JHS 154 ETRS89-järjestelmään liittyvät karttaprojektiot, tasokoordinaatistot ja karttalehtijako, Liite 2: Esimerkit
- Versio: 6.6.2008
- Julkaistu:
- Voimassaoloaika: Toistaiseksi
Esimerkkeinä projektiolaskuista esitetään muunnos geodeettisista koordinaateista tasokoordinaateiksi ja päinvastoin välituloksineen ETRS-TM35FIN – koordinaatistossa. Lisäksi esitetään lopputulokset muunnoksille geodeettisista koordinaateista ETRS-GK – koordinaatiston eri kaistoihin.
Esimerkki 1: Projektiolaskut ETRS-TM35FIN – koordinaatistossa
Lähtötiedot: Pisteen G4 (Geta) EUREF-FIN – koordinaatit:
|
φ |
= |
60 ° 23’ 06.38474” |
= |
1.053918934088933 rad |
|
λ |
= |
19 ° 50’ 53.29237” |
= |
0.346415337012956 rad |
|
h |
= |
118.309 m |
GRS80 – vertausellipsoidin parametrit:
|
a |
= |
6 378 137.0 m |
|
f |
= |
1/298.257222101 |
Karttaprojektion parametrit:
|
k0 |
= |
0.9996 |
|
λ 0 |
= |
27 ° |
|
E 0 |
= |
500 000 m |
Apusuureet:
|
n |
= |
0,001679220395 |
|
A 1 |
= |
6367449,145771 |
|
e 2 |
= |
0,006694380023 |
|
e’ 2 |
= |
0,006739496775 |
|
V 2 |
= |
1,00164579775 |
|
h 1 |
= |
0,000837732168164 |
|
h 2 |
= |
0,000000059058696 |
|
h 3 |
= |
0,000000 000167349 |
|
h 4 |
= |
0,000000000000217 |
|
h 1 ’ |
= |
0,000837731824734 |
|
h 2 ’ |
= |
0,000000760852779 |
|
h 3 ’ |
= |
0,000000001197638 |
|
h 4 ’ |
= |
0,000000000002443 |
|
Geodeettisista koordinaateista tasokoordinaateiksi |
Tasokoordinaateista geodeettisiksi koordinaateiksi |
|||||
|
φ |
= |
1.053918934088933 |
E |
= |
106256,35958 |
|
|
λ |
= |
0.346415337012956 |
N |
= |
6715706,37705 |
|
|
Q' |
= |
1,330479626914950 |
ξ |
= |
1,055115412897463 |
|
|
Q'' |
= |
0,071251194462820 |
η |
= |
-0,061861695615107 |
|
|
Q |
= |
1,324649911823168 |
||||
|
ξ 1 ’ |
= |
0,000724281930916 |
||||
|
l |
= |
-0,124823561025513 |
ξ 2 ’ |
= |
-0,000000053657596 |
|
|
β |
= |
1,051030767588720 |
ξ 3 ’ |
= |
0,000000000008501 |
|
|
ξ 4 ’ |
= |
0,000000000000203 |
||||
|
η ’ |
= |
-0,061915076853879 |
||||
|
ξ ’ |
= |
1,054391184619376 |
η 1 ’ |
= |
0,000053374333729 |
|
|
η 2 ’ |
= |
0,000000006973167 |
||||
|
ξ 1 |
= |
0,000724918454654 |
η 3 ’ |
= |
-0,000000000063479 |
|
|
ξ 2 |
= |
-0,000000690230193 |
η 4 ’ |
= |
0,000000000000062 |
|
|
ξ 3 |
= |
0,000000000055283 |
||||
|
ξ 4 |
= |
0,000000000002298 |
ξ ’ |
= |
1,054391184615438 |
|
|
η ’ |
= |
-0,061915076858586 |
||||
|
η 1 |
= |
0,000053291297517 |
||||
|
η 2 |
= |
0,000000090400064 |
β |
= |
1,051030767584305 |
|
|
η 3 |
= |
-0,000000000454791 |
l |
= |
-0,124823561034060 |
|
|
η 4 |
= |
0,000000000000692 |
||||
|
Q |
= |
1,324649911814278 |
||||
|
ξ |
= |
1,055115412901418 |
Q’ |
= |
1,330469999534920 |
|
|
η |
= |
-0,061861695610397 |
Q’ |
= |
1,330479611087242 |
|
|
Q’ |
= |
1,330479626880053 |
||||
|
Q’ |
= |
1,330479626906003 |
||||
|
Q’ |
= |
