小地區(qū)控制測量-閉合導(dǎo)線（園林工程測量）

閉合導(dǎo)線例題講解1.繪制計算草圖，在圖上填寫已知數(shù)據(jù)和觀測數(shù)據(jù)。115.106100.092108.32394.38267.581ABCDEXA=500.000mYA=500.000m

A1

48°43′20″

A

1

2

3

4

112°22′22″97°03′00″

105°17′05″

101°46′23″

123°30′05″

點號轉(zhuǎn)折角

(右)

°′″改正后轉(zhuǎn)折角

°′″方位角

°′″邊長

D(米)

坐標增量(米)XY改正后增量(米)XY坐標(米)XY點號ABCDEAB9703001051705101462312330051122222484320

500.000500.000115.106100.092108.32394.38267.5812.角度閉合差的計算與調(diào)整（1）計算角度閉合差

=

測-

理=

測-(n-2)

180°

=539°58′55″

-(5-2)

180°

=539°58′55″

-540°00′00″

=539°58′55″

-539°59′60″

=-65″（2）計算限差f

容=±40√n=±40√5=±89″

判斷：f

<f

容，符合精度要求。（3）按反符號平均分配原則，計算各個角的改正數(shù)v

=-f

/n=+65″/6=+13

″

（4）計算改正后新的角值

i改=

i+v

點號轉(zhuǎn)折角

(右)

°′″改正后轉(zhuǎn)折角

°′″方位角

°′″邊長

D(米)

坐標增量(米)XY改正后增量(米)XY坐標(米)XY點號ABCDEAB9703001051705101462312330051122222484320

500.000500.000+13+13+13+13+139703131051718101463612330181122235115.106100.092108.32394.38267.5813.按新的角值，推算各邊坐標方位角

連接角為右角，推算坐標方位角的公式為：ɑ前=ɑ后-

i改+180°注意：使用改正后的角度值。ɑBC=ɑAB-

B+180°

=48°43′20″-97°03′13″+180°=131°40′07″ɑCD=ɑBC-

C+180°

=131°40′07″-105°17′18″+180°=206°22′49″ɑDE=ɑCD-

D+180°

=206°22′49″-101°46′36″+180°=284°36′13″ɑEA=ɑDE-

E+180°

=284°36′13″-123°30′18″+180°=341°05′55″ɑAB=ɑEA-

A+180°

=341°05′55″-112°22′35″+180°=408°43′20″-360°=48°43′20″(檢核)點號轉(zhuǎn)折角

(右)

°′″改正后轉(zhuǎn)折角

°′″方位角

°′″邊長

D(米)

坐標增量(米)XY改正后增量(米)XY坐標(米)XY點號ABCDEAB9703001051705101462312330051122222484320

500.000500.000+13+13+13+13+1397031310517181014636123301811222351314007206224928436133410555

484320115.106100.092108.32394.38267.5814.按坐標正算公式，計算各邊坐標增量ΔxAB=DAB*cosɑAB

=115.106*cos48°43′20″=75.937mΔyAB=DAB*sinɑAB

=115.106*sin48°43′20″

=86.504m4.按坐標正算公式，計算各邊坐標增量ΔxBC=DBC*cosɑBC

=100.092*cos131°40′07″=-66.543mΔyBC=DBC*sinɑBC

=100.092*sin131°40′07″

=74.769m4.按坐標正算公式，計算各邊坐標增量ΔxCD=DCD*cosɑCD

=108.323*cos206°22′49″=-97.043mΔyCD=DCD*sinɑCD

=108.323*sin206°22′49″

=-48.131m4.按坐標正算公式，計算各邊坐標增量ΔxDE=DDE*cosɑDE

=94.382*cos284°36′13″=23.797mΔyDE=DDE*sinɑDE

=94.382*sin284°36′13″=-91.333m4.按坐標正算公式，計算各邊坐標增量ΔxEA=DEA*cosɑEA

=67.581*cos341°05′55″=63.937mΔyEA=DEA*sinɑEA

=67.581*sin341°05′55″=-21.892m

=-48.131m點號轉(zhuǎn)折角

(右)

°′″改正后轉(zhuǎn)折角

°′″方位角

°′″邊長

D(米)

坐標增量(米)XY改正后增量(米)XY坐標(米)XYABCDEAB9703001051705101462312330051122222484320

500.000500.000+13+13+13+13+1397031310517181014636123301811222351314007206224928436133410555

484320115.106100.092108.32394.38267.581+75.937-66.543-97.043+23.797+63.937+86.504+74.769-48.131-91.333-21.892485.4845395855

+0.085

-0.0835.坐標增量閉合差的計算與調(diào)整（1）計算坐標增量閉合差fx=

Δx測-

Δx理=

Δx測=+85mm

fy=

Δy測-

Δy理=

Δy測=

-83mm（2）計算導(dǎo)線全長絕對閉合差f=√fx2+fy25.坐標增量閉合差的計算與調(diào)整（3）計算導(dǎo)線全長相對閉合差

k=f/D=1/4086（4）判斷1/4086<1/2000，符合精度要求

（5）分配坐標增量閉合差VΔxAB=-fx*DAB/D=-0.085*115.106/485.484=-0.020mVΔyAB=-fy*DAB/D=0.083*115.106/485.484=0.020m點號轉(zhuǎn)折角

(右)

°′″改正后轉(zhuǎn)折角

°′″方位角

°′″邊長

D(米)

坐標增量(米)XY改正后增量(米)XY坐標(米)XYABCDEAB9703001051705101462312330051122222484320

500.000500.000+13+13+13+13+1397031310517181014636123301811222351314007206224928436133410555

484320115.106100.092108.32394.38267.581+75.937-66.543-97.043+23.797+63.937+86.504+74.769-48.131-91.333-21.892485.4845395855

+0.085

-0.083-20-18-19-16-12+20+17+19+16+11檢核，使

VΔx=-fx

VΔy=-fy點號轉(zhuǎn)折角

(右)

°′″改正后轉(zhuǎn)折角

°′″方位角

°′″邊長

D(米)

坐標增量(米)XY改正后增量(米)XY坐標(米)XYABCDEAB9703001051705101462312330051122222484320

500.000500.000+13+13+13+13+1397031310517181014636123301811222351314007206224928436133410555

484320115.106100.092108.32394.38267.581+75.937-66.543-97.043+23.797+63.937+86.504+74.769-48.131-91.333-21.892485.4845395855

+0.085

-0.083-20-18-19-16-12+20+17+19+16+116.計算改正后的坐標增量+75.917-66.561-97.062+23.781+63.925+86.524+74.786-48.112-91.317-21.881檢核，使

Δx改=0

Δy改=000點號轉(zhuǎn)折角

(右)

°′″改正后轉(zhuǎn)折角

°′″方位角

°′″邊長

D(米)

坐標增量(米)XY改正后增量(米)XY坐標(米)XYABCDEAB97030010