Top: expanding shock front, colour ∝ local overpressure. Bottom: Friedlander overpressure-time trace at the observer marker.
This simulator models the fluid dynamics of a point-source blast wave expanding into a uniform atmosphere — the same idealised problem G. I. Taylor and Leonid Sedov solved independently in the 1940s to describe how a shock front grows from a sudden, localised release of energy. The shock-front radius follows the Sedov–Taylor self-similar scaling law R(t) = ξ₀·(E·t²/ρ₀)^(1/5), the peak overpressure at the front falls off steeply with distance, and at any chosen observer point the pressure-time history follows the classic Friedlander waveform: a sharp jump at arrival followed by an exponential decay through a brief negative phase.
A plan-view of the shock front expanding from a point source, coloured by local overpressure, alongside a live-traced overpressure-versus-time chart at a fixed observer distance — exactly the two curves blast-engineering textbooks use to size protective structures.
Set the energy yield (a log-scale TNT-equivalent slider, purely a unit of released energy), the ambient air density, and the observer distance. Watch the shock radius, its instantaneous velocity, the peak and current overpressure at the observer, and the arrival time all update live as the ring expands.
Because R(t) scales with the fifth root of energy, releasing 100× more energy only pushes the shock front out about 2.5× further at a given time — this weak scaling is exactly why blast-resistant design focuses so heavily on standoff distance rather than energy alone.
It is a self-similar solution to the fluid-dynamics equations describing a strong shock wave driven outward by a sudden, localised release of energy into a uniform gas. It predicts that the shock radius grows as R(t) ∝ (E·t²/ρ₀)^(1/5), a result derived independently by G. I. Taylor and L. Sedov and later confirmed against real blast-test photography.
In the far field, peak side-on overpressure from a point-source blast decays roughly as the inverse cube of distance (Δp ∝ R⁻³), because the same total energy is spread over an ever-larger spherical shock front. This simulation uses a simplified curve with that correct far-field asymptotic, smoothed near the source to avoid an unphysical singularity.
It is the standard idealised shape used in blast engineering for the pressure-time history at a fixed point: pressure jumps sharply to its peak at the shock's arrival, then decays roughly exponentially through a positive phase and briefly dips below ambient pressure before recovering.
No — because the shock radius scales with the fifth root of energy (R ∝ E^(1/5)), each additional order of magnitude of energy produces a comparatively modest increase in shock-front reach at a given time, which is why standoff distance dominates blast-resistant structural design far more than raw energy does.
The surrounding air is the medium the shock pushes against; denser air (lower altitude, colder temperature) resists the expanding shock more, so for the same energy release the shock front grows more slowly and stays smaller at a given time, exactly as the ρ₀ term in the Sedov–Taylor formula predicts.