The spherical radius Вс of a small circle with с¹с²с³ is called the theoretical range of the visible horizon.

The value of the spherical radius depends on the height of the observer's eye above sea level.

So, if the observer's eye is at point A1 at a height BA¹ = e¹ above sea level, then the spherical radius Bc" will be greater than the spherical radius Bc.

To determine the relationship between the height of the observer's eye and the theoretical range of its visible horizon, consider the right triangle AOc:

Ac² \u003d AO² - Os²; AO = OB + e; OB=R,

Then AO = R + e; Os = R.

Due to the insignificance of the height of the observer's eye above sea level in comparison with the dimensions of the Earth's radius, the length of the tangent Ac can be taken equal to the value of the spherical radius Bc and, denoting the theoretical range of the visible horizon through D T, we obtain

D 2T = (R + e)² - R² = R² + 2Re + e² - R² = 2Re + e²,

Rice. eight

In this case, the beam from point A to c does not go along the straight line Ac, but along the curve ASm "(see Fig. 8). Therefore, to the observer, the point c appears to be visible in the direction of the tangent AT, i.e., raised by an angle r \u003d L TAc , called the angle of the earth's refraction. The angle d \u003d L HAT is called the inclination of the visible horizon. And in fact, the visible horizon will be a small circle m", m "2, mz", with a slightly larger spherical radius (Bm "\u003e Bc).

The value of the earth's refraction angle is not constant and depends on the refractive properties of the atmosphere, which change with temperature and humidity, the amount of suspended particles in the air. Depending on the time of year and the date of the day, it also changes, so the actual range of the visible horizon compared to the theoretical one can increase up to 15%.

In navigation, an increase in the actual range of the visible horizon compared to the theoretical one is taken by 8%.

Therefore, denoting the actual, or, as it is also called, geographical, range of the visible horizon through D e , we get:

If the actual height of the eye does not match the numerical values ​​indicated in the table, then the range of the visible horizon can be determined by linear interpolation between two values ​​close to the actual height of the eye.

Range of visibility of objects and lights

To facilitate the determination of the visibility range of objects, use the table. 22-c (MT-63), calculated by formula (5a): To determine from this table from what distance an object will open, it is necessary to know the height of the observer's eye above the water level and the height of the object in meters.

The visibility range of an object can also be determined by a special nomogram (Fig. 10). For example, the height of the eye above the water level is 5.5 m, and the height h of the sign is 6.5 m, in order to determine D n, a ruler is applied to the nomogram so that it connects the points corresponding to h and e on the extreme scales. The point of intersection of the ruler with the middle scale of the nomogram will show the desired visibility range of the object D n (in Fig. 10 D n = 10.2 miles).

In navigation manuals - on maps, in sailing directions, in descriptions of lights and signs - the visibility range of objects DK is indicated at an observer's eye height of 5 m (on English maps - 15 feet).

In the case when the actual height of the observer's eye is different, it is necessary to introduce the correction AD (see Fig. 9).

Rice. nine

Therefore, the lights have their own "optical" range of visibility, which may be greater or less than the range of visibility of the horizon from the height of the fire.

Navigation manuals indicate the actual (mathematical) range of visibility of lights, but if it is greater than the optical one, then the latter is indicated.

The visibility range of coastal signs of the navigation situation depends not only on the state of the atmosphere, but also on many other factors, which include:

A) topographic (determined by the nature of the surrounding area, in particular, the predominance of a particular color in the surrounding landscape);

B) photometric (brightness and color of the observed sign and the background on which it is projected);

C) geometric (distance to the sign, its size and shape).

Synonyms: firmament, outlook, sky, skyscraper, sunset of the sky, eyes, eyes, veil, close, mischief, see, look around.

Distance to visible horizon

• If visible horizon define as the boundary between heaven and earth, then calculate geometric range the visible horizon is possible using the Pythagorean theorem:

Visibility range

In the figure on the right, the visibility range of an object is determined by the formula

$D\_\backslash mathrm(BL)\; =\; 3.57\backslash ,(\backslash sqrt(h\_\backslash mathrm(B))\; +\; \backslash sqrt(h\_\backslash mathrm(L)))$,

where $D\_\backslash mathrm(BL)$- visibility range in kilometers,
$h\_\backslash mathrm(B)$ and $h\_\backslash mathrm(L)$- the height of the observation point and the object in meters.

For an approximate calculation of the visibility range of objects, the Struisky nomogram is used (see illustration): on the two extreme scales of the nomogram, points are marked corresponding to the height of the observation point and the height of the object, then a straight line is drawn through them and at the intersection of this straight line with the average scale, the object visibility range is obtained.

