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Honking a bicycle as a non-holonomic Fermi-like acceleration (Advert Reference: SF19/EE/MPEE/KIRILLOV)

   Faculty of Engineering and Environment

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  Dr O Kirillov, Dr Stephane Régnier, Dr B Huard  Applications accepted all year round  Self-Funded PhD Students Only

About the Project

Honking means cycling out of the saddle. Cyclists use this way of riding to accelerate. In this process, the body of the cyclist moves rhythmically side to side with respect to the plane of the bicycle, while the frame of the bicycle rocks or sways with respect to the vertical position. It is known, however, that the commonly accepted modern bicycle models, stemming from the Whipple model of 1899, are non-holonomic and conservative. On one hand, this implies the conservation of energy, and on the other, non-conservation of the phase volume, which results in the possibility of the asymptotic stability of a straight vertical position of a bicycle that is riding along a straight path if the forward velocity is high enough, which is a well-known empirical fact. A natural question is: where the energy of dying leaning and steering motions flows? Actually, the energy in the lean and steer oscillations is transferred via a nonlinear coupling to the forward speed rather than being dissipated. It can therefore be conjectured that when cycling out of the saddle, the periodical movement of the cyclist’s mass pumps energy into the forward motion leading to the desired acceleration. Recently, acceleration due to a periodic motion of an internal mass has been theoretically discovered in a non-holonomic Chaplygin sleigh model and linked to the mechanism of acceleration of particles moving between periodically oscillating walls in a Fermi-Ulam model. The present project aims to verify the conjecture that acceleration due to honking is indeed a non-holonomic Fermi-like acceleration via a creation of a new nonlinear model of a bicycle with a periodically moving mass. The project will combine numerical, analytical and experimental approaches to engineer of a prototype demonstrating for the first time the non-holonomic Fermi-like acceleration in the laboratory.

This project is supervised by Dr. Oleg Kirillov.

Please note eligibility requirement:
• Academic excellence of the proposed student i.e. 2:1 (or equivalent GPA from non-UK universities [preference for 1st class honours]); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
• Appropriate IELTS score, if required.

For further details of how to apply, entry requirements and the application form, see

Please note: Applications that do not include a research proposal of approximately 1,000 words (not a copy of the advert), or that do not include the advert reference (e.g. SF19/EE/MPEE/KIRILLOV) will not be considered.

Start Date: 1 March 2020 or 1 October 2020

Northumbria University takes pride in, and values, the quality and diversity of our staff. We welcome applications from all members of the community. The University holds an Athena SWAN Bronze award in recognition of our commitment to improving employment practices for the advancement of gender equality and is a member of the Euraxess network, which delivers information and support to professional researchers.

Funding Notes

This is an unfunded research project.


O.N. Kirillov (2018) Locating the sets of exceptional points in dissipative systems and the self-stability of bicycles. Entropy, 20(7): 502.
D. Bigoni, O.N. Kirillov (2018) Dynamic Stability and Bifurcation in Nonconservative Mechanics, CISM International Centre for Mechanical Sciences 586, Springer, Berlin
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