Kõrgem geodeesia, kõik kodused tööd lahendatud. Vello Kala (0)

Overview

Sheet1
Sheet2
Sheet3
kt_4SS
kt5
Sheet4

Sheet 1: Sheet1

Punktid Vasakpoolsed nurgad rad dir nurgad Kaugused (m) sin cos dx dy x y
7
RPV240
119.72
67346.75 14185.23
-1.7520802005 -1.0521618034 D 7
RPV241 137º15' 2.3954643984 77.0º
0.9742521471 0.2254612025 45.0922404915 194.8504294259 67247 14360 0.6788007455
-60.2844307013 5
137.25 1.3433799253 200
119.7155692987
PP1 165º00' 2.8797932658 62.0º
0.8827016571 0.4699338087 93.9867617378 176.5403314204 67292.0922404915 14554.8504294259
689.0846851648
165 1.1º 200
PP2 206º30' 3.6041049054 88.5º
0.999643 0.026700364 5.3400728094 199.9286963454 67386.0790022294 14731.3907608463
559.0561565499
206.5 1.5º 200
PP3 222º00' 3.8746309394 130.5º
0.7607459116 -0.6490498117 -129.8099623382 152.1491823105 67391.4190750388 14931.3194571918
399.4518139018
222 2.3º 200
PP4 186º00' 3.2463124087 136.5º
0.6887342865 -0.72501385 -145.0027699966 137.7468572902 67261.6091127006 15083.4686395023
200
186 2.4º 200
PP5 152º10' 2.6558081816 108.6º
0.9475644685 -0.3195646696 -63.9129339286 189.512893695 67116.606342704 15221.2154967924
0
152. 1666
1.9º 200 0 1 200 0
RPV242
0 1 200 0 67052.6934087754 15410.7283904874
18.6561140992
1068.9166
67249.6427402771 14898.9961677494
19.5
5 25
33
17 85
10
24 120
1
30
4 20
57.295780
33
18 90
206264.806247096
25.100
68
ro^2 42545170296.1522
890 37.0833333333
36.006240
890 111.25
6.001
Punktide nr.nr. Vasakpoolsed nurgad Direktsiooni-nurgad α Joonte pikkused Koordinaatide juurdekasvud Koordinaadid Punktide nr.nr.
mõõdetud arvutatud
º ' º ' ± Δx ± Δy ± x ± y D D2
RPV240
119.96
201.730
67347.75
14185.23
119 58
67247.00
14360.00
1065.028 1134283.96932482
RPV241 137 15 77.212
200
44.268
195.039
77 13
PP1 165 0
67291.268
14555.039
886.332 785584.78572192
Kõrgema geodeesia I iseseisev töö
62.2122419938
200
93.240
176.936
62 13
Andmed:
x y
PP2 207 30
67384.508
14731.975
756.657 572529.711633297
RPV240 67347.75 14185.23
89.7122419938
200
1.004
199.997
RPV241 67247.00 14360.00
89 43
PP3 222 0
67385.512
14931.973
586.832 344372.267423522
E = 7
131.7122419938
200
-133.078
149.299
I = 7 = 119.9622 º
131 43
P = 5
PP4 186 0
67252.434
15081.272
388.118 150635.807428717
137.7122419938
200
-147.955
134.571
Lahendus:
137 43
1. Punktide ligikaudsed koordinaadid
PP5 152 10
67104.479
15215.843
200.000 40000 .0000000006
109.7122419938
200
-67.459
188.280
Punkt Dir.nurk α vasak.nurk x y s
109 43
PP1 77.0º 137º15' 67292.0922404915 14554.8504294259 200
RPV242
67037.020
15404.123
PP2 62.0º 165º00' 67386.0790022294 14731.3907608463 200
3027406.54153227
PP3 88.5º 206º30' 67391.4190750388 14931.3194571918 200
PP4 130.5º 222º00' 67261.6091127006 15083.4686395023 200
PP5 136.5º 186º00' 67261.6091127006 15221.2154967924 200
RPV242 108.6º 152º10' 67116.606342704 15410.7283904874 200
α=αPP1 + β – 180
X=XPP1 + Δx
Y=YPP1 + Δy
Δx=s·cosα
Δy=s·sinα
3. Raskuskeskme koordinaadid
Xo=
Xo= 67277.5334500935
Yo= 14812.68
4. Teravnurgad diagonaali ja käigu joonte vahel
β1= 23º
β2= 38º
β3= 9º
β4= 33º
β5= 36º
Keskmine nurk β' = 27,8º
5. Punktide kaugused raskuskeskme paralleelist:
l1 = 30 m
l4 = 20 m
l2 = 90 m
l5 = 90 m
l3 = 125 m
lkeskmine = 71 m
6. Käik ei ole piklik, kuna punktide keskmine hälve on suurem, kui 1/24 diagonaali
pikkus. Maksimaalne hälve on suurem, kui 1/8 diagonaali pikkus;
lõikenurgad on üle 8º, keskmine üle 24º
7. Lõpp-punkti KRV
= 49x6 = 294 mm
M'2 =
= 660.93203 mm2
M' = 25.7086 mm (Lõpp-punkti KRV)
kõige nõrgema punkti äärmine viga =
2 x 25 = 50 mm
käigu suhteline sulgemisviga = 1:
24,000

