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Air mass: Difference between revisions
→{{header|Nim}}
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90 34.32981136 34.36666557
</pre>
=={{header|Nim}}==
{{trans|Wren}}
<lang Nim>import math, strformat
const
Re = 6371000 # Radius of earth in meters.
Dd= 0.001 # Integrate in this fraction of the distance already covered.
Fin = 1e7 # Integrate only to a height of 10000km, effectively infinity.
func rho(a: float): float =
## The density of air as a function of height above sea level.
exp(-a / 8500)
func height(a, z, d: float): float =
## Height as a function of altitude (a), zenith angle (z)
## in degrees and distance along line of sight (d).
let aa = Re + a
let hh = sqrt(aa * aa + d * d - 2 * d * aa * cos(degToRad(180-z)))
result = hh - Re
func columnDensity(a, z: float): float =
## Integrates density along the line of sight.
var d = 0.0
while d < Fin:
let delta = max(Dd, Dd * d) # Adaptive step size to avoid it taking forever.
result += rho(height(a, z, d + 0.5 * delta)) * delta
d += delta
func airmass(a, z: float): float =
columnDensity(a, z) / columnDensity(a, 0)
echo "Angle 0 m 13700 m"
echo "------------------------------------"
var z = 0.0
while z <= 90:
echo &"{z:2} {airmass(0, z):11.8f} {airmass(13700, z):11.8f}"
z += 5</lang>
{{out}}
<pre>Angle 0 m 13700 m
------------------------------------
0 1.00000000 1.00000000
5 1.00380963 1.00380965
10 1.01538466 1.01538475
15 1.03517744 1.03517765
20 1.06399053 1.06399093
25 1.10305937 1.10306005
30 1.15418974 1.15419083
35 1.21998076 1.21998246
40 1.30418931 1.30419190
45 1.41234169 1.41234567
50 1.55280404 1.55281025
55 1.73875921 1.73876915
60 1.99212000 1.99213665
65 2.35199740 2.35202722
70 2.89531368 2.89537287
75 3.79582352 3.79596149
80 5.53885809 5.53928113
85 10.07896219 10.08115981
90 34.32981136 34.36666557</pre>
=={{header|Perl}}==
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