Crashworthiness

Crashworthiness is the ability of a structure to manage a collision through controlled deformation and energy dissipation while limiting transmitted loads and intrusion into the space it protects. A crushable member can use plastic deformation to spread the loss of kinetic energy over a useful stopping distance. High static strength alone does not specify this response: the complete force-displacement curve and the available deformation stroke matter.

For an original one-dimensional model, a $100\mathrm{kg}$ carriage approaches a stationary crush member at $4\mathrm{m}{\mathrm{s}}^{-1}$. Neglect rebound, friction elsewhere and external work during crushing. The member must absorbA constant resisting force over $s=0.20\mathrm{m}$ is $4000\mathrm{N}$; over $0.40\mathrm{m}$ it is $2000\mathrm{N}$. A triangular force-displacement curve rising from zero over the shorter stroke needs a peak of $8000\mathrm{N}$ to absorb the same energy. Thus equal absorbed energy does not imply equal peak load. Doubling the approach speed quadruples the required energy. The long-stroke design is useful only if that stroke is physically available without unacceptable intrusion.

A physical test must record the load history as well as the final crushed shape. One primary example used two vertical drop tests at $12.8\mathrm{m}{\mathrm{s}}^{-1}$ with an energy-absorbing aircraft-seat prototype, a test dummy and acceleration measurements, using crash pulses informed by twelve light-aircraft crash tests. This tests a dynamic load path rather than merely a material's static strength.^[ref] The carriage calculation above is an idealized energy budget, not a reconstruction of those tests.

A crash pulse is an acceleration time history associated with a collision. It must specify a measurement location, direction and reference frame: a vehicle structure, test platform and supported component can have different histories. NASA's 1981 aircraft-seat study explicitly described crash pulses as deceleration time histories and used them to inform crashworthiness testing.^[ref]

For one-dimensional motion, the signed area under the acceleration curve is the change in velocity:Consider two original ideal stopping pulses, both lasting $T=0.10\mathrm{s}$ and reducing velocity from $8\mathrm{m}{\mathrm{s}}^{-1}$ to zero. A constant pulse needs $a=-80\mathrm{m}{\mathrm{s}}^{-2}$. A symmetric triangular pulse that begins and ends at zero needs a peak magnitude of $160\mathrm{m}{\mathrm{s}}^{-2}$, because its area is half its peak times its duration:They have the same average acceleration but different peaks and different time histories.

For a constant $100\mathrm{kg}$ mass following either prescribed history, Newton's second law gives the same total impulse, $m\Delta v=-800\mathrm{N}\mathrm{s}$, while the peak net force magnitude is $8000\mathrm{N}$ for the constant pulse and $16000\mathrm{N}$ for the triangular pulse. Equal pulse area therefore does not imply equal peak loading. Component motion can also differ from the motion prescribed at its support because of mechanical compliance and dynamic response.

As a historical apparatus example, the NASA study analyzed twelve light-aircraft crash tests and conducted two vertical drop tests with an energy-absorbing seat prototype at $12.8\mathrm{m}{\mathrm{s}}^{-1}$ and $36g_n$ peak deceleration, where $g_n$ denotes standard gravity. Those test conditions are distinct from the synthetic example above.^[ref]