On nautical charts, in sailing directions and other navigational aids, the visibility range of beacons and lights is indicated for an observation point height of 5 m. If the height of the observation point is different, then a correction is introduced.

Horizon on the Moon

It must be said that the distances on the moon are very deceptive. Due to the absence of air, distant objects are seen more clearly on the Moon and therefore always appear closer.

artificial horizon- an instrument used to determine the true horizon.

For example, it is easy to determine the true horizon if you bring a glass of water to your eyes so that the water level is visible as a straight line.

Horizon in philosophy

The concept of the horizon is introduced into philosophy by Edmund Husserl, and Gadamer defines it as follows: "The horizon is the field of view, embracing and embracing everything that can be seen from any point"

see also

Write a review on the article "Horizon"

Notes

1. .
2. The article "Horizon" in the Great Soviet Encyclopedia
3. Ermolaev G. G., Andronov L. P., Zoteev E. S., Kirin Yu. P., Cherniev L. F. Maritime navigation / under the general editorship of the sea captain G. G. Ermolaev. - 3rd edition, revised. - M .: Transport, 1970. - 568 p.
4. . Interpretations of the expression "visible horizon". .
5. . Horizon. Space and astronomy. .
6. Dal V.I. Explanatory dictionary of the living Great Russian language. - M .: OLMA Media Group, 2011. - 576 p. - ISBN 978-5-373-03764-8.
7. Veryuzhsky N. A. Nautical astronomy: Theoretical course. - M .: RConsult, 2006. - 164 p. - ISBN 5-94976-802-7.
8. Perelman Ya. I. Horizon // Interesting geometry. - M .: Rimis, 2010. - 320 p. - ISBN 978-5-9650-0059-3.
9. Calculated using the formula "distance = 113 roots of height", thus, the influence of the atmosphere on the propagation of light is not taken into account and it is assumed that the Earth is spherical.
10. Nautical tables (MT-2000). Adm. No. 9011 / editor-in-chief K. A. Yemets. - St. Petersburg: GUN i O, 2002. - 576 p.
11. . Calculation of the distance to the horizon and line of sight online. .
12. . What is the next horizon?. .
13. Lukash V. N., Mikheeva E. V. Physical cosmology. - M .: Physical and mathematical literature, 2010. - 404 p. - ISBN 5922111614.
14. Klimushkin D. Yu.; Grablevsky S.V. . space horizon (2001). .
15. . Chapter VII. Navigation.
16. . Apparent horizon and visibility range. .
17. . Have Americans been to the moon?. .
18. . Interpretations of the expression "true horizon". .
19. Zaparenko Victor. Great encyclopedia of drawing Viktor Zaparenko. - M .: AST, 2007. - 240 p. - ISBN 978-5-17-041243-3.
20. Truth and Method. P.358

Literature

• Vitkovsky V.V.// Encyclopedic Dictionary of Brockhaus and Efron: in 86 volumes (82 volumes and 4 additional). - St. Petersburg. , 1890-1907.
• Horizon // Great Soviet Encyclopedia: [in 30 volumes] / ch. ed. A. M. Prokhorov. - 3rd ed. - M. : Soviet encyclopedia, 1969-1978.

An excerpt characterizing the Horizon

- What's wrong with you, Masha?
“Nothing ... I felt so sad ... sad about Andrei,” she said, wiping her tears on her daughter-in-law's knees. Several times, during the morning, Princess Marya began to prepare her daughter-in-law, and each time she began to cry. These tears, for which the little princess did not understand the reason, alarmed her, no matter how observant she was. She didn't say anything, but looked around uneasily, looking for something. Before dinner, the old prince, whom she had always feared, entered her room, now with a particularly restless, angry face, and, without saying a word, went out. She looked at Princess Marya, then thought with that expression of eyes of inward-turning attention that pregnant women have, and suddenly burst into tears.
Did you get anything from Andrew? - she said.
- No, you know that the news could not come yet, but mon pere is worried, and I'm scared.
- Oh nothing?
“Nothing,” said Princess Marya, looking firmly at her daughter-in-law with radiant eyes. She decided not to tell her and persuaded her father to hide the terrible news from her daughter-in-law until her permission, which was supposed to be the other day. Princess Marya and the old prince, each in his own way, carried and hid their grief. The old prince did not want to hope: he decided that Prince Andrei had been killed, and despite the fact that he sent an official to Austria to look for his son's trace, he ordered a monument to him in Moscow, which he intended to erect in his garden, and told everyone that his son is killed. He tried not to change his former way of life, but his strength betrayed him: he walked less, ate less, slept less, and became weaker every day. Princess Mary hoped. She prayed for her brother as if she were alive, and waited every minute for news of his return.

- Ma bonne amie, [My good friend,] - said the little princess on the morning of March 19 after breakfast, and her sponge with a mustache rose from the old habit; but as in all not only smiles, but the sounds of speeches, even gaits in this house, from the day the terrible news was received, there was sadness, even now the smile of the little princess, who succumbed to the general mood, although she did not know its cause, was such that she even more reminiscent of the general sadness.
- Ma bonne amie, je crains que le fruschtique (comme dit Foka - cook) de ce matin ne m "aie pas fait du mal. [My friend, I'm afraid that the current frischtik (as Chef Foka calls it) would not make me feel bad. ]
What about you, my soul? You are pale. Oh, you are very pale, said Princess Marya in fright, running up to her daughter-in-law with her heavy, soft steps.
“Your Excellency, why not send for Marya Bogdanovna?” - said one of the maids who were here. (Marya Bogdanovna was a midwife from a district town, who had been living in Lysy Gory for another week.)
“And indeed,” Princess Marya picked up, “perhaps, for sure. I will go. Courage, mon ange! [Don't be afraid, my angel.] She kissed Lisa and wanted to leave the room.
- Oh, no, no! - And besides pallor, the face of the little princess expressed a childish fear of inevitable physical suffering.
- Non, c "est l" estomac ... dites que c "est l" estomac, dites, Marie, dites ..., [No, this is the stomach ... tell me, Masha, that this is the stomach ...] - and the princess began to cry childishly, suffering, capriciously and even somewhat feignedly, breaking their little arms. The princess ran out of the room after Marya Bogdanovna.
— Mon Dieu! Mon Dieu! [My God! My God!] Oh! she heard behind her.
Rubbing her full, small, white hands, the midwife was already walking towards her, with a considerably calm face.
- Maria Bogdanovna! It seems to have begun, ”said Princess Marya, looking at her grandmother with frightened open eyes.
“Well, thank God, princess,” said Marya Bogdanovna without adding a step. You girls don't need to know about this.
“But why hasn’t the doctor arrived from Moscow yet?” - said the princess. (At the request of Lisa and Prince Andrei, they were sent to Moscow for an obstetrician by the deadline, and they were waiting for him every minute.)
“It’s okay, princess, don’t worry,” said Marya Bogdanovna, “and without a doctor everything will be fine.”
Five minutes later the princess heard from her room that something heavy was being carried. She looked out - for some reason the waiters were carrying into the bedroom a leather sofa that stood in Prince Andrei's office. There was something solemn and quiet on the faces of the carrying people.
Princess Marya sat alone in her room, listening to the sounds of the house, occasionally opening the door when they passed by, and looking closely at what was going on in the corridor. Several women walked to and fro with quiet steps, looked back at the princess and turned away from her. She did not dare to ask, shut the door, returned to her room, and either sat down in her chair, or took up her prayer book, or knelt before the kiot. To her misfortune and surprise, she felt that prayer did not calm her excitement. Suddenly the door of her room quietly opened and on the threshold appeared her old nurse, Praskovya Savishna, tied with a handkerchief, who almost never, due to the prince's prohibition, did not enter her room.
“I came to sit with you, Mashenka,” said the nanny, “yes, she brought the prince’s wedding candles in front of the saint to light, my angel,” she said with a sigh.
“Oh, how glad I am, nanny.
“God is merciful, dove. - Nanny lit candles entwined with gold in front of the icon-case and sat down at the door with a stocking. Princess Mary took the book and began to read. Only when footsteps or voices were heard did the princess look frightened, inquiringly, and the nanny looked at each other reassuringly. At all ends of the house, the same feeling that Princess Mary experienced while sitting in her room was overflowing and possessed everyone. According to the belief that the fewer people know about the sufferings of the puerperal, the less she suffers, everyone tried to pretend to be ignorant; no one talked about it, but in all people, except for the usual degree and respectfulness of good manners that reigned in the prince's house, there was one kind of general concern, softened heart and consciousness of something great, incomprehensible, happening at that moment.
There was no laughter in the big girls' room. In the waiter's room, all the people sat in silence, ready for something. On the courtyard they burned torches and candles and did not sleep. The old prince, stepping on his heel, walked around the study and sent Tikhon to Marya Bogdanovna to ask: what? - Just tell me: the prince ordered to ask what? and come and tell me what she will say.
“Report to the prince that the birth has begun,” said Marya Bogdanovna, looking significantly at the messenger. Tikhon went and reported to the prince.
“Very well,” said the prince, shutting the door behind him, and Tikhon no longer heard the slightest sound in the study. A little later, Tikhon entered the office, as if to fix the candles. Seeing that the prince was lying on the sofa, Tikhon looked at the prince, at his upset face, shook his head, silently approached him and, kissing him on the shoulder, went out without adjusting the candles and without saying why he had come. The most solemn sacrament in the world continued to be performed. The evening passed, the night came. And the feeling of expectation and softening of the heart before the incomprehensible did not fall, but rose. Nobody slept.

It was one of those March nights when winter seems to want to take its toll and pour out its last snows and snowstorms with desperate anger. To meet the German doctor from Moscow, who was expected every minute and for whom a set-up was sent to the main road, to the turn into a country road, horsemen with lanterns were sent to lead him along the potholes and gaps.
Princess Mary had long since left the book: she sat in silence, fixing her radiant eyes on the wrinkled, familiar to the smallest detail, face of the nanny: at the lock of gray hair that had come out from under the scarf, at the hanging bag of skin under the chin.
Nanny Savishna, with a stocking in her hands, in a low voice, without hearing and not understanding her own words, told hundreds of times about how the deceased princess in Chisinau gave birth to Princess Marya, with a Moldavian peasant woman, instead of a grandmother.
“God have mercy, you never need a doctor,” she said. Suddenly a gust of wind blew on one of the exposed frames of the room (by the prince’s will, one frame was always set up with larks in each room) and, having beaten off the poorly pushed bolt, ruffled the damask curtain, and smelling of cold, snow, blew out the candle. Princess Mary shuddered; the nanny, putting down her stocking, went up to the window, and leaning out began to catch the open frame. A cold wind ruffled the ends of her handkerchief and gray, stray strands of hair.
- Princess, mother, someone is driving along the prefecture! she said, holding the frame and not closing it. - With lanterns, it must be, dokhtur ...
- Oh my god! Thank God! - said Princess Mary, - we must go to meet him: he does not know Russian.
Princess Marya threw on her shawl and ran to meet the travelers. When she passed the front hall, she saw through the window that some kind of carriage and lamps were standing at the entrance. She went out onto the stairs. A tallow candle stood on the railing post and flowed from the wind. The waiter Philip, with a frightened face and with another candle in his hand, was standing below, on the first landing of the stairs. Even lower, around the bend, on the stairs, steps could be heard moving in warm boots. And some kind of familiar voice, as it seemed to Princess Mary, was saying something.
- Thank God! said the voice. - And the father?
“Go to sleep,” answered the voice of the butler Demyan, who was already downstairs.
Then a voice said something else, Demyan answered something, and steps in warm boots began to approach faster along an invisible turn of the stairs. "This is Andrey! thought Princess Mary. No, it can’t be, it would be too unusual, ”she thought, and at the same moment as she thought this, on the platform on which the waiter was standing with a candle, the face and figure of Prince Andrei in a fur coat with a collar sprinkled with snow. Yes, it was him, but pale and thin, and with a changed, strangely softened, but anxious expression on his face. He entered the stairs and hugged his sister.
- You didn't get my letter? he asked, and without waiting for an answer, which he would not have received, because the princess could not speak, he returned, and with the obstetrician, who came in after him (he had gathered with him at the last station), with quick steps again entered the ladder and hugged his sister again. - What a fate! - he said, - Masha is dear - and, throwing off his fur coat and boots, he went to the half of the princess.

