# Exercise 2: the dynamometer readings as forces on a disc.
import math

LBF_N = 4.4482216
FT_M = 0.3048
IN_FT = 1 / 12
DISC_IN = 3.0                       # ASSUMED, illustrative: the pages I read give no disc size
READINGS = {"summer mean": 611, "winter mean": 2086, "Bell Rock best": 3013, "Skerryvore best": 4335, "design figure": 6000}

area_ft2 = math.pi * (DISC_IN * IN_FT / 2) ** 2
print("disc area:", round(area_ft2, 4), "ft2 =", round(area_ft2 * FT_M ** 2 * 10000, 1), "cm2")
for name, p in READINGS.items():
    force_lbf = p * area_ft2
    print(name.ljust(16), p, "lb/ft2 -> force on the disc:", round(force_lbf, 1), "lbf =", round(force_lbf * LBF_N), "N")

# Fraction by which each reading falls short of the design figure.
for name, p in READINGS.items():
    print(name.ljust(16), "is", round(p / 6000 * 100, 1), "per cent of 6000")

# The one-fourth claim, and a 'fourth below' check on each pair.
print("Bell Rock / Skerryvore:", round(3013 / 4335, 3), "; three quarters would be", round(0.75 * 4335))
print("4335 in tonnes-force per m2:", round(4335 * LBF_N / FT_M ** 2 / 9.81 / 1000, 1))
print("6083 vs 6000:", round((6083 / 6000 - 1) * 100, 2), "per cent higher")
# disc area: 0.0491 ft2 = 45.6 cm2
# summer mean      611 lb/ft2 -> force on the disc: 30.0 lbf = 133 N
# winter mean      2086 lb/ft2 -> force on the disc: 102.4 lbf = 455 N
# Bell Rock best   3013 lb/ft2 -> force on the disc: 147.9 lbf = 658 N
# Skerryvore best  4335 lb/ft2 -> force on the disc: 212.8 lbf = 947 N
# design figure    6000 lb/ft2 -> force on the disc: 294.5 lbf = 1310 N
# summer mean      is 10.2 per cent of 6000
# winter mean      is 34.8 per cent of 6000
# Bell Rock best   is 50.2 per cent of 6000
# Skerryvore best  is 72.2 per cent of 6000
# design figure    is 100.0 per cent of 6000
# Bell Rock / Skerryvore: 0.695 ; three quarters would be 3251
# 4335 in tonnes-force per m2: 21.2
# 6083 vs 6000: 1.38 per cent higher