You are hereBlogs / pmallory's blog / Peter Mallory's Blog

Peter Mallory's Blog

By pmallory - Posted on 20 June 2012

16 March 2012

My good friend Evan Snyder of West End & St. Georges Rowing Club in Auckland, New Zealand recently wrote to me:

Dear Peter,

I want to tell you that I am thoroughly enjoying your four-volume compilation, The Sport of Rowing, which I had purchased and brought back to New Zealand with me just a few weeks ago. I am surprised they did not charge me for the extra weight!!

I am an avid single sculler, and there is so much information on sculling techniques and style and how both of these have evolved over time.

One thing that I discovered as the owner of a single, apart from the rowing itself, was a certain quirk about the dimensions of the average single shell. If you are familiar with the Fibonacci number sequence: 0 1 1 2 3 5 8 13 21 34 55 89 144 . . . , you will know that if you divide the last number by the one proceeding it, after 13 numbers in this sequence you will get a constant ratio (to 3 significant figures) of 1.618, known as the Golden Ratio.

Now if you take the length of an average single shell - I based this on measurements taken of over 30 different boats from around a dozen manufacturers - and divide that length by the distance from the bow ball to the toe of the foot stretcher, guess what? You get a ratio of nearly 1.618. The same happens if you divide the distance from the bow ball to the toe by the distance from the toe to the stern. Again, nearly the golden ratio. Isn’t mathematical symmetry wonderful????

It is my belief that if a sculler has the right size boat for their height (and weight), if they set the foot stretcher to where this ratio is achieved, then set the wing rigger and seat slide of the boat accordingly, they should maximize their performance. Not enough data yet to prove this, but it's a work in progress, and so far it is looking valid.



Wow! I had to look all this stuff up.

Leonardo of Pisa, aka Fibonacci, came up with the Fibonacci sequence in a book he wrote in AD 1202. If you define the first two numbers as 0 and 1, then each successive number is the sum of the previous two in the sequence. Fibonacci numbers rise in a spiral, and fibonacci spirals appear all over our natural world, like in a sunflower or a nautilus shell or a succulent . . . and in all sorts of unexpected places . . . all the way up to the structure of galaxies. Computer programmers use fibonacci numbers in ways you and I will probably never understand or even be aware of . . . but if it works for them and for plants and for hurricanes, well why not single shells as well?

Now I'm not particularly religious, but this is real Hand of God stuff. And I have to admit that this isn't the first time the hairs on the back of my neck have stood on end when contemplating the universe with a pair of sculls or a megaphone in my hands.

How about parabolas? You make a parabola by slicing a cone . . . or by graphing the formula x² = 4py . . . or by recording Kris Korzeniowski's force curve while rowing!

Or the force curve of 1920 Olympic Men’s Singles and Doubles Champion John B. Kelly, Sr. Or 1956, 1960 and 1964 Olympic Men’s Singles Champion Vyacheslav Ivanov. Or 1960 Olympic Men's Coxless-Fours Champion Ted Nash. Or 1967 and 1969 European Men’s Coxless-Pairs Champion Larry Hough and Tony Johnson. Or 1969 European Men’s Doubles Champion John Van Blom and Tom McKibbon. Or 1974 World Men’s Eights Champion Al Shealy. Or 1984 Olympic Men’s Doubles Champion Brad Alan Lewis and Paul Enquist. Or 1988 and 1992 Olympic Men’s Singles Champion Thomas Lange. Or 1996 Olympic Men’s Eights Champion Michiel Bartman. Or 2004 Olympic Men's Eights Champion Bryan Volpenhein. Or 2004 and 2008 Olympic Women's Doubles Champions Caroline and Georgina Evers-Swindell.

What's going on here? For Heaven's sake, it's a slice of a cone! What could that possibly have to do with rowing?

If you could ask legendary coach Steve Fairbairn what the ideal force profile would be for moving a rowing shell down the course, he would describe to you a parabola, my friends. As would Charles Courtney of Cornell. And Hiram Conibear of the University of Washington. And Jumbo Edwards of Great Britain. And Karl Adam of Ratzeburg. And Dr. Theo Körner of the German Democratic Republic. And Harry Mahon and Dick Tonks of New Zealand.

Seriously, what is going on here? Why a parabola of all curves?

Coaches have been trying to explain that for 200 years, and I have done my best to include their most eloquent efforts in The Sport of Rowing. My own tongue-in-cheek first effort was in my first book, An Out-of-Boat Experience, and it was this: "God is a rower, and He rows like me!" If I had chosen to be a bit less juvenile back then I might have said something about how when we hear the boat sing beneath us, we truly touch the Divine, that traveling over water relying on our own body power has truly cosmic implications, that only a perfect curve, only a parabola, is good enough for rowers like us.