A section of a train wheel tread is formed into a continuous hyperbolic curve to respond asymptotically to changes in the path of a rail, thus, dampening lateral oscillation of the train wheels back and forth across rail. The hyperbolic curve at a minimum extends from a taping line to a wheel lift point. However, for further dampening effects the hyperbolic curve is extended from a fillet section across the taping line toward the field side of the wheel. Two tires having the same hyperbolic profile work in conjunction as a feedback system to dampen lateral oscillation while at the same time saving energy, reducing tire and rail wear.