# How Bridges Work 8, Exercise 1: how many stays? fan or harp?
# A tower 150 m above the deck carries a half-span of 325 m, with a total deck
# load of 80,000 kN on that side, shared equally by n stays at equal spacing.
# For n = 6, 10 and 14 compare the fan layout (all stays meet at the tower
# top) and the harp layout (parallel stays): the largest stay force, the total
# horizontal push on the deck, and the steel volume of all the stays at 600 MPa.
import math

def stays(layout, n, d, height, p):
    out = []
    for i in range(1, n + 1):
        x = i * d
        y = height if layout == "fan" else height * x / (n * d)
        length = math.hypot(x, y)
        t = p * length / y
        out.append((x, y, length, t, t * x / length))
    return out

half, height, total = 325, 150, 80000
for n in (6, 10, 14):
    for layout in ("fan", "harp"):
        rows = stays(layout, n, half / n, height, total / n)
        h_sum = sum(r[4] for r in rows)
        steel = sum(r[3] * r[2] for r in rows) / 600e3
        print(n, layout, round(max(r[3] for r in rows)), round(h_sum), round(steel, 1))

# Output when run:
# 6 fan 31817 101111 59.6
# 6 harp 31817 173333 66.4
# 10 fan 19090 95333 56.1
# 10 harp 19090 173333 62.6
# 14 fan 13636 92857 54.7
# 14 harp 13636 173333 61.0
#
# Columns: number of stays, layout, largest stay force (kN), total horizontal
# push on the deck (kN), steel volume (m3). With the same total load, more stays
# means smaller forces in each (31,817 kN with 6 stays, 13,636 kN with 14) and a
# little less steel (59.6 to 54.7 m3 for the fan), which also makes each stay
# easier to handle and replace. The harp always pushes the deck with 173,333
# kN: that is the total load times the horizontal reach over the height
# (80,000 x 325 / 150), whatever n is. The fan pushes less (95,333 kN at n = 10)
# because most of its stays are steep. In this simple model the fan wins on both
# deck push and steel; designers still choose harps or semi-fans for looks
# and to space out the connections on the tower.