Roller Coaster G-Force Lab (2D)

Track

Track shape

Hill / valley radius scale 1.00×

Launch speed v₀ 12.0 m/s

Cart + riders mass 280 kg

Ready to launch.

Apparent Weight (rider G-force)

-1g0g1g3g5g

Speed

0.0 m/s

G-force

1.00 g

Normal force N

0 N

Local radius r

∞ m

G-force vs Track Position (analytic)

G(s) for current v₀1g reference

How it works

At every point of the track, the cart follows a circular arc of some local radius r with signed curvature κ = ±1/r (positive for a valley, whose center of curvature sits above the track; negative for a hill crest, whose center sits below). Newton's second law along the track-normal direction gives the exact rail (normal) force per unit mass: N/m = v²·κ + g·cosθ, where θ is the track's angle from horizontal. The rider's felt G-force is simply G = N/(mg).

On a valley bottom κ is positive, so G rises above 1g with speed — that's the "squashed into your seat" feeling. On a hill crest κ is negative: if v²/r exceeds g·cosθ, the equation gives N < 0 — the rail can only push, never pull, so the cart is momentarily weightless or the restraint has to hold you down. That's genuine airtime, the same physics real coasters engineer on purpose with tight-radius camelback hills.

The track is frictionless here so speed along it is exact from energy conservation, v(s) = √(v₀² + 2g(h₀ − h(s))) — which is why the G(s) graph can be drawn analytically for the whole track before the cart even moves, instead of only trailing a history. Sharpen the radius scale slider and the same launch speed produces much bigger G swings — proof that G-force is driven by curvature, not by energy content.