88 lines
2.4 KiB
ReStructuredText
88 lines
2.4 KiB
ReStructuredText
Coordinate System
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=================
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NavalToolbox uses a **right-handed coordinate system** consistent with standard naval architecture conventions.
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Axes Definition
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---------------
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.. list-table::
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:widths: 15 40 25
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:header-rows: 1
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* - Axis
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- Direction
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- Sign Convention
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* - **X**
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- Longitudinal (length)
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- Positive towards bow (forward)
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* - **Y**
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- Transverse (beam)
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- Positive towards port (left when facing bow)
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* - **Z**
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- Vertical (height)
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- Positive upward
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.. note::
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The origin is typically at the intersection of the aft perpendicular (AP),
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centerline, and baseline (keel), but may vary depending on the hull geometry file.
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Rotations
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---------
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Rotations follow the **right-hand rule**: curl your fingers around the axis in the
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direction of positive rotation, and your thumb points in the positive axis direction.
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.. list-table::
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:widths: 15 30 35
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:header-rows: 1
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* - Rotation
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- Axis
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- Positive Direction
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* - **Heel (φ)**
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- Around X-axis
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- Port UP / Starboard down
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* - **Trim (θ)**
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- Around Y-axis
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- Bow down / Stern up
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Physical Interpretation
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-----------------------
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**Heel:**
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- **Positive heel** (φ > 0): Port side goes UP, starboard side goes DOWN
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- **Negative heel** (φ < 0): Port side goes DOWN, starboard side goes UP
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**Trim:**
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- **Positive trim** (θ > 0): Bow goes DOWN, stern goes UP
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- **Negative trim** (θ < 0): Bow goes UP, stern goes DOWN (stern trim)
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Equilibrium Angles
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------------------
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When calculating equilibrium from a center of gravity (COG) offset:
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- **TcG > 0** (weight on port): Results in **negative heel** (port goes down)
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- **TcG < 0** (weight on starboard): Results in **positive heel** (starboard goes down)
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- **LcG > LCB** (weight forward of buoyancy): Results in **positive trim** (bow down)
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- **LcG < LCB** (weight aft of buoyancy): Results in **negative trim** (stern down)
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GZ Curve Convention
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-------------------
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The righting arm GZ is calculated as:
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.. math::
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GZ = G_y^{world} - B_y^{world}
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Where :math:`G_y^{world}` and :math:`B_y^{world}` are the Y-coordinates of the
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center of gravity and center of buoyancy in the world frame (waterplane horizontal).
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- **Positive GZ**: Restoring moment (ship tends to return upright)
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- **Negative GZ**: Capsizing moment (ship tends to heel further)
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At small heels, this simplifies to: :math:`GZ \approx GM \cdot \sin(\phi)`
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