The little princess was lying on pillows, in a white cap. (Suffering had just let go of her.) Black hair curled in strands around her inflamed, sweaty cheeks; her ruddy, lovely mouth, with a sponge covered with black hairs, was open, and she smiled joyfully. Prince Andrei entered the room and stopped in front of her, at the foot of the sofa on which she was lying. Brilliant eyes, looking childish, frightened and agitated, rested on him without changing their expression. “I love you all, I didn’t harm anyone, why am I suffering? help me,” her expression said. She saw her husband, but did not understand the meaning of his appearance now before her. Prince Andrei walked around the sofa and kissed her on the forehead.
“My dear,” he said, a word he had never spoken to her. - God is merciful. She looked inquiringly, childishly reproachfully at him.
- I expected help from you, and nothing, nothing, and you too! her eyes said. She was not surprised that he came; she did not understand that he had come. His arrival had nothing to do with her suffering and its relief. The torment began again, and Marya Bogdanovna advised Prince Andrei to leave the room.
The obstetrician entered the room. Prince Andrei went out and, meeting Princess Marya, again approached her. They started talking in a whisper, but every minute the conversation fell silent. They waited and listened.
- Allez, mon ami, [Go, my friend,] - said Princess Mary. Prince Andrei again went to his wife, and sat down in the next room waiting. Some woman came out of her room with a frightened face and was embarrassed when she saw Prince Andrei. He covered his face with his hands and sat there for several minutes. Pathetic, helpless animal moans were heard from behind the door. Prince Andrei got up, went to the door and wanted to open it. Someone held the door.
- You can't, you can't! said a frightened voice from there. He began to walk around the room. The screams ceased, a few more seconds passed. Suddenly a terrible scream - not her scream, she could not scream like that - was heard in the next room. Prince Andrei ran to the door; the cry ceased, the cry of a child was heard.
“Why did they bring a child there? Prince Andrei thought at first. Child? What? ... Why is there a child? Or was it a baby? When he suddenly understood all the joyous meaning of this cry, tears choked him, and, leaning on the windowsill with both hands, he sobbed, sobbing, as children cry. The door opened. The doctor, with his shirt sleeves rolled up, without his coat, pale and with a trembling jaw, left the room. Prince Andrei turned to him, but the doctor looked at him in bewilderment and, without saying a word, passed by. The woman ran out and, seeing Prince Andrei, hesitated on the threshold. He entered his wife's room. She lay dead in the same position in which he had seen her five minutes earlier, and the same expression, despite the fixed eyes and the pallor of her cheeks, was on that lovely, childish face with a sponge covered with black hairs.
“I love you all and have done no harm to anyone, and what have you done to me?” her lovely, pitiful, dead face spoke. In the corner of the room, something small and red grunted and squeaked in Marya Bogdanovna's white, trembling hands.

Two hours later, Prince Andrei with quiet steps entered his father's office. The old man already knew everything. He stood at the very door, and as soon as it opened, the old man silently, with senile, hard hands, like a vise, clasped his son's neck and sobbed like a child.

Three days later, the little princess was buried, and, saying goodbye to her, Prince Andrei ascended the steps of the coffin. And in the coffin was the same face, although with closed eyes. "Oh, what have you done to me?" everything said it, and Prince Andrei felt that something had come off in his soul, that he was guilty of guilt, which he could not correct and not forget. He couldn't cry. The old man also entered and kissed her wax pen, which lay high and calm on the other, and her face said to him: “Ah, what and why did you do this to me?” And the old man turned away angrily when he saw that face.

Five days later, the young Prince Nikolai Andreevich was baptized. Mammy held the diapers with her chin, while the priest smeared the boy's wrinkled red palms and steps with a goose feather.
The godfather, the grandfather, fearing to drop, shuddering, carried the baby around a crumpled tin font and handed it over to the godmother, Princess Marya. Prince Andrei, trembling with fear lest the child be drowned, sat in another room, waiting for the end of the sacrament. He joyfully looked at the child when his nanny carried him out, and nodded his head approvingly when the nanny informed him that the wax with hairs thrown into the font did not sink, but floated along the font.

Rostov's participation in the duel between Dolokhov and Bezukhov was hushed up through the efforts of the old count, and Rostov, instead of being demoted, as he expected, was appointed adjutant to the Moscow governor general. As a result, he could not go to the village with the whole family, but remained at his new position all summer in Moscow. Dolokhov recovered, and Rostov became especially friendly with him at this time of his recovery. Dolokhov lay ill with his mother, who passionately and tenderly loved him. Old Marya Ivanovna, who fell in love with Rostov for his friendship with Fedya, often spoke to him about her son.

Horizon visibility range

The line observed in the sea, along which the sea, as it were, connects with the sky, is called visible horizon of the observer.

If the observer's eye is at a height eat above sea level (ie. BUT rice. 2.13), then the line of sight going tangentially to the earth's surface defines a small circle on the earth's surface aa, radius D.

Rice. 2.13. Horizon visibility range

This would be true if the Earth were not surrounded by an atmosphere.

If we take the Earth as a ball and exclude the influence of the atmosphere, then from a right-angled triangle OAa follows: OA=R+e

Since the value is extremely small ( for e = 50m at R = 6371km – 0,000004 ), then we finally have:

Under the influence of the earth's refraction, as a result of the refraction of the visual beam in the atmosphere, the observer sees the horizon further (in a circle centuries).

(2.7)

where X- coefficient of terrestrial refraction (» 0.16).

