The sizing formula#
A drone-in-a-box (DiaB) aircraft cycles between three states: transiting, on station, and charging in its dock. Let be sortie length, transit time each way and recharge time. Each aircraft is useful for out of every minutes, so continuous coverage of one point needs
For a typical 35-minute sortie with 4-minute transits and a 55-minute recharge, . One dock covers at most of the day. Vendor brochures that show one dock “protecting a site 24/7” are describing availability to launch, not time on watch.
Adding weather#
The formula assumes the aircraft can always fly. Real sites have wind and rain. We simulated a year at one-minute resolution (dib_fleet.py, seed 7):
- Wind: hourly mean wind follows a Weibull distribution (shape 2, scale 6 m/s) with hour-to-hour persistence from an AR(1) process (). Mean wind 5.13 m/s; 1.7% of hours exceed 12 m/s.
- Rain: a two-state Markov chain with 8.0% of hours wet and a mean wet spell of three hours.
- Flight limits: DiaB flies only when wind < 12 m/s and dry. That leaves 90.4% of the year flyable.
- Perching sentry: stays on watch while perched up to 15.3 m/s sustained wind (0.15% of hours exceed it), re-perches every four hours, and only needs a flyable window to move. If it can't move, it stays put.
Result 1: the scheduler matters as much as the fleet#
We first tried the obvious schedule: stagger docks evenly across the 90-minute cycle and, when weather blocks a launch, retry every five minutes. Coverage stayed between 27.6% and 31.9% no matter how many docks we added.
The cause is resynchronization. Every weather hold makes all waiting aircraft launch in the same flyable minute. After a few holds the whole fleet flies together, recharges together and leaves the site uncovered together — the fleet behaves like one very expensive drone. Over a simulated year this happens dozens of times.
A relief scheduler fixes it: launch the next charged aircraft only so that it arrives on station as the current one departs.
for t in range(minutes):
if station_until - t <= TRANSIT and flyable[t]:
i = argmin(ready) # earliest-charged aircraft
if ready[i] <= t:
start = max(t + TRANSIT, station_until)
end = t + SORTIE - TRANSIT
covered[start:end] = True
station_until = end
ready[i] = t + SORTIE + RECHARGEResult 2: the weather ceiling#
| Docks | Ideal (no weather) | Naive stagger | Relief scheduling |
|---|---|---|---|
| 1 | 30.0% | 27.6% | 27.6% |
| 2 | 60.0% | 27.7% | 55.2% |
| 3 | 90.0% | 27.8% | 82.4% |
| 4 | 100.0% | 30.9% | 91.1% |
| 5 | 100.0% | 31.9% | 91.1% |
| 6 | 100.0% | 27.8% | 91.1% |
| 7 | 100.0% | 31.9% | 91.1% |
With relief scheduling, coverage climbs almost linearly to 91.1% at four docks and then stops: five, six or seven docks buy nothing, because the remaining 8.9% of the year is weather in which no aircraft may fly. That gap does not close with money. It closes only with an aircraft that can watch without flying.
A single perching sentry in the same weather is on watch 99.1% of the year. It loses time only during relocations and the 0.15% of hours above its perched wind limit. When transit is blocked by rain, it simply stays where it is — still watching.
Sensitivity: sortie and recharge time#
The sizing formula is cheap to evaluate, so it is worth seeing how sensitive it is. The table holds transit at 4 minutes each way and varies the other two parameters.
| Sortie ↓ · Recharge → | 30 min | 55 min | 90 min |
|---|---|---|---|
| 25 min | 4 docks · 31%/dock | 5 docks · 21%/dock | 7 docks · 15%/dock |
| 35 min | 3 docks · 42%/dock | 4 docks · 30%/dock | 5 docks · 22%/dock |
| 45 min | 3 docks · 49%/dock | 3 docks · 37%/dock | 4 docks · 27%/dock |
Two things follow. Recharge time matters as much as flight time: halving recharge from 55 to 30 minutes saves a dock at every sortie length, which is why battery-swap docks exist. And short sorties are punished twice — transit eats a larger share of a short flight, so a 25-minute aircraft spends 32% of every sortie getting to and from station.
From one point to a whole site#
Everything above is for one point of interest. A site with separate areas needing persistent watch, more than one sensor footprint apart, needs aircraft in rotation, and each additional area adds its own transit time. Patrol routes that visit several areas trade time on watch per area for coverage breadth: an aircraft visiting four areas on a 27-minute station time gives each area under 7 minutes per 90-minute cycle — about 7% time on watch. Most real DiaB deployments are therefore alarm-response systems with excellent launch latency rather than persistent-watch systems, and they should be bought and judged as such.
What this means for buyers#
Ask any DiaB vendor three questions. First, what is time on watch — not availability to launch — for one point on your site? Second, how does their scheduler behave after a weather hold; do aircraft relaunch together? Third, what is the flyable fraction at your site, from local wind and precipitation records? If the answer to the third is 80%, no fleet size will deliver more than 80% coverage from the air.
DiaB remains an excellent tool for alarm response and inspection. It is the wrong tool for persistent watch, which is exactly what our alternatives comparison lays out.
Limitations#
The weather model is synthetic. Weibull scale 6 m/s with shape 2 is plausible for an exposed inland site, but coastal and mountain sites differ substantially; use local data. We did not model visibility, icing, night-flight restrictions, airspace closures, aircraft faults or maintenance downtime, all of which reduce DiaB coverage further. We modeled one point of interest; covering a large site with several points multiplies the fleet. The perching model assumes a valid perch is always available within range and ignores relocation blindness beyond two minutes per move.
Frequently asked questions#
How many drone docks are needed for 24/7 coverage?
Ceil((sortie + recharge) / (sortie − 2 × transit)). For a 35-minute sortie, 4-minute transits and 55-minute recharge, that is four docks — before weather.
Can drone-in-a-box provide 24/7 coverage?
Only up to the site's flyable fraction. In our model, four docks reached 91% of the year; additional docks added nothing because the remaining time was unflyable weather.
Why does adding docks sometimes not improve coverage?
If the scheduler simply retries after weather holds, aircraft resynchronize and fly together. A relief scheduler that times launches to hand over on station avoids this.
References#
- J. Gordon Leishman, Principles of Helicopter Aerodynamics, 2nd ed., Cambridge University Press, 2006. Momentum theory, ideal hover power and figure of merit.
Reproducibility: model code is published at /research-code/ with a README. Results are model outputs under the assumptions stated above, not field trials.