VOR/DME groundspeed, fuel and inbound tracking
You are the pilot of a twin-engine IFR aircraft tracking outbound on R-090 from the KAI VOR at 8,000 ft. TAS is 150 kt and fuel flow is 40 L/h. At 1410 the DME reads 25 NM, the CDI is centred, and the heading is 098°M. At 1420 the DME reads 40 NM, the CDI is still centred, and the heading is 094°M. The next planned checkpoint is DME 80 on the same radial. You have 120 L usable fuel remaining and require a 45-minute reserve. ATC has cleared you to maintain 8,000 ft and expects the next position report at DME 80. There is no GNSS on board; the VOR/DME is the only approved navigation aid. The forecast wind is not available, and the area QNH is 1013 hPa.
1. Calculate the actual groundspeed and ETA at DME 80. Show your calculation.
Read the worked answer
Between 1410 and 1420 the DME changed from 25 to 40 NM, so the aircraft covered 15 NM in 10 minutes. That is 15 × 6 = 90 kt groundspeed. Remaining distance to DME 80 is 80 − 40 = 40 NM. Time = 40 / 90 h = 0.444 h = 26.7 minutes. ETA = 1420 + 26 min 40 s ≈ 1447. Because the radial is constant and the CDI is centred, the DME distance is essentially along-track; slant-range error at 8,000 ft and 40 NM is negligible for this calculation. Plan the next position report at about 1447, not at the original flight-plan ETA.
2. Assess fuel at DME 80 against the required 45-minute reserve. Can you continue?
Read the worked answer
Fuel flow is 40 L/h = 0.667 L/min. Fuel to DME 80 = 26.7 × 0.667 = 17.8 L. Remaining fuel at DME 80 = 120 − 17.8 = 102.2 L. The 45-minute reserve is 45 × 0.667 = 30 L. Margin above reserve = 72.2 L. The leg is fuel-positive. As a sanity check, if groundspeed fell 20% to 72 kt, the time would be 40 / 72 h = 33.3 min and burn 22.2 L, leaving 97.8 L - still well above reserve. Continue, but update the fuel and groundspeed at DME 80 because the along-track wind component is clearly significant.
3. What wind effect is indicated, and what heading would you fly inbound on R-270? State your assumptions.
Read the worked answer
Outbound track is 090°M and heading is 094°M, so the aircraft is crabbed 4° right of track. That indicates wind from the right, on the south side. For inbound track 270°M the same crosswind will be from the left, so crab left by about 4°: heading 266°M. This assumes TAS remains 150 kt and the crosswind component is unchanged. Crosswind check: 150 × sin 4° ≈ 10.5 kt. If groundspeed changes inbound, the drift angle remains about arcsin(10.5 / 150) ≈ 4° because TAS is unchanged; only the along-track component changes. Do not simply reverse the outbound heading - reverse the correction.