C2 link and detect-and-avoid

Example 1 Three aircraft on the display

The pipeline drone is at the origin. Three aircraft are shown: one head-on 4 km away at a similar height, one crossing that will pass 2 km away, and one head-on but 200 m higher (hypothetical data).

import numpy as np

FT = 0.3048
DMOD, HMD, ZTHR, TAU = 4000 * FT, 4000 * FT, 450 * FT, 35.0   # DO-365 well-clear values (Phase 1)

def check(p_rel, v_rel, dz):
    r = np.linalg.norm(p_rel)
    rdot = p_rel @ v_rel / r
    tau_mod = (DMOD**2 - r**2) / (r * rdot) if rdot < 0 else float("inf")
    t_cpa = max(0.0, -(p_rel @ v_rel) / (v_rel @ v_rel))
    hmd = np.linalg.norm(p_rel + v_rel * t_cpa)
    horiz = (r <= DMOD or 0 <= tau_mod <= TAU) and hmd <= HMD
    lowc = horiz and abs(dz) <= ZTHR
    return tau_mod, hmd, lowc

cases = {   # intruder relative position (m), relative velocity (m/s), height difference (m)
    "head-on 4 km": (np.array([4000.0, 0]), np.array([-70.0, 0]), 30),
    "crossing, passes 2 km": (np.array([3000.0, 2000]), np.array([-60.0, 0]), 30),
    "head-on 4 km, 200 m above": (np.array([4000.0, 0]), np.array([-70.0, 0]), 200),
}
for name, (p, v, dz) in cases.items():
    start = next((s for s in range(0, 121) if check(p + v * s, v, dz)[2]), None)
    tau, hmd, _ = check(p, v, dz)
    msg = f"loss of well clear in {start} s" if start is not None else "stays well clear"
    print(f"{name:26s} now: tau_mod {tau:5.1f} s  HMD {hmd:5.0f} m  -> {msg}")

head-on 4 km               now: tau_mod  51.8 s  HMD     0 m  -> loss of well clear in 15 s
crossing, passes 2 km      now: tau_mod  64.0 s  HMD  2000 m  -> stays well clear
head-on 4 km, 200 m above  now: tau_mod  51.8 s  HMD     0 m  -> stays well clear

The head-on aircraft at the same level will lose well clear in 15 seconds, though it is still 4 km away. The crossing aircraft at 2 km and the one 200 m higher (above the ZTHR of about 137 m) stay well clear. Judging by current range alone is wrong in both directions; direction and relative velocity matter.

Example 2 How far away must we see?

Using assumed times for each step, compare closing speeds of 60 and 90 m/s, with avoidance complete before entering DMOD.

DMOD = 4000 * 0.3048          # m
steps_pilot = {"detect and track": 8, "C2 downlink + display": 1.5, "pilot decides": 12,
               "C2 uplink": 0.5, "manoeuvre takes effect": 8}
steps_onboard = {"detect and track": 8, "onboard decision": 1, "manoeuvre takes effect": 8}

for name, steps in [("pilot in the loop", steps_pilot), ("onboard avoidance", steps_onboard)]:
    t = sum(steps.values())
    for v_close in (60, 90):  # closing speed m/s
        r = v_close * t + DMOD
        print(f"{name:18s} timeline {t:4.1f} s  closing {v_close} m/s -> detect by {r/1000:.2f} km")

pilot in the loop  timeline 30.0 s  closing 60 m/s -> detect by 3.02 km
pilot in the loop  timeline 30.0 s  closing 90 m/s -> detect by 3.92 km
onboard avoidance  timeline 17.0 s  closing 60 m/s -> detect by 2.24 km
onboard avoidance  timeline 17.0 s  closing 90 m/s -> detect by 2.75 km

With the pilot deciding over C2, the sensor must see aircraft 3–4 km away, while onboard avoidance needs 2.2–2.8 km. Many sensors on small drones cannot see light aircraft that far. An ADS-B receiver only helps with aircraft carrying a transmitter; the rest need ground radar, observers or the strategic mitigations from Module 1.