The way a yacht performs and behaves at sea is often due to subtle details that are far from obvious. This article explains the basics.
For some reason, good performance — by which, for the moment, we mean speed — is considered indecent by many cruising sailors. This strikes me as very odd, for there seems to be considerable benefit in completing passages quickly. For example, the difference between averaging five and six knots could shave two hours off the 60 nautical mile trip from our home port of Poole (England) to Cherbourg (France) and four days off a tradewind trans-Atlantic passage. Expressed another way, you could sail twenty percent further in any given time — perhaps an extra 250 miles during the course of a three week cruise.
The practical significance of this sort of arithmetic arose for me and my wife, Chele, when recently we were returning from our annual cruise. The final stage was from Lannion, North Britanny, to Poole — about 140nm distant diagonally across the English Channel. We intended to do it in a single hop.
It was high summer and the days were long. The winds were fresh and favourable and we knew we were in for a fast run. But how fast? Differences in average speed would fundamentally inﬂuence the planning of our crossing, as can be seen below:
5 knots: A twenty-eight-hour trip, including one full night at sea. Leaving at 0400, to allow us to pick our way through the rocks in gaining light, we would cross the busy shipping lanes north of the Casquets in the dark. With only two people aboard, watches would be essential if we were to remain alert.
6 knots: A little over twenty-three hours. Again, a night at sea, but we would be just about through the traffic before darkness fell. Watches would still be advisable.
7 knots: Twenty hours. Our dawn departure would have us arriving about midnight. The traffic lanes would be crossed entirely in daylight. Full watches could be abandoned. An experienced crew in a well found boat can easily function efficiently over such a period, taking turns to rest on an unscheduled basis.
8 knots: Seventeen and a half hours. Stretching it in our then thirty-two foot [9.75m] sloop, but this sort of average could comfortably be achieved by a larger, swifter vessel. A busy day’s work for the crew, but hardly an ordeal. You would be alongside well before the pubs closed.
It can be seen that an increase in speed will completely transform the nature of this fairly typical passage. Accomplished at five knots, it would be quite demanding; at eight knots it would be barely more than an exhilarating jaunt. And speed may help you beat any bad weather home. Even in the foulest conditions there are lulls between the blasts, during which a fast boat might safely make a run for it.
If anything, good performance should be of more importance to the cruising sailor than it is to the racer. To be successful in handicap racing, boats have only to perform better than their rating prediction, Indeed, the last boat over the line can win on handicap. But cruisers live in ‘real time’, and the implications of their performance is absolute, good or bad. Within reason, speed is a thoroughly good thing. Boats dance to the rhythms of natural laws, trapped on the interface between two ﬂuids, air and water. There is no opting out from the rules which govern that ever-shifting world. All must comply. The trick is to comply well.
Expressed in the simplest terms, a sailing boat is a machine in which the forward propulsive drive generated by the sails must overcome the total resistance of the hull. The more the drive and the less the resistance, the better will be the performance — and, of course, vice-versa. To understand how and why, it is necessary to have some grasp of the limitations involved. It isn’t essential to plough through all of the sums (though, if you have the stomach for it, you would find it useful), but no one can have an informed opinion on sailboat design without taking aboard the basic principles.
We shall be looking at rigs elsewhere. For the moment let’s concentrate on hulls — or, more specifically, on monohulls. The merits of the better multihulls are indisputable but their design is more properly the subject of another article. Single-hulled vessels comprise the vast majority of cruising yachts and it is difficult to see when this would ever be otherwise.
Before we plunge into the technicalities of hull design, it is worth spending some time dwelling on the problems associated with comparing boats of different sizes.
To illustrate this, let’s assume that we have a twenty-five foot (7.62m) LWL yacht which we want to scale up to fifty feet (15.24m) LWL, with all other measurements being doubled up similarly. If we did this, would we then have a boat exactly twice the size of the original in every way. Well, in some respects, yes: Length, beam, and draught would certainly have doubled (times two); but sail area and wetted surface area would have increased by the square (times four), displacement by the cube (times eight], and the stability by the power of four (times sixteen). For we have strayed into that area embraced by the law of mechanical similitude, where not everything is as straightforward as it might seem. Follow the link for more on this subject.
Incidentally, it was this mathematical reality which helped kill off the commercial sailing ship. The economics of carrying freight made bigger and bigger ships desirable. It took almost the same number of men to crew a 500—tonner as one of 1,000 tons. Unfortunately, as displacement increased by the power of three (cubed), sail area was only increasing by the square. Before long, naval architects found that it was impossible to set enough sail to propel the ships they were building. The grotesque six and seven-masted schooners were their last desperate attempts to cheat the law of mechanical similitude.
When assessing performance, these matters again arise when we try to compare speeds for boats of different length. For example, six knots would be respectable for a twenty-five foot (7 .62m) LWL boat but paltry for one of fifty feet (15.24m) LWL. But a more meaningful comparison can be made by expressing the relative speed of a hull in terms of the Speed/Length Ratio (S/L Ratio). This is determined by dividing any given boat speed (in knots) by the square root of the waterline length (in feet).
