Pinball Machine - 2D Table View

A ball on a tilted table

A pinball table is tilted by a few degrees, so gravity along the table is a = g sinθ. With position z measured down the table, a free ball follows z(t) = z₀ + v₀t + ½at², a parabola, until it hits something. The slider sets a directly (the 3D page uses 21.6 length-units/s²). The mechanical energy per unit mass, E = ½v² − a z, is constant in free flight and in perfectly elastic collisions, so the energy graph is a staircase that only jumps when a bumper or flipper does work on the ball.

Collisions

A collision with a smooth surface of unit normal n flips the normal velocity component and keeps the tangential one: v′ = v − (1 + e)(v·n)n, with restitution e (walls 0.7, flippers 0.5). A powered bumper then multiplies the speed by the gain (1.3 on the 3D page), which injects energy. Flippers are capsules rotating at 24 rad/s: the ball bounces off the relative velocity, so a flipper swinging up hands extra speed to the ball.

Honest simplifications: the ball slides and does not roll (no rotational inertia), the table is perfectly smooth, there is no friction, spin or magnus effect, and the 3D page's vertical hops are not modelled in this top-down view. The speed cap of 72 units/s mirrors the 3D page. Units are the table units of the 3D sim, not metres.

• Switch autoplay off and use A / D, the arrow keys, or press the left / right half of the table to flip.
• Choose Dead bumpers (gain 1) and watch the speed graph stop climbing after hits; choose Super bouncy to see the speed cap line.
• Compare Steep table and Shallow table on the energy graph.
• Run the three model checks in the left panel.