Professor Snake does his calculus

Vital formulae for the aspirant yachtie

As a child, The Snake was forced to comply with a number of sensible, advisory guidelines: 1) Don’t talk to strangers (“My Mother said, I never should / Play with the gypsies in the wood”). 2) The non-consumption of vegetables severely reduces the prospect of pudding. 3) Pulling ugly facial expressions can cause permanent disfiguration should the wind change mid-gurn. 4) An anchor chain must be seven times the depth below the boat….and so on. Much to the disgust of The Snake’s grey whiskered old nanny, speaking to forest dwelling travelling folk is no longer taboo and chocolate is now more readily available than broccoli. While facial contortion is a vital element of sailing - especially in fluctuating wind strengths and direction - the anchoring mantra has survived the ravages of time unaltered and is easily expressed as an equation: ac = d X 7

This early familiarity with yachting formula has provoked a lasting, personal interest in all technically sensitive components of the sport; a curiosity that has been taxed by the increasingly complex advances in many areas of sailing. However, seeking enlightenment from within the covers of yachting magazines is often counterproductive. For although multicoloured and visually appealing bar graphs and flow charts illustrating sailing yacht dynamics, velocity predictions and hydrodynamic forces are the staple diet of naval architects, they can often result in internal bleeding for 99% of the readership. Furthermore, computer generated images of transom vortex separation and pressure distribution on hulls and appendages may send an erotic ripple of stimulation through a posse of America's Cup design technicians, but can produce brain trauma in the lay-sailor, leaving him slumped over the article with cerebrospinal fluid trickling from his ears onto the glossy, colourful graphics. Obviously, browsing these articles is a matter of choice and personal censorship, but (as is the case with pornography) many people find themselves helplessly drawn to these intriguing pictures.



Intricate principles are not confined to yacht design and are employed throughout the sport at every level; particularly in handicap rating where countless man hours are spent refining, debating and squabbling over IMS, IRC, PHRF, Americap, IRM etc. In an attempt to clarify the current state of yachting formulae there follows a brief gallop through the history of this science and also incorporates many new and essential equations for the modern yachtsman, including, for example, the definitive calculation for precisely how many post-race drinks a crewmember is expected to buy the bellowing egomaniac who verbally abused him on every upwind leg, transforming an entire regatta into a whole new world of pain…

It is evident from Man’s earliest attempts at marine construction that yacht design required some form of regulation and control. This said, Noah confronted unique problems when building the Ark and was faced with a novice naval architect (creating the universe in six days is slick, but…) demanding an extraordinary build programme with a vengeful penalty clause should the project overrun. Many lessons were learnt from the original Ark blueprint handed to Noah: With a design specification of 300 cubits length X 50 cubits beam X 30 cubits height, the length overall (LOA) could vary between 129 m or 155.2 m dependant upon the choice of Egyptian or Sumerian calculations of a cubit.

Unwilling to question the wisdom of such a broad and vague plan for fear of a righteous smiting, Noah had to stumble nervously through the vessel’s fabrication with minimal divine guidance. However, he wisely complied with the desired 'tebah' (box) hull shape to maximise both stability and internal volume and fitted a door capable of admitting a pachyderm. With astonishing imprecision a “tsohar” (light aperture) was requested with directions to “complete it to the extent of a cubit upwards” suggesting only a basic understanding of ventilation required on a commercial vessel shipping large numbers of paired livestock.

For centuries, yacht and ship building continued in a haphazard chaos with differing designs developing in cultural isolation: Egyptian barges, Pacific rafts, Phoenician galleys, Roman and Greek biremes, triremes, quadreremes, even the Qiunquereme of Ninevah from distant Ophir and lateen rigged Arab trading craft proliferated unchecked and unregulated. In the 16th century, naval architecture was a secretive, unpublished profession and a century later the collective maritime brains trust was distracted and totally absorbed with the problems of accurate navigation and the design of reliable, seaworthy time keeping instruments. These quests allowed regulators to concentrate their statutory skills on shipboard conduct.

A quotation attributed to Winston Churchill, First Lord of The Admiralty in 1911, is unlikely to be aired during the UK’s forthcoming Festival of The Sea and Trafalgar Day celebrations. The great man observed that naval tradition consists of little more than “rum, sodomy and the lash” and much highly detailed literature suggesting how much of the first should be dispensed and when, and to what extent the third should be applied if the first caused the second, supports this claim.

To extend this practice to a formula: In 1740 Admiral Edward “Old Grog” Vernon decreed that the regulation “tot” on fighting ships of 1 pint of neat rum per man per day (half a pint for boys) be diluted with a quart (2 pints) of water and issued in two halves, twice a day. When the maximum, legal number of lashes with a cat-o’-nine-tails was limited to twelve, a simple equation is produced;

R + S = 12L

However, seven years prior to Vernon’s attempt at maintaining onboard sobriety, a new method of calculating a vessel’s harbour and mooring dues was introduced; The Builders Old Measurement:

(L-3/5B) X B X 1/2B
94

Using beam ( B) and with a length ( L) measurement that included the keel’s profile, the system soon became outdated as sleeker craft swiftly evolved. The Builders Old Measurement was also the only available method of handicapping racing yachts leading, predictably, to designers producing radical, heavily canvassed boats with insufficient keels; potentially dangerous craft customised to gain a favourable rating and fill the trophy cabinet. In 1855, the Thames Measurement (TM) was established by the Royal Thames Yacht Club (RTYC) to quickly cap this trend by subtly altering the old equation in what is possibly the first instance of wisely adjusting yachting rules to keep pace with technology:

TM: (L-B) X B X 1/2B
94



Rating and general design rules display an historical pattern that meanders between the absurdly complicated and the refreshingly simple. With brevity reminiscent of Noah’s remit in The Book of Genesis, the American Universal Rule of 1930 was implemented solely to speed the J Class weapons build-up and produced a total of 10 extraordinary yachts. The rule (waterline length 79’-87’, LOA 120’+, displacement up to 160 tons) was perhaps partly driven by convoluted equations and mind-numbing figures holding scant appeal for yacht owners who spent much of their time studying share prices, property values, tea export figures and the latest developments in aircraft technology.



