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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]

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.

Emilio Alfaro-Bou contributed experimental crashworthiness research at NASA Langley, including the use of measured aircraft crash pulses to test energy-absorbing seat structures. The publisher names him in full as the first author of the 1981 paper whose citation abbreviates the name to E. Alfaro-Bou.^[ref]

The study analyzed acceleration histories from twelve light-aircraft crash tests. It then used two vertical drop tests at $12.8\mathrm{m}{\mathrm{s}}^{-1}$ to assess an energy-absorbing seat prototype under a specified impact pulse, comparing instrumented dummy and structural response with a finite element method model.^[ref] The physical question is how a load path changes the acceleration-time history; a static strength measurement alone does not answer it.

For an original ideal pulse comparison, take a rigid test mass initially moving at $12\mathrm{m}{\mathrm{s}}^{-1}$. A constant opposing acceleration of $200\mathrm{m}{\mathrm{s}}^{-2}$ stops it in $0.060\mathrm{s}$ over $0.36\mathrm{m}$. Halving that acceleration to $100\mathrm{m}{\mathrm{s}}^{-2}$ doubles the time to $0.120\mathrm{s}$ and the stopping distance to $0.72\mathrm{m}$:Both pulses remove the same momentum per unit mass, $\int adt=12\mathrm{m}{\mathrm{s}}^{-1}$, but require different deformation strokes. These stipulated constant pulses illustrate the tradeoff; they are not measured histories from the paper.

Tomasz Wierzbicki is an applied-mechanics researcher and MIT emeritus professor whose work concerns plastic deformation, structural failure and crashworthiness. His MIT curriculum vitae lists research comparing experimental sheet fracture and tearing with numerical predictions; the laboratory account identifies dynamic plasticity and structural failure as central research themes.^[ref]

His structural-mechanics teaching makes the relation between measurement and model explicit. A uniaxial tensile test measures axial force, extension and lateral contraction. Those observations determine Young's modulus and Poisson's ratio under the stated loading conditions, rather than treating material parameters as properties of a specimen's shape.^[ref]

An original work calculation illustrates a related structural-design distinction. A constant resisting force of $3\mathrm{kN}$ over a compression stroke of $0.1\mathrm{m}$ takes input work $300\mathrm{J}$. A triangular force–displacement curve with the same peak and stroke has area $150\mathrm{J}$. Equal peak loads therefore need not imply equal energy input. The area under the measured curve, together with unloading behaviour, helps distinguish total work from recoverable elastic energy.

These are illustrative curves, not measurements from a Wierzbicki experiment. His work on structural failure and constitutive models addresses the broader task of connecting geometry, material response and observed load histories.