Sheet 2: Sheet2

Punktide nr.nr. vasakpoolsed nurgad Direktsiooni-nurgad α Joonte pikkused (m) Koordinaatide juurdekasvud Koordinaadid Punktide nr.nr.
Kõrgema geodeesia II iseseisev töö
mõõdetud arvutatud lõplikud
Polügonomeetriakäigu arvutus
º ' º ' ± Δx ± Δy ± Δx ± Δy ± x ± y
koordinaatsidumise puhul
RPV 11
-1.1429445412
7436.377
5830.895 RPV 11
114.514102
Andmed: E = 7
RPV 12 181º04'57''
114 30.833
7415.285
5877.147 RPV 12
M = 7
181 4.95 2.0175413018
49.235
-21.271
44.403
-21.276
# VALUE !
7415.106
5875.298
P = 5
3.160485843
115.596602
7415.101
# VALUE !
PP1 179º33'17''
115 35.80
7394.009
5921.550 PP1 3. Käigu diagonaal RPV12-RPV17
praktiline
179 33.283333333 2.0097697382
50.113
-21.299
45.362
-21.304
#VALUE!
7393.807
5920.660
3.13382109
115.151324
7393.797
#VALUE!
α= 116.05745 = 116º03'27'' Δx = -109.698000
PP2 180º56'43''
115 9.06
7372.705
5966.912 PP2
180 55.716666666 2.0262679476
50.278
-22.117
45.152
-22.122
#VALUE!
7371 .691
5965.812
s= 249.727 m Δy = 224.343000
3.158090863
116.096602
7371.675
#VALUE!
PP3 179º28'57''
116 5.78
7350.583
6012.064 PP3 4. Diagonaali pikkus ja direktsiooninurk esialgsetel andmetel
teoreetiline
179 28.95 2.0172358691
50.296
-21.716
45.366
-21.721
#VALUE!
7349.975
6011.179
3.132560575
115.579102
7349.954
#VALUE!
α'= 116.05190 = 116º03'07'' Δx = -109.671241
PP4 182º15'39''
115 34.73
7328.862
6057.431 PP4
182 15.65 2.0566948545
49.827
-23.269
44.060
-23.275
#VALUE!
7326.706
6055.238
s'= 249.715267 m Δy = 224.343338
3.181051639
117.839935
7326.679
#VALUE!
RPV 17
117 50.40
7305.587
6101.490 RPV 17 6. Direktsiooninurga parand
7305.587
6101.490
δα = α – α' = 0º00'20''
249.749
-109.67
224.34
Suhteline erinevus
0.0114
-0.0268
0.00
δs = s – s' = 0.0114 m
Δx = -0.026759 m -0.00535185
Δy = -0.000338 m -0.00006763
7. Lõplikud juurdekasvud
Δxi = #VALUE!
Δyi = #VALUE!

