Fuel reserve decision with a headwind that grows with altitude
You are planning a VFR cross-country in a single-engine piston aircraft. Still-air cruise fuel burn is 34 L/h at 6,500 ft and 30 L/h at 9,500 ft. Distance is 340 NM. Forecast wind: at 6,500 ft, 290/25; at 9,500 ft, 300/40. TAS is 118 kt at 6,500 ft and 112 kt at 9,500 ft. Usable fuel at start is 160 L. You require a 45-minute fixed reserve plus 10% of the planned trip fuel as contingency. Departure and destination are both near sea level; no alternate is required. The aircraft has no fuel totaliser, and the dipstick reads are known to be accurate to about ±5 L.
1. Compute the wind-corrected ground speed, trip fuel and total required fuel for each altitude, and state which altitude is legal and preferable.
Read the worked answer
Convert winds to components. Track is 270° (due west).
6,500 ft: wind 290/25 gives a 20° angle. Headwind component = 25 × cos20° ≈ 23 kt. Crosswind ≈ 8.6 kt. GS ≈ √(118² − 8.6²) − 23 ≈ 117.7 − 23 ≈ 94.7 kt. Time = 340/94.7 ≈ 3.59 h. Trip fuel = 3.59 × 34 ≈ 122 L.
9,500 ft: wind 300/40 gives a 30° angle. Headwind = 40 × cos30° ≈ 34.6 kt. Crosswind = 20 kt. GS ≈ √(112² − 20²) − 34.6 ≈ 110.2 − 34.6 ≈ 75.6 kt. Time = 340/75.6 ≈ 4.50 h. Trip fuel = 4.50 × 30 ≈ 135 L.
Reserves: 45 min at the respective cruise burn: 25.5 L (6,500 ft) or 22.5 L (9,500 ft). Contingency 10%: 12.2 L or 13.5 L.
Totals: 6,500 ft ≈ 122 + 12.2 + 25.5 ≈ 160 L. 9,500 ft ≈ 135 + 13.5 + 22.5 ≈ 171 L.
At 9,500 ft the requirement exceeds the 160 L on board, so it is not legal. At 6,500 ft the requirement is essentially equal to the fuel on board, leaving no margin for the ±5 L dipstick uncertainty. The lower altitude is the only defensible choice, and even then the flight should be replanned (or a fuel stop added) because the margin is inside the measurement error.
2. The dipstick could be 5 L low. What operational decision follows, and what in-flight trigger would make you divert?
Read the worked answer
If the dipstick over-reads by 5 L, usable fuel is 155 L against a 160 L requirement: a 5 L (about 9 minutes) deficit before any error in wind or burn. That is not a legal dispatch. Options, in order of preference:
- Reduce the trip: shorten the leg, add a fuel stop, or pick a closer destination.
- Re-check the actual wind aloft (the headwind may be weaker than forecast) and recompute; only accept if the total requirement falls at least 15–20 minutes below available fuel.
- Fly the 6,500 ft profile but lean aggressively and use a measured power setting rather than the book figure.
In-flight trigger: compare fuel remaining at each waypoint with the plan. If actual fuel at the midpoint is more than about 8–10 L below plan, or if groundspeed is more than 10 kt below the planned 95 kt, divert. Also set a hard bingo: the point at which remaining fuel equals reserve plus 20 minutes. Crossing it before the destination is reached means divert now, not later.
3. Why is it wrong to simply accept the 9,500 ft option because it burns less fuel per hour?
Read the worked answer
Fuel per hour is not the planning quantity; fuel per nautical mile is. At 9,500 ft the aircraft burns 30 L/h but only makes 75.6 kt over the ground, i.e. about 0.40 L/NM. At 6,500 ft it burns 34 L/h at 94.7 kt, about 0.36 L/NM. The stronger headwind at altitude more than cancels the lower burn rate, so the higher level costs about 13 L more trip fuel despite the better specific consumption.
The general lesson: on a headwind leg, the optimum altitude is usually lower than the still-air best-range altitude, because wind gradient dominates. Always compare litres per nautical mile over the ground, not litres per hour.