Crash pulse 2026-11-05
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 and reducing velocity from to zero. A constant pulse needs . A symmetric triangular pulse that begins and ends at zero needs a peak magnitude of , because its area is half its peak times its duration:
They have the same average acceleration but different peaks and different time histories.
Figure 1.
Ideal crash pulses with equal velocity change and different peak deceleration
. Own synthetic stopping examples, not measured crash-test data. The vertical axis shows the positive deceleration magnitude, so its integral is speed lost. Time labels are milliseconds; the calculation uses seconds. Details.
For a constant mass following either prescribed history, Newton's second law gives the same total impulse, , while the peak net force magnitude is for the constant pulse and 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 and peak deceleration, where denotes standard gravity. Those test conditions are distinct from the synthetic example above.[ref]
Specific impulse 2026-11-05
Specific impulse measures the impulse delivered by a rocket per unit propellant consumed. In its conventional seconds form, divide total axial thrust impulse by propellant mass and standard gravity :
For constant conditions this becomes , where is the positive expelled mass flow rate. Multiplying by gives the effective exhaust velocity. The conventional value is a unit convention, not a requirement that the engine operate near Earth.[ref] [ref]
For a worked example, a steady engine consuming has and effective exhaust velocity . A ten-second firing supplies using of propellant. The unit of seconds does not mean that this engine can burn for 305.9 seconds: duration also depends on the available propellant and its flow rate.
In a laboratory illustration, integrate the force recorded on a calibrated engine stand and measure the mass consumed during the same firing. Report the ambient pressure, since nozzle pressure forces contribute to thrust. At fixed specific impulse, doubling the mass flow rate doubles thrust; a large specific impulse alone does not specify a large force. For varying performance, the burn-integrated value is weighted by propellant flow, rather than generally equaling a simple time average.
Standard gravity 2026-11-05
Standard gravity is the conventional reference acceleration
exactly. It supplies a fixed reference for unit conversions and for expressing an acceleration as a multiple of . It is distinct from the locally measured gravitational acceleration, which depends on location and height.[ref]
For example, . If a vertical force on a mass of is calculated using this reference, . The same calculation using a measured local value gives instead. The reference value's exactness does not remove measurement uncertainty from a real force or from the actual local gravitational field.
One can measure local gravitational acceleration by tracking a body in free fall with an optical interferometer, taking positive downward and fitting its vertical position to after instrumental corrections. Such an experiment estimates at the apparatus; it does not determine the already stipulated number .[ref]