Rowing and the samesum problem have their moments
Abstract
We consider the optimal positioning of an even number of identical crew members in a coxless racing boat so as to avoid the presence of a sideways wiggle as the boat is propelled forward through the water. We show that the traditional (alternate port and starboard) positioning always possesses an oscillating nonzero transverse moment and associated wiggling motion and that the problem of finding the zeromoment positions is related to a special case of the subset sum problem. We find the one (known) zeromoment rig for a racing Four and show that there are four possible such rigs for a racing Eight, of which only two are known. We show that only balanced boats with crew numbers that are divisible by four can have the zeromoment property and give the 29 zeromoment solutions for racing Twelves, which have zero transverse moments. Some aspects of unbalanced boats in which the numbers of port and starboard oars are unequal are also discussed.
 Publication:

American Journal of Physics
 Pub Date:
 July 2010
 DOI:
 10.1119/1.3318808
 arXiv:
 arXiv:0911.3551
 Bibcode:
 2010AmJPh..78..728B
 Keywords:

 boats;
 force;
 mechanical stability;
 method of moments;
 optimisation;
 sport;
 teaching;
 01.80.+b;
 45.00.00;
 Physics of games and sports;
 Classical mechanics of discrete systems;
 Physics  Popular Physics;
 General Relativity and Quantum Cosmology;
 Physics  Classical Physics
 EPrint:
 11 pages, 7 figures, additional notes and refs