The performance of a given hull is dependent on length and shape, plus available propulsive energy



Scout's hull is a classic displacement design with relatively fine entry and exit (canoe form) in ideal calm water conditions. She also has wing flare extensions rising to a raised deck - creating instability, which is resolved by weight placement in an elongated keel.


Scout is therefore subject to conventional 'speed-length-ratio', or Froude calculations - but with complications arising from additional drag from wash spray drag, due to its small scale in relation to open ocean size waves.


Basically, any very small displacement vessel will have serious performance limitations from the environment - because, by design, it is not well suited to surpass nature, where waves are large - if that is, efficient transport is the case in point. In this case it is not. The objective is to prove autonomous navigation is possible. While efficiency has been a consideration, hull innovation is not the main objective. In the circumstances, Scout's hull compromise is commendable.



Froude's experimental wooden model boat hulls, Science Museum, London


The wooden Swan and Raven experimental model boat hulls of William Froude, seen in the Science Museum in London.  All the postulation in the world in nothing compared to physical testing and proof of concept.





Hull speed, or displacement speed, can be thought of the speed at which the wavelength of a boat's bow wave is equal to the boat length. This is applicable to surface vessels in displacement mode.


As boat speed increases, the size of the bow wave increases, and therefore so does its wavelength. When hull speed is reached, a boat in pure displacement mode will appear trapped in a trough behind its very large bow wave, from which traditional designs cannot escape. 


Generally, increasing the length of a displacement hull will increase its economic speed. One was of escaping this rule is to lift a hull out of the water so it planes across the waves. But this is not possible under a certain power to weight ratio. A solar powered boat will not have sufficient power to achieve planing speeds.

From a technical perspective, at hull speed the bow and stern waves interfere constructively, creating relatively large waves, and thus a relatively large value of wave drag. Though the term "hull speed" seems to suggest that it is some sort of "speed limit" for a boat, in fact drag for a displacement hull increases smoothly and at an increasing rate with speed as hull speed is approached and exceeded, with no noticeable inflection at hull speed. However a normal design displacement boat that is not light in weight will begin to climb its own bow wave as its hull speed approaches and it will not be able to climb out of the trough created and so will never reach its hull speed.

The concept of hull speed is not used in modern naval architecture, where considerations of speed-length ratio or Froude number are considered more helpