Триангуляция

Московский колледж геодезии и картографии

Работу выполнил Комосов Д.Ю.

Студент группы АГС – 41.

1.Исходные данные……………………………………………………………… 3

2.Решение треугольников……………………………………………… 5

3.Вычисление сферических избытков…………………… 5

4.Вычисление поправок за центрировку и

редукцию……………………………………………………………………………………… 6

5.Список сферических треугольников………………… 7

6.Оценка точности измерений в сети………………… 7

7.Вычисление приближенных координат……………… 8

8.Вычислене поправок за редуцирование………… 9

Круглово

Севастьяново Прокатная

Каменка

Речица

Горнечки Лазорки

Вариант I.

| | |Х |У | |

|1 |Каменка |6 239 843 |5 376 563 |18 675 м. |

|2 |Лазорки |6 224 833 |5 387 671 | |

|Каменка |Речица |0о 00’ 00.00” |0о 00’ 00.00” |

|Lc = 0.021 m |Лазорки |31o 17’ 36.64” |31o 17’ 38.08” |

|?c = 186o 31’ |Горнечки |86o 39’ 32.25” |86o 39’ 33.40” |

|Lr = 0.008 m |Севастьяново |146o 03’ 16.98” |146o 03’ 18.18” |

|?r = 9o 38’ |Круглово |233o 01’ 53.80” |233o 01’ 55.60” |

| |Прокатная |295o 38’ 59.70” |295o 39’ 01.71” |

|Lc = 0.074 m |Алеево |0о 00’ 00.00” |0o 00’ 00.00” |

|?c = 289o 26’ |Горнечки |173o 34’ 57.81” |173o 35’ 01.13” |

|Lr = 0.007 m |Каменка |228o 23’ 14.01” |228o 23’ 17.73” |

|?r = 162o 58’ |Речица |260o 15’ 08.79” |260o 15’ 10.53” |

|Lc = 0 |Лазорки |0о 00’ 00.00” |0о 00’ 00.00” |

|?c = 0 |Севастьяново |245o 37’ 44.40” |245o 37’ 44.83” |

|Lr = 0.013 m |Каменка |290o 10’ 13.01” |290o 10’ 13.15” |

|?r =20o 24’ | | | |

|Lc = 0 |Горнечки |0о 00’ 00.00” |0о 00’ 00.00” |

|?c = 0 |Круглово |231o 09’ 54.31” |231o 09’ 54.64” |

|Lr = 0.032 m |Каменка |283o 56’ 13.55” |283o 56’ 13.80” |

|?r = 58o 51’ | | | |

|Lc = 0 |Каменка |0о 00’ 00.00” |0о 00’ 00.00” |

|?c = 0 |Севастьяново |40o 15’ 04.83” |40o 15’ 04.59” |

|Lr = 0.019 m |Прокатная |307o 33’ 14.34” |307o 33’ 14.51” |

|?r = 0o 10’ | | | |

|Lc = 0.040 m |Речица |0о 00’ 00.00” |0о 00’ 00.00” |

|?c = 328o 52’ |Каменка |51o 37’ 13.42” |51o 37’ 13.27” |

|Lr = 0.011 m |Круглово |116o 33’ 22.34” |116o 33’ 22.43” |

|?r = 38o52’ | | | |

|Lc = 0,070 m |Каменка |0о 00’ 00.00” |0о 00’ 00.00” |

|?c = 116о 00’ |Прокатная |64o 01’ 51.55” |64o 01’ 50.51” |

|Lr = 0,114 m |Лазорки |243o 09’ 30.94” |243o 09’ 29.81” |

|?r = 315о 07’ | | | |

|1 | | | |18 675.00 |303.6201778 |

| |Горнечки |69o 49’ 46.85” |0.938671769 |16 369.59 |249.8171213 |

| |Каменка |55o 21’ 55.61” |0.822793775 |16 258.13 |? = 0.63” |

| |Лазорки |54o 48’ 16.60” |0.817191286 | | |

| | |179o 59’ 59.06”|k=19895.1(3) | | |

|2 | | | |16 258.13 |191.0284752 |

| |Севастьяново |76o 03’ 46.19” |0.970560446 |14 417.90 |164.4190375 |

| |Каменка Горнечки|59o 23’ 44.73” |0.860704339 |11 749.72 |? = 0.42” |

| | |44o 32’ 28.32” |0.701421966 | | |

| | |179o 59’ 59.24”|k=16751.280 | | |

|3 | | | |11 749.72 |170.1251359 |

| |Круглово |40o 15’ 04.59” |0.646140963 |18 159.15 |169.8883890 |

| |Каменка |86o 58’ 36.81” |0.998608348 |14 479.08 |? = 0.43” |

| |Севастьяново |52o 46’ 19.16” |0.796234242 | | |

| | |180o 00’ 00.57”|k=18184.453 | | |

|6 | | | |18 675.00 |206.3449305 |

| |Речица |116o 50’ 29.06”|0.892259752 |10 871.51 |107.1801664 |

| |Каменка | |0.519422339 |11 049.26 |? = 0.27” |

| |Лазорки |31o 17’ 36.64” |0.527914687 | | |

| | |31o 51’ 52.80” |k=20930.004 | | |

| | |179o 59’ 58.50”| | | |

|5 | | | |11 049.26 |140.0140129 |

| |Прокатная |51o 37’ 13.27” |0.783914053 |12 706.01 |126.2164384 |

| |Каменка |64o 21’ 00.29” |0.901455746 |12 671.80 |? = 0.32 |

| |Речица |64o 01’ 50.51” |0.899028782 | | |

| | |180o 00’ 04.08”|k=14094.989 | | |

|4 | | | |12 671.80 |183.4734716 |

| |Круглово |52o 26’ 45.48” |0.792778890 |14 193.22 |162.9175387 |

| |Каменка |62o 37’ 05.90” |0.887962370 |14 478.88 |? = 0.41” |

| |Прокатная |64o 56’ 09.16” |0.905834248 | | |

| | |180o 00’ 00.54”|k=15984.028 | | |

|15 |14 |13 |12 |11 |10 |9 |8 |7 |6 |5 |4 |3 |2 |1 |№ |

|(c |(c |r” |c” |K1 |Sin|M1 |M1 |?1 |L1 |S |K =|Sin|M +|M |Элемен|

|+ |+ | | |= |(M1|+ | | | | |L .|(M+|? | |ты |

|r)0|r)”| | |L1 |+?1|?1 | | | | |? |?) | | |Формул|

|” | | | |. ?|) | | | | | | | | | | |

|0.0|-1.|-1.|-0.|235|-0.|315|0o |315|0.1|11 |433|-0.|186|0o |Речица|

|0” |54”|50”|04”|14.|705|o |00’|o |14 |049|1.5|113|o |00’| |

| | | | |21 |665|07’|00.|07’| |.26|65 |492|31’|00.| |

| | | | | |493| |00”| | | | |227| |00”| |

|+1.|-0.| |-0.|14 |+0.|31o|228|162|0.0|18 |433|-0.|217|31o|Лазорк|

|44”|10”|0.0|14”|43.|520|21’|o |o |07 |675|1.5|613|o |17’|и |

| | |4” | |855|322|14.|23’|58’| | |65 |047|48’|36.| |

| | | | | |574|01”|14.| | | | |403|36.|64”| |

| | | | | | | |01”| | | | | |64”| | |

|+1.|-0.|-0.|-0.|268|-0.|310|290|20o|0.0|16 |433|-0.|273|86o|Горнеч|

|15”|39”|12”|27”|1.4|759|o |o |24 |13 |258|1.5|998|o |39’|ки |

| | | | |45 |608|34’|10’| | |.13|65 |464|10’|32.| |

| | | | | |763|13.|13.| | | | |421|32.|25”| |

| | | | | | |01”|01”| | | | | |25”| | |

