High-Density-Altitude Departure with a Tailwind and a Deadline
A private pilot in a two-place gyroplane plans a midday departure from a 3,000-ft asphalt runway at field elevation 4,600 ft. The surface wind is reported 180° at 7 kt, and the only available runway is 18. OAT is 30°C and the altimeter is 29.92. The aircraft empty weight is 820 lb with an empty-arm moment of 74,620 lb-in; maximum gross weight is 1,430 lb, and the CG envelope is 86.0 to 98.0 in aft of datum. Pilot and passenger weigh 195 lb and 215 lb and sit at arms of 76 in and 116 in. Baggage of 20 lb is loaded at 132 in, and 24 gal of fuel at 6 lb/gal is loaded at 104 in. The POH gives a sea-level, ISA, max-gross takeoff distance over a 50-ft obstacle of 1,100 ft and a density-altitude factor of 2.6 at 7,500 ft. The pilot has no alternate runway and a passenger who must arrive by 1500.
1. Compute total weight and center of gravity. Are they within limits?
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Total weight = 820 + 195 + 215 + 20 + (24 × 6) = 1,394 lb. Maximum gross is 1,430 lb, so the aircraft is 36 lb under-legal but with little margin.
Moments:
- Empty: 74,620 lb-in
- Pilot: 195 × 76 = 14,820
- Passenger: 215 × 116 = 24,940
- Baggage: 20 × 132 = 2,640
- Fuel: 144 lb × 104 = 14,976
Total moment = 131,996 lb-in. CG = 131,996 ÷ 1,394 = 94.7 in. The envelope is 86.0–98.0 in, so the CG is within limits. It is well aft in the envelope, which reduces pitch stability and makes control forces lighter; this matters because the takeoff performance is already marginal.
2. Estimate density altitude and takeoff distance. How do they compare with the runway?
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Standard temperature at 4,600 ft is about 15 − (2 × 4.6) = 5.8°C. Density altitude ≈ 4,600 + 120 × (30 − 5.8) = 7,500 ft.
POH distance: 1,100 ft × 2.6 = 2,860 ft over a 50-ft obstacle. That leaves only 140 ft on a 3,000-ft runway before any wind correction. With a 7-kt tailwind, a common planning rule adds about 10% per 2 kt: 2,860 × 1.35 ≈ 3,860 ft. Even the milder 10% per 3 kt gives about 3,520 ft. Either exceeds the runway.
The high density altitude also reduces engine power and rotor efficiency, so initial climb will be flat and the margin for error is gone.
3. What should the pilot do, and why is offloading fuel not a complete fix?
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Do not depart as loaded. The legal weight and CG are acceptable, but performance is not. The pilot should wait until evening when the temperature and density altitude fall, use a longer or into-wind runway, or reduce load and fuel. Offloading 9 gal saves 54 lb and slightly shortens the takeoff, but the tailwind and 7,500-ft density altitude remain the dominant factors; 54 lb will not turn a 3,500–3,900-ft requirement into a safe 3,000-ft takeoff. Offloading also moves the CG forward, which is fine but not a performance cure.
The passenger deadline is external pressure-classic get-there-itis. A professional decision is to delay, change airports, or drive. If the pilot does attempt the takeoff, brief a reject point and abort if liftoff is not achieved by it, but the better choice is no-go.