How Gearbox Ratios Influence Lap Time and Driving Style. An Analysis Based on Time-Optimal Maneuvers. 2003-32-0056

This paper presents an analysis of time-optimal maneuvers of a race motorcycle in the circuit of Adria (Italy) with different choices of gearbox ratios. The minimum lap time is found by means of the Optimal Maneuver Method, whose theoretical basis is presented in [1], [3], [4], [10]. The method essentially solves a two-point boundary value optimal control problem by finding the driver's inputs that minimize an objective function (i.e. the minimum-lap time). The good agreement between the method results and data acquired by a measurement system mounted on board a motorcycle driven by expert drivers justifies its use as a tool for vehicle set up and design parameters analysis. In the past the method was extensively used to analyze the influence, on racing vehicle performance, of geometry, mass properties distribution, tire and engine power characteristics as shown in papers [2], [6], [7].

In this work the importance of the gear ratios and their dependence on the specific characteristic of a circuit (number and types of curves and straight runs) is investigated. The motorcycle power train is modeled by specifying the envelope curve of the engine torque at the rear wheel. It is assumed that any time the engaged gear is that which yields the maximum thrust, although throttling may occur in some part of the circuit. Comparisons among optimal maneuvers obtained with different ratio sets point out the importance of this technical choice. Not only the final effect on lap time is pointed out, but it is also shown how gearbox ratio selection affects driving style in different part of the circuit. A set with wrong ratios may result in time losses in some curves or straights, not balanced by gains in the remaining parts, which ultimately spoils the overall performance. Tuning the gear ratios to the most critical curves of the circuit makes the difference. Finally, information helping drivers to improve can be drawn from simulated maneuvers.