Hot Day, Heavy Gimbal
Site elevation is 1,400 ft AMSL, QNH 1013 hPa, shade temperature 32 °C. Your 9.5 kg MTOW multirotor's published data gives hover at 62% of maximum thrust at MTOW in ISA sea-level conditions, with 25 minutes of hover endurance at that mass. Today you want to fit a 1.5 kg gimbal, taking off at 11.0 kg. The job needs a 2.0 km transit out and back at 15 m/s cruise, plus 2.5 minutes of stationary hover for sensor calibration. Wind is 12 kt, roughly straight down the transit line. Your operations manual sets a minimum 20% battery reserve and a rule that hover must not exceed 75% of available thrust.
1. Calculate density altitude and the hover thrust fraction at 11.0 kg. Does the flight meet your 75% rule?
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Work in steps and keep the assumptions visible.
Pressure altitude: QNH equals 1013, so PA = 1,400 ft.
ISA temperature at 1,400 ft: 15 − (2 × 1.4) ≈ 12.2 °C.
ISA deviation: 32 − 12.2 = 19.8 °C.
Density altitude: PA + (120 × deviation) = 1,400 + 2,376 ≈ 3,780 ft (about 1,150 m).
Density ratio: σ ≈ (1 − 6.8756×10⁻⁶ × 3,780)^4.2559 ≈ 0.894. In plain terms, the rotors produce about 10.6% less thrust for the same power, and the aircraft must run at a higher power setting for the same lift.
Thrust required:
- At 9.5 kg sea level, hover = 62%.
- Scaling for mass: 62 × (11.0 / 9.5) = 71.8%.
- Scaling for thin air: 71.8 / 0.894 = 80.3%.
That is well over the 75% limit. The aircraft would hover with only about 20% of thrust in reserve for gusts, and 12 kt with a gust spread on a hot day is exactly when you need that reserve. Verdict: not compliant with your own rule, and not sensible regardless.
2. Work out the transit and hover time with the wind, and say whether endurance or thrust is the binding limit.
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Convert everything to the same units.
- Cruise 15 m/s = 54 km/h.
- Wind 12 kt ≈ 22 km/h ≈ 6.2 m/s.
- Outbound ground speed: 15 − 6.2 = 8.8 m/s.
- Inbound ground speed: 15 + 6.2 = 21.2 m/s.
Times:
- Outbound 2,000 m at 8.8 m/s ≈ 227 s.
- Hover for calibration: 150 s.
- Inbound 2,000 m at 21.2 m/s ≈ 94 s.
- Total ≈ 471 s ≈ 7.9 minutes.
Against a nominal 25-minute hover endurance, 7.9 minutes looks trivial and a 20% reserve is easily met. That is the trap: the endurance figure is a sea-level, MTOW hover number, and you are hovering at 80% of available thrust, where current draw is far higher than the number assumes. Run the hover at 80% and the usable endurance shrinks substantially.
So the binding limit is thrust margin, not battery. Endurance arithmetic would wave this flight through; the thrust calculation stops it. That is why both numbers get checked on every hot, heavy sortie.
3. The client cannot move the job to another day. What changes would legitimately make the flight work, and what would not?
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Test each proposed change against the 75% rule rather than against how the aircraft feels.
Waiting for a cooler part of the day - not enough on its own. At 21 °C: deviation = 21 − 12.2 = 8.8 °C, so density altitude ≈ 1,400 + 1,056 = 2,456 ft, σ ≈ 0.930. Hover becomes 71.8 / 0.930 ≈ 77%. Still over the limit. A dawn start helps, but the 1.5 kg gimbal is the real problem.
Reducing mass - works. Back at 9.5 kg on the same 21 °C morning: 62 / 0.930 ≈ 67%. Comfortable. Even at 32 °C, 9.5 kg gives 62 / 0.894 ≈ 69%, which is inside the rule.
So the legitimate options are:
- Fit a lighter camera payload so take-off mass stays near MTOW, and fly the planned sortie.
- Keep the heavy gimbal but split the work into two sorties with the calibration hover done on the lighter configuration, or drop the hover segment.
- Fly early, with the lighter payload, and accept a shorter transit by repositioning the launch point closer to the middle of the line.
What would not work: treating the 25-minute endurance figure as proof of capability, or shaving the 75% rule 'just for this job'. The rule exists because the gust response at 80% hover is where these aircraft get written off.