This purity of purpose disappeared entirely in the austere, post World War II period when the America’s Cup recommenced in 1958 after a 21 year suspension. J Class-sized budgets were unsustainable and the will to promote a 'one design' boat and foster close racing saw the advent of the 12 metre rule…..and things suddenly began to get really complicated (sensitive readers of thedailysail should ensure that a paramedic is on standby before continuing further with this article). The rule involves calculations of length ( L), sail area ( Sa), a girth measurement ( 2d), freeboard ( F) and can provoke tremors, clamminess, a blinding pain behind the eyes and a shortness of breath:

L + ?(Sa) + 2d – F
2.37

The equation above does not include additional 12 metre parameters involving mast height, headsail height, etc.

This, though, appears as little more than harmless, 1950’s flirting with formulae when we encounter the brazen boffinry of the International America’s Cup Class
(IACC) Version 4, introduced in 2000. As an exercise in comparison, one of the equations below is IACC and one is Euclidean Geometry, a system used to find a co-ordinate in space. Which equation involves yachts? A or B….answers on a post card, please:

A) L + 1.25 X ? S – 9.8 X ³?DSP <= 24.000 metres
0.679


B) ? X ? = ? x.x = ? n
? (xi – xi)² .
i = 1

That Version 4 covers 51 pages becomes understandable when each element of the equation above is subject to an individual definition. For example, length is interpreted as:

8
L = LM X (1 + 0.01 X (LM – 21.2) ) + FP + DP + WP +BP

The updated rules in IACC Version 5 launched 2003, by contrast, are relatively straightforward and require only (sic) that all yachts fit a lighter bulb and longer keel fin to produce “…wholesome, fast and manoeuverable day sailing monohulls” (IACC Version 5 intro). Although technical ACC formulae have stabilised, mathematicians and physicists are currently working ceaselessly on an equation to explain the unparalleled legal twists and labyrinthine employment arrangements surrounding this event; fascinating characteristics that have provided endless material for commentators.

While all the rules and their associated formula in documents of this type are essential, many yachtsmen have more temporal concerns. Although it is absolutely clear that battens 'shall be approximately straight within a tolerance of 100 mm either side of a straight line' (Version 5, Rule 34.2(e)), such minutiae have little relevance to the lay-sailor.

At the beginning of this article, the dilemma of buying drinks for abusive crewmembers was raised. In reality, there is no appropriate formula for this scenario as drinks should never be stood for foul mouthed, bullying sociopaths. A caveat can be made, though, if the drink is spiked with a highly aggressive purgative that may render the recipient incapable of racing the following day.

Another useful regatta equation concerns rafting yachts in crowded marinas. The total number of yachts rafted in a line is counted and the yacht nearest the pontoon takes the highest value (i.e. If 6 yachts are rafted together, the pontoon yacht takes the value 6, while the yacht on the outside of the raft takes the value 1) expressed as ?. Variables include items found on the yacht’s foredeck or in the cockpit at dawn and the average sleep (expressed as S, measured in hours) of the yacht’s crew:



Variables:

C = contraceptives
V = vomit
U = articles of clothing belonging to persons other than the yacht’s crew
E = empty bottles/beer cans
Cu = Cohiba #5 butt ends

C + V + U + E + Cu X ?
S

Research shows that an average coefficient for an 'inside' boat during Cowes Week Regatta is 12:

0 + 2 + 1 + 1 + 0 X 6
2

This formula successfully illustrates that yachts rafted together exhibit a decreasing coefficient as distance from the pontoon increases; an anomaly caused by a reduction in garbage, garments, bodily fluids etc. being deposited on boats further from the pontoon coupled with higher sleep averages for those rafted 4, 5 or 6 boats deep, as their crews can slumber undisturbed by the nocturnal stumblings of transients.

Possibly the most revealing (and alarming) equation is the Time Afloat Continuum (TAC); an accurate formula that most yachtsmen choose to ignore. All variables are measured in hours and include:

Time spent…..

….in bars discussing yachting (pre-sailing) B
….in bars “Swinging the Lantern” (post-sailing) BS
….organising crew OC
….trying to book a restaurant table for 12 people R
….in a chandlery C
….waiting for the travel lift TL
….on the water W

Time Afloat Continuum:

BS X OC + R + C + TL
B W


An exhaustive study of European, American and Southern Hemisphere yachts shows that the average TAC coefficient for these countries is 5. Should this figure exceed 10, it is clearly an appropriate time to find another sport.

To study a scarily long but compelling article about how Noah's Ark was built 5,200 years ago by aliens using titanium (complete with much formulae by way of proof) - click here.