Crate navcore_math 

Pure navigation math.

The bottom layer of the navigation core: great circle and rhumb line sailings, cross-track error, the wind triangle, the current triangle, VMG and laylines, and a boat’s own performance polar. Every item here is a plain function of its arguments – no clock, no I/O, no state, no dependencies. That is what lets the layers above replay a recorded log deterministically.

Units and conventions

There is one convention throughout, and it is worth reading once:

• Angles are degrees, never radians. Radians exist only inside a function body.
• Bearings, headings and courses are degrees true, 0.0..360.0, clockwise from north. Magnetic variation is deliberately not handled here: it is a property of a place and a date, so it belongs to the layer that knows where and when the vessel is.
• Relative angles (true and apparent wind angle) are signed, -180.0..=180.0, measured from the bow, positive to starboard.
• Distances are nautical miles, speeds are knots.
• Cross-track error is positive when the vessel is to starboard of the track.

Nothing enforces these at the type level. Newtypes were considered and rejected: they make formulae meant to be read against a textbook harder to read, without preventing the mistakes this crate actually risks. Function and field names carry the unit instead – distance_nm, bearing_deg, speed_kn.

Earth model

A sphere of radius EARTH_RADIUS_NM, not the WGS84 ellipsoid. Over the distance of a single leg, the difference is well under the error in the fix that starts the leg. One consequence worth noting: one degree of latitude comes out as 60.04 NM rather than exactly 60, because the nautical mile is a fixed 1852 m while a minute of arc on the mean sphere is 1853.25 m.

Re-exports

pub use position::Position;

Modules

angle

Angle normalisation.

current

The current triangle: deriving set and drift, and steering to beat them.

great_circle

Great circle sailing – the shortest path between two positions.

polar

Boat performance polars, and the tactical numbers built on one.

position

A geographic position.

rhumb

Rhumb line (loxodrome) sailing – the path of constant bearing.

sailing

Velocity made good and laylines.

track

Position relative to a route leg: cross-track error and along-track distance.

wind

The wind triangle: converting between apparent and true wind.

Constants

EARTH_RADIUS_NM

Mean radius of the earth in nautical miles.

METRES_PER_FOOT

The international foot, exactly – a fixed definition, like METRES_PER_NM. Distance and speed stay nautical miles and knots throughout this crate (see “Units and conventions” above); this constant exists for converting a length or depth to feet when a display preference requires it.

METRES_PER_NM

The international definition of the nautical mile, exactly 1852 m. Exported so other crates converting a distance_nm result into metres for the wire (Signal K’s resources are metric) use this value instead of restating the literal.

METRES_PER_STATUTE_MILE

The statute mile, exactly – 5280 × METRES_PER_FOOT, a fixed international definition. Distinct from METRES_PER_NM: used for an imperial (non-nautical) display preference, as opposed to a nautical-imperial one.