方位角

Lost at sea — saved by a bearing 方位角

• Before GPS, sailors navigated using bearings — a precise angle from north.
• A single mistake (reading anticlockwise instead of clockwise, or writing "45" instead of "045") could put a ship miles off course.

What is a bearing?

• A bearing gives a direction as a three-figure angle, measured clockwise from north.
• Due north $= 000^{\circ}$ (or $360^{\circ}$); due east $= 090^{\circ}$; due south $= 180^{\circ}$; due west $= 270^{\circ}$.
• Always write three figures: $5^{\circ}$ becomes $005^{\circ}$, $45^{\circ}$ becomes $045^{\circ}$.

Bearings are always measured clockwise from north, and always written as three figures.

Back bearings 反方位角

• The back bearing (the return direction) differs from the forward bearing by $180^{\circ}$.
• If the bearing is under $180^{\circ}$, add $180^{\circ}$; if over, subtract $180^{\circ}$.
• Bearing of $B$ from $A$ is $025^{\circ}$ → bearing of $A$ from $B$ is $025 + 180 = 205^{\circ}$.

Bearings are measured clockwise from north as three figures; the back bearing differs by $180^\circ$

Worked example — three-figure bearings

• A ship sails on bearing $135^{\circ}$ for $20$ km, then turns to bearing $225^{\circ}$.
• The angle turned through $= 225 - 135 = 90^{\circ}$ — a right-angle turn to starboard.

Bearings in the real world

• Aviation: runways are numbered by their bearing divided by 10 (Runway 27 faces roughly $270^{\circ}$).
• Hiking: a compass bearing tells you which direction to walk, even in fog.

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