done in several ways:

1. Just multiply the number of nodes by 1.852 in any way you can, for example using a calculator.
2. Make a rough calculation in your head by multiplying the number of nodes by 1.85.
3. Apply special translation tables from the Internet.

Having made a similar recalculation, it is easy to compare the speeds of movement of ships and other vehicles.

Record holders among ships

The speed of sea-going passenger ships is usually higher than that of merchant ships. The last official record ("Blue Ribbon of the Atlantic") belongs to the American high-speed transatlantic liner United States... It was installed in 1952. Then the liner crossed the Atlantic from average speed 35 knots (64.7 km / h).

The infamous "Titanic" on its only voyage at the moment of collision with an iceberg on the night of April 14-15, 1912 was almost at the limit of its technical capabilities at a speed of 22 knots. The highest then speed passenger liners("Mauritania" and "Lusitania") was equal to 25 knots (46.3 km / h).

Here are some of the ships that once held the Atlantic Blue Ribbon:

1. Great Western (Great Britain) in 1838.
2. Britain (Great Britain) in 1840.
3. Baltic (Great Britain) in 1873.
4. "Kaiser Wilhelm der Grosse" (Germany) in 1897.
5. Lusitania (Great Britain) in 1909.
6. "Rex" (Italy) in 1933.
7. Queen Mary (Great Britain) in 1936.

Exists separate category vessels - hydrofoils, which are used for passenger transportation and the coast guard. They can reach speeds in excess of 100 km / h (60 knots), but their field of application at sea is highly limited exclusively to the coastal zone and low economic performance.

Change of priorities

With the development of aviation, such an active rivalry among ocean-going passenger ships has lost its relevance. Passengers to cross the Atlantic began to prefer airplanes, and shipowners had to reorient themselves to serving tourists. For cruise liners the most important indicators were reliability, comfort and economic efficiency.

The optimum speed for modern ocean-going cruise ships is typically 20 to 30 knots, and for cargo ships it is around 15 knots. United States' record-breaking achievement at the time remains the highest in history. For merchant ships, the priority indicators today are primarily economic. The pursuit of records has finally become a thing of the past.

Video

In this video selection you will find many interesting information about measuring the speed of sea transport.

The constant knowledge by the navigator of the reliable speed of his vessel is one of the most important conditions for trouble-free sailing.

The movement of the vessel relative to the bottom at a speed called absalty, is considered in navigation as a result of the addition of the vessel's speed vector relative to the water and the current vector acting in the navigation area.

In turn, the vector of the ship's speed relative to the water (referbodilyspeed) is the result of the work of ship propellers and the effect of wind and waves on the ship.

In the absence of wind and waves, it is most easily determined by the rotational speed of the propellers.

Knowing the speed makes it possible to determine the distance traveled by the vessel S about in miles:

S about = V about t, (38)

where V about - the speed of the vessel, determined by the rotational speed of the propellers, knots; t- sailing time of the vessel, h.

However, this method is inaccurate, since it does not take into account the change in the state of the vessel (fouling of the hull, change in draft), the effect of wind and waves. The following factors affect the speed of a boat relative to the water.

1. Degree of loading, list and trim of the vessel. The speed of the vessel changes with the change in draft. Usually, in good weather conditions, a vessel in ballast has a slightly higher speed than when fully loaded. However, as wind and waves intensify, the speed loss of a ship in ballast becomes much greater than that of a fully loaded ship.

Trim has a significant effect on speed change. Generally, nose trim will reduce speed. A significant stern trim leads to the same results. The optimal trim option is selected based on experience.

The presence of the ship's roll causes its systematic departure from the given course towards the raised side, which is a consequence of the violation of the symmetry of the contours of the part of the hull submerged in the water. For this reason, it is necessary to resort to shifting the rudder more often to keep the boat on course, and this in turn leads to a decrease in the speed of the boat.

2. Wind and waves usually affect the vessel at the same time and usually cause a loss in speed. Headwinds and waves create significant resistance to the movement of the vessel and worsen its controllability. The loss in speed in this case can be significant.

Winds and excitement of a passing direction reduce the speed of the vessel mainly due to a sharp deterioration in its controllability. Only with a weak tailwind and insignificant waves in some types of ships a slight increase in speed is observed.

