Abstract: A variably curved track-mounted amusement ride having, in a first embodiment, at least one outside curve and at least one inside curve, each lying substantially within a vertical plane and each having an axis of symmetry which is substantially horizontal. The vertical distance occupied by an outside curve is less than that occupied by an inside curve. The track can retain a cart which runs on the track no matter what the orientation of the body of the cart is with respect to the track. Any means that is well known in the art can be used to raise the cart to the beginning of the track. No portion of the track, except optionally the lowest level, lies directly below at least the farthest outside portion of an outside curve. A second embodiment has only outside curves.