#!/usr/bin/env ruby
include Math

def d2r(d)
  d*Math::PI/180.0
end

def r2d(r)
  r*180.0/Math::PI
end

# from Candlekeep discussion with Ed Greenwood 31 December 2004
# http://www.forum.candlekeep.com/topic.asp?TOPIC_ID=1901&whichpage=80&SearchTerms=axial%2Ctilt
AXIAL_TILT_DEGREES = 28.883333
SOLAR_DAYS_PER_YEAR = 365.0

HOURS_PER_SOLAR_DAY = 24.0
DEGREES_PER_HOUR = 360.0 / HOURS_PER_SOLAR_DAY

# calculations based on:
# http://www.jgiesen.de/astro/solarday.htm
# (site contains errors, which have been corrected here)

def delta_from_day_of_year(northern_spring_equinox_day_of_year, day_of_year)
  orbital_position_degrees = (day_of_year-northern_spring_equinox_day_of_year)/SOLAR_DAYS_PER_YEAR

  -1 * AXIAL_TILT_DEGREES * sin(2*PI*orbital_position_degrees)
end

def hours_of_sunlight(northern_spring_equinox_day_of_year, latitude_degrees, day_of_year)
  delta = delta_from_day_of_year(northern_spring_equinox_day_of_year, day_of_year)
  r2d(acos(tan(d2r(latitude_degrees))*tan(d2r(delta)))) / (DEGREES_PER_HOUR / 2.0)
end

# based on http://stackoverflow.com/questions/4136248/how-to-generate-a-human-readable-time-range-using-ruby-on-rails
def humanize(mins)
  [[60, :m], [24, :h], [1000, :d]].map{ |count, name|
    if mins > 0
      mins, n = mins.divmod(count)
      "#{n.to_i}#{name}"
    end
  }.compact.reverse.join(' ')
end

FDate = Struct.new(:name, :day_of_year) do
  def at_latitude_degrees(northern_spring_equinox_day_of_year, latitude_degrees)
    "#{name}: #{humanize(60*hours_of_sunlight(northern_spring_equinox_day_of_year, latitude_degrees, day_of_year))}"
  end
end

FYear = Struct.new(:northern_spring_equinox_day_of_year, :dates) do
  def print_date_day_lengths(latitude_degrees)
    dates.each { |date| puts date.at_latitude_degrees(northern_spring_equinox_day_of_year, latitude_degrees)}
  end
end

# FRCS p77
FrcsYear = FYear.new(
  80,
  [
    FDate.new('Hammer 15', 15),
    FDate.new('Midwinter', 31),
    FDate.new('Alturiak 15', 46),
    FDate.new('Ches 15', 76),
    FDate.new('Ches 19 Equinox', 80),
    FDate.new('Tarsakh 15', 106),
    FDate.new('Greengrass', 122),
    FDate.new('Mirtul 15', 137),
    FDate.new('Kythorn 15', 167),
    FDate.new('Kythorn 20 Solstice', 172),
    FDate.new('Flamerule 15', 197),
    FDate.new('Midsummer/Shieldmeet', 213),
    FDate.new('Eleasis 15', 228),
    FDate.new('Eleint 15', 258),
    FDate.new('Eleint 21 Equinox', 263),
    FDate.new('High Harvestide', 274),
    FDate.new('Marpenoth 15', 289),
    FDate.new('Uktar 15', 319),
    FDate.new('The Feast of the Moon', 335),
    FDate.new('Nightal 15', 350),
    FDate.new('Nightal 20 Solstice', 355)
  ]
)

# SCAG p15
ScagYear = FYear.new(
  122,
  [
    FDate.new('Hammer 15', 15),
    FDate.new('Midwinter Solstice', 31),
    FDate.new('Alturiak 15', 46),
    FDate.new('Ches 15', 76),
    FDate.new('Tarsakh 15', 106),
    FDate.new('Greengrass Equinox', 122),
    FDate.new('Mirtul 15', 137),
    FDate.new('Kythorn 15', 167),
    FDate.new('Flamerule 15', 197),
    FDate.new('Midsummer/Shieldmeet Solstice', 213),
    FDate.new('Eleasis 15', 228),
    FDate.new('Eleint 15', 258),
    FDate.new('High Harvestide', 274),
    FDate.new('Marpenoth 15', 289),
    FDate.new('Marpenoth 30 Equinox', 304),
    FDate.new('Uktar 15', 319),
    FDate.new('The Feast of the Moon', 335),
    FDate.new('Nightal 15', 350)
  ]
)

ARGV.each do |arg|
  latitude_degrees = arg.to_f
  puts "FRCS (pre 1488 DR) Latitude: #{latitude_degrees}"
  FrcsYear.print_date_day_lengths(latitude_degrees)
  puts
  puts "SCAG (post 1488 DR) Latitude: #{latitude_degrees}"
  ScagYear.print_date_day_lengths(latitude_degrees)
  puts
end

quote:

---

Originally posted by Aelf

For my current game, we wanted to know how many hours of daylight there were in various locales and seasons on Toril.
This is complicated by the long winter of 1488 DR (SCAG p15.)

