Waterline length is not the defining factor in maximum boat speed that we all think it is. Julian Wolfram busts the hull speed myth
Waterline length is not the defining factor in maximum boat speed that we all think it is. Julian Wolfram busts the hull speed myth
Every sailor is delighted when the breeze picks up and the boat really starts to get going with a bone in her teeth.
The crew will want to know how fast she will go and perhaps surreptitiously race her against any similar sized boat in the vicinity.
Speculation may start about what allows one boat to go faster than another – is it the hull shape or the sails?
It is easy to spot good, well-trimmed sails but what about the hull?
The important part is not visible below the water surface. However there is one key indicator that is often very apparent – the waves generated by the sailing yacht.
When a yacht picks up speed the wave pattern around it grows and the greater the speed the bigger the waves.
The energy in these waves is proportional to the square of their height – double the height and the energy goes up by a factor of four.
This energy comes from the wind, via the sails and rig, making the hull push water out of the way.
If less of this wind energy was wasted in producing waves the yacht would go faster.
When a typical displacement monohull reaches a speed-to-length ratio of around 1.1 to 1.2 (speed in knots divided by the square root of the waterline in feet) up to half the wind energy driving it is usually wasted in generating waves.
The hull speed myth: Half angle of entrance
So how can we tell if a yacht will sail efficiently, or have high wave resistance and waste a lot of energy generating waves?
The answer starts back in the 19th century with the Australian J H Michell.
In 1898 he wrote one of the most important papers in the history of naval architecture in which he developed a formula for calculating wave resistance of ships.
This showed that wave resistance depended critically on the angle of the waterlines to the centreline of the ship – the half angle of entrance.
The smaller the angle the smaller the height of the waves generated and the lower the wave-making drag.
A knife blade can slice through water with minimal disturbance – drag the knife’s handle through and you generate waves.
The big hull speed myth
For a displacement hull the so-called ‘hull speed’ occurs when the waves it generates are the same length as the hull.
This occurs when the speed-length ratio is 1.34.
It is claimed that hulls cannot go significantly faster than this without planing. It is called ‘the displacement trap’ but is a myth.
As an example, consider a 25ft (7.6m) boat that goes at 10 knots in flat water.
This is a speed-length ratio of two. That is the average speed over 2,000m for a single sculls rower in a world record time.
The reason for this high speed is a half angle of entrance of less than 5º. Hobie Cats, Darts and many other catamarans have similarly low angles of entrance and reach even higher speed-length ratios with their V-shaped displacement hulls.
These hulls also have almost equally fine sterns, which is also critically important to their low wave resistance.
The monohull problem
Now a monohull sailing yacht needs reasonable beam to achieve stability and, unless waterline length is particularly long, the half angle of entrance will inevitably be much larger than those on rowing skulls and multihulls.
In his 1966 Sailing Yacht Design Douglas Phillips-Birt suggests values of 15º to 30º for cruising yachts.
Many older cruising yachts with long overhangs and short waterline lengths, for their overall length, have values around the top of this range.
Newer sailing yachts, with plumb bows, have somewhat smaller half angles and a modern 12m-long fast cruiser may have a value around 20º and a racing yacht 17º or 18º.
Size matters here as, to achieve stability, a little yacht is likely to have a bigger half angle than a large one, such as the German Frers-designed 42m (138ft), Rebecca which has a half angle of entrance of under 13º.
Rebecca also has a fine, elegant stern which helps minimise the stern wave – I’ll come back to sterns and stern waves.
Interestingly the half angle of entrance is not mentioned in the otherwise excellent 2014 Principles of Yacht Design by Larsson et al, although it is currently used as one of the parameters in the preliminary estimation of wave resistance for ships.
While it is still particularly applicable to very slender hulls, naval architects are not generally familiar with Michell’s work.
His formula for wave resistance involves quadruple integrals of complex functions.
These are not ‘meat and drink’ for your average naval architect, and only a few mathematically inclined academics have much interest in theoretical wave resistance.
Michell’s work is rarely, if ever, covered in naval architecture courses now.
Nowadays the emphasis is much more on numerical methods, high-speed computers and computational fluid mechanics (CFD) using the so called Navier-Stokes equations.
Examining these equations, which apply to any fluid situation, does not give any insights into wave resistance, albeit they can model wave resistance very well when used in the piecewise manner of CFD.
It is very easy to measure the half angle of entrance at the design waterline when a yacht is out of the water.
Take a photograph directly upwards from the ground under the centreline at the bow.
Now blow this up on a computer screen, or print it off at a large scale, and measure the angle with a protractor.
Alternatively, if you have a properly scaled accommodation plan drawn for a level close to the design waterline this will yield a reasonable approximation of the half angle of entrance.
Unfortunately there is not a simple relationship between the fineness of the bow and the wave drag.
But, all other things being equal, the smaller the half angle the better.
It is easy to measure and is a useful parameter to know when comparing yachts.