3. Hull fouling is observed when vessels navigate in any conditions, both in fresh and salt water. Fouling occurs most intensively in warm seas. The consequence of fouling is an increase in the resistance of the water to the movement of the vessel, i.e. decrease in speed. In middle latitudes, after six months, the decrease in speed can reach 5-10%. The fight against fouling is carried out by systematic cleaning of the ship's hull and painting it with special non-
overgrown paints.

4. Shallow water. The effect of shallow water on a decrease in vessel speed
begins to affect at depths in the sailing area

H≤4Tcp + 3V 2 / g,

where N - depth, m.

Tcp, - average draft of the vessel, m;

V- vessel speed, m / s;

g- acceleration of gravity, m / s 2.

Thus, the dependence of the ship's speed on the rotational speed of the propellers determined for specific sailing conditions will be violated under the influence of the listed factors. In this case, the calculations of the distance traveled by the vessel, made according to formula (38), will contain significant errors.

In the practice of navigation, the speed of the vessel is sometimes calculated using the known relationship

V = S/ t,

where V- vessel speed relative to the ground, knots;

S - distance traveled with constant speed, miles; t - time, h.

Accounting for the speed and distance traveled by the vessel is carried out most accurately using a special device - a log.

To determine the speed of the vessel, measuring lines are equipped, for the areas of location of which the following requirements are imposed:

lack of influence of shallow water, which is ensured at a minimum depth determined from the ratio

N / T≥ 6,

where N- the depth of the area of ​​the measuring line, m; T- draft of the vessel, m;

protection from the prevailing winds and waves;

the absence of currents or the presence of weak constant currents coinciding with the directions of the runs;

the ability to freely maneuver ships.

Rice. 23. Measuring line

The equipment of the measuring line (Fig. 23), as a rule, consists of several parallel cross-sections and one leading, perpendicular to them. The distances between the cross sections are calculated with high precision. In most cases, the line of movement of vessels is indicated not by the leading line, but by buoys or landmarks placed along it.

Typically, measurements are taken at full load and in ballast for the main operating modes of the engines. During the period of measurements on the measuring line, the wind should not exceed 3 points, and the excitement - 2 points. The vessel should not be heel and the trim should be within optimal limits.

To determine the speed of the vessel, it is necessary to lie on the compass on a course perpendicular to the lines of the secant sections, and to develop a given speed of rotation of the propellers. The duration of the run is usually measured using the readings of three stopwatches. At the moment of crossing the first secant alignment, stopwatches are started and every minute the tachometer readings are noticed. The stopwatches stop when the second cross section is crossed.

Having calculated the average time of the duration of the run according to the readings of the stopwatches, the speed is determined by the formula

V = 3600S / t, (39)

where S is the length of the run between the cross sections, miles;

t- the average duration of the run between the cross sections, s; V- vessel speed relative to the ground, knots.

The rotational speed of the propellers is determined as the arithmetic mean of the tachometer readings during the run.

If there is no current in the area of ​​the measuring line, then the velocities relative to the ground and water are equal. In this case, just one run is enough. If there is a current constant in direction and speed in the area of ​​maneuvering, it is necessary to make two runs in opposite directions. The relative speed of the vessel V 0 and the frequency of rotation of the propellers P in this case will be determined by the formulas:

Vo = (V 1 + V 2) / 2, (40)

n = (n 1 + n 2) / 2, (41)

Rice. 24. The graph of the dependence of the speed on the frequency of rotation of the propellers

where V 1, V 2 - the speed of the vessel relative to the bottom on the first and second runs; n 1 and n 2 - the frequency of rotation of the propellers on the first and second runs.

When operating in the area of ​​the measuring line of a uniformly changing current, it is recommended to make a third run in the same direction as the first, and the speed, free from the influence of the current, is calculated nO approximate formula

V 0 = (V 1 + 2V 2 + V 3) / 4. (42)

If the nature of the change in the flow is unknown or they want to get a more accurate result, then four runs are made and the speed is calculated by the formula

V 0 = (V 1 + 3V 2 + 3V 3 + V 4) / 8. (43)

The average rotational speed of the propellers in these cases is calculated for three and four runs, respectively:

n = (n 1 + 2n 2 + n 3) / 4; (44)

n = (n 1 + 3n 2 + 3n 3 + n 4) / 8. (45)

Thus, the speed and frequency of rotation of the propellers are determined for several modes of operation of the main engines in cargo and in ballast. Based on the data obtained, graphs of the dependence of the speed on the rotational speed of the propellers are plotted for various loading of the vessel (Fig. 24).

