= 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 $4\,\mathrm{m\,s^{-1}}$. Neglect rebound, friction elsewhere and external work during crushing. The member must absorb
$$
E=\frac12mv^2=800\,\mathrm{J},\qquad \int_0^s F(x)\,dx=E.
$$
A 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 \b[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.
\Image[/crashworthiness-equal-work.png]
{title=Original ideal crush-force curves: both absorb 800 J over 0.20 m, but their peak loads differ by a factor of two}
A physical test must record the load history as well as the final crushed shape. One primary example used two vertical drop tests at $12.8\,\mathrm{m\,s^{-1}}$ 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.<Determination of crash test pulses and their application to aircraft seat analysis by E. Alfaro-Bou and others>[NASA NTRS record 19810058363, author abstract; SAE paper 810611 (1981)]{ref} The carriage calculation above is an idealized <energy> budget, not a reconstruction of those tests.
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