Wellington to Christchurch: Manual DR and Fuel Margin
You are planning a twin-turboprop revenue flight from Wellington (NZWN) to Christchurch (NZCH), 175 nm, planned true track 175°T. The aircraft TAS is 260 kt and total fuel flow is 520 kg/h. Forecast wind is 290°T/40 kt. Magnetic variation is 21°E. Fuel on board is 720 kg; company reserves are 45 minutes holding plus 10% trip contingency. No alternate is required. The FMS is unserviceable, so you must use manual DR. The aircraft is cleared into controlled airspace and must land with the reserve intact. QNH is standard and there is no icing. The crew plans to depart with the minimum fuel and asks you to validate the flight plan. You must determine the drift, heading and groundspeed, then decide whether the fuel load is acceptable. Show the wind-triangle reasoning, not just the final figures.
1. Calculate the drift, true heading, magnetic heading and groundspeed for the planned leg.
Read the worked answer
Track is 175°T and wind is 290°T/40 kt. The angle between track and wind direction is 115°.
Crosswind component = 40 × sin 115° = 36.3 kt. The wind is from the right, so drift is left.
Drift = asin(36.3 / 260) = 8.0° left.
True heading = 175° + 8° = 183°T. With 21°E variation: magnetic heading = 183° − 21° = 162°M.
Along-track wind component: the wind toward 110°T makes an angle of 65° with the 175°T track, giving 40 × cos 65° = 16.9 kt tailwind.
Groundspeed = 260 × cos 8° + 16.9 = 257.5 + 16.9 = 274.4 kt, approximately 274 kt.
2. Using the calculated groundspeed, determine whether 720 kg of fuel is sufficient for the trip plus reserves.
Read the worked answer
Leg time = 175 / 274.4 = 0.638 h = 38.3 min.
Trip fuel = 520 × 0.638 = 331.8 kg.
45-minute holding reserve = 520 × 45/60 = 390 kg.
10% trip contingency = 33.2 kg.
Total required = 331.8 + 390 + 33.2 = 755 kg.
Fuel on board is 720 kg, so the aircraft is 35 kg short before any taxi fuel. The planned load is not acceptable. You would need additional fuel, reduced payload or a revised plan. The heading itself is acceptable, but the fuel margin is negative.