Metrically, the same results can be obtained by multiplying the square root of the waterline length (this time in metres) by 1.8 before dividing it into the boat speed. Thus:
Now, for reasons which we will shortly discuss, the maximum practical speed for any displacement hull tops out at an S/L Ratio of about 1.4 (seven knots for a twenty-five footer and nearly ten knots for the fifty footer). So, if both boats were making only six knots then the smaller would be at eighty-six per cent stretch whilst the larger would be loping along at just over half its potential. But if the same two boats were sailing at different speeds but identical S/L Ratios, then they would be at the same point within their own speed ranges and would be experiencing much the same hydrodynamic conditions — at least in ﬂat water, ignoring wave size.
The value of the S/L Ratio is that we can now talk about boat speed in purely relative terms without the need to specify lengths. But, from here on, if you want to think in absolute speeds for a specific boat you have in mind, make a note of its LWL and simply multiply by the S/L Ratios as we go along.
The reluctance of a hull to move through the water is caused by the total resistance arising from three distinct sources. These are:
- Skin drag
- Wave-making resistance
For the purposes of this section, we can ignore the windage for now, but let’s look at the other two in some depth.
This is caused by the friction between the underwater surface of the hull (aptly known as its ‘wetted surface area’) and the water. Frictional resistance is the major drag component at low speeds — as much as sixty-five percent of the total at an S/L Ratio of 1.0, dropping to about ten per cent at an S/L Ratio of 1.5.
The drag penalty imposed by friction is greatly exacerbated by roughness to the underwater surfaces. It is not the major swoops and hollows that do the damage, but the little imperfections such as weed fouling, protruding skin-fittings, or pitted antifouling paint. The water directly in contact with the hull has some forward velocity imparted to it by friction. This effect is transferred outwards by the interlocking of the water molecules, diminishing to zero at some distance from the hull’s surface. This layer of water is carried along with the hull and is known as the boundary layer.
While the boundary layer remains attached and laminar — flowing parallel to the hull’s surface — frictional drag is minimised; but once it becomes turbulent, drag increases considerably. Laminar ﬂow is easily destroyed by roughness. Even a pimpling of infant barnacles will have a detrimental effect upon light weather performance.
Nothing is created without cost, and the generation of waves (including all the little eddies and vortices caused by the various appendages that dangle beneath a hull) costs energy. As speed rises, the hull’s efforts to shoulder aside the water results in a rapid increase in this form of resistance. Somewhere around S/ L Ratio 1.5 it will peak at about ninety per cent of the total. When a displacement type hull reaches this point, it will be sailing at what is known as its hull speed.
The best way to understand hull speed is to know something about the wave dynamics that cause it. The faster that waves travel across deep water, the greater will be the distance between crests. This relationship can be mathematically expressed as:
Imagine a boat accelerating from rest. As it starts to move forward, a bow wave is generated, with a shallow trough and secondary wave forming a little way behind it.
As speed increases, so does the wavelength in accordance with the above formula...
The secondary wave moves progressively towards the stern. By S/ L Ratio 1.34, the secondary wave will have moved right aft and, obviously, the wavelength and the waterline length will then be equal.
Now the hull is supported fore and aft by the crests of the two waves. The widest, most buoyant central part of the hull coincides with the trough, and the boat sinks lower. If speed then continues to build, the quarter wave will move clear astern, and the hull will squat still deeper into the trough. From here on it is literally uphill work. Increasingly, between S / L ratios 1.34 and 1.65, the boat will find itself faced ever more with the daunting task of having to sail over its own bow wave — something only the lightest, most powerfully rigged boats can achieve.
This is a compelling argument in favour of generous sail area and light displacement. Although all displacement hulls (when in that mode rather than if planing) will eventually be limited by their hull speed, the exact point where they ‘hit the wall’ will vary from boat to boat. And clearly there is benefit in delaying this limitation as long as possible. For a boat of twenty—five feet (7.62m) LWL, the difference between S/L Ratios 1.34 and 1.65 is over 1.5 knots — definitely worth having!
Once this was considered the exclusive territory of surfboards, dinghies, and the lighter multihulls. Monohulled yachts — especially cruisers — were expected to remain respectably embedded in the water, pinned back by the limitations of hull speed. But, it has been known for some time that larger yachts will plane handsomely if designed for the task and given the right conditions. Yet we have continued to discourage it.
Racing is the natural seedbed for the development of the fastest yachts but, unfortunately, it was in the odious grip of the International Offshore Rule (known as IOR) during much of the sixties, seventies, and eighties. This rule was a hybrid cobbled from the British RORC rule and the American CCA rule, and it exerted a stiﬂing inﬂuence on racing yacht design for far too many years. To be advantaged under IOR, it was necessary to design boats with grotesque sectional shapes, pinched sterns, and very little in the way of initial stability — none of which did much to promote genuinely good and sea-kindly performance. Happily, this is all now astern and the International Measurement System (IMS) and other more localised systems (CHS) have emerged from the wake to shine a much kindlier light on future development. Today’s racing yacht is a very fast beast indeed, and designers are naturally delighted that they can turn aside from the sea-lawyer’s fine print and can at last concentrate more on speed and efficiency.
