Uneingeschränkter Zugang

Proposed single-zone map projection system for Turkey

Faruk Yildirim
Faruk Yildirim
 und 
Fatih Kadi
Fatih Kadi
   | 03. Jan. 2022
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Article Category: Original Article
Online veröffentlicht: 03. Jan. 2022
Seitenbereich: 35 - 45
Eingereicht: 12. Aug. 2021
Akzeptiert: 29. Nov. 2021
DOI: https://doi.org/10.2478/rgg-2021-0006
Schlüsselwörter
© 2021 Faruk Yildirim et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

UTM zones for Turkey
UTM zones for Turkey

Figure 2

Distortion sizes for Mittermayer method: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2°; (d) the distance (S – s) distortion, contour intervals 75 cm.
Distortion sizes for Mittermayer method: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2°; (d) the distance (S – s) distortion, contour intervals 75 cm.

Figure 3

Distortion sizes for LCC2: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2″; (d) the distance (S – s) distortion, contour intervals 40 cm.
Distortion sizes for LCC2: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2″; (d) the distance (S – s) distortion, contour intervals 40 cm.

Figure 4

Distortion sizes for CP: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2″; (d) the distance (S – s) distortion, contour intervals 40 cm.
Distortion sizes for CP: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2″; (d) the distance (S – s) distortion, contour intervals 40 cm.

Figure 5

Distortion sizes for double projection: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2″; (d) the distance (S – s) distortion, contour intervals 40 cm.
Distortion sizes for double projection: (a) scale factor, counter interval 0.0005; (b) meridian convergence, contour intervals 1°; (c) the arc to chord (T – t) distortion, contour intervals 0.2″; (d) the distance (S – s) distortion, contour intervals 40 cm.

Figure 6

Correction values based on correction formulas for accuracy analysis in CP: (a) Ss difference for 1 km, counter interval 2 mm; (b) Ss difference for 2 km, counter interval 2 mm; (c) Tt difference for 1 km, contour intervals 0.001″; (d) Tt difference for 2 km, contour intervals 0.001″.
Correction values based on correction formulas for accuracy analysis in CP: (a) Ss difference for 1 km, counter interval 2 mm; (b) Ss difference for 2 km, counter interval 2 mm; (c) Tt difference for 1 km, contour intervals 0.001″; (d) Tt difference for 2 km, contour intervals 0.001″.

Figure 7

Scale correction factor for CP
Scale correction factor for CP

(B, L) Ellipsoid geographical latitude and longitude;
(φ, λ) Sphere geographical latitude and longitude;
(B0, L0) Central meridian (latitude) and longitude of central meridian;
(x, y) Projected coordinates or plane coordinates;
(N, E) Northing, Easting map of scale or sheet coordinates;
q Isometric latitude for ellipsoid: atanh(sin B) – e atanh(e sin B);
ω Isometric latitude for sphere: atanh(sin φ);
q, l Isometric coordinates;
l L – L0;
A Ellipsoid azimuth;
S Ellipsoid geodetic or distance on ellipsoid;
s Plane or projection distance;
t Plane or projection azimuth;
γ Grid convergence of ellipsoid;
(T – t) The arc to chord distortion of projection (A–t–γ);
(S – s) Distance distortion of projection (S–s);
(T – t)map The arc to chord correction calculated from (x, y);
(S – s)map Distance correction calculated from (x, y);
a Semi-major axis of ellipsoid;
b Semi-minor axis of ellipsoid;
c Polar radius of curvature;
e2 Eccentricity of ellipsoid squared;
e′2 Second eccentricity of ellipsoid squared;
e 2.71828182845904523. . . Euler's number;
G Meridian arc length from equator to latitude, meridian distance;
M Radius of curvature in the meridian:
c/(1 + e′2 cos2 B)3/2;
N Radius of curvature in the prime vertical: c/(1 + e′2 cos2 B)1/2;
R Radius of Gauss sphere: (MN)1/2 = c/(1 + e′2 cos2 B);
r Radius of curvature of the parallel (N cos B);
η2 e′2 cos2 B;
t tan B;
m Point grid scale factor;
m0 Grid scale factor assigned to central meridian (longitude) or parallels (latitude);
(B1, B2) Standard parallels for Lambert conformal conic.

