Next time you lose your paddle whilst canoeing - don't despair. There is another way to push your canoe forwards: by jumping on it! Gunwale bobbing refers to the act of standing on the gunwales (side walls) of a canoe and forcing it into oscillations with one's legs. When forced at the right frequency, the canoe can surf from crest to crest of the generated wave field by pushing into positive surface gradients.
Recently myself, Oxford Mathematician Graham Benham, and co-authors, Jerome Neufeld (Cambridge), Olivier Devauchelle (Paris) and Stephen Morris (Toronto), have created the first hydrodynamical explanation for gunwale bobbing. The theory, which is partly inspired by studies on bouncing droplets, uses linear wave theory with a forcing term that is a combination of heaving and out-of-phase pitching. With this forcing term, a horizontal thrust force can be generated that balances the drag on the canoe, such that cruising speeds of $\sim$ 1-1.5 m/s can be achieved. The theoretical prediction for the wave field is shown below next to a photograph. The angle of the waves is given by $\tan^{-1} (g/U\omega)\approx 51^\circ$, where $g$ is gravity, $U$ is the boat speed and $\omega$ is the bobbing frequency.
This study not only links together canoeing and the nonlinear dynamics of wave-driven particles, but it also has interesting implications for competitive sports. In rowing and canoe races the boat undergoes a significant vertical force each time the athlete heaves their body during a stroke. However, it is unknown how this vertical force interacts with the surrounding wave field, nor whether this helps or hinders performance. Hence, this study is a first step towards optimising boat-wave interactions during a rowing race.
You can find more details in this recently published article in Physical Review Fluids (Editors' suggestion).
Further videos can be found below:
Video 1 - Short video explanation (Oxford version)
Video 2 - Longer video explanation by Jerome Neufeld (Trinity College Cambridge)
Video 3 - Jerome Neufeld gunwale bobbing with a passenger
Video 4 - Miles Neufeld (Jerome's son) gunwale bobbing on a paddle board
Video 5 - Jerome Neufeld gunwale bobbing from a long shot perspective (showing waves)
Video 6 - Graham Benham gunwale bobbing on an Oxford punt in formal attire. It should be noted that the forward speed is very slow due to the length and flatness of the punt, making it difficult to bob on. Canoes are much more effective.
Graham Benham is a Departmental Lecturer in Applied Mathematics in the Mathematical Institute in Oxford.