Stern shape and hull speed
The half angle of entrance cannot be taken alone as a measure of wave drag, and the fairness of the hull and in particular the run aft is also critical.
Just as the half angle of entrance dictates the height of the bow wave, so the fineness of the stern is a key influence on the height of the stern wave.
Consider the water flowing around both sides of the hull and meeting at the stern.
If these streams meet at a large angle the water will pile up into a high stern wave.
On the other hand if they meet at a shallow angle there will be less piling up. A fine stern can maintain a streamline flow of water.
However if the sides of the hull meet at the stern at a large angle then the streamline flow will tend to separate from the hull, leaving a wide wake full of drag-inducing eddies.
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In many modern designs the hull sides are not far off parallel at the stern and it is then the upward slope of the buttock lines that are critical and, again, the shallower the slope the better from a hull drag perspective.
The slope of the buttocks can easily be measured if the lines plan is available and a good indication can be obtained from a profile drawing or a photo taken beam on with the boat out of the water.
Drawing a chalk line parallel to the centreline and half a metre out from it will provide a buttock line that can be checked visually for fairness when the boat is viewed from abeam.
Again, the smaller the angle the better – provided the transom is clear of the water.
An angle of more than 17º will lead to separated flow and eddy making. This also happens if the transom is immersed.
The greater the immersion the greater the drag, so weight in stern lockers on modern boats can be critical.
Modern hull design
The modern wedge shape attempts to resolve the conflicting demands of a small angle of entrance, good stability and a fine stern.
The plumb bow extends the waterline forward and, with the maximum beam taken well aft, the hull forward can be relatively narrow, providing a low half angle of entrance.
The stern is wide, which helps achieve good stability, but at the same time the buttocks rise slowly at a shallow angle to the water surface.
This gives a smooth and gradual change in the hull’s cross section area ensuring the water flow remains attached to the hull and that the stern wave is kept low.
This wide, flat stern also helps surfing down waves and possibly planing.
Some designs have chines just above the design waterline which increases usable internal volume and gives a little more form stability when heeled.
However, as soon as the chine is immersed there will be separation along the chine edge as water will not flow smoothly around a sharp edge.
It is just not possible to get the chine perfectly aligned with the streamlines of the water flow in all sailing conditions and there will be some extra drag at times.
There are two downsides to the wedge- shaped hull.
First the boat has to be sailed at a small angle of heel to keep the rudder properly immersed and to avoid broaching. This can be offset to some extent by using twin rudders.
The second is that the weight must be kept relatively low.
This is because a relatively small increase in weight causes a big increase in wetted surface area at the stern and hence in the frictional drag which makes the boat slower, particularly in light airs.
This is the downside of slowing rising buttocks and the reason why dinghy sailors get their weight forward in a light breeze.
Displacement Length Ratios
Traditionally for sailing yachts the displacement-length ratio has been used as a measure of speed potential, partly because it is easy to calculate from the yacht particulars.
It is waterline length (in metres) divided by the cube root of displacement (in cubic metres or tonnes).
A heavy boat, such as the Heard 35, will have a value of about 4 to 4.8.
A more moderate displacement boat, such as the Hallberg Rassy 342 or Dufour 32 Classic, will have a value in the range 5 to about 5.5; whilst a racing boat may a value of up to, and even over, 7.
However the displacement length ratio can be misleading as making a hull 20% deeper and 20% narrower will keep the displacement the same but will significantly reduce the half angle of entrance and the wave drag.
It is interesting to note a Thames barge in racing trim has the same length-displacement ratio as a J class yacht, but their speed potential is vastly different.
Finally I should mention the older ‘length-displacement’ ratio, which is quoted in imperial units.
This is calculated by dividing a boat’s displacement in tons (2,240 pounds) by one one-hundredth of the waterline length (in feet) cubed.
It is still used in the USA and should be treated with caution.
The myth that your boat’s speed is only restricted by it waterline length does a disservice to its designers, and does little to help you understand how to get the best from her when the wind picks up.
Have a look at how the boat is loaded, how you sail on the wind, your boat handling and how much canvas you ask her to carry and you may discover more speed than you expect.
The remarkable John Henry Mitchell
Pioneer of wave theory
It’s worth saying a little more about the remarkable John Henry Michell.
He produced a series of ground-breaking papers including one that proved a wave would break when its height reached a seventh of its length.
He was the son of Devon miner who had emigrated to the gold mining area near Melbourne.
He showed such promise that he got a scholarship to Cambridge.
He was later elected a fellow of the Royal Society at the age of 35 – not bad for the son of a Devonshire miner.
His brother George was no slouch either – he invented and patented the thrust bearing that is named after him.
The half angle of entrance became the traditional factor for assessing the fineness of hulls.
It is defined as the angle the designed waterline makes with the centreline at the bow.It varies from less than 5º for very fine hull forms up to 60º or more for a full-form barge.
At higher speeds, modest increases in the half angle can give rise to substantial increases in wave resistance.
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