Select a person to inspect their forces.Seed 12 · 160 people
One person. Many forces.
Click a particle. Follow the push and pull.
Same scale for every arrow.
Net force is white.
Person #7383 kg
- Speed
- 1.31 m/s
- Velocity (x, y)
- -1.17, 0.59 m/s
- Preferred heading
- 153°
- Personal gap
- 0.35 m
- Nearby people
- 5
Heading: 0° right, 90° down.
Dashed halo: half the desired gap.
| Force | x (N) | y (N) | Size (N) |
|---|---|---|---|
| Self-propulsion | -35.5 | 17.9 | 39.7 |
| Neighbor alignment | 199.4 | -63.7 | 209.3 |
| Personal space / avoidance | 0.0 | 0.0 | 0.0 |
| Circle-route preference | 340.1 | 3.0 | 340.1 |
| Body contact | 0.0 | 0.0 | 0.0 |
| Damping | 31.2 | -15.7 | 34.9 |
| Boundary response | 0.0 | 0.0 | 0.0 |
| Resultant force | 535.2 | -58.6 | 538.4 |
Acceleration = net force ÷ mass. Values are model units expressed in N; they are not measurements of real people.
Why does a pit move?
Simple rules. Collective behavior.
People supply the motion
Each person tries to reach a preferred velocity. Muscles turn chemical energy into movement; feet push against the floor, which pushes back. Music motivates movement—it is not a mechanical force in this model.
Contact passes a push along
Overlapping bodies act like soft, damped springs. A pair feels equal and opposite contact forces. Walls also push back, exchanging momentum with the venue.
Steering is a choice
Personal space and looking a little ahead encourage avoidance. Alignment nudges a person toward nearby velocities. Circle mode adds a gentle preference to run around the center; no person follows a fixed track.
Energy in. Energy out.
Drive and steering can add or remove kinetic energy. Damping and inelastic contacts dissipate it. Switch self-propulsion off: all active steering stops, and the crowd settles. People are an active system, so crowd momentum and kinetic energy are not conserved on their own.
Under the hood: equations & limits
m a = Fdrive + Falign + Favoid + Froute + Fcontact + Fdamp + FwallDrive: m(v₀e − v)/τ, with τ = 1.5 − 0.85I seconds. Intensity I also increases random heading changes. Damping: −0.32mv. At zero preferred speed, avoidance may still reposition people; turn propulsion off to remove all active behavior. Alignment matches the mean velocity within 1.8 m. Avoidance uses the desired edge-to-edge gap plus a 0.45 s look-ahead.
Contacts use a 30,000 N/m spring and 450 N·s/m normal dashpot, clamped to repel only. Agents have masses 55–100 kg and radii 0.22–0.255 m. These are illustrative choices, not fitted measurements.
Circle mode steers headings toward a selected tangent and adds a soft radial preference near 3.15 m from the center. It deliberately supplies a route and turning direction. Collective spacing and disruptions emerge from local forces; this does not demonstrate spontaneous direction selection.
The solver uses fixed 1/120 s steps and semi-implicit Euler integration. Boundary impulses prevent escape; an 8 m/s numerical speed ceiling prevents blow-ups. Long frame gaps are discarded instead of jumping the physics. Reset reproduces the same seed; New crowd changes it.
Circulation is the mean signed tangential fraction of velocity: −1 is counterclockwise, +1 clockwise. It is a coherence score, not angular velocity. Density counts particle centers per 1 m² cell. Contacts counts touching pairs at the current physics step.
No fear, fatigue, falling, limbs, consent, obstacles, exits, music response, or real human decision-making. No parameter has been calibrated for injury or crowd-safety prediction.