# Exercise 3: wave height from fetch, and fetch from wave height.
import math

FT_M = 0.3048
MILE_KM = 1.609344

def height_m(fetch_km):
    fetch_miles = fetch_km / MILE_KM
    return 1.5 * math.sqrt(fetch_miles) * FT_M

def fetch_km_for(height_in_m):
    feet = height_in_m / FT_M
    return (feet / 1.5) ** 2 * MILE_KM

print("heights from fetch (km):")
for km in (5, 20, 50, 100, 200):
    note = "" if km <= 100 else "  (beyond the 100 km the observations were for)"
    print(" ", km, "km ->", round(height_m(km), 2), "m" + note)
print("fetch needed for a given height:")
for h in (2, 4, 6, 8, 10):
    print(" ", h, "m ->", round(fetch_km_for(h)), "km")
print("largest height from observed fetches up to 100 km:", round(height_m(100), 2), "m")
print("fetch ratio for double the height:", round(fetch_km_for(4) / fetch_km_for(2), 2))
# heights from fetch (km):
#   5 km -> 0.81 m
#   20 km -> 1.61 m
#   50 km -> 2.55 m
#   100 km -> 3.6 m
#   200 km -> 5.1 m  (beyond the 100 km the observations were for)
# fetch needed for a given height:
#   2 m -> 31 km
#   4 m -> 123 km
#   6 m -> 277 km
#   8 m -> 493 km
#   10 m -> 770 km
# largest height from observed fetches up to 100 km: 3.6 m
# fetch ratio for double the height: 4.0