Right-sizing protective packaging is a real trade-off: too little cushion and the product breaks; too much and you waste material, weight and shipping volume. This model treats the cushion pad as a nonlinear spring-damper compressed by the falling product's kinetic energy.
Impact velocity: v = √(2·g·h)
Cushion stress: σ(ε) = E₀·ε + Ef·ε^n (ε = compression / thickness)
Contact force: F = σ(ε)·A + c·(dx/dt)
Deceleration: a = F / m → reported as G = a / g
The E₀ term is the cushion's initial soft response; the Ef·ε^n term is the steep "knee" as the material approaches its densification strain and stiffens sharply — the same shape as a real manufacturer's cushion curve. Each material below uses distinct stiffness and densification constants:
- EPE foam — soft, high densification strain (~75%), the industry default for electronics.
- Molded fiber pulp — stiffer and greener (recycled paper pulp), less travel before bottoming out.
- Recycled cardboard honeycomb — very stiff, thin, low material volume, but a hard "knee" — needs enough thickness or it transmits a spike.
- Air pillow — very soft and reusable-air-based, but bulky (large volume for the same protection).
The fragility rating is the maximum G a product can survive (a common packaging-engineering spec — fragile electronics are often rated around 40 G, glass and ceramics around 75 G, and rugged hardware 150 G or more). If the simulated peak G exceeds the rating, or the cushion fully "bottoms out" before absorbing the impact, the product is flagged damaged. The goal of eco-friendly packaging design is the thinnest, lowest-volume cushion of the greenest material that still keeps peak G under the product's rating — minimizing material (Reduce) without risking the product.