Based on these graphs, a table is drawn up to match the speed of the propeller rotation frequency or the table to match the rotational speed of the propellers to the ship's speed.

If, according to the results of passing the measuring line, any speed and the corresponding rotational speed of the screws are known, then you can calculate the speed value for any intermediate value of the rotational speed of the screws using the Afanasyev formula

V И = V 0 (n 1 / n 0) 0, 9, (46)

where V 0 - known speed at the speed of rotation of the propeller n 0 ; V И, - the required speed for the speed of rotation of the propeller n 1 .

Thus, having determined the speed of your vessel according to the graph of its dependence on the rotational speed of the propellers, you can calculate the distance traveled in nautical miles using the formula

where V 0 - vessel speed, knots; t- swimming time, min.

If the distance traveled is known, then the swimming time is calculated: v

These formulas are used to compile the tables "Distance by time and speed" and "Time by distance and speed" in MT - 75 Appendices 2 and 3, respectively.

Calculations of the distance traveled using the speed determined from the rotational speed of the screws V o6 are performed only in the absence of a lag or to control its operation.

The speed of the vessel in the process of speed tests is found in various ways.

It is widespread to determine the speed of a vessel on special measuring lines equipped with coastal secant (transverse) sections, the distance between which is precisely known. On the gauge line, the speed of the vessel is determined by the time the vessel passes a known distance between the lines. This method is one of the most accurate ways to measure the speed of the vessel.

Known applications are also cable measuring lines, which are a kind of the above-mentioned measuring lines with transverse cross-sections. On a cable gauge line, the vessel passes over electrical cables laid at the bottom of the fairway across the direction of movement of the vessel. Electric current is passed through cables, the distance between which must be precisely known. Special electronic equipment installed on the ship records the moment the ship passes over the cable.

Recently, various radio navigation systems, in particular phase ones, have begun to be widely used to measure the speed of a ship.

The ship's speed, with relatively less accuracy, can also be measured using the ship's own radar station, which successively at short intervals measures the distance to any specific object that reflects radio waves well.

Measurement of the ship's speed using a fan of bearings of two objects or using other navigational methods, for example, using beacons, the distance between which is known, does not have sufficient accuracy.

All of the above and many other methods, including the main method for determining the speed of the vessel on the gauge line, have one common drawback, which is that the speed of the vessel is found relative to the shore, not the water. At the same time, the influence of wind or tidal currents, which is difficult to accurately assess, is superimposed on the measurements. Meanwhile, when conducting high-speed tests and for further using the data obtained, it is necessary to know the speed of the vessel relative to the surrounding water, i.e., in the absence of a current. Therefore, the conditions and place of testing are selected so that the influence of the flow is the least or is directed as far as possible along the measuring section. In these cases, the runs of the vessel in the measuring sections are carried out in mutually opposite directions and in a certain sequence.

Despite some difficulty in determining the speed of a ship on the gauge line or using radio navigation aids, one should always prefer to measure speed using standard ship and special logs or hydrometric propellers due to the low accuracy of the latter, although they measure the speed of the ship directly relative to the water.

For speed testing, gauge lines should be used that are close to the ship's construction or base, which will save time and fuel required to approach the gauge line. In addition, due to the fuel consumption when moving to a distant gauge line, it is difficult to provide a predetermined value of the displacement of the vessel.

The depth of water in the area of ​​the measuring line, that is, its measuring section and on the approach to it (from both sides), as well as in the area of ​​the vessel turning on the return course, should be sufficient to exclude the influence of shallow water on the resistance of water to the movement of the vessel , and consequently, on its speed.

It is known that the wave system created by a vessel when it is moving in shallow water differs from the wave system in deep water and depends on the regime characterized by the so-called Froude number in shallow water

Where σ is the speed of the vessel, m / s; g is the acceleration of free fall, m / s2; Н - fairway depth, m.

A change in the nature of wave formation leads to an increase or decrease in the resistance to the movement of the vessel and, therefore, affects its speed.

