Sub-skill of mooring-analysis: 5. Installation and Pretensioning (+1).
Pretension Optimization:
def calculate_pretension(
water_depth: float,
horizontal_distance: float,
target_touchdown_tension: float,
weight_per_length: float
) -> dict:
"""
Calculate required pretension for target touchdown tension.
Args:
water_depth: Water depth
horizontal_distance: Horizontal distance to anchor
target_touchdown_tension: Desired horizontal tension at seabed
weight_per_length: Line weight per length
Returns:
Required pretension
"""
# Calculate catenary profile
a = target_touchdown_tension / weight_per_length
# Suspended length
s = catenary_suspended_length(
water_depth,
horizontal_distance,
target_touchdown_tension,
weight_per_length
)
# Top tension
vertical_load = weight_per_length * water_depth
pretension = np.sqrt(target_touchdown_tension**2 + vertical_load**2)
return {
'pretension_kN': pretension,
'touchdown_tension_kN': target_touchdown_tension,
'suspended_length_m': s,
'catenary_parameter_m': a
}
Low Frequency Motion:
def estimate_low_frequency_offset(
mean_wave_drift: float, # kN
mooring_stiffness: float # kN/m
) -> float:
"""
Estimate vessel low-frequency offset.
Simple static approximation:
offset = Force / Stiffness
Args:
mean_wave_drift: Mean wave drift force
mooring_stiffness: Total horizontal stiffness
Returns:
Offset in meters
"""
return mean_wave_drift / mooring_stiffness
def calculate_mooring_stiffness(
num_lines: int,
pretension: float, # kN per line
fairlead_depth: float,
weight_per_length: float,
line_azimuth: list # degrees for each line
) -> float:
"""
Calculate total horizontal mooring stiffness.
Args:
num_lines: Number of mooring lines
pretension: Pretension per line
fairlead_depth: Depth of fairlead below waterline
weight_per_length: Weight per unit length
line_azimuth: Azimuth of each line
Returns:
Total horizontal stiffness in kN/m
"""
# Simplified: K = (T/a) for catenary
# where a = H/w
stiffness_per_line = weight_per_length * pretension / fairlead_depth
# Resolve in each direction
total_stiffness = 0
for azimuth in line_azimuth:
# Component in surge direction
component = stiffness_per_line * np.cos(np.radians(azimuth))
total_stiffness += component
return total_stiffness