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&[DATE] &[TIME] - &[FILENAME]

Calculating Visibility of Distant Objects

lapserates No Refraction Standart Atmospheric Rate Custom Rate Calculation 31 mat :

A CycleColors M A 1 matrix : k 1 A range M k el : for M mat2sys.1 31 line :

Lapse Rate Formula γ lapse 1 ≡ 0 K km / * lapse 2 ≡ 6.5 K km / * lapse 3 ≡ T T.H - H h - / 0 try if 11 line :

d.eff R.eff h + (2^R.eff (2^- sqrt 11 line : d.eff_H R.eff H + (2^R.eff (2^- sqrt 11 line : smallH d.H 2^1 k - (2 R * / * 11 line : z h d.H 2^1 k - (2 R * / * + 11 line : altrad H z - d.H / atan 11 line : altdeg altrad deg / 11 line : altmin altdeg 60 * 11 line : diprad h 2 * 1 k - (* R / sqrt 11 line : dipdeg diprad deg / 11 line : dipmin dipdeg 60 * 11 line : dipsum diprad altrad + 11 line : dipsumdeg dipsum deg / 11 line : dipsummin dipsumdeg 60 * 11 line : 131 line

Curvature Ratio k lapse 1 ≡ 135 γ km K / * - 150 / h H + 16 km * / - exp * if 11 line :

Refractive Radius R.eff lapse 1 ≡ R R 1 k - / if 11 line :

Earth Radius R 6371 km * :

r# 1 : r# 2 ^ x 2 ^ - sqrt x 0.1 0.95 lele cases 2 1 line 5 CycleColors r# 1.09 : r# 2 ^ x 2 ^ - sqrt x 0.38 0.67 lele cases 2 1 line r# 1.05 : r# 2 ^ x 0.15 - ( 2 ^ - sqrt x 0.39 0.70 lele cases 2 1 line 0 0 0.1 0.995 2 2 mat 5 CycleColors 0 0 0.95 0.3122 2 2 mat 0 0 0.35 0.9367 2 2 mat 5 CycleColors 0 0 0.61 0.79 2 2 mat 0.35 0.9367 0.38 1.02 2 2 mat 5 CycleColors 0.61 0.79 0.7 0.9 2 2 mat 0.34 1.06 h 0.17 0.6 R 0.38 0.5 R 0.71 0.92 H 0.5 0.92 d 0.57 1.03 R' 6 3 mat 14 1 sys

Observer Elevation h 1.8 m * :

Target Elevation H 150 m * :

Observer Temperature T 22 °C * :

Target Temperature T.H 21 °C * :

Adiabatic Lapse Rate γ.A 10 K km / * :

Target Distance d.H 15 km * :

"No\0020\Refraction"
"Standart\0020\Atmospheric\0020\Rate"
"Custom\0020\Rate\0020\Calculation"

Lapse Rate Selection

lapse

Lapse Rate γ K km / 6.7476

temizleme makinası yoksa hız 0.75'den az olmalıdır. mekanik temizlenenler için hız 1.5 m/s'ye çıkarılabilir.

lapse 3 ≡ T.H 58 °C * > ( T 58 °C * > ( | Temperatures are greater than 58°C. Reduce it. k 1 > The observer is in a duct. Horizon is infinite. γ γ.A ≤ Lapse Rate is OK γ γ.A > Lapse rate exceeds the adiabatic value. Reduce it. if No condition applied. if lapse 3 ≡ T.H 58 °C * > ( T 58 °C * > ( | Black k 1 > Black γ γ.A ≤ DarkGreen γ γ.A > Black if Darkgreen if lapse 3 ≡ T.H 58 °C * > ( T 58 °C * > ( | Red k 1 > Red γ γ.A ≤ White γ γ.A > Red if White if WhiteFrame 1 4 mat

1) We first find lapse rate for specified conditions. A manual rate can be determined.
\[REGION[dbe86dc97005426db1e4c8657ef73c0f]]\
2) Having determined the lapse rate, we find the ratio of curvatures of horizontal rays and the Earth's surface.
\[REGION[0784491ebfbb4388b269e8a66e171205]]\
3) We adopt an effective curvature for the Earth that's the difference of curvatures of the actual surface and the circular ray.
\[REGION[5b45c927ba2946ae8ea9baa0d943cd64]]\
4) Finding horizon distances is simple gemotery after determining curvature ratio.
\[REGION[9fdb5de46d0b4699af683a441df19b7a]]\

γ T T.H - H h - / ≡

k 35 γ km K / * - 150 / h H + 28 * km * / - exp * ≡

R.eff R 1 k - / ≡

d.eff R.eff h + (2^R.eff 2^- sqrt ≡

Curvature Ratio k 0.1866

lapse 1 ≡ k 1 : d.eff d.H ≥ result The target is closer than horizon, it is easily visible. : d.eff d.eff_H + d.H > result The target is above the horizon, it is visible. : d.eff d.eff_H + d.H ≤ result The target is below the horizon, it is hidden. : if 21 line lapse 3 ≡ k 1 > k 1 : result The distance to the horizon is infinite, because the observer is in a duct. : altrad altdeg altmin diprad dipdeg dipmin dipsum dipsumdeg dipsummin Clear 31 line T 58 °C * > (T.H 58 °C * > (| result Temperatures are greater than 58°C. Reduce it. : γ γ.A > k 1 : result Lapse rate exceeds adiabatic value, reduce it. : altrad altdeg altmin diprad dipdeg dipmin dipsum dipsumdeg dipsummin Clear 31 line if if dipsum 103 -^> result The target is above horizon, it is easily visible. : dipsum 0 > result The target is above horizon, it is visible. : dipsum 0 ≤ d.eff d.H < result The target is below the horizon, it is hidden. : result The target is closer than horizon, it is visible. : if if 21 line if

Refractive Radius R.eff km 7832.2713

Observer Horizon Distance d.eff R.eff h + (2^R.eff 2^- sqrt : km 5.31

Target Horizon Distance d.eff_H R.eff H + (2^R.eff 2^- sqrt : km 48.4737

Line of Sight d.T d.eff d.eff_H + : km 53.7838

Apparent altitude of target is \[REGION[0906c671778b4897a735b4a942d8e79a]]\ minutes of arc = \[REGION[99facbdebeeb4942a97cc4d9881dda54]]\ degrees of arc.
Dip of sea horizon is \[REGION[65a7c08ad1a44977a922c28051d44d73]]\ minutes of arc = \[REGION[29f99a70761d4db080ca3a3f4f21b628]]\ degrees of arc.
These values place the target \[REGION[d62bce13bf2f49c3b6cda81c4057f70c]]\ minutes of arc = \[REGION[229409901e7e4b8daa86ac416f081f93]]\ degrees of arc.

\[REGION[5b2f6f78a2094504ad4a47cc1fd03a34]]\

altmin 30.6722

altdeg 0.5112

dipmin 2.3307

dipdeg 0.0388

dipsummin 33.0029

dipsumdeg 0.55

result The target is above horizon, it is easily visible.

https://aty.sdsu.edu/explain/atmos_refr/altitudes.html