At the same time, a counter flow of water develops, increasing the speed of the flow around the hull and, consequently, the frictional resistance of the vessel. The complete elimination of the influence of shallow water requires large depths of the measuring line, which are not always possible to ensure (Table 1).

Table 1. Values ​​of the minimum depth of the measuring line, m

As a result, when determining the minimum required depths, they usually proceed from the loss of speed due to the influence of shallow water, which is 0.1% of the measured value. To comply with these conditions, the value of Frh≥0.5 should be taken for the wave resistance, and for the frictional resistance
It is on the basis of this approach that the test rules developed by the 12th International Conference of Experimental Pools recommend taking the minimum allowable depth on the measuring line greater than that calculated by the formulas
where B and T are the vessel's width and draft, respectively. A similar method is recommended by the domestic standard ОН-792-68, however, the formulas are written in the form
The measured line, if possible, should be located in an area protected from the prevailing winds and sea waves. Finally, a prerequisite is the presence of sufficient space at both ends of the measurement line, necessary for free maneuvering of the vessel at the end of the run on the measurement section, turn on the return course and accelerate after the turn.

The permissible deviations of the water depth at the approaches to the measuring section of the measuring line should not exceed ± 5%.

The ship's track on the gauge line must be at least two to three miles from coastal hazards. Failure to comply with this condition creates the threat that the vessel at high speeds, even in the case of correct maneuvering, may run aground if the rudder is jammed.

It is not always possible to satisfy all the requirements listed above, therefore the number of full-fledged measuring lines is very limited.

Table 2 shows some data characterizing the measured lines of a number of foreign countries. As can be seen from the table, the length of the measuring sections of these lines is different, and the depths of many of them are insufficient for testing relatively high-speed vessels.

In fig. 3 shows a diagram of the measuring line near Rockland (USA), on which a large number of high-speed tests of ships, including research ones. This line satisfies most of the above requirements, but it is not protected from westerly winds and the waves they cause. The measuring section is one nautical mile (1852 m) long, the length of each booster section is three nautical miles. The measuring line is equipped with two coastal transverse (secant) sections perpendicular to the measuring section. One of the cross sections is equipped with three signs (shields), the other - two.

Rice. 3. Diagram of the measuring line in Rockland (USA). Δ - leading sign.

In addition, milestones are placed along the run line for the navigator's orientation, indicating the boundaries of the accelerating and measuring sections.

Many measuring lines are equipped with so-called leading alignments, on the line of which the measuring section is located. Currently, the presence of a leading alignment is not considered mandatory, although there is still an opinion that it is necessary in cases where there is a current in the area of ​​the measuring line that does not coincide with the direction of the measuring line. However, this opinion is wrong: simple geometric constructions show that in this case, when steering the ship along the leading alignment, as well as on the compass, the ship travels a path longer than the distance between the alignment lines. That is why the requirement is put forward that the direction of the flow coincides with the direction of the measuring line or, in any case, makes an angle with it not exceeding 15-20 °.

Leading signs (Fig. 4) of the measuring lines are shields that are installed at such a height that they can be clearly seen from the sea. Usually, the front shield, that is, the shield located closer to the measuring section of the measuring line, is installed slightly lower than the rear one in such a way that at the moment the vessel passes the alignment, the shields overlap each other, making up almost one whole in the vertical direction. In the middle of the shields, vertical brightly colored stripes are applied, which should also be clearly visible from the sea.

Rice. 5. Linear sensitivity of sections.

1 - front alignment mark; 2 - rear alignment mark.

Nevertheless, an observer on a ship crossing the transverse sections of the measuring line at right angles practically cannot absolutely accurately determine the moment of passage of the alignment line, that is, the moment when the middle strips of the shields are on one vertical straight line, as if constituting a continuation of each friend.

The magnitude of the error in determining the moment of complete coverage of the middle strips of the alignment shields depends on the so-called linear sensitivity of the alignment (Fig. 5).

The resolving power of a normal eye is equal to one arc-minute. Let's draw on the line of the ship's run along the measured line (Fig. 5) segment A1A2, corresponding to one arc minute. In the interval A1A2, the angle between the two signs turns out to be less than one minute, and, therefore, any point in this interval can serve as a mark for the beginning of measuring the speed. The value ОА1 = ОА2 is called the linear sensitivity of the alignment and is denoted hereinafter by the letter W.

