# How Lighthouses Work 5, Exercise 2: a rotating lens and its characteristic
import math

def flash_interval(period_s, panels):
    return period_s / panels

# 4 equally spaced bull's-eye panels, one turn in 20 s
print("interval:", flash_interval(20, 4), "s, rate:", 60 / flash_interval(20, 4), "per minute")
# Dwell time of a 1.25 degree beam at 20 s per turn
print("dwell:", round(1.25 / 360 * 20, 3), "s")
# Fl 5 s from 4 panels: period of one turn
print("turn for Fl 5s from 4 panels:", 5 * 4, "s")
# Fl(2) 10 s: panel pair spacing for flash starts 2 s apart at a 10 s turn
spacing_deg = 2 / 10 * 360
print("pair spacing:", spacing_deg, "deg")
# Beam width a flash of 1 s needs at 20 s per turn and at 5 s per turn
for t in (20, 5):
    print("1 s flash at", t, "s per turn needs a beam", 1 / t * 360, "deg wide")
# Speed of the beam over the sea at a ship 10 nm away (nominal range)
speed_deg_s = 360 / 20
nm = 1852.0
v = math.radians(speed_deg_s) * 10 * nm
print("beam sweep speed at 10 nm:", round(v), "m/s")

# Output:
# interval: 5.0 s, rate: 12.0 per minute
# dwell: 0.069 s
# turn for Fl 5s from 4 panels: 20 s
# pair spacing: 72.0 deg
# 1 s flash at 20 s per turn needs a beam 18.0 deg wide
# 1 s flash at 5 s per turn needs a beam 72.0 deg wide
# beam sweep speed at 10 nm: 5818 m/s
#
# A lens with 4 equally spaced panels turning once in 20 s gives a flash every 5 s (12 per minute), the
# interval of Fl 5s. A 1.25 degree beam (the first-order figure from How Lighthouses Work 4) sweeps past an
# observer in 0.069 s at that speed, so a 1 s flash needs a beam 18 degrees wide (72 degrees if the turn takes 5 s).
# That is the general trade-off: a narrow beam gives a short flash, a wide beam is weaker. I could not find a source
# for how real lights reconcile the two, so treat the 1 s figure as the stated characteristic and not as a measured
# beam. For Fl(2) the two flash starts are 2 s apart in a 10 s turn, so the panel pair sits 72 degrees apart. The
# sweep speed at 10 nm is 5,818 m/s, which shows why the beam passes in a moment. All values come from the model,
# not from any real light.