A rider moving on a circle of radius R with angular speed ω = 2π/T has centripetal acceleration a = ω²R = v²/R directed toward the hub. The seat force is the weight plus whatever supplies that acceleration: at the top N = m(g − ω²R), at the bottom N = m(g + ω²R). The rider feels lightest at the top; N = 0 when ω²R = g, i.e. period T = 2π√(R/g).
The gondola hangs from a pivot on the rim, so it is a pendulum with an accelerating support: l φ'' = −(g sin φ + ap·eφ) − c l φ', and the hanger tension (what the rider feels) is T = m(−ap·er + lφ'² + g cos φ). Eight gondolas are integrated with a fixed 1/240 s step (semi-implicit Euler).
Simplifications: rigid wheel, point-mass rider, linear damping, no wind, constant speed (no start-up). Real wheels turn so slowly that ω²R is only a few percent of g; the fast presets are for illustration.