To find an expression for W, we use the relation
tanα = tan (β-γ). (1.2)
converted to form

After substituting the values ​​tan β and tan γ into expression (1.3) and simple transformations, we will have

The first term on the right-hand side of expression (1.4) can be neglected, since it will be of a higher order of smallness in comparison with the next two. Then equation (1.4) takes the form
dW = tan αDc (Dc + d), (1.5)
where

Replacing the tangent of the angle with the arc and the angle with the value of the eye's resolving power, as well as introducing the illumination factor of the alignment a "(for daylight α" = 2 and for night light α "= 3.5), we obtain the value of the linear sensitivity of the alignment (in meters)

Where
Dс - distance from the front sign of the secant alignment to the running gear of the measuring line, m; ao - the angle of the eye resolution; d - distance between leading signs, m.

Here are the values ​​of the sensitivity of cross sections of one of the foreign measurement lines:

If we take the sensitivity of a pair of sections equal to half the possible absolute error, then the relative error in the length of the measured section of the line (sections 2-3) will be equal to 0.4%.

As can be seen from formula (1.6), in order to reduce the error in determining the distance between sections and, consequently, to increase the sensitivity of sections, it is necessary that the ratio Dc: d be as small as possible. In practice, however, this ratio is usually not less than three.

To assess the effect of the error in timing, as well as the effect of the sensitivity of the crossings and the length of the run line on the speed measurement results, it is necessary to consider the dependence of the ship's speed on the track and time.
ν = s / t (1.9)
where v is the arithmetic mean of several speed measurements, m / s; s is the arithmetic mean value of the path, m; t is the arithmetic mean of the travel time, s.

As you know, the error in the result of indirect measurements (the speed is calculated according to the measured path and time) is the sum of the errors in the results of each direct measurement included in the indirect one. With indirect measurements, the relative error (root-mean-square, probable or marginal) of each direct measurement is found and the total relative error of the indirect measurement is calculated. So, in this case

where εν is the relative error in measuring the speed,.%; εs - relative error of path measurement; εt is the relative error in measuring the travel time.

Expressing relative errors in terms of probable ones, we get

or, after the substitution t = s / v.

Where ρs is the probable error in measuring the path, m; ρt is the probable error in measuring the travel time, s (according to ρt = 0.5 s). Probable path measurement error

if the sensitivity of both sections is taken to be the same and equal to the half-sum of their sensitivities, and the number of runs in the mode is equal to three.

Substituting these values ​​into formula (1.12) and transforming it, we obtain

Thus, the magnitude of the error will depend on three components: the sensitivity of the cross-sections, the length of the run along the measured line, and the speed of the vessel.

As an example, in table. 3 shows data on the accuracy of measuring the speed of the vessel on one of the measuring lines. Based on these data, it can be concluded that the measured speeds, regardless of the speed of the vessel, are determined with a high degree of accuracy. So, in the section of the measuring line between the second and third sections, the errors in measuring the speed are 0.35-0.40%. With an increase in the length of the measuring line (the section between the first and second sections is equal to one mile, between the second and third sections - two miles, and between the first and third - three miles), the error in measuring the speed decreases sharply.

However, this does not mean that it is more expedient to make runs on long measuring lines, since this increases the errors caused by the possible uneven operation of the main mechanisms over a large distance of the path and the influence of disturbing external influences leading to a deviation of the course from the straight line.

When assigning the length of the measuring section of the measuring line, it should also be borne in mind that during high-speed tests (in the absence of automatic equipment for recording instrument readings), it is sometimes necessary to measure the torque on the propeller shaft at least eight to ten times or to remove indicator diagrams once or twice, and also several times to measure the rotational speed of the propeller shafts and to determine some parameters of the power plant operation. All this takes at least four minutes. Thus, the minimum path length s on the measuring line, which is a function of the time required to perform these measurements and determine the speed of the vessel, can be calculated by the formula
s = 0.067νs (1.15)
where νs is the speed of the vessel, knots, s is the range of the vessel, miles.

A dimensional factor of 0.067 corresponds to approximately 4 minutes, which is the time required to take measurements.