1,330479626906045 |
||||
|
Tasokoordinaatit: |
||||||
|
E |
= |
106256,35961 |
φ |
= |
1,053918934084532 |
|
|
N |
= |
6715706,37708 |
= |
60°23’06.384739” |
||
|
λ |
= |
0,346415337004409 |
||||
|
= |
19°50’53.292368” |
|||||
|
Meridiaanikonvergenssi ja mittakaavakerroin |
||||
|
γ |
= |
-0,108655736 |
= |
-6,225515089° |
|
k |
= |
1,001501684 |
(1502 ppm) |
|
Esimerkki 2: Projektiola skut ETRS-GK –koordinaatistoissa
Lähtötiedot: Pisteen G42 (Kymi) EUREF-FIN – koordinaatit:
|
φ |
= |
60 ° 31’ 15.86470” |
= |
1.056292000 rad |
|
λ |
= |
26 ° 54’ 25.76350” |
= |
0.469618474 rad |
|
h |
= |
71.214 m |
GRS80 – vertausellipsoidin parametrit:
|
a |
= |
6 378 137.0 m |
|
f |
= |
1/298.257222101 |
Karttaprojektion parametrit:
|
k0 |
= |
1.0 |
|
λ 0 |
= |
19 ° - 31 ° |
|
E 0 |
= |
500 000 m |
Pisteen G42 koordinaatit, meridiaanikonvergenssi ja mittakaavakerroin ETRS-GK –koordinaatiston eri kaistoissa:
|
19 ° |
E |
= |
933549.030 |
m |
γ |
= |
+0.120324829 |
rad |
= |
+6°53’39” |
|
N |
= |
6738233.823 |
m |
k |
= |
1.002306100 |
(2306 ppm) |
|||
|
20 ° |
E |
= |
878867.261 |
m |
γ |
= |
+0.105069207 |
rad |
= |
+6°01’12” |
|
N |
= |
6732045.175 |
m |
k |
= |
1.001759690 |
(1760 ppm) |
|||
|
21 ° |
E |
= |
824125.258 |
m |
γ |
= |
+0.089829144 |
rad |
= |
+5°08’49” |
|
N |
= |
6726693.699 |
m |
k |
= |
1.001287047 |
(1287 ppm) |
|||
|
22 ° |
E |
= |
769331.899 |
m |
γ |
= |
+0.074602387 |
rad |
= |
+4°16’28” |
|
N |
= |
6722178.673 |
m |
k |
= |
1.000888173 |
(888 ppm) |
|||
|
23 ° |
E |
= |
714495.986 |
m |
γ |
= |
+0.059386685 |
rad |
= |
+3°24’09” |
|
N |
= |
6718499.484 |
m |
k |
= |
1.000563066 |
(563 ppm) |
|||
|
24 ° |
E |
= |
659626.265 |
m |
γ |
= |
+0.044179783 |
rad |
= |
+2°31’53” |
|
N |
= |
6715655.628 |
m |
k |
= |
1.000311727 |
(312 ppm) |
|||
|
25 ° |
E |
= |
604731.429 |
m |
γ |
= |
+0.028979431 |
rad |
= |
+1°39’37” |
|
N |
= |
6713646.713 |
m |
k |
= |
1.000134156 |
(134 ppm) |
|||
|
26 ° |
E |
= |
549820.136 |
m |
γ |
= |
+0.013783374 |
rad |
= |
+0°47’23” |
|
N |
= |
6712472.461 |
m |
k |
= |
1.000030353 |
(30 ppm) |
|||
|
27 ° |
E |
= |
494901.020 |
m |
γ |
= |
-0.001410639 |
rad |
= |
-0°04’51” |
|
N |
= |
6712132.709 |
m |
k |
= |
1.000000318 |
(0.3 ppm) |
|||
|
28 ° |
E |
= |
439982.705 |
m |
γ |
= |
-0.01660486 |
rad |
= |
-0°57’05” |
|
N |
= |
6712627.410 |
m |
k |
= |
1.000044051 |
(44 ppm) |
|||
|
29 ° |
E |
= |
385073.814 |
m |
γ |
= |
-0.031801546 |
rad |
= |
-1°49’20” |
|
N |
= |
6713956.632 |
m |
k |
= |
1.000161552 |
(162 ppm) |
|||
|
30 ° |
E |
= |
330182.986 |
m |
γ |
= |
-0.047002944 |
rad |
= |
-2°41’35” |
|
N |
= |
6716120.560 |
m |
k |
= |
1.000352820 |
(353 ppm) |
|||
|
31 ° |
E |
= |
275318.884 |
m |
γ |
= |
-0.062211309 |
rad |
= |
-3°33’52” |
|
N |
= |
6719119.494 |
m |
k |
= |
1.000617857 |
(618 ppm) |