Referencing Ed's reply on December 31st, 2004, and doing a bit of trig :)
http://www.forum.candlekeep.com/topic.asp?TOPIC_ID=1901&whichpage=80

Waterdeep 45 deg N, pre 1488 DR

Hammer 15: 8h 6m
Midwinter: 8h 53m
Alturiak 15: 9h 47m
Ches 15: 11h 44m
Ches 19 Equinox: 12h 0m
Tarsakh 15: 13h 42m
Greengrass: 14h 42m
Mirtul 15: 15h 31m
Kythorn 15: 16h 26m
Kythorn 20 Solstice: 16h 27m
Flamerule 15: 15h 54m
Midsummer/Shieldmeet: 15h 7m
Eleasis 15: 14h 14m
Eleint 15: 12h 17m
Eleint 21 Equinox: 11h 58m
High Harvestide: 11h 14m
Marpenoth 15: 10h 15m
Uktar 15: 8h 29m
The Feast of the Moon: 7h 50m
Nightal 15: 7h 32m
Nightal 20 Solstice: 7h 32m

Waterdeep 45 deg N, post 1488 DR

Hammer 15: 7h 45m
Midwinter Solstice: 7h 32m
Alturiak 15: 7h 44m
Ches 15: 9h 3m
Tarsakh 15: 10h 56m
Greengrass Equinox: 12h 0m
Mirtul 15: 12h 59m
Kythorn 15: 14h 52m
Flamerule 15: 16h 14m
Midsummer/Shieldmeet Solstice: 16h 27m
Eleasis 15: 16h 16m
Eleint 15: 14h 57m
High Harvestide: 13h 59m
Marpenoth 15: 13h 1m
Marpenoth 30 Equinox: 12h 1m
Uktar 15: 11h 2m
The Feast of the Moon: 10h 0m
Nightal 15: 9h 5m

Silverymoon 51 deg N, pre 1488 DR

Hammer 15: 7h 3m
Midwinter: 8h 6m
Alturiak 15: 9h 14m
Ches 15: 11h 40m
Ches 19 Equinox: 12h 0m
Tarsakh 15: 14h 7m
Greengrass: 15h 22m
Mirtul 15: 16h 26m
Kythorn 15: 17h 42m
Kythorn 20 Solstice: 17h 43m
Flamerule 15: 16h 57m
Midsummer/Shieldmeet: 15h 55m
Eleasis 15: 14h 47m
Eleint 15: 12h 22m
Eleint 21 Equinox: 11h 57m
High Harvestide: 11h 3m
Marpenoth 15: 9h 50m
Uktar 15: 7h 35m
The Feast of the Moon: 6h 41m
Nightal 15: 6h 17m
Nightal 20 Solstice: 6h 16m

Silverymoon 51 deg N, post 1488 DR

Hammer 15: 6h 34m
Midwinter Solstice: 6h 16m
Alturiak 15: 6h 33m
Ches 15: 8h 19m
Tarsakh 15: 10h 41m
Greengrass Equinox: 12h 0m
Mirtul 15: 13h 13m
Kythorn 15: 15h 36m
Flamerule 15: 17h 24m
Midsummer/Shieldmeet Solstice: 17h 43m
Eleasis 15: 17h 27m
Eleint 15: 15h 42m
High Harvestide: 14h 28m
Marpenoth 15: 13h 16m
Marpenoth 30 Equinox: 12h 2m
Uktar 15: 10h 48m
The Feast of the Moon: 9h 31m
Nightal 15: 8h 21m

If you would like other locales run, let me know and I will post a reply.
I will also look at automating the process on a webpage.

Note also that these calculations agree with Jerryd's midwinter length of day number for Silverymoon.
(There are a number of assumptions here that will cause some inaccuracy, but it is a small amount.)

Finally, I will post the code to the script I wrote for those who might enjoy math and/or programming.

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quote:

---

Originally posted by Sleyvas
Ok, I'm going to go with... you goodsir are officially a geek

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quote:

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Originally posted by Markustay
... and I realize I may have come off a bit ...

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quote:

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Originally posted by Ayrik

Are these calculations based off data for Earth/Sun orbits, rotations, latitude, etc?

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