|+1.|-0.|-0.|-0.|660|-0.|342|283|58o|0.0|11 |433|-0.|332|146|Севаст|

|20”|34”|17”|17”|0.4|295|o |o |51’|32 |749|1.5|460|o |o |ья-нов|

| | | | |8 |923|47’|56’| | |.72|65 |643|34’|03’|о |

| | | | | |167|13.|13.| | | | |151|16.|16.| |

| | | | | | |55”|55”| | | | | |98”|98”| |

|+1.|+0.|0.0|+0.|391|+0.|0o |0o |0o |0.0|14 |433|+0.|59o|233|Кругло|

|80”|26”|0” |26”|9.0|002|10’|00’|10’|19 |478|1.5|862|32’|o |во |

| | | | |35 |908|00.|00.| | |.98|65 |056|53.|01’| |

| | | | | |877|00”|00”| | | | |509|80”|53.| |

| | | | | | | | | | | | | | |80”| |

|+2.|+0.|+0.|+0.|226|+0.|90o|51o|38o|0.0|12 |433|+0.|122|259|Прокат|

|01”|47”|18”|29”|8.9|999|29’|37’|52’|11 |671|1.5|846|o |o |ная |

| | | | |15 |963|13.|13.| | |.80|65 |503|09’|38’| |

| | | | | |867|43”|43”| | | | |812|59.|59.| |

| | | | | | | | | | | | | |70”|70”| |

|№ |Название вершин |Сферические углы |W |W2 |?? |

|1 |Горнечки |69o 49’ 46.85” |-0.60 |0.36 |0.14 |

| |Каменка |55o 21’ 55.32” | | | |

| |Лазорки |54o 48’ 16.60” | | | |

| | |179o 59’ 58.77” | | | |

| | |? = + 0.63” | | | |

|2 |Севастьяново |76o 03’ 46.19” |-0.27 |0.0729 |0.06 |

| |Каменка |59o 23’ 44.78” | | | |

| |Горнечки |44o 32’ 28.32” | | | |

| | |179o 59’ 59.30” | | | |

| | |? = + 0.42” | | | |

|3 |Круглово |40o 15’ 04.59” |+1.60 |2.56 |0.38 |

| |Каменка |86o 58’ 37.42” | | | |

| |Севастьяново |52o 46’ 19.16” | | | |

| | |180o 00’ 01.17” | | | |

| | |? = + 0.43” | | | |

|4 |Прокатная |64o 56’ 09.16” |+1.16 |1.3456 |0.27 |

| |Каменка |62o 37’ 06.11” | | | |

| |Круглово |52o 26’ 45.48” | | | |

| | |180o 00’ 00.76” | | | |

| | |? = + 0.41” | | | |

|5 |Речица |64o 01’ 50.51” |+2.39 |5.7121 |0.56 |

| |Каменка |64o 20’ 58.29” | | | |

| |Прокатная |51o 37’ 13.27” | | | |

| | |180o 00’ 02.07” | | | |

| | |? = + 0.32” | | | |

|6 |Лазорки |31o 51’ 52.80” |+1.33 |1.7689 |0.31 |

| |Каменка |31o 17’ 38.08” | | | |

| |Речица |116o 50’ 30.19” | | | |

| | |180o 00’ 01.07” | | | |

| | |? = + 0.27” | | | |

Точность всей сети составляет ?? = 0,81

|№ |Название вершин |Сферические |X1 |Ctg2 |Y1 |

| | |углы |X2 |Ctg1 |Y2 |

| | |приведенные к |X3 |Ctg2+ctg1 |Y3 |

|1 | |54o 48’ 16.60” |6 224 833 |0.6974629400 |5 387 671 |

| |Лазорки |55o 21’ 55.32” |6 239 843 |0.7053018800 |5 376 563 |

| |Каменка |69o 49’ 46.85” |6 224 460 |1.3960481750 |5 371 307 |

|2 | |44o 32’ 28.32” |6 224 460 |0.5914979520 |5 371 307 |

