170 lines
4.7 KiB
ReStructuredText
170 lines
4.7 KiB
ReStructuredText
Stability Tutorial
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==================
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This tutorial covers GZ curve calculations for intact stability analysis.
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Introduction
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------------
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The GZ (righting arm) curve shows how a vessel's stability changes with heel angle.
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Positive GZ values indicate the vessel will return to upright.
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Basic GZ Calculation
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--------------------
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.. code-block:: python
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from navaltoolbox import Hull, Vessel, StabilityCalculator
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# Load hull
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hull = Hull("dtmb5415.stl")
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vessel = Vessel(hull)
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# Create stability calculator
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calc = StabilityCalculator(vessel, water_density=1025.0)
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# Define loading condition
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# Note: This is the vessel mass EXCLUDING dynamic tank fluids.
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# The calculator will add the mass of any active tanks to this value.
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displacement = 8635000 # kg (8635 tonnes)
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cog = (71.67, 0.0, 7.555) # LCG, TCG, VCG in meters (Base/Lightship COG)
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# Heel angles to calculate
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heels = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]
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# Calculate GZ curve
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curve = calc.calculate_gz_curve(displacement, cog, heels)
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# Print results
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print("Heel (°) GZ (m)")
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print("-" * 20)
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for heel, gz in zip(curve.heels(), curve.values()):
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print(f"{heel:6.1f} {gz:+.3f}")
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Analyzing the Curve
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-------------------
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Extract key stability metrics:
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.. code-block:: python
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# Get GZ values
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heels = curve.heels()
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gz_values = curve.values()
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# Find maximum GZ
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max_gz = max(gz_values)
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max_gz_idx = gz_values.index(max_gz)
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max_gz_heel = heels[max_gz_idx]
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print(f"Maximum GZ: {max_gz:.3f}m at {max_gz_heel:.1f}°")
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# Check positive range
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positive_range = [h for h, gz in zip(heels, gz_values) if gz > 0]
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print(f"Positive GZ range: 0° to {max(positive_range):.0f}°")
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# Initial GM (from slope at 0°)
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# GZ ≈ GM × sin(φ) for small angles
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if len(gz_values) > 1 and heels[1] > 0:
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gm_approx = gz_values[1] / math.sin(math.radians(heels[1]))
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print(f"Approximate GM: {gm_approx:.2f}m")
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Effect of VCG
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-------------
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VCG (vertical center of gravity) significantly affects stability:
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.. code-block:: python
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# Compare different VCG values
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vcg_values = [6.5, 7.0, 7.5, 8.0, 8.5]
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print("VCG (m) Max GZ (m) Max GZ Angle")
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print("-" * 45)
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for vcg in vcg_values:
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cog = (71.67, 0.0, vcg)
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curve = calc.calculate_gz_curve(displacement, cog, [0, 10, 20, 30, 40, 50])
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gz_vals = curve.values()
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max_gz = max(gz_vals)
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max_idx = gz_vals.index(max_gz)
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print(f"{vcg:6.1f} {max_gz:.3f} {curve.heels()[max_idx]:.0f}°")
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DTMB 5415 Reference Values
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--------------------------
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NavalToolbox has been validated against reference data from Ariffin (2017).
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+--------+-------------+---------------+
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| Heel | Reference | NavalToolbox |
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+========+=============+===============+
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| 10° | 0.339 m | 0.333 m |
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+--------+-------------+---------------+
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| 20° | 0.674 m | 0.669 m |
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+--------+-------------+---------------+
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| 30° | 0.993 m | 0.982 m |
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+--------+-------------+---------------+
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| 40° | 1.077 m | 1.052 m |
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+--------+-------------+---------------+
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**Maximum error: 2.5cm**
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Plotting Results
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----------------
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Visualize the GZ curve using matplotlib:
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.. code-block:: python
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import matplotlib.pyplot as plt
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heels = curve.heels()
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gz_values = curve.values()
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plt.figure(figsize=(10, 6))
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plt.plot(heels, gz_values, 'b-o', linewidth=2, markersize=6)
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plt.axhline(y=0, color='k', linestyle='-', linewidth=0.5)
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plt.xlabel('Heel Angle (degrees)')
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plt.ylabel('GZ (m)')
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plt.title('Stability Curve (GZ)')
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plt.grid(True, alpha=0.3)
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plt.xlim(0, max(heels))
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plt.show()
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Including Tanks
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---------------
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Free surface effects reduce effective GM:
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.. code-block:: python
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from navaltoolbox import Tank
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# Add a fuel tank
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fuel_tank = Tank.from_box(
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"Fuel Tank",
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x_min=50, x_max=70,
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y_min=-5, y_max=5,
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z_min=0, z_max=4,
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fluid_density=850.0
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)
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fuel_tank.fill_percent = 50 # Partial fill = free surface
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vessel.add_tank(fuel_tank)
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# Free surface correction
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fsm = fuel_tank.free_surface_moment_t
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fs_correction = (fsm * fuel_tank.fluid_mass / fuel_tank.fill_volume) / displacement
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print(f"Free surface moment: {fsm:.1f} m⁴")
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print(f"GM reduction (virtual VCG rise): {fs_correction:.3f}m")
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print(f"GM reduction (virtual VCG rise): {fs_correction:.3f}m")
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# Note: Both HydrostaticsCalculator and StabilityCalculator apply this
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# correction automatically if tanks are present in the vessel.
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# The GZ curve computed above ALREADY includes this reduction.
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# No manual adjustment of VCG is required.
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