Sheet 3: Sheet3

Kõrgema geodeesia III iseseisev töö
Polügonomeetria andmete taandus
ellipsoidile ja kaardiprojektsiooni
Andmed: E = 7
M = 7
P = 5
Punkt X (m) Y (m) H (m)
Y'2= 271063.8
1 6552325 770756 70
-229244 -229090.1 Y'3= 271248.4
X'2 = 178170.7
2 6553170.7 771063.8 50
-228936.2 -228997.8 Y'1= 270756.0
X'3 = 177411.800
3 6552411.8 771248.4 70
-228751.6
Ym= 270909.9
Ym2= 271002.2
2. Joonte pikkused
l1-2= 899.972 m
l1-3= 499.992 m
3. Joonte pikkused ellipsoidil GRS-80
Hm = 60
Rm = 6387952
= -0.011130 m
s1-3 = -0.006966 m
l'1-2= 899.961 m
l'1-3= 499.985 m
4. Joonte pikkuste taandamine Mercatori projektsiooni
d1-2 = 900.411 m
d1-3 = 500.236 m
Märkus . Jooned on taandatud telgmeridiaanile
nurk 1.2.3.
β1.2.3. = (1.3 – 1.2.) + δ1..3 – δ1..2
= 60º+(-0,06'')-(-0,58'')
= 60º00'00,52''
δ1..2 =
rho = 206264.806247096
δ1..2 = -0.5790459866 ''
δ1..3 = -0.0594517155 ''
6. Taandamine Lambert -Est projektsiooni
d=s'm
m = 0,99993243 + 1,22565*10-14*r2 + 1,042*10-21*r3
m = 0.9999525
0.9999517
r = 40395.502 m 39625.490 m
joon - 1.2
1.3
d = 899.918 m 499.961 m
δ1..2 = 0.03842 ''
Rk = 6387521 m
δ1..3 = 0.06115 ''
Xk = 6503225 m
summa delt 0.0227277
β1.2.3. = (1.3 – 1.2.) + δ1..3 – δ1..2 =
60°00'00,02''

Sheet 4: kt_4SS

Kõrgema geodeesia IV iseseisev töö
Üleminek Krassovski ellipsoidilt
WGS-84 koordinaatidele
B: L:
Andmed: B = 59º00´00,00´´
1.0297442587 0.436332313
L = 25º00´00,00´´
Krassovski:
H (m) = 100
a = 6378245
e2 = 0.0066934216200
Telgmeridiaan 24º
KRV = ± 0,3 m
WGS84:
a = 6378137
1. Üleminek geodeetilistelt koordinaatidelt
e2 = 0.0066943800000
geotsentrilistele ruumilistele koordinaatidele





