Cyclone avoidance and equal-time point on a Pacific sector
A Boeing 737-800 is planned Auckland (NZAA) to Nadi (NFFN), 1,150 NM, FL350, TAS 450 kt. Forecast wind: average headwind 40 kt outbound and tailwind 40 kt on return. Cruise fuel flow is 2,400 kg/h; final reserve 1,200 kg; alternate Nausori fuel 800 kg. Tropical cyclone Lena is at 17.5°S 175.0°E, forecast to move 250° at 10 kt with 35 kt winds extending 180 NM from the centre. The planned track passes 90 NM north of the forecast 12-hour position. Company policy requires 100 NM clearance outside the 35 kt radius. The captain proposes carrying 800 kg extra fuel and deviating 60 NM south of track.
1. Calculate the equal-time point (ETP) between Auckland and Nadi with the stated winds, and the fuel needed from the ETP to each airport.
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Ground speeds:
- Outbound: 450 − 40 = 410 kt
- Return: 450 + 40 = 490 kt
Distance from Auckland to the ETP is:
D × GS_return ÷ (GS_out + GS_return) = 1,150 × 490 ÷ (410 + 490) = 626 NM.
Time to the ETP = 626 ÷ 410 = 1.53 h. Fuel to the ETP = 1.53 × 2,400 = 3,665 kg.
From the ETP:
- Back to Auckland: 626 ÷ 490 = 1.28 h → 3,066 kg
- On to Nadi: (1,150 − 626) = 524 NM ÷ 410 = 1.28 h → 3,066 kg
The times and trip fuels are equal by definition. At the ETP, the aircraft must still hold final reserve 1,200 kg; if continuing to Nadi it also needs the Nausori alternate fuel 800 kg. The ETP is therefore a planning aid, not a point at which the aircraft is automatically committed.
2. Assess the cyclone clearance and the proposed 60 NM southerly deviation. What extra fuel is needed?
Read the worked answer
The 12-hour forecast position is about 120 NM from the current centre along 250°: roughly 19.4°S 174.3°E. The planned track passes only 90 NM from the centre, but the required clearance is:
35 kt radius 180 NM + company buffer 100 NM = 280 NM.
The track is short by about 190 NM. A 60 NM southerly deviation is therefore inadequate; it may also put the aircraft closer to the dangerous semicircle. A deviation of at least 200 NM on the safe side is needed.
Extra distance for a 200 NM lateral offset near the midpoint is approximately:
2 × √(575² + 200²) − 1,150 = 2 × 608.8 − 1,150 = 68 NM.
At 410 kt ground speed, that is 68 ÷ 410 = 0.166 h, and 0.166 × 2,400 = 398 kg. The proposed 800 kg extra fuel is sufficient for the deviation and some holding, but the route must be re-filed with at least 280 NM clearance and the ETP recalculated. The captain should not depart on the planned track with only a 60 NM deviation.