Fuel Margin on a Windy Cross-Country
You plan a 95 NM cross-country in a two-seat gyroplane with a 90 L tank. At 75% power the POH gives 28 L/h and 85 kt TAS. Forecast wind is 250/25 at cruise altitude; your track is 340 magnetic. Before departure you note the fuel gauge reads just under half, and the last refuel was 40 L. Cruise altitude is 2500 ft, field elevation 400 ft. You have a 15-minute reserve policy plus 10 minutes for the climb. During run-up you notice the engine idles slightly rough but clears at 2000 rpm. Your passenger weighs 95 kg and you weigh 85 kg; the aircraft empty weight is 310 kg with a 560 kg MTOW.
1. Compute the still-air and wind-corrected fuel required for the cruise leg, and state whether the planned departure is legal and prudent under your reserve policy.
Read the worked answer
Heading and groundspeed. Track 340, wind from 250 at 25 kt. The wind angle to track is 90 degrees, so it is essentially a full crosswind. The wind correction angle is arcsin(25/85) ≈ 17 degrees, giving a heading of about 357. The along-track component is 25 × cos(17) ≈ 24 kt headwind, so groundspeed ≈ 85 − 24 = 61 kt.
Time and fuel. 95 NM at 61 kt ≈ 1.56 h ≈ 94 min. Cruise fuel = 1.56 × 28 ≈ 44 L. Add climb allowance (10 min ≈ 4.7 L) and 15-min reserve (7 L): total ≈ 56 L.
Available fuel. Tank 90 L; gauge just under half suggests roughly 40–44 L. The last refuel of 40 L into an unknown residual is not a reliable quantity check.
Judgement. 56 L required against ~42 L indicated means the flight is not legal or prudent as planned. Refuel to a known quantity, verify with dipstick, and recompute. The rough idle is a separate airworthiness concern to resolve before flight.
2. If you refuel to full, what is the payload margin, and how does that interact with the fuel decision?
Read the worked answer
Empty 310 kg + pilot 85 + passenger 95 = 490 kg. MTOW 560 kg leaves 70 kg for fuel. At 0.72 kg/L, full 90 L ≈ 65 kg, so you are just inside MTOW with full tanks - but only if the empty weight includes oil and unusable fuel as stated in the POH.
This shows the tension: the fuel needed for the wind (~56 L ≈ 40 kg) fits comfortably, but filling to 90 L consumes nearly the whole payload margin. The correct decision is to carry the fuel required plus reserve (about 56–60 L), confirm the CG remains within limits with that load, and record the actual dipstick quantity rather than relying on the gauge. Never trade reserve fuel for payload.