Coefficients for correction formulas

k tk sk
1 −1.230817046856762e-14 3.410737419053955e-04
2 −4.102723489522539e-15 −1.230817046856762e-14
3 −1.560602822242498e-21 −1.230817046856762e-14
4 −7.675969852812854e-22 −5.117313235208569e-22
5 7.803014111212491e-22 1.560602822242498e-21
6 −2.882524686831016e-28 7.799576438254665e-29
7 9.649191199496467e-29 2.876383454639922e-28
8 2.882524686831016e-28 −4.824471121337579e-29

ak coefficients in metres

GK LCC2 CP
k Hayford (ED50 Datum) GRS80 (ITRF Datum) Hayford (ED50 Datum) GRS80 (ITRF Datum) Hayford (ED50 Datum) GRS80 (ITRF Datum)
1 4963550.54140 4963327.33863 4961856.51702 4961633.36122 4961858.21105 4961635.05520
2 −1561831.78385 −1561761.55083 −1561480.06295 −1561409.82430 −1561480.41467 −1561410.17603
3 −174039.01315 −174022.53500 327595.12206 327580.38357 327093.48792 327078.78065
4 344383.18219 344355.40058 −51546.55823 −51544.23875 −51150.62849 −51148.33911
5 −97650.60029 −97639.86801 6488.61350 6488.32148 6384.47429 6384.19329
6 −37371.53049 −37368.38135 −680.64850 −680.61786 −717.33938 −717.30563
7 39232.35134 39,226.49432 61.19939 61.19663 100.37054 100.36193
8 −7671.34989 −7668.97005 −4.81481 −4.81460 −12.48135 −12.47875
9 −6850.12639 −6849.30900 0.33671 0.33670 −6.51375 −6.51295
10 5154.82567 5153.41787 −0.02119 −0.02119 5.13365 5.13225

Numerical values for CP (for 1 km) (k1 = 0.001, k2 = 1 − k1)

B [°] L [°] XCP[m] YCP[m] M m0=1m {m_0} = {1 \over m} γ [°] (T – t) [″] (T-t)map Tt[m] (S – s) [m] (S-s)map Ss [m]
35.5 26.0 −343547.200 −861653.097 1.001502 0.998500 −5.97880628 0.6806 0.6805 0.0000 −1.499 −1.489 −0.010
36.0 26.5 −292879.879 −810972.322 1.001018 0.998983 −5.66419331 0.5850 0.5852 −0.0002 −1.015 −1.005 −0.010
36.5 27.0 −241925.869 −760876.119 1.000607 0.999394 −5.34957328 0.4890 0.4893 −0.0003 −0.604 −0.595 −0.009
37.0 27.5 −190685.986 −711365.636 1.000269 0.999731 −5.03494624 0.3924 0.3927 −0.0003 −0.267 −0.259 −0.008
37.5 28.0 −139161.028 −662442.072 1.000005 0.999995 −4.72031223 0.2952 0.2955 −0.0003 −0.004 0.003 −0.007
38.0 28.5 −87351.773 −614106.679 0.999816 1.000184 −4.40567130 0.1974 0.1976 −0.0002 0.185 0.191 −0.006
38.5 29.0 −35258.976 −566360.762 0.999702 1.000298 −4.09102350 0.0989 0.0990 −0.0001 0.299 0.303 −0.005
39.0 29.5 17116.629 −519205.677 0.999662 1.000338 −3.77636888 −0.0002 −0.0002 0.0000 0.338 0.341 −0.003
39.5 30.0 69774.333 −472642.839 0.999699 1.000301 −3.46170748 −0.1000 −0.1002 0.0002 0.301 0.303 −0.002
40.0 30.5 122713.451 −426673.712 0.999812 1.000188 −3.14703936 −0.2006 −0.2009 0.0003 0.187 0.188 −0.001
40.5 31.0 175933.327 −381299.820 1.000002 0.999998 −2.83236456 −0.3019 −0.3024 0.0005 −0.003 −0.004 0.001
41.0 31.5 229433.329 −336522.741 1.000269 0.999731 −2.51768313 −0.4040 −0.4047 0.0007 −0.271 −0.273 0.002
42.0 32.0 338751.594 −290207.607 1.001040 0.998961 −2.20301786 −0.6108 −0.6117 0.0009 −1.043 −1.047 0.004
42.5 32.5 392851.626 −246933.182 1.001545 0.998457 −1.88831991 −0.7155 −0.7166 0.0011 −1.548 −1.553 0.005
35.5 33.0 −385425.899 −227133.656 1.001494 0.998508 −1.57336268 0.6816 0.6812 0.0004 −1.490 −1.484 −0.006
36.0 33.5 −331015.720 −180494.967 1.001010 0.998991 −1.25870410 0.5861 0.5855 0.0005 −1.007 −1.002 −0.005
36.5 34.0 −276364.523 −134461.147 1.000600 0.999401 −0.94403851 0.4900 0.4894 0.0007 −0.597 −0.593 −0.004
37.0 34.5 −221473.213 −89033.279 1.000263 0.999737 −0.62936594 0.3934 0.3926 0.0008 −0.261 −0.258 −0.003
38.0 35.0 −110853.214 −43907.730 0.999811 1.000189 −0.31468987 0.1983 0.1974 0.0009 0.189 0.191 −0.002
39.0 35.5 0.000 0.000 0.999659 1.000341 0.00000000 0.0007 −0.0004 0.0011 0.341 0.341 0.000
39.5 36.0 55609.954 42993.428 0.999696 1.000304 0.31470008 −0.0992 −0.1004 0.0012 0.303 0.303 0.001
40.0 36.5 111461.668 85375.887 0.999810 1.000190 0.62940691 −0.1997 −0.2010 0.0013 0.189 0.188 0.002
40.5 37.0 167554.386 127145.900 1.000000 1.000000 0.94412043 −0.3010 −0.3024 0.0014 −0.002 −0.004 0.002
41.0 37.5 223887.372 168301.932 1.000268 0.999732 1.25884059 −0.4031 −0.4047 0.0015 −0.270 −0.273 0.003
41.5 38.0 280459.918 208842.389 1.000615 0.999386 1.57356734 −0.5061 −0.5077 0.0016 −0.617 −0.621 0.004
42.0 38.5 337271.342 248765.618 1.001040 0.998961 1.88830062 −0.6099 −0.6116 0.0018 −1.043 −1.047 0.004
42.5 39.0 394320.989 288069.904 1.001545 0.998457 2.20304037 −0.7145 −0.7164 0.0019 −1.549 −1.554 0.005
35.5 39.5 −380561.376 363342.720 1.001495 0.998507 2.51738164 0.6827 0.6812 0.0015 −1.491 −1.484 −0.007
36.0 40.5 −320609.223 451047.199 1.001012 0.998989 3.14676397 0.5872 0.5856 0.0016 −1.009 −1.002 −0.007
36.5 41.0 −262583.287 492747.097 1.000603 0.999398 3.46148011 0.4912 0.4895 0.0016 −0.600 −0.593 −0.007
37.0 41.5 −204364.419 533824.364 1.000266 0.999734 3.77620340 0.3946 0.3929 0.0017 −0.264 −0.258 −0.006
37.5 42.0 −145953.593 574277.932 1.000004 0.999996 4.09093380 0.2974 0.2956 0.0018 −0.003 0.004 −0.006
38.0 42.5 −87351.773 614106.679 0.999816 1.000184 4.40567130 0.1996 0.1977 0.0019 0.185 0.191 −0.006
38.5 43.0 −28559.910 653309.428 0.999703 1.000297 4.72041584 0.1011 0.0991 0.0020 0.298 0.304 −0.006
39.0 43.5 30421.060 691884.946 0.999665 1.000335 5.03516738 0.0020 −0.0002 0.0023 0.335 0.341 −0.006
39.5 44.0 89590.217 729831.941 0.999703 1.000297 5.34992587 −0.0978 −0.1003 0.0025 0.297 0.303 −0.006
40.0 44.5 148946.655 767149.065 0.999817 1.000183 5.66469127 −0.1983 −0.2012 0.0029 0.182 0.189 −0.007
42.5 45.0 429557.127 780679.388 1.001552 0.998451 5.97971209 −0.7135 −0.7181 0.0046 −1.555 −1.551 −0.004

