Impact & Structural Integrity Model

This section describes the simplified impact and structural integrity model used in the Moonlander simulation. The model evaluates touchdown events by relating the vertical impact energy to a predefined safe landing reference.

The approach is intentionally low-order and deterministic. It does not attempt to model material deformation, landing gear mechanics, or detailed crash dynamics. Instead, it provides a robust and extensible abstraction for simulation state transitions.

Impact Energy Model

At touchdown, the impact severity is estimated from the kinetic energy associated with the vertical impact velocity.

E_{impact} = \frac{1}{2} m v_{impact}^{2}

Where:
• $E_{impact}$ is the impact kinetic energy [J]
• $m$ is the current spacecraft mass [kg]
• $v_{impact}$ is the vertical impact velocity [m/s]

This formulation ensures that both spacecraft mass and touchdown velocity contribute to the resulting impact load.

Reference Energy

A reference energy is computed using the maximum safe landing velocity. It represents the impact energy that the spacecraft is assumed to tolerate without structural damage.

E_{ref} = \frac{1}{2} m v_{safe}^{2}

Where:
• $E_{ref}$ is the safe reference impact energy [J]
• $v_{safe}$ is the maximum safe vertical landing velocity [m/s]

Damage Ratio

Structural loading is represented by a normalized damage ratio. This ratio compares the actual impact energy to the safe reference energy.

D = \frac{E_{impact}}{E_{ref}}

Where:
• $D$ is the normalized damage ratio [-]

A value of $D = 1$ corresponds to an impact at the predefined safe landing limit. Values greater than one indicate that the impact energy exceeds the nominal safe reference.

Structural Integrity Update

The spacecraft structural integrity is modeled as a normalized state variable in the interval $[0, 1]$ .

I \in [0, 1]

The updated integrity value is computed by subtracting the damage ratio from the previous integrity value:

I_{new} = I_{old} - D

To avoid invalid numerical states, the resulting value is clamped to the physically meaningful interval:

I_{new} = \max\left(0,\min\left(1, I_{old} - D\right)\right)

Where:
• $I = 1$ represents a fully intact spacecraft
• $I = 0$ represents complete structural failure

Spacecraft State Classification

The continuous integrity value is mapped to discrete spacecraft states. This allows the simulation to derive operational consequences from the damage model.

Destroyed

I \leq 0

The spacecraft has lost all structural integrity. This is treated as a terminal failure state.

Crashed

0 < I < I_{structural}

The spacecraft is not completely destroyed, but its structural integrity is below the minimum required threshold. Mission continuation is no longer possible.

Landed

z \leq 0 \; \land \; I \geq I_{structural}

The spacecraft has reached the ground while remaining above the structural integrity threshold.

Operational

z > 0 \; \land \; I > I_{structural}

The spacecraft remains above the surface and retains sufficient structural integrity for continued operation.

Model Assumptions

Only the vertical impact velocity is considered.
The spacecraft is treated as a lumped mass during impact evaluation.
Landing gear deformation and material-specific crash mechanics are neglected.
The safe landing velocity defines the reference energy threshold.
Integrity is represented as a normalized scalar state.

Design Rationale

The model separates impact physics, structural degradation, and discrete spacecraft state transitions. This keeps the implementation transparent and suitable for real-time simulation while preserving a physically interpretable relationship between touchdown velocity and vehicle damage.

The formulation can later be extended toward multi-axis impact evaluation, component-level damage, landing gear absorption models, or probabilistic structural failure criteria.

Summary

Impact severity is estimated using vertical kinetic energy.
A safe reference energy is derived from the maximum allowed landing velocity.
Structural damage is represented by a normalized energy ratio.
Spacecraft integrity is clamped to the interval $[0,1]$ .
Discrete spacecraft states are derived from integrity and altitude.