= 6393986.860430 m


= 2984651.1615 m
1391765.6935 m
5444117.4286 m
2984651.16149902 1391765.6935282 5444117.42857774 2. Üleminek Krassovski geotsentrilistelt koordinaatidelt
x y z
WGS-84 geotsentrilistele ruumilistele koordinaatidele
e''x = -1.01378 -3025779.65450447 -1410944.22478502 -5519137.36674355
rad
x (m) = 21.58719
e''x = -1.01378 -0.0000049
e''y = -0.58117 -1734589.71552838 -808852.468107786 -3163957.72596653
y (m) = -97.54127
e''y = -0.58117 -0.0000028
e''z = -0.23480 -700796.092719969 -326786.584840422 -1278278.77223005
z (m) = -60.92546
e''z = -0.23480 -0.0000011
m -4.6121 -13765509.6219496 -6418962.55512142 -25108813.9923434
m+1
m = -0.0000046
m+1 -3.6121 -10780858.4604506 -5027196.86159322 -19664696.5637657
m/1000 -0.004612 -13765.5096219496 -6418.9625551214 -25108.8139923434 2984672.7382 m
m/1000000 -0.000005 -13.7655096219 -6.4189625551 -25.1088139923
m+1/1000 -0.003612 -10780.8584604506 -5027.1968615932 -19664.6965637657 1391638.3733 m
m+1/1000000 -0.000004 -10.7808584605 -5.0271968616 -19.6646965638
5444029.8252 m
3. Üleminek WGS-84 geotsentrtilistelt koordinaatidelt
WGS-84 geodeetilistele koordinaatidele
= 24.997834 º = 3293163.94 0.46626163
0.43629450 24.9978337255
0.42258400 3293163.93701947
= 6393880.817 m
0.90632377 3293163.93701947 B = 59 59.44825 59.58
rad B 1.0297442587 1.037567697 1.0398671683
sin 0.8571673007 0.8611703964 0.8623369776
sin 2 0.7347357814 0.7416144516 0.7436250629
5480719.17
Ti-1 = 5480719.1704
N 6393880.856152 6394028.803048 6394072.049348
Bi = 24.99783
cos 0.51503807 0.50831639 0.50633481
= 58.9998831 º Bi = 58.999879996
B1 58.999883116
0.000120004
lubatud viga = 1'' ehk 0.000277778 º
0.000116884
q/b 6394020.35974639 6478571.27401096 6503925.64207565
58.999722222
h 139.5423342139 84690.4565987885 110044.824663471
= 117.8338607531 m

Sheet 5: kt5

Kõrgema geodeesia V iseseisev töö
Kaare pikkuse, mõõtkava ja
meridiaanide koonduvuse arvutamine
Andmed: B = 58º00´00,00´´
sin Bm 0.8526402 e2 = 0.0066943800
L = 25º00´00,00´´
sin B1 0.8480481 N 6393714.385
X (m) = 6430460.059
sin B2 0.8571673 a 6378137
Y (m) = 618207.902
sin Bm2 0.7269952499
rho 206264.806247096
1. Meridiaani 1º kaare pikkus
B2 = 59º00'00''
B võtta sekundites
M = 6381972.101 m
X = 111386.426 m
N1 = 6393546.439 m
= 3593.48320473 ''
cos B 1 0.52991926
ehk 0.9981898 º
2. TM-Balti mõõtkava
a 6378137
e' = 0.082094465431 b 6356752.3
tasandiliste koordinaatide abil:
e2 = 0.006694384442 a2 40680631590769
e'2 0.006739501254 b2 40408299803555.3
R = 6387504.9728 m
e = 0.081819218048
mo = 0.999600
M 6381469.20504
y'm = 118207.9020 m
N 6393546.44935
μ = 0.9997712430
geodeetiliste koordinaatide abil:
rho min 1
l = 0.0174533 rad
l min 0.0174532925
η = 0.0435034387
2 = 0.0000428514283
μ = 0.99964285
3 = -0.000000000482
mju = 0.99964285095
3. Meridiaanide koonduvus
rad sek degrees
geodeetiline koonduvus:
1 206264.806247096 57.2957795
0.0174533 3600 1
60
γ' = 50.884339372272 ' ehk = 0.84807 º
58.002620
sek min
rho 206264.806247096 3437.7467707849
Gaussi meridiaanide koonduvus:
γ' = 50.884344874302 ' ehk = 0.84807 º
Lamberti koonduvus:
α = 0.85417585805
L1 - Lo = 60 '
γ' = 51.250551483000 ' ehk = 0.85418 º

Sheet 6: Sheet4

прямая задача
x y
1
2
обратная задача
x y dx dy s alpha 1 6552325 770756 86.7999999998 492.4 499.991999936 80.002641 2 6552411.8 771248.4