06 / analyses · 22 September 2026

Swarm arithmetic

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A time budget calculated for a single drone is the easiest case. When drones arrive one after another, each finds the defence still busy with the last. This piece calculates how many of ten drones one defence point handles in time. The answer depends on the intervals, the engagement time and the human role.

The earlier analyses calculated time for a single target, and real attacks rarely look like that. When there are several or a dozen drones, the result depends on the sum of the times, not on the time of a single engagement. This piece shows how quickly that sum outgrows what one defence point can do.

Three attacks, three scales

On the night of 5 to 6 January 2018, 13 simple drones attacked the Russian bases at Khmeimim and Tartus in Syria. That is the figure given by the Russian defence ministry. Ten flew at the air base and three at the port. The Russians said they shot down seven and took control of six with electronic warfare.

In September 2019 the oil processing plant at Abqaiq in Saudi Arabia was hit by 18 drones, according to the Saudi defence ministry. The same strike used seven cruise missiles, four of which hit the Khurais oil field. The attack halted about half of Saudi oil production for a time.

On the night of 9 to 10 September 2025, Poland recorded 19 violations of its airspace by drones, from about 23.30 to about 6.30. Three were confirmed shot down, and according to the prime minister probably a fourth as well. On average that is one violation every twenty minutes or more, but it was not an attack on a single site.

The exact intervals between drones in the first two attacks have not been disclosed. What is known is that a coordinated strike on one site cuts them to seconds or to zero. That is the case this piece calculates.

The model

Ten drones of medium speed, 21 metres per second, are detected at equal intervals, each at the same distance. Each first passes the technical links of the model, meaning detection, classification and an automatic check of whether the flight is authorised. The model then calculates three variants. In variant A a human in the loop decides on the drones in turn, one after another, and passes the order to the shooter. In variant B the decisions run in parallel, as if each drone had its own decision-maker. In variant C the human is on the loop, and the system engages each drone unless a veto comes within ten seconds.

The defence point has one effector, which engages drones one at a time. The time the effector spends on one drone is set, for illustration, at 3, 6 or 12 seconds. The effector takes the drone with the least time left and skips any drone it can no longer hit in time.

Human or effector

The first table covers ten drones detected at one kilometre, with an effector that needs six seconds per drone. It shows how many the defence point engages in time.

Interval between dronesA, one operator in turnB, decisions in parallelC, on the loop, 10 s veto
0 s0.21.55.0
5 s0.21.910.0
10 s0.21.910.0
20 s0.22.010.0

Mean number of drones engaged in time, out of ten. Illustrative model, 4,000 draws per cell with a fixed random seed.

02468100 s5 s10 s15 s20 sinterval between dronesmean hit in time, out of 10C, on the loop, 10 s vetoB, decisions in parallelA, one operator in turn

Ten drones detected at one kilometre, effector 6 seconds per drone. Mean number of drones engaged in time by interval between them, for three human roles. Illustrative model.

With a human in the loop and detection at one kilometre, the defence point hardly gets anything in time, whatever the staffing. Even parallel decisions give two drones at most, while with a human on the loop the picture reverses. With ten drones at once the defence point engages half of them, and with five-second intervals all of them. The bottleneck moves from the human to the effector.

What an effector second weighs

The second table takes variant C and ten drones at once. It varies the effector time and the detection distance.

Effector time per droneDetection at 2 kmDetection at 1 kmDetection at 500 m
3 s10.010.02.0
6 s10.05.01.0
12 s6.02.00.0

Variant C, ten drones at once, mean number of drones engaged in time, out of ten.

When the human does not slow the procedure, the number of drones engaged depends almost entirely on two things. These are the time the effector spends on one target and the time left after detection. Once the effector is the bottleneck, every doubling of the engagement time cuts the number of drones handled by half or more. With detection at 500 metres, even the fastest of the three effectors handles only two.

A swarm as compressed time

A swarm is not just a number of targets. It is the same time budget shared among many targets at once. In the role with a human in the loop, the human shares it out, so it runs short already with the first targets. In the role with a human on the loop, the effector shares it out, so every second of engagement counts. Both roles have a common denominator, the detection distance, because it sets the whole time to be shared.

What the model leaves out

The model has one effector and assumes that every shot hits. Several effectors or missed shots would change the result in opposite directions. In variant C it also does not account for whether one person can follow ten veto windows at once. Nobody has measured this, and with ten targets it is doubtful. The effector times are illustrative values, not data from any real system.

Model code and inputs (ZIP, Python)

Declaration of interest. The author is the founder of Silesian Advanced Systems, a team developing an autonomous counter-drone system ahead of incorporating a company. The system is intended to operate in the role this piece calls supervision on the loop. This gives the author a direct interest in the subject. The model, the code and the full grid of results are published so that the reasoning can be checked independently.

Sources

  1. CBC News and Reuters. 2025. "Poland Shoots Down at Least 3 Russian Drones in Its Airspace." 10 September. ↗
  2. CNBC. 2018. "Russia Says It Killed Rebels behind Swarm Drone Attack in Syria, but Experts See More Such Strikes Ahead." 12 January. ↗
  3. Defense Update. 2019. "Attack on Saudi Oil Refineries Proves the Devastating Potential of Iranian Cruise Missiles." 20 September. ↗
  4. DFRLab. 2018. "#PutinAtWar. Drone Attack at Khmeimim." Medium, 22 January. ↗
  5. NBC News. 2025. "Poland Says It Shot Down Russian Drones That Violated Its Airspace during Attack on Ukraine." 10 September. ↗
  6. Radio Free Europe/Radio Liberty. 2018. "Russia Says 13 Drones Used in Attack on Its Air Base, Naval Facility in Syria." 8 January. ↗
  7. The War Zone. 2019. "Here's All the New Info You Need to Know in the Aftermath of the Saudi Oil Facilities Attacks." 19 September. ↗
  8. UN News. 2025. "UN Warns of Escalation Risk after Large-Scale Russian Drone Incursion into Poland." 12 September. ↗

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