bk coefficients

GK LCC2 CP
k Hayford (ED50 Datum) GRS80 (ITRF Datum) Hayford (ED50 Datum) GRS80 (ITRF Datum) Hayford (ED50 Datum) GRS80 (ITRF Datum)
1 2.01468684898033e-07 2.01477745023166e-07 2.01537468197565e-07 2.01546532602613e-07 2.01537399414265e-07 2.01546463815034e-07
2 1.27719412250272e-14 1.27730899691869e-14 1.27821479148768e-14 1.27832976273027e-14 1.27821377081870e-14 1.27832874196446e-14
3 1.90606580617672e-21 1.90630871057434e-21 1.08091269101801e-21 1.08105852690209e-21 1.08173784413317e-21 1.08188377708576e-21
4 2.33217785338216e-28 2.33259302576196e-28 1.02832386626856e-28 1.02850885526054e-28 1.02962772025567e-28 1.02981293943104e-28
5 3.40288110341843e-35 3.40362666718644e-35 1.04351317940802e-35 1.04374783445450e-35 1.04587254733203e-35 1.04610771328723e-35
6 4.92399104670312e-42 4.92529126527513e-42 1.10304880523434e-42 1.10334646159951e-42 1.10686974747581e-42 1.10716840640319e-42
7 7.46687045549524e-49 7.46916636213681e-49 1.19929486733841e-49 1.19967244054757e-49 1.20556244292657e-49 1.20594193446916e-49
8 1.14705437919241e-55 1.14745779438984e-55 1.33110423181849e-56 1.33158317899727e-56 1.34124367137860e-56 1.34172617376217e-56
9 1.79545605447638e-62 1.79616622523578e-62 1.50085099606334e-63 1.50145853535200e-63 1.51730470561204e-63 1.51791873906901e-63
10 2.84208801069137e-69 2.84333725613141e-69 1.71339747802719e-70 1.71416813538263e-70 1.74010496065608e-70 1.74088733980856e-70
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