The Flight Budget, Carried to Full Precision

The Flight Budget, Carried to Full Precision

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

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.

Try

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. Calculate this case.

Observe

This audit recomputes the flight budget carried to full precision, to see whether summing pre-rounded legs is safe. Check shows this.

Explain

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 handafter hover time is included. Check confirms it.

See the relationship before changing it

The figure reads from left to right. The blue input is hover per node. The middle card names the page’s rule. The green output is battery used. The arrow matters: change the input, apply the rule once, then read the result with its unit.

Walk the arrow. Hover time is paid at every node, while route flight time stays fixed.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 10 s.

2. 2

   Name the relationship. mission = 370.1786/10 + 5 x hover; used = mission/1800 x 100

3. 3

   Substitute with units. (37.0179 + 50) / 1800 x 100 = 4.83%

4. 4

   Read the result. Keep the unit beside the value, then use the result only inside the technical boundary below.

Predict, then change hover per node

Try Predict how battery used responds when hover per node moves. Calculate hover per node; compare battery used with that prediction.

Hover per node

10 s

Chapter baseline

Battery used

Observe Return to 10 s. Recheck battery used with hover per node at its chapter value.

Explain Hover time is paid at every node, while route flight time stays fixed.

Check yourself

What should you do before trusting a moved-slider result?

Answer: Predict its direction, apply the displayed relationship, keep the units, and compare the reset value with the chapter’s worked baseline.

What does this small model leave out?

Answer: Only hover per node moves here. The battery used calculation excludes field effects listed below.

Honesty note. The battery used result holds hover per node as the only changing input. It is not a field prediction.

Technical boundaries

Beyond the scope of “The Flight Budget, Carried to Full Precision” sit wind, climb and hover transients, battery voltage sag, reserve policy, route obstacles, communications loss, or payload-dependent aerodynamics; “The Flight Budget, Carried to Full Precision” therefore reports only its named fixtures.

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.