| |Горнечки |59o 23’ 44.78” |6 239 483 |1.0161447670 |5 376 563 |

| |Каменка |76o 03’ 46.19” |6 237 452 |1.6076427190 |5 365 060 |

|3 | |52o 46’ 19.16” |6 237 452 |0.0528092460 |5 365 060 |

| |Севастьяново |86o 58’ 37.42” |6 239 483 |0.7598121530 |5 376 563 |

| |Каменка |40o 15’ 04.59” |6 253 843 |0.8126214000 |5 372 873 |

|6 | |31o 17’ 38.08” |6 239 843 |1.6087777530 |5 376 563 |

| |Каменка |31o 51’ 52.80” |6 224 833 |1.6451048730 |5 387 671 |

| |Лазорки |116o 50’ 30.19”|6 235 668 |3.2538826260 |5 386 792 |

|5 | |64o 20’ 58.29” |6 239 483 |0.4870695440 |5 376 563 |

| |Каменка |64o 01’ 50.51” |6 235 668 |0.4802033620 |5 386 792 |

| |Речица |51o 37’ 13.27” |6 248 345 |0.9672729060 |5 385 957 |

|4 | |62o 37’ 06.11” |6 239 483 |0.4675708630 |5 376 563 |

| |Каменка |64o 56’ 09.16” |6 235 668 |0.5179442050 |5 385 957 |

| |Прокатная |52o 26’ 45.48” |6 253 842 |0.9856615069 |5 372 874 |

|Название |Х км |У км |Х1 – Х2 |2У1 + У2 |У1 + 2У2|?1-2” |?2-1” |

|Каменка |6 239,843 |-123,437|+15,010 |-359,203 |-348,095|-4.55 |+4.41 |

|Лазорки |6 224,833 | |+15,383 |-357,567 | |-4.87 |+4.94 |

|Горнечки |6 224,460 |-112,329|+02,391 |-381,814 |-380,823|-0.77 |+0.79 |

|Севастьяново |6 237,452 | |-13,999 |-374,000 | |+4.42 |-4.46 |

|Круглово |6 253,842 |-128,693|-08,502 |-360,917 |-393,317|+2.59 |-2.52 |

|Прокатная |6 248,345 | |+04,175 |-360,082 | |-1.27 |+1.23 |

|Речица |6 235,668 |-134,940| | |-377,689| | |

| | | | | | | | |

| | |-127,126| | |-351,523| | |

| | | | | | | | |

| | |-114,043| | |-349,853| | |

| | | | | | | | |

| | |-113,208| | | | | |

|Лазорки |6 224,833 |-112,329|+00,373 |-353,351 |-369,715|-0.11 |+0.12 |

|Горнечки |6 224,460 | |-10,835 |-337,866 | |+3.09 |-3.10 |

|Речица |6 235,668 |-128,693| | |-338,745| | |

| | | | | | | | |

| | |-113,208| | | | | |

|Севастьяново |6 237,452 |-134,940|-16,390 |-397,006 |-389,192|+5.49 |-5.38 |

|Круглово |6 253,842 | |+12,992 |-398,573 | |-4.37 |+4.30 |

|Горнечки |6 224,460 |-127,126| | |-392,326| | |

| | | | | | | | |

| | |-128,693| | | | | |

|Прокатная |6 248,345 |-114,043|+12,677 |-341,294 |-340,459|-3.65 |+3.64 |

|Речица |6 235,668 | |-05,497 |-355,212 | |+1.65 |-1.71 |

|Круглово |6 253,842 |-113,208| | |-368,295| | |

| | | | | | | | |

| | |-127,126| | | | | |

Круглово

Севастьяново Прокатная

Каменка

Речица

Горнечки Лазорки

МЕНЮ

Триангуляция

Триангуляция

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