Of course, the more extreme racing boats will never make acceptable cruising yachts, but it’s inevitable that their inﬂuence will slowly change our general perceptions of what is a ‘good’ sailboat. The modern racing yacht will plane like a dinghy and, as this deplorable behaviour becomes more acceptable, so soon will more cruising yachts. The critical consideration is weight, which takes us on to the next topic.
To determine whether a boat is ‘light’ or ‘heavy’ for its length, another ratio is employed. This is the Displacement/Length Ratio (D/L Ratio) which is arrived at by the following calculation:
Where: D = Displacement in tons of 2240 lbs.
LWL = Waterline length in feet.
D/L Ratios of around 100 would be ultra—light; 200 would still be considered light; 300 would put us into the medium displacement range; and by the time we get to the 450 mark. things are getting seriously heavy. For those who become glassy eyed at the sight of formulae, I have calculated the various D/L Ratios for yachts of various waterline lengths.
But, however you do the sums, I commend you to heed the D/L Ratio when choosing a boat. The role of weight as a performance killer is readily understood when talking of, say, automobile design or jogging. But among sailors there remains an ingrained, almost perverse resistance to accepting what is, after all, an obvious and demonstrable truth. Admittedly, displacement can affect the characteristic way in which each boat rolls and pitches its way through the water, but an excess of it never made a yacht sail fast. The propulsion of mass requires energy — the more mass you have, the more energy you need.
To state the obvious, when not under auxiliary power the motive force which propels any yacht is derived solely from its sails. The larger the sail area, the more power you have at hand. And yet another calculation relates sail area to displacement and gives an indication of how powerfully rigged a yacht might be. In any other field this could be thought of simply as a power/weight ratio, but specific to yachting it is called, as one might guess, the Sail Area/ Displacement Ratio. This is derived thus:
Where: SA = Sail area in feet.
D = Displacement in pounds.
Most boats will be found to have an SA/D Ratio of between 14 and 20, with the higher figure at the more powerfully canvassed end of this range. Again, for those not blessed with a slide-rule mentality, there's a graph below which allows approximation for boats of varying sizes.
I would ask you to believe that all of the foregoing is not an attempt to ‘blind with science’. If our boat is to perform creditably in the circumstances for which it’s intended, then these and other matters must be optimised by the designer, and should be weighed up carefully by any prospective purchaser. No one would buy a car without carefully assessing such considerations as performance and fuel consumption, but it is astonishing how some folk blunder into boat ownership with hardly a notion of what they’re getting.
Before we close the chapter on performance related design considerations, let’s take a look at this vital but obscure little number, the meaning and significance of which isn’t always understood.
The word ‘prismatic’ is confusing. The prism in question is actually the maximum underwater section extended longitudinally to equal LWL. The volume of the prism so produced is said to have a value of one (1) and the actual volume of the tapered hull is then expressed as a proportion of it. For instance, a hull whose prismatic coefficient is .50 has fifty percent of the volume of the prism, a prismatic coefficient of .55 would represent fifty-five percent of the prism volume, and so on. In practical terms, the prismatic coefficient is a measure of how fine or full are the ends of a hull.
Much of the credit for recognising the importance of prismatic coefficients is due to an American, Admiral David W. Taylor, who was working on the design of warships at the time. He found that for every S/ L Ratio there was an optimum prismatic coefficient. For example, a hull travelling through the water at an S/ L Ratio of 1.0 would have the least wave making resistance if it had a coefficient of .52. If the S/L Ratio was around 1.4 [hull speed) the ideal coefficient would then be .64.
And to further illustrate the importance of the coefficient, consider this: If that last boat with its tubby coefficient of .64 was slopping along at the lesser S/L Ratio of 1.0, its resistance would be approximately double that of the finer hull.
The problem for the yacht designer is that his creation will eventually be sailing at S/L Ratios of anywhere between barely moving and ﬂat out. Somehow he has to decide which speed range his boat will most often be performing in and choose the prismatic coefficient accordingly. If he knows the boat will sail in an area where light airs predominate and speeds will generally be low (say the Mediterranean or the Gulf of Mexico) he may choose a lower than average coefficient — and, of course, vice-versa. To some extent this accounts for why yachts can gain reputations for being ‘dogs in light airs’ or ‘demons when it blows’, and also why a yacht can be startlingly successful in one area and a disappointment in another. The inescapable compromise a yacht designer makes when he selects the prismatic coefficient is part of his ‘black art’ — the combination of technical knowledge and empirical guesswork. And of all the design details he is likely to release, this is amongst the last he will want published.
Therefore, to summarise: the factors that most profoundly inﬂuence performance are:
The longer the better, though this could incur greater wetted surface area which
can be deleterious in light conditions.
The less the better, particularly in regions where light conditions predominate.
Within reason, also the less the better, though load carrying and structural requirements must obviously prevail.
Optimised for conditions and usage. Most cruising designs will have coefficients compromised to provide the broadest possible range of operational efficiency.
The more the better, again within reason. Remember, you can always reduce sail as the wind rises. To have to reef early is nothing like as exasperating as wishing you had an extra metre on the mast in light airs.