Rowing and the Same-Sum Problem Have Their Moments

TL;DR

This paper investigates optimal crew positioning in racing boats to eliminate sideways wiggling, linking the problem to the Subset Sum problem and identifying specific zero-moment configurations for various crew sizes.

Contribution

It introduces a novel connection between boat rig configurations and the Subset Sum problem, providing explicit solutions for certain crew sizes and conditions for zero transverse moments.

Findings

Traditional rigs always produce oscillating moments.

Identified all zero-moment rigs for racing Four, Eight, and Twelve.

Only boats with crew numbers divisible by four can have zero transverse moments.

Abstract

We consider the optimal positioning of an even number of crew members in a coxless racing boat in order to avoid the presence of a sideways wiggle as the boat is propelled forwards through the water. We show that the traditional (alternate port and starboard) rig of racing boats always possesses an oscillating non-zero transverse moment and associated wiggling motion. We show that the problem of finding the zero-moment rigs is related to a special case of the Subset Sum problem. We find the one (known) zero-moment rig for a racing Four and show there are four possible such rigs for a racing Eight, of which only two (the so called 'Italian' and 'German' rigs) appear to be already known. We also give the 29 zero-moment solutions for racing Twelves but refrain from explicitly listing the 263 Sixteens and 2724 Twenties which have zero transverse moments. We show that only balanced boats with crew numbers that are divisible by four can have the zero-moment property. We also discuss some aspects of unbalanced boats, in which the number of port and starboard oars are unequal.