Traffic Pattern Geometry, Crab Angle, and Mental Rotation
You are flying left-hand traffic for runway 09 in a light airplane at 100 kt true airspeed. On downwind your heading indicator reads 270° and the runway lies off your left wing about 1 nm away. You turn left onto base, then left onto final. There is no wind on the downwind and base legs. On short final the tower reports wind 360° at 15 kt, which is a pure crosswind. During downwind you noted a large water tower sitting at your 10 o'clock position. The runway is 45 m wide. On very short final you notice you are lined up not on the runway but on the parallel taxiway, which sits 150 m to the right of the runway centerline.
1. State your heading on each leg and where the runway appears in the windscreen on each leg. Explain the turn direction rather than just naming headings.
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Runway 09 = landing heading 090° true.
| Leg | Heading | Runway position | Reason |
|---|---|---|---|
| Downwind | 270° | off the left wing | Reciprocal of landing heading; on left traffic the runway is on your left |
| Base | 180° | ahead and slightly left | Left turn from 270° to 180°; flying south with the field to the east |
| Final | 090° | dead ahead | Left turn from 180° to 090°; on centerline |
Check by turn direction: every turn in left traffic is to the left - 270 → 180 → 090 is two 90° left turns, consistent with the runway staying on the left until you roll out aligned. If the runway had appeared on your right on downwind, you would be in right-hand traffic and every turn would reverse.
Sanity check on the downwind geometry: flying west with the field to the south means you are north of the runway. Turning left (south) on base, then left (east) on final puts you rolling out on 090° - correct.
2. Using the reported wind, compute the heading required to hold the 090° ground track on final, and state the resulting groundspeed. Which way do you point the nose and why?
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Setup: TAS = 100 kt, wind from 360° at 15 kt, desired track 090°.
Wind angle relative to the nose: wind from 360° while tracking 090° is a direct left crosswind, 90° off the desired track.
Crab angle: sin θ = crosswind ÷ TAS = 15 ÷ 100 = 0.15 → θ = 8.6°
Heading to fly: 090° − 8.6° ≈ 081° - the nose points left, into the wind, so the airplane tracks straight down the extended centerline. Pointing the nose right (099°) would double the drift and blow you off the right side.
Groundspeed: with a perpendicular wind, GS = √(100² − 15²) = √(10,000 − 225) = 98.9 kt
Why this matters practically: at 98.9 kt, the airplane covers 45 m of runway width in about 0.9 s. An 8.6° crab error uncorrected at touchdown translates to roughly 1.5 m of sideways drift per second of rollout - enough to matter on a 45 m runway, and enough to explain a 150 m lineup error if the wrong surface is being tracked.
3. Mentally rotate the scene: the water tower was at your 10 o'clock on downwind. After the two left turns, where is it? Then explain what the 150 m taxiway lineup on short final tells you to do.
Read the worked answer
Mental rotation:
- 10 o'clock = 60° left of the nose (300° relative bearing).
- Two left turns total 180° of rotation. Your nose swings 180° left, so every fixed object's relative bearing shifts 180° to the right of where it was.
- 60° left → 60° − 180° = −120° → 120° right of the nose = 4 o'clock, i.e. behind you and to the right.
Rule of thumb: after a 180° turn, anything that was forward-left is now aft-right. If you had said "still on the left," you rotated the airplane but not the world.
The taxiway lineup:
- On short final at low altitude and low airspeed, the airplane is already committed in pitch and energy. A late, steep S-turn or a sideways scramble to reach the runway centerline trades a misalignment problem for a loss-of-control problem.
- Go around. Climb straight ahead on runway heading, fly the pattern, and re-enter final correctly lined up with the runway edge lights and the aiming point.
- The 150 m offset is a strong cue that the wrong surface was being tracked from base leg or earlier: correct the lineup at the point where it is cheap - before turning final - not at 50 ft.