How Far Was the Drone? Estimating Distance to Taipei 101 from a News Broadcast Image

Image Overview

High‑resolution aerial image released by the PLA Eastern Theater Command shows the Danjiang Bridge tower in the lower‑left corner, providing a dual‑landmark for triangulation.

Known Parameters

Landmark heights

Taipei 101: 509.2 m (official, including spire)

Danjiang Bridge tower: 211 m (as of Sep 2025)

Geographic coordinates

Danjiang Bridge tower: 25.165° N, 121.415° E

Taipei 101: 25.0339° N, 121.5645° E

Ground distance between landmarks

Using the Haversine formula the great‑circle distance is approximately 21 km.

Mathematical Model

Dual‑landmark triangulation principle

Let D be the distance from the drone to the Danjiang Bridge tower (unknown). The distance to Taipei 101 is D+L, where L is the horizontal separation between the two landmarks (≈21 km). For a pinhole camera the pixel height p of an object of real height H at distance d satisfies p = f·H/d, where f is the focal length in pixel units. Taking the ratio of the two landmarks eliminates f:

k = p₁ / p₂ = (H₁ / (D+L)) / (H₂ / D) = H₁·D / (H₂·(D+L))

Solving for D gives: D = (k·H₂·L) / (H₁ - k·H₂) where H₁=509.2 m, H₂=211 m, L≈21 km, and k is the measured pixel‑height ratio.

Pixel‑height measurements

Taipei 101: p₁ = 177 px (center line x=488, tip y=118, base y=295)

Danjiang Bridge tower: p₂ = 130 px (center line x≈100, top y=422, base y=552)

Pixel‑height ratio k = 177 / 130 ≈ 1.362.

Distance Calculation

Substituting the values into the formula yields:

D ≈ 27.1 km   (drone to Danjiang Bridge)

D+L ≈ 48.1 km (drone to Taipei 101)

Error Analysis

Assuming a ±10 % uncertainty on the pixel measurements, a sensitivity analysis produces the following representative results:

p₁=159, p₂=143 → D≈17.9 km, D+L≈38.9 km

p₁=168, p₂=137 → D≈21.9 km, D+L≈42.9 km

p₁=177, p₂=130 → D≈27.1 km, D+L≈48.1 km

p₁=186, p₂=124 → D≈34.3 km, D+L≈55.3 km

p₁=195, p₂=117 → D≈46.8 km, D+L≈67.7 km

Resulting confidence intervals:

Drone‑to‑bridge: 18 km – 47 km (best estimate 27 km)

Drone‑to‑Taipei 101: 39 km – 68 km (best estimate 48 km)

Drone‑to‑coastline (bridge is ~3 km from shore): 15 km – 44 km (best estimate 24 km)

12‑nautical‑mile assessment

The 12‑nm (22.22 km) limit is compared with the drone‑to‑coast distance:

Best estimate 24 km > 22.22 km → outside 12 nm

Minimum estimate 15 km < 22.22 km → could be inside

Maximum estimate 44 km > 22.22 km → outside

Thus the most likely position is beyond the 12‑nm limit, though measurement uncertainty does not completely rule out a location near the limit.

Model Discussion

Advantages of the dual‑landmark method

No need for camera intrinsic parameters (focal length, field‑of‑view).

Systematic optical distortions cancel because both landmarks are captured in the same frame.

The pixel‑height ratio has a theoretical upper bound, providing a built‑in validation check.

High repeatability: any analyst can reproduce the result by measuring pixel heights.

Primary error sources

Pixel measurement error (≈±10 %).

Partial occlusion of the base of Taipei 101 by surrounding buildings.

Atmospheric refraction affecting line‑of‑sight over distances > 40 km.

Earth curvature causing ~125 m line‑of‑sight drop.

All calculations are based on perspective geometry and can be independently reproduced from the publicly released image.