Christchurch to Hokitika: mountain wave, headwind and fuel
You are planning a VFR crossing from Christchurch (NZCH) to Hokitika (NZHK), 85 NM, planned track 270°M at 10,500 ft in a C172. TAS is 100 kt. The forecast wind at 10,000 ft is 300/45, freezing level 8,000 ft, and there is lenticular cloud and moderate turbulence over the Southern Alps. You have 110 L usable fuel, burn 32 L/h, allow 8 L taxi and a 45-minute reserve. The route via Arthur’s Pass requires terrain clearance; the alternative via Lewis Pass is longer. You are not pressurised and have no oxygen; 10,500 ft is within the aircraft’s capability but you will be above 10,000 ft for some time. The cloud base is forecast 6,000 ft with mountain tops obscured. You must calculate the wind effect, fuel, and decide whether the crossing is acceptable.
1. Calculate the magnetic heading and groundspeed for the leg, and the ETA.
Read the worked answer
Track is 270°M and wind is 300°/45, so the wind is 30° from the right and ahead of the aircraft.
Crosswind = 45 × sin 30° = 22.5 kt from the right. Headwind = 45 × cos 30° = 39.0 kt.
Wind correction angle = arcsin(22.5/100) = 13.0° right. Magnetic heading = 270 + 13 = 283°M.
Groundspeed = TAS × cos(WCA) − headwind = 100 × cos 13° − 39.0 = 97.4 − 39.0 = 58.4 kt.
ETA = 85/58.4 = 1.46 h = 88 minutes. This is a very slow leg; the headwind is the dominant factor.
2. Calculate fuel required including taxi and reserve, and the margin. If the wind is 20 kt stronger than forecast, does the flight remain viable?
Read the worked answer
At 58.4 kt, trip fuel = 32 × 1.46 = 46.7 L. Taxi = 8 L. Reserve = 45 min at 32 L/h = 24 L. Total required = 46.7 + 8 + 24 = 78.7 L. Margin with 110 L = 31.3 L. On the forecast wind, fuel is adequate.
With wind 300/65, headwind = 65 × cos 30° = 56.3 kt. Crosswind = 65 × sin 30° = 32.5 kt. WCA = arcsin(32.5/100) = 19°. Groundspeed = 100 × cos 19° − 56.3 = 94.6 − 56.3 = 38.3 kt.
ETA = 85/38.3 = 2.22 h = 133 min. Trip fuel = 32 × 2.22 = 71.0 L. Total required = 71.0 + 8 + 24 = 103 L. Margin = 7 L, which is too small for a mountain crossing with turbulence and possible holding. On the stronger wind, the flight is not viable without a shorter route or a refuelling stop.
3. What meteorological and terrain cues would make you divert via Lewis Pass or turn back, and how does mountain wave affect your navigation?
Read the worked answer
Lenticular cloud, rotor cloud, strong turbulence, and mountain tops obscured are warnings that wave activity is present. In mountain wave, you can expect strong updraughts and downdraughts, altimeter errors, and severe turbulence on the lee side. Navigation becomes harder because your actual track and groundspeed change rapidly, and the visual horizon may be distorted.
Divert via Lewis Pass or turn back if you cannot maintain VFR at a safe terrain clearance, if the cloud base is below your planned minimum, if downdraughts prevent you holding altitude, or if the turbulence is beyond your experience. Do not enter a valley hoping to stay visual; set a hard decision point before the mountains. If the crossing is marginal on wind, fuel, or cloud, the correct decision is to delay or use a lower, longer route.