The Flight Budget, Carried to Full Precision

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

The Flight Budget, Carried to Full Precision

The chapter plans a five-node drone sortie and reports 370.1 m of flight, 37.0 s in the air, and a 4.8% battery draw at 10 m/s cruise with 10 s of hover per node. A go/no-go launch decision rides on that route budget and its 1,800 s battery. This audit recomputes the flight budget carried to full precision, to see whether summing pre-rounded legs is safe.

Companion to the chapter CoRAD Drone Data Collection — every number here comes from that chapter.

Ada: A go/no-go launch decision hangs on this route budget, so it is exactly where rounding discipline matters. The chapter’s five-node sortie reports 370.1 m of flight, 37.0 s in the air, and a 4.8% battery draw. Let me recompute each leg as a straight-line distance and hold full precision until the final round, using the chapter’s stated visit order and drone specs (10 m/s cruise, 10 s hover per node, 1,800 s battery).

  • Leg distances: sqrt(50^2+30^2)=58.3095, sqrt(30^2+30^2)=42.4264, sqrt(40^2+30^2)=50.0000, sqrt(80^2+40^2)=89.4427, sqrt(120^2+50^2)=130.0000 m.
  • Full-precision total: 58.3095 + 42.4264 + 50 + 89.4427 + 130 = 370.1786 m (the chapter’s 370.1 comes from summing already-rounded legs; the honest total is 370.18 m).
  • Flight time: 370.1786 / 10 = 37.0179 s, which rounds to 37.0 s either way.
  • Hover: 5 nodes x 10 s = 50 s; mission total 37.02 + 50 = 87.0 s.
  • Battery used: 87.02 / 1,800 = 4.83%, leaving 95.2%.
  • Reserve check: usable budget is 0.8 x 1,800 = 1,440 s; the 87 s mission clears it with the full 360 s (20%) reserve untouched.

The audit confirms the mission is feasible and illustrates the habit that keeps it honest: summing pre-rounded legs lost 0.08 m here, harmless at this scale but the kind of drift that compounds across a 42-node cluster. The number that actually gates the launch is not the 87-second mission time but the reserve — the sortie flies only because it finishes with 1,713 s in hand against a 1,440 s ceiling.

Every number above is taken from the chapter’s own material and re-derived step by step.