If we take the range of the visible horizon D e in miles, and the height of the observer's eye above sea level ( eat) in meters and substitute the value of the Earth's radius ( R=3437,7 miles = 6371 km), then we finally obtain a formula for calculating the range of the visible horizon

(2.8)

For example: 1) e = 4 m D e = 4,16 miles; 2) e = 9 m D e = 6,24 miles;

3) e = 16 m D e = 8,32 miles; 4) e = 25 m D e = 10,4 miles.

According to formula (2.8), table No. 22 "MT-75" (p. 248) and table No. 2.1 "MT-2000" (p. 255) according to ( eat) from 0.25 m¸5100 m. (see table 2.2)

Range of visibility of landmarks at sea

If an observer whose eye height is at a height eat above sea level (ie. BUT rice. 2.14), observes the horizon line (i.e. AT) on distance D e(miles), then, by analogy, and from a landmark (i.e., B), whose height above sea level hM, visible horizon (ie. AT) is observed at a distance Dh(miles).

Rice. 2.14. Range of visibility of landmarks at sea

From fig. 2.14 it is obvious that the range of visibility of an object (landmark) having a height above sea level hM, from the height of the observer's eye above sea level eat will be expressed by the formula:

Formula (2.9) is solved using table 22 "MT-75" p. 248 or Table 2.3 "MT-2000" (p. 256).

For example: e= 4 m, h= 30 m, D P = ?

Decision: for e= 4 m® D e= 4.2 miles;

for h= 30 m® D h= 11.4 miles.

D P= D e + D h= 4,2 + 11,4 = 15.6 miles.

Rice. 2.15. Nomogram 2.4. "MT-2000"

Formula (2.9) can also be solved using Apps 6 to "MT-75" or nomograms 2.4 "MT-2000" (p. 257) ® fig. 2.15.

For example: e= 8 m, h= 30 m, D P = ?

Decision: Values e= 8 m (right scale) and h\u003d 30 m (left scale) we connect with a straight line. The point of intersection of this line with the average scale ( D P) and gives us the desired value 17.3 miles. ( see table. 2.3 ).

Geographic range of visibility of objects (from Table 2.3. "MT-2000")

Note:

The height of the navigational landmark above sea level is selected from the navigational manual for navigation "Lights and Signs" ("Lights").

2.6.3. Range of visibility of the landmark light shown on the map (Fig. 2.16)

Rice. 2.16. Beacon light visibility ranges shown

On nautical nautical charts and in navigation aids, the range of visibility of the landmark light is given for the height of the observer's eye above sea level. e= 5 m, i.e.:

If the actual height of the observer's eye above sea level differs from 5 m, then to determine the visibility range of the landmark fire, it is necessary to add to the range shown on the map (in the manual) (if e> 5 m), or subtract (if e < 5 м) поправку к дальности видимости огня ориентира (DD K) shown on the map for the height of the eye.

(2.11)

(2.12)

For example: D K= 20 miles, e= 9 m.

D O = 20,0+1,54=21,54miles

then: DO = D K + ∆ D To = 20.0+1.54 =21.54 miles

Answer: D O= 21.54 miles.

Tasks for calculating visibility ranges

A) the visible horizon ( D e) and landmark ( D P)

B) Lighthouse opening fire

findings

1. The main ones for the observer are:

a) planes:

The plane of the true horizon of the observer (pl. IGN);

The plane of the true meridian of the observer (pl. IMN);

The plane of the first vertical of the observer;

b) lines:

The plumb line (normal) of the observer,

Line of the true meridian of the observer ® noon line N-S;

Line E-W.

2. Direction counting systems are:

Circular (0°¸360°);

Semicircular (0°¸180°);

Quarter (0°¸90°).

3. Any direction on the surface of the Earth can be measured by an angle in the plane of the true horizon, taking the line of the true meridian of the observer as the origin.

4. True directions (IR, PI) are determined on the vessel relative to the northern part of the true meridian of the observer, and KU (heading angle) - relative to the bow of the longitudinal axis of the vessel.

5. Range of the visible horizon of the observer ( D e) is calculated by the formula:

.

6. The visibility range of a navigational landmark (daytime in good visibility) is calculated by the formula:

7. Range of visibility of the fire of a navigational landmark, according to its range ( D K) shown on the map is calculated by the formula:

, where .

