Impact & Structural Integrity Model

This page describes how landing impacts are evaluated in the Moonlander simulation. The model connects physical impact energy with structural integrity and derives discrete spacecraft states from this continuous damage representation.

The approach is intentionally simplified, focusing on clarity, robustness, and extensibility rather than material-specific crash mechanics.

Level 1 — Energy Model

Landing damage is evaluated using the kinetic energy of the spacecraft at the moment of ground contact.

E = 1 / 2 · m · v²

m — total spacecraft mass
v — vertical impact velocity

This formulation ensures that both velocity and mass naturally influence the resulting structural load.

Reference Energy (Safe Landing)

A reference energy is computed using a predefined maximum safe landing velocity. This value represents the highest impact energy the structure can absorb without damage.

E_ref = 1 / 2 · m · v_safe²

Impact Energy

The actual energy at touchdown is calculated from the measured impact velocity:

E_impact = 1 / 2 · m · v_impact²

Level 2 — Integrity Model

Structural damage is expressed as a normalized ratio between impact energy and reference energy:

D = E_impact / E_ref

The spacecraft integrity is reduced proportionally to this damage value:

I_new = I_old − D

To maintain numerical stability, integrity is clamped to a physically meaningful range:

I ∈ [0, 1]

I = 1.0 — fully intact
I = 0.0 — complete structural failure

Level 3 — Spacecraft State Machine

The spacecraft state is derived deterministically from the current integrity value and the vertical position of the lander.

Destroyed (Terminal)

I ≤ 0

The spacecraft is completely destroyed. This is a terminal state and the simulation ends.

Crashed (Terminal but Stable)

0 < I < I_structural

Structural failure occurred, but the spacecraft remains physically stable. Mission continuation is no longer possible.

Landed (Successful Touchdown)

z ≤ 0 ∧ I ≥ I_structural

The spacecraft touched down successfully within structural limits.

Operational

z > 0 ∧ I > I_structural

The spacecraft remains controllable. If I < 1, the system is considered operational but damaged.

Design Rationale

This three-layer model cleanly separates physical impact energy, structural damage, and discrete system behavior. It avoids arbitrary thresholds while remaining intuitive, testable, and extensible.

The structure is well suited for future extensions such as multi-axis impacts, component-based damage models, or material-specific absorption limits.