Shock waves and the Mach cone around a body. Watch pressure waves bunch up as Mach number rises, an oblique shock spring off a wedge, and a bow shock stand ahead of a blunt body.
This simulator renders pressure waves emitted by a body moving through air, showing how they behave as the Mach number crosses 1. Below Mach 1 the waves outrun the body; above it they can no longer escape ahead and pile up into a cone. Drag the Mach slider or the wedge half-angle, or switch between wedge, cone and blunt body shapes to see the oblique shock steepen, detach into a bow shock, and watch the θ-β-M relation and Rankine-Hugoniot jump conditions update live.
Circular pressure waves expanding at the speed of sound from a moving body. Past Mach 1 they merge into a Mach cone with half-angle μ = arcsin(1/M); a wedge or cone shape produces an attached oblique shock at angle β, while a blunt body forces a detached bow shock standing off its nose.
Use the Mach number and wedge half-angle sliders, pick a body shape (Wedge, Cone, Blunt), or jump to a preset (Subsonic, Sonic boom, Sharp wedge, Blunt re-entry) to see the shock geometry and stats panel (μ, β, p₂/p₁, ρ₂/ρ₁, M₂) update instantly.
Every wedge angle has a maximum θ beyond which no attached oblique shock solution exists — push past θmax in this sim and the shock detaches into a curved bow shock, exactly as happens on real re-entry capsules.
It's the cone-shaped shock front trailing a body flying faster than sound, with half-angle μ = arcsin(1/M). At M = 2 that works out to about 30°; the cone narrows as Mach number rises.
The θ-β-M relation only has a solution up to a maximum deflection angle θmax for a given Mach number. Turn the flow more sharply than that (a blunter wedge or higher θ) and the shock can't stay attached to the tip — it stands off as a curved bow shock instead.
They're the pressure and density ratios across the shock, computed from the Rankine-Hugoniot relations applied to the shock-normal Mach number. Stronger shocks (higher Mach, steeper β) produce bigger jumps.
A 3D cone lets flow relieve sideways in every direction around its axis, so it produces a weaker shock than a 2D wedge of the same half-angle — this sim applies roughly a 0.78 scaling factor to approximate that effect.
It's the transonic regime around M = 1, where pressure waves that would normally spread out ahead of the body instead pile up right at the nose before finally forming a proper shock — the "Sonic boom" preset shows this compression building.