Some technical insight...
Take a spoon, any spoon, and hold it so that it is suspended in the water flowing from a running tap - the rounded side into the flow. You’ll notice that the spoon is ‘sucked’ into the flow of the water. If the spoon represents the bottom of a short, fat ‘displacement’ hull running through water it is not hard to imagine that that same ‘suction’ effect draws the boat downwards into the water.
This silly-simple exercise demonstrates one small component of the very complex catalogue of the drag forces that combine to resist the forward motion of a hull passing through the water.
Resistance…
The resistance of a boat can be split into three main components - frictional, residuary and air resistance. The relative importance of these components changes as the boat length, displacement and speed increase. For now we can ignore air resistance as it is relatively small.
Frictional resistance is associated with the viscous drag of the underwater surface of the boat and therefore the size of that wetted surface is important, along with its roughness
Residuary resistance is mostly associated with the energy lost by the boat in the generation of waves – the wave-making drag. The waves generated by the boat will have a speed equal to the boat speed.
A full displacement hull is restrained by wave-making drag so that its speed is absolutely limited to a speed which is function of its waterline length. This function is called Speed/Length ratio and turns out to be about 1.3 x the sq. root of the waterline length in ft.
The most common way to escape this natural speed limit is to design the hull so that it is flat enough underneath to cause it to ‘plane’ on the surface of the water. By ‘planing’ (‘skimming would be another word) it is no longer floating and therefore no longer held captive by wave-making drag.
For reasons explained in the BOAT INTERNATIONAL article, in embracing LDL technology we have chosen to explore and further develop a different way to reduce wave-making drag – a way that intentionally uses very little of the ‘dynamic’ lift available through planing.
Instead it involves ‘drawing out’ the hull lines of that short, fat displacement hull so that the length-wise curvature of the hull is much less pronounced, and therefore much less inclined to attract wave-making drag.
Apart from getting rid of some of the curvature, extending the hull offers other drag-reducing benefits:
• As the drag of non-planing hulls is governed by a formula in which the expression ‘sq. root of the waterline length’ is dominant, so that simply increasing that length also increases speed
• For a similar displacement (or weight) the maximum cross-section of the hull reduces as the length over which it is spread increases. It comes as no surprise that pushing a smaller cross-section through the water uses less energy than pushing a bigger one.
Waves and Speed…
There is a fundamental law governing waves in deep water - the speed of a wave is proportional to the square root of its wavelength. In other words the faster a boat moves the further apart are the waves generated.
Consider a boat moving at a speed such that it has wave crests at the bow and the stern then the wavelength is about equal to the waterline length of the boat. This speed is known as the displacement speed and is the maximum speed at which a boat can travel whilst not climbing out of its own wave system. Therefore there is a fixed relationship between the displacement speed and the waterline length of a boat. A boat will have a higher displacement speed simply by being longer.
When discussing different hydrodynamic phenomena it is worth emphasizing that the boundaries between design characteristics are not demarked by any sudden changes. As a hull is ‘drawn out’, for example, the drag we are trying to reduce (wave-making drag) is reduced progressively as the Displacement/Length ratio is reduced.
A vessel whose DL ratio is below 100 is likely to benefit from some significant decline in wave-making drag. Below that the results just get progressively better.
The Displacement/Length ratio is determined by the following formula:
DL ratio = Displ. / (0.01 x WL)3
Where:
Displ. is the displacement in long tons
(2240 lbs)
WL is the waterline length in feet.
With a DL ratio of only 25 the trimaran ‘iLANVOYAGER‘ is an extreme expression of this approach to hull design. The vessel has a working displacement of some 6 tonnes and yet is capable of 28 knots on 235 hp. (more data in ‘Yachts’).
As an example of a more moderate LDL vessel the ‘RANGEBOAT’ has a DL of about 98 and is best suited to a cruise speed of between 13 and 16 knots (SL ratio 2.2 to 2.7). As the specification shows the extra power needed to get to from 13 knots to 16 is considerable and will have a significant effect on both fuel burn - and therefore range. (more data in ‘Yachts’).
Speed and Length…
It is important to note that boat speeds can only properly be compared in terms of speed/length ratio (see box) or more formally Froude number. If this quantity is the same for boats of different sizes then they are operating in the same kind of wave system and can be compared. For example a 40ft boat moving at 9 knots will be operating in the same wave system as an 80ft boat moving at about 13 knots.
In order to break out of its wave system and exceed its displacement speed a boat will need a suitable hull shape and sufficient propulsive power. The hull will need to be light and designed to generate lift as speed increases. This dynamic lift progressively supports more of the weight of the hull as speed increases, thus diminishing the support provided by the buoyancy of the hull and releasing the hull from its speed limiting wave system.
A hull capable of speeds where boat weight is partly supported by the displacement of the hull and partly by dynamic lift is referred to as a semi-displacement hull. And a hull capable of speeds where boat weight is mostly supported by dynamic lift is called a planing design.
For the purposes of this website it is important to note that direct comparisons of DL of are only really useful when considering boats of roughly similar displacement.
In our work to date we have considered boats of between 5 and 150 tonnes although LDL principles can be effectively applied to larger yachts that are required to operate at relatively high speeds.
The best application for LDL technology appears to be in vessels that are required to travel at ‘medium speed’, which in practice could lie between SL ratios of around 1.3 up to around 3.
The Speed/Length ratio is determined by the following formula:
SL ratio = V / vWL
Where:
V is the boat speed in knots
WL is the waterline length in feet.