Moonlander – Impact & Structural Integrity | Spaceflight Dynamics Framework

This section describes the simplified impact and structural integrity model used in the Moonlander simulation framework.

The implemented approach represents a deterministic low-order energy-based impact assessment model intended for real-time simulation and autonomous landing research.

Instead of resolving detailed structural mechanics, material deformation, or landing gear dynamics, the model estimates landing severity from the translational kinetic energy associated with the touchdown event.

The resulting impact severity is then mapped to a normalized spacecraft integrity state that controls simulation state transitions such as operational landing, crash, or complete destruction.

Impact Energy Model

The impact model assumes that the translational kinetic energy associated with the vertical touchdown velocity is converted into structural loading during impact.

The vertical impact energy is computed as:

E_{impact} = \frac{1}{2} mv_{impact}^{2}

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

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

Reference Impact Energy

A reference impact energy is computed from the maximum allowed safe landing velocity.

This reference defines the nominal structural loading level that the spacecraft is assumed to tolerate without critical damage.

E_{ref} = \frac{1}{2} mv_{safe}^{2}

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

Normalized Damage Metric

Structural loading is represented by a normalized impact severity metric comparing actual impact energy to the safe reference energy.

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

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

The ratio acts as a dimensionless measure of impact severity.

Interpretation:

D > 1 \Rightarrow E_{impact} > E_{ref}

Thus, values greater than one indicate that the touchdown energy exceeds the predefined safe landing condition.

Structural Integrity State

Spacecraft structural condition is represented by a normalized integrity state variable:

I \in [0,1]

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

The integrity variable does not represent a directly measurable physical material property. Instead, it acts as a normalized survivability state used for simulation logic and mission-state evaluation.

Integrity Degradation Model

Structural degradation is modeled by reducing the integrity state according to the normalized damage metric.

A configurable damage scaling coefficient is introduced:

k_D \in [0,1]

The updated structural integrity becomes:

I_{new} = I_{old} - k_D D

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

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

The coefficient $k_D$ allows tuning the effective structural robustness of the spacecraft model without modifying the underlying impact energy formulation.

Spacecraft State Classification

The continuous integrity state is mapped to discrete spacecraft operational states.

This enables the simulation framework to derive mission-level consequences from impact severity.

Destroyed

I \leq 0

The spacecraft has lost all structural survivability and is treated as completely destroyed.

Crashed

0 < I < I_{structural}

The spacecraft remains partially intact but below the minimum structural survivability threshold required for continued mission operation.

Landed

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

The spacecraft has successfully reached the lunar surface while remaining above the required structural integrity threshold.

Operational

z > 0 \land I > I_{structural}

The spacecraft remains airborne and structurally operational.

Model Assumptions and Limitations

The current implementation intentionally simplifies the physical impact process in favor of deterministic real-time execution and transparent simulation behavior.

The model currently neglects:

lateral impact velocity components
rotational impact momentum
landing gear compression and damping
distributed structural loading
plastic deformation mechanics
fracture propagation and material failure models
terrain-dependent impact effects

Consequently, the model should be interpreted as a low-order impact-assessment framework rather than a high-fidelity structural crash simulation.

Design Rationale

The implemented formulation separates:

impact physics estimation
structural degradation modeling
simulation-state classification

This modular structure keeps the implementation computationally efficient, numerically robust, and extensible for future research campaigns.

The framework can later be extended toward:

multi-axis impact analysis
component-level damage models
landing gear energy absorption
terrain interaction models
probabilistic structural failure estimation
high-fidelity crash dynamics

Key Characteristics

Energy-based impact severity estimation
Deterministic low-order structural survivability model
Normalized damage metric formulation
Configurable structural robustness scaling
Discrete spacecraft state classification
Real-time capable implementation

Impact & Structural Integrity Model