# Rocking the boat: The physics of kayaks, canoes and rowing

In this talk I will present two topics related to the physics of boat sports: The first explains the shape of a kayak – and why it’s different to a dolphin. The second explains how to beat Olympic records by choosing the correct water depth!

More than a century ago, J.H. Michell derived an integral formula for the wave drag on a moving body, using the approximation of a slender body in an irrotational, inviscid fluid (Michell 1898). The major shortcoming of this formula is that, due to the reversibility of the steady potential flow formulation, it predicts no difference in the wave drag when an object with front-back asymmetry moves forwards or backwards. However, anyone who has tried to row a dinghy in the wrong direction would argue differently! In the first part of my talk, I will discuss recent experimental observations investigating the effects of body asymmetry on wave drag, and show that these effects can be replicated by modifying Michell’s theory to include the growth of a symmetry-breaking boundary layer. I will demonstrate that asymmetry can have either a positive or a negative effect on drag, depending on the depth of motion and the Froude number, explaining the difference in shape between a kayak and a dolphin.

Another factor which strongly affects the wave drag is the water depth. Olympic race courses have a minimum depth requirement of 3m, but with boats as long as 18m, rowers are likely to generate waves in both the deep (dispersive) and shallow (non-dispersive) regimes at various moments during a race. Entering from deep to shallow water is accompanied by a focusing of the wave drag near the shallow wave speed – and hence the emergence of co-existing fast and slow solution branches. In the second half of my talk, I will describe the non-linear dynamics of such motion, including sketches of possible bifurcation patterns and hysteresis routes during a race. I will demonstrate the existence of both dead and anti-dead regions of shallow water – and how they may be responsible for recent Olympic records.

This talk is part of the Institute for Energy and Environmental Flows (IEEF) series.