Harpoon Capture of Tumbling Space Debris (2D)

Harpoon Launch

Launch velocity 20 m/s

Target tumble rate 18°/s

Target plate mass 120 kg

Tether breaking strength 2200 N

Telemetry

Armed — aim and fire

Impact velocity (normal)

— m/s

Tether tension

0 N

Target angular rate

0.0°/s

Distance to servicer

— m

How it works

A harpoon-and-tether capture (as flight-tested by ESA's RemoveDEBRIS mission in 2019, and studied for ClearSpace-style active debris removal) has to solve two problems in sequence: penetrating the target, then arresting its tumble without snapping the line. This 2D version views the encounter from directly above the plane the debris tumbles in, so the single rotation axis (perpendicular to the screen) is exact — not the isotropic-inertia approximation a full 3D rigid body needs.

1. Penetration — Poncelet's criterion. The harpoon embeds only if its kinetic energy along the impact-surface normal exceeds the plate's penetration resistance:

E_impact = ½ m_harpoon (v · n̂)²
Capture succeeds if  E_impact ≥ k_pen · M_target

A glancing hit (small v·n̂ because the panel is tumbling away from the shot) or too heavy/tough a target plate produces a bounce, not a capture — exactly why real missions aim for the flattest, most perpendicular moment of the tumble.

2. Tether dynamics — spring-damper + angular momentum transfer. Once embedded, the tether pulls only (it cannot push):

T = max(0, k(L − L₀)) + c·dL/dt
F = T·(servicer − anchor)/|…|,   τ = r_x F_y − r_y F_x
dω/dt = τ / I,  I = (1/12) M (W² + H²)

The torque τ comes from the lever arm r between the harpoon anchor point and the target's centre of mass — this is what despins the tumbling debris, exactly as conservation of angular momentum requires. If tension T exceeds the tether's rated breaking strength before the tumble is damped, the line snaps and the target escapes still tumbling. Once tension and spin settle, the sim reels in the restraint length L₀ to bring the target home.