An investigation into bicycle steering and roll responses

Prince, John
Al-Jumaily, Ahmed
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Master of Engineering
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Auckland University of Technology

This research studies the dynamics of bicycles, in particular how they corner, balance upright and maintain directional control. It examines the design and performance of single front wheel steering, the geometry of which has up till now, been based on established practice rather than scientific investigation.

A computer simulation model for bicycle dynamics was developed using Simulink™. The model combines all the key elements of a moving bicycle, the steering torque, the physical parameters that define the design and is based on Euler’s Equations of Motion. It can simulate a wide range of bicycle manoeuvres, particularly counter-steered cornering. The model can be changed to simulate different bicycles and riders so that comparisons can be made between different bicycle designs and different conditions of cornering.

After running the computer model it is found that, the most important torque terms for yawing are; the castor torque, the Jones’ torque and the steering torque input by the rider. The most important torque terms for rolling are; the gravitational and centrifugal torques. The next most important terms are the various new torques added in this study due to the steering geometry. The negligible terms are the Coriolis torque and the gyroscopic torques (again the gyroscopic torques are shown to be unimportant).

To validate the computer model it was compared firstly to existing theory and then secondly to the results of an experimental investigation. The experimental investigation used a bicycle fitted with sensors to measure steering and roll angles. The steering angle was measured with an electrical potentiometer mounted directly on the steering stem and the roll angle was measured using an infra-red (IR) distance measuring sensor mounted at the rear of the bicycle. A data logger recorded the steering and roll responses to a series of cornering manoeuvres.

A main research objective was to improve steering performance in terms of the response, system stability and frequency response. It was found that small changes in system inputs and bicycle geometry can have a large effect on dynamic behaviour. Head tube angle, rake, trail, steering torque and damping are all important factors and to some extent interrelated. The computer model allows combinations of these factors to be trialed so that their effect can be quantified.

Procedures for the design of bicycles have been prepared so that unstable designs can be avoided and steering problems with existing bicycles can be examined. A graph of rake against trail allows unstable combinations to be shown in an easily interpreted form. This graph allows bicycle designers and cycling enthusiasts to quickly grasp the importance of selecting appropriate geometry.

The research has successfully achieved its objectives and identified areas for future developement. The computer model could be improved by adding rider steering feedback and by plotting the bicycle’s course. The experimental investigation could be improved by making the equipment easier to calibrate and use.

Bicycles -- Performance , Bicycles -- Design and construction
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