# How Lighthouses Work 3, Exercise 3: lamps compared, and a range check
# Filament against LED over ten years, and the Souter and Bell Rock intensities through the range model.
import math

NM = 1852.0

def transmissivity(visibility_nm):
    return 0.05 ** (1 / visibility_nm)

def luminous_range_nm(intensity_cd, visibility_nm, threshold_lx=2e-7):
    t = transmissivity(visibility_nm)
    lo, hi = 0.01, 200.0
    for _ in range(100):
        mid = (lo + hi) / 2
        e = intensity_cd * t ** mid / (mid * NM) ** 2
        if e > threshold_lx:
            lo = mid
        else:
            hi = mid
    return (lo + hi) / 2

def geographic_range_nm(light_m, eye_m):
    return 3.86 * (math.sqrt(light_m) + math.sqrt(eye_m)) / 1.852

# Assumptions: 1,500 lm wanted, 4,380 dark hours a year, efficacy and lifetime from the chapter
HOURS = 4380
for name, eff, life in (("Filament", 15, 1000), ("LED", 102, 50000)):
    watts = 1500 / eff
    kwh_year = watts * HOURS / 1000
    lamps_10y = math.ceil(10 * HOURS / life)
    print(name, round(watts, 1), "W", round(kwh_year), "kWh a year", lamps_10y, "lamps in 10 years")
print(round(102 / 15, 1), "x the lumens per watt")

# Souter's quoted 800,000 cd against the Bell Rock's current 1,900,000 cd
print(round(luminous_range_nm(800_000, 10), 1), round(luminous_range_nm(1_900_000, 10), 1))
print(round(1_900_000 / 800_000, 2), "x the intensity")

# Output when run:
# Filament 100.0 W 438 kWh a year 44 lamps in 10 years
# LED 14.7 W 64 kWh a year 1 lamps in 10 years
# 6.8 x the lumens per watt
# 25.1 27.4
# 2.38 x the intensity
#
# Lines 1 and 2: the 15 lm/W filament draws 100 W, uses 438 kWh a year, and needs 44 lamps of
# 1,000 hours in 10 years; the 102 lm/W LED draws 14.7 W, uses 64 kWh a year, and needs one.
# Line 3: that is 6.8 times the lumens per watt. Line 4: the model gives 25.1 nm for Souter's
# 800,000 cd and 27.4 nm for 1,900,000 cd. Line 5: 2.38 times the intensity gives only about 9
# per cent more range. The Wikipedia page for the Bell Rock lists a range of 18 nmi, less than
# the 27.4 nm of this model; I do not know how the listed figure was set (the geographic range
# for a 28 m focal height and an eye 5 m up is about 15.7 nm), so treat the gap as unexplained
# and not as a finding.