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Dec142011

Mathematician Solves Rowing Boat "Wiggle" Problem

By: John D. Barrow 

(Submitted on 18 Nov 2009 (v1), last revised 16 Aug 2010 (this version, v3))

Website: Technology Review


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. 

A mathematician has discovered two entirely new arrangements of rowers in a racing eight in which the rowing forces cancel to make the boat wiggle-free.

kfc 11/20/2009

They take their rowing seriously at the University of Cambridge. So seriously, in fact, that the university has press-ganged John Barrow at the Center for Mathematical Sciences to study the serious problem of oscillating non-zero transverse moment in racing boats, otherwise known as wiggle.
 
The placement of the rowers, the "rig" of the boat, obviously has consequences for the motion of the boat. The question is how best to arrange an even number of crew members in a coxless racing boat in a way that minimizes or eliminates wiggle.
 
The traditional way of rigging a boat places rowers alternately pulling oars on each side of the boat. "The traditional rig appears symmetrical and simple in ways that might tempt you into thinking it is in every sense optimal. However, this is not the case," says Barrow who goes on to show that the balance of forces in this rig as the oars are pulled through the water always produces a wiggle.
 
But there is an arrangement in which the transverse forces cancel. This rig consists of one rower pulling on the port side of the boat followed by two on the starboard with a final rower on port. In the rowing world, this arrangement is known as the Italian rig because it was discovered by the Moto Guzzi Club team on Lake Como in 1956. The Moto Guzzi crew went on to win gold representing Italy at the Melbourne Olympic Games later that year.
 
Barrow next considers a crew of eight and identifies four possible rigs that have a zero transverse moment. These are shown above. The interesting thing is that only two of these rigs are known to the racing world. Rig b is called the "bucket," or "Ratzeburg rig," first used by crews training at the famous German rowing club of the same name in the late 1950s.

Rig c is simply the Italian rig repeated twice. It was used by the Italian Eights in the 1950s after their success with the Fours. It's also known as the triple tandem rig.

The other two, rigs a and d, are brand spanking new and don't seem to have ever been discussed. However, Rig d is a combination of a zero-moment Italian Four with its mirror image.
 
Barrow goes on to generalize the idea for any number of crew, proving along the way that only crew numbers divisible by four can be wiggle-free. (Assuming that they are evenly spaced.)

He also goes on to show that unbalanced boats in which there are unequal numbers of oars on each side, can also be wiggle free if the spacing between the rowers can be altered. As an example, he shows how a Three could have a zero transverse moment.
 
Barrow ends by saying that his work is not intended to revolutionize rowing tactics. That seems overly modest. Clearly, Barrow's paper should be recognized as a master stroke.
 
Will we see at least one of the new rigs at the 2012 Olympics in London?

Ref: arxiv.org/abs/0911.3551: Rowing and the Same-Sum Problem Have Their Moments. 

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Reader Comments (2)

I've seen rig (d) plenty of times, and rowed with it myself. Rig (a) however is new to me. Is there an argument that (a) could be damaging to the boat or is that encompassed by the zero wiggle i.e. zero moment? Does this assume that a boat is 100% stiff? Just thinking off the hoof so haven't thought it through fully yet!

December 16, 2011 | Unregistered CommenterArnold

Interesting, but not exactly new. Brearley, M.N., Oar arrangements in rowing eights. in: Lanady, S.P., and R. E. Machol (eds.) Optimal Strategies in Sports (Studies in Management Science and Suystems; v. 5), Elsevier, North-Holland, inc. New York. pp 184-185, (1977)

March 8, 2012 | Registered CommenterWalter Martindale
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