4.1 Direction Sense

4.1 Direction Sense

Quick Answer: Treat every walk as a vector with a length and a bearing. Add the North-South and East-West components separately, then combine them for net displacement. Turns are relative to the figure's current facing — not to North.

Direction-sense problems are a staple of the PAF GD Pilot Initial Test verbal intelligence domain because they measure the same spatial orientation skill a pilot uses when reading a heading indicator. Each question describes a person walking some distance, turning, and walking again; you must find the final position, the straight-line distance from start, or the direction of one point from another.

The Cardinal Convention

Draw the standard compass with North up, East right, South down, and West left. Bearings are measured clockwise from North:

North-East (NE) is 45°, South-East (SE) is 135°, South-West (SW) is 225°, North-West (NW) is 315°.

The Relative-Turn Rule

A turn is described relative to the figure's current facing, not to absolute North. This is the single most common trap.

An about-turn (or "turn back") reverses the facing by 180° but does not move the figure — position is unchanged, only the heading flips.

Worked Example: The 3-4-5 Triangle

A man walks 3 km North, turns right, and walks 4 km. How far is he from the start, and in what direction?

Step 1 — Track the legs:

• Leg 1: 3 km North → North component = +3, East component = 0.
• Turn right from North → faces East.
• Leg 2: 4 km East → North component = +3, East component = +4.

Step 2 — Net displacement:

• Distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km.
• Direction: both components positive → North of start and East of start → North-East.

The 3-4-5 right triangle is the examiner's favourite — recognise it and skip the arithmetic.

Finding the Bearing

When the legs are not a clean Pythagorean triple, use tan θ = (East-West component) / (North-South component) and read θ from the appropriate quadrant. For 5 km North + 2 km East: tan θ = 2/5 = 0.4, so θ ≈ 21.8° East of North — the figure is North-North-East of start.

Common Traps

1. Relative vs absolute facing. "Turn right" does not mean "face East" — it means rotate 90° clockwise from wherever you are currently looking.
2. About-turn confusion. A figure that walks North, about-turns, and walks South is back at the start — not 2× further North.
3. Direction from vs direction to. "A is North of B" means if you stand at B and look at A, you look North. Reversing the reference flips the answer.
4. Mixed units. Distances given in metres and kilometres must be unified before applying Pythagoras.

Worked Example: Four-Leg Bearing Problem

A navigator starts at base and flies the following legs: 6 km on a bearing of 090°, then 8 km on a bearing of 180°, then 6 km on a bearing of 270°, then 2 km on a bearing of 000°. Find the final position and the straight-line distance from base.

Step 1 — Convert each bearing to components (North +, East +):

• Leg 1: 090° (East) → N = 0, E = +6.
• Leg 2: 180° (South) → N = −8, E = +6.
• Leg 3: 270° (West) → N = −8, E = +6 − 6 = 0.
• Leg 4: 000° (North) → N = −8 + 2 = −6, E = 0.

Step 2 — Sum components: North = −6 (i.e. 6 km South), East = 0.

Step 3 — Displacement: distance = √((−6)² + 0²) = 6 km. Direction: pure South component → final point is 6 km due South of base.

This problem illustrates a key bearing-sense habit: every leg must be decomposed into North-South and East-West components before you sum. Trying to chain arrows visually with four legs invites sign errors; the component table keeps the bookkeeping honest.

Bearings Beyond the Cardinals

Real PAF items sometimes use three-figure bearings (e.g. 045°, 135°, 225°, 315° for the inter-cardinal points). For a leg of length d on bearing θ measured clockwise from North:

• North component = d × cos θ
• East component = d × sin θ

Example: 10 km on bearing 135° (SE). North = 10 × cos 135° ≈ −7.07; East = 10 × sin 135° ≈ +7.07. The leg contributes roughly 7 km South and 7 km East.

Additional Traps

1. Shadow/sunrise misdirection. "A man walks 5 km towards the sunrise" — in Pakistan the sun rises in the East, so the walk is East, not North. Do not assume a default direction.
2. Bearing vs facing. A bearing of 090° describes where the figure goes, not where it looks. A figure can face North yet walk on bearing 090° if the question states a bearing, not a turn.
3. Left/right from inter-cardinal facings. A figure facing North-East (045°) turning right faces South-East (135°), not East. The 90° clockwise rotation applies to the bearing number: 045° + 90° = 135°.

Practice Procedure

1. Draw a quick cross with N/E/S/W labels.
2. Plot each leg as a labelled arrow, noting the figure's facing after each turn.
3. Sum the North-South and East-West components separately.
4. Apply Pythagoras for distance; use the signs of the components to pick the quadrant for direction.

Master this procedure and most direction-sense items collapse into 20-second mental arithmetic.