Micrometeorite Shield Test (3D test bench)

Hypervelocity impact on a Whipple shield. Orbital debris and micrometeoroids hit at 3 to 20 km/s, far above the speed of sound in metal, so the target behaves like a fluid and a thin sacrificial plate (the bumper) is enough to shatter a particle many times its own thickness. The fragments then spread across the standoff gap, so the same momentum lands on a much larger area of the rear wall.

Stage 1, bumper. Penetration scale: P = d (rp/rw)^1/2 (vn/c)^2/3 with vn = v cos(theta) and c = 5.4 km/s. A thin plate is perforated when t/cos(theta) is below 1.8 P. The shattered fraction is f = [1 - exp(-(vn/3 km/s)^2)] [1 - exp(-(t/(d cos theta))/0.12)]: a thick, fast bumper makes a cloud, a thin or slow one leaves an intact slug.

Conservation. The projectile plus the bumper plug it punches out (mass mp + mb) split into a cloud (fraction f) and a slug (1 - f). Their forward momentum can never exceed the incident normal momentum mp vn (the bumper rim takes the rest) and their kinetic energy is below the incident energy; the missing part becomes heat, melt and vapour.

Stage 2, standoff. The cloud half-angle is tan(phi) = 0.12 + 0.2 [1 - exp(-vn/6 km/s)], so after a standoff S its radius is Rc = dh/2 + S tan(phi). Parabolic areal loading gives a peak impulse I = 2 Mc vc / (pi Rc^2), which falls roughly as 1/S^2: doubling the gap cuts the load about four times.

Stage 3, rear wall. The wall absorbs the impulse as plastic work: I^2/(2 rw t) = sigma_y t eps_f, so I_crit = L sqrt(2 eps_f) t sqrt(rw sigma_y) with eps_f = 0.15 and a localisation factor L = 0.35 (peak loading is concentrated, so the wall fails below its plate-average capacity). I/I_crit above 1 perforates the wall, above 0.55 it bulges and spalls. An intact slug is judged separately with the same penetration scale.

Honest limits. This is a transparent scaling model with illustrative constants, not a hydrocode and not a certified ballistic limit equation; real shields add MLI blankets, Nextel or Kevlar layers and are qualified by light-gas-gun tests and simulation. No particular spacecraft is represented. Real numbers: ISS modules use bumpers of about 1 to 2 mm with 100 mm or more standoff.

What to try

• Load Thin bumper (fails): the bumper no longer shatters the particle and the slug perforates the wall. Raise the bumper to 1 mm and watch f approach 1.
• Drag Standoff from 30 to 300 mm and watch the peak impulse drop like 1/S^2.
• Raise the speed at fixed size: the cloud cone widens and the critical diameter curve turns over.
• Tilt the impact to 60 deg: the cloud axis moves sideways by S tan(theta) and the effective bumper gets thicker.