In conditions of ideal visibility, that is, standing in an open area, an absolutely flat plain, without grass and trees, in the absence of fog and other atmospheric phenomena, a person of average height sees the horizon at a distance of about 4-5 kilometers. If you rise higher, then the horizon line will move away, if, on the contrary, go down to the lowland, then the horizon will become much closer. there is a special formula that allows you to calculate the distance to the horizon, but I don’t think it’s worth doing, because in each case it will be different. The shortest distance to the horizon will be in the city - usually to the wall of the nearest house.

In fact, how subjective the horizon is from us depends on what kind of landscape, mountains, desert, or even water, as well as conditions like precipitation, fog, and so on. But nevertheless, there is a formula that is designed to calculate the distance to the horizon. However, the formula works correctly only in conditions of a completely flat, for example, water surface.

Formula for calculating the distance to the horizon:

S = (R+h)2 - R21/2

In this formula:

letter S the height of the observer's eyes in meters

letter R the radius of the Earth is indicated, usually it is: 6367250 m

letter h denotes the height of the observer's eyes above the surface in meters

Using this formula, you can get a similar table.

The visible horizon is often called the line along which the sky is seen bordering on the surface of the Earth. Also called the visible horizon and the celestial space above this boundary, and the surface of the Earth visible to man, and still the space visible to man, to its final limits.

The distance to the visible horizon is calculated depending on the height of the observer above the earth's surface, and the radius of the earth is also taken into account in the calculation. The table shows the results of the calculations.



There is even a special formula for calculating the distance to the horizon. And approximately we can say that if a person has an average height, then the horizon line from him is at a distance of approximately 5 kilometers. The higher you go, the farther the horizon line will be. So, for example, if you climb a lighthouse 20 meters high, you can observe the water surface at a distance of 17 kilometers. But on the Moon, a person of average height will be at a distance of 3.3 kilometers from the horizon line, and on Saturn already at 14.4 kilometers.

The apparent distance to the horizon line depends on the terrain, but if we keep in mind that no objects block the horizon, for example, in the steppe or at sea, then objects are visible at 5 kilometers. This is if you look from the height of the growth of the average person.

If a sailor climbs an eight-meter mast, he will be able to look at objects at a distance of 10 kilometers.

From the television tower in Ostankino, the horizon will expand to 80 km, it is at this distance that there is a stable prim radio signal.

From a plane flying at an altitude of 10 kilometers, a distance of 350 kilometers can already be seen, and astronauts from a space station in orbit can see up to 2 thousand kilometers.

The horizon is visible and true, so the distance will be different if you put people on different points.

If a person looks in a standing position, then approximately the distance is 5 km.

If you climb a mountain 8 km high, then the distance to the horizon will be about 10 km.

At an altitude of 10 thousand meters, the distance increases to 350 km.

That is, everyone has a different distance to the horizon they see.

On a flat area (water surface) about 6 km. The higher the viewpoint, the farther the horizon.

If you mean the line of the visible horizon, then the distance to does not depend on the height of the observer's eyes. From the navigation bridge of the ship on which I had to serve, the horizon line was at a distance of 5 miles (1852 x 5 meters). Through the navigational periscope raised on the surface, the distance to the horizon line was already 11 miles ...

Nothing at all. An hour of walking. It is very interesting to sit on the horizon, dangling legs and dangling them. You can, of course, climb the rainbow, only for this you need a ladder. And the horizon is right there. And you don't have to take anything with you.

The visible horizon line also depends on the conditions of observation (weather, atmospheric phenomena, etc.). So, from the same point of view (for me, for example, an embankment on the high bank of the Volga), depending on visibility, a certain horizon is visible in the direction of water meadows, sometimes for 8-9, sometimes more than 30 kilometers.

The distance to the horizon depends on many parameters. For example, from your vision. And even more important is the height at which you are. So, from Everest, the horizon will be visible at a distance of 336 kilometers. But from the lowland it can be seen even after 5 kilometers.

Rice. 4 Basic lines and planes of the observer

For orientation in the sea, a system of conditional lines and planes of the observer is adopted. On fig. 4 shows the globe, on the surface of which at the point M the observer is located. His eye is at the point BUT. letter e the height of the observer's eye above sea level. The line ZMn drawn through the place of the observer and the center of the globe is called a plumb or vertical line. All planes passing through this line are called vertical, and perpendicular to it - horizontal. The horizontal plane HH / passing through the observer's eye is called true horizon plane. The vertical plane VV / passing through the place of the observer M and the earth's axis is called the plane of the true meridian. At the intersection of this plane with the Earth's surface, a large circle РnQPsQ / is formed, called the true meridian of the observer. The straight line obtained from the intersection of the plane of the true horizon with the plane of the true meridian is called true meridian line or midday line N-S. This line defines the direction to the north and south points of the horizon. The vertical plane FF / perpendicular to the plane of the true meridian is called the plane of the first vertical. At the intersection with the plane of the true horizon, it forms the line E-W, perpendicular to the line N-S and defining the directions to the eastern and western points of the horizon. Lines N-S and E-W divide the plane of the true horizon into quarters: NE, SE, SW and NW.

Fig.5. Horizon visibility range

In the open sea, the observer sees a water surface around the ship, bounded by a small circle CC1 (Fig. 5). This circle is called the visible horizon. The distance De from the position of the vessel M to the line of the visible horizon CC 1 is called visible horizon. The theoretical range of the visible horizon Dt (segment AB) is always less than its actual range De. This is explained by the fact that, due to the different density of the layers of the atmosphere along the height, the beam of light does not propagate in it in a straight line, but along the AC curve. As a result, the observer can additionally see some part of the water surface located behind the line of the theoretical visible horizon and limited by a small circle SS 1 . This circle is the line of the visible horizon of the observer. The phenomenon of refraction of light rays in the atmosphere is called terrestrial refraction. Refraction depends on atmospheric pressure, temperature and humidity. In the same place on the Earth, refraction can change even during one day. Therefore, in the calculations, the average value of refraction is taken. Formula for determining the range of the visible horizon:

As a result of refraction, the observer sees the horizon line in the direction AC / (Fig. 5), tangent to the AC arc. This line is raised at an angle r above the direct line AB. Injection r also called terrestrial refraction. Injection d between the plane of the true horizon HH / and the direction to the visible horizon is called apparent horizon inclination.

RANGE OF VISIBILITY OF OBJECTS AND LIGHTS. The range of the visible horizon allows you to judge the visibility of objects located at the water level. If an object has a certain height h above sea level, then the observer can detect it at a distance:

On nautical charts and in navigational aids, a pre-calculated range of visibility of lighthouse lights is given. Dk from the observer's eye height of 5 m. From this height De equals 4.7 miles. At e other than 5 m should be corrected. Its value is:

Then the visibility range of the beacon Dn is equal to:

The range of visibility of objects, calculated according to this formula, is called geometric, or geographical. The calculated results correspond to some average state of the atmosphere in the daytime. In fog, rain, snowfall or foggy weather, the visibility of objects naturally decreases. On the contrary, under a certain state of the atmosphere, the refraction can be very large, as a result of which the visibility range of objects turns out to be much greater than the calculated one.

Visible horizon distance. Table 22 MT-75:

The table is calculated by the formula:

De = 2.0809 ,

Entering the table 22 MT-75 with item height h above sea level, get the visibility range of this object from sea level. If we add to the obtained range the range of the visible horizon found in the same table according to the height of the observer's eye e above sea level, then the sum of these distances will be the visibility range of the object, without taking into account the transparency of the atmosphere.

To get the range of the radar horizon Dr. accepted selected from the table. 22 increase the range of the visible horizon by 15%, then Dp=2.3930 . This formula is valid for standard atmospheric conditions: pressure 760 mm, temperature +15°C, temperature gradient - 0.0065 degrees per meter, relative humidity, constant with altitude, 60%. Any deviation from the accepted standard state of the atmosphere will cause a partial change in the range of the radar horizon. In addition, this range, i.e. the distance from which reflected signals can be seen on the radar screen, depends to a large extent on the individual characteristics of the radar and the reflective properties of the object. For these reasons, use the coefficient 1.15 and the data in Table. 22 should be followed with caution.

The sum of the ranges of the radar horizon of the antenna Ld and the observed object of height A will be the maximum distance from which the reflected signal can return.

Example 1 Determine the detection range of the beacon with height h=42 m from sea level from the height of the observer's eye e=15.5 m.
Decision. From Table. 22 choose:
for h = 42 m..... . Dh= 13.5 miles;
for e= 15.5 m. . . . . . De= 8.2 miles,
hence the beacon detection range
Dp \u003d Dh + De \u003d 21.7 miles.

The visibility range of an object can also be determined by the nomogram placed on the insert (Appendix 6). MT-75

Example 2 Find the radar range of an object with height h=122 m, if the effective height of the radar antenna Hd = 18.3 m above sea level.
Decision. From Table. 22 select the visibility ranges of the object and the antenna from sea level, respectively, 23.0 and 8.9 miles. Summing up these ranges and multiplying them by a factor of 1.15, we get that an object under standard atmospheric conditions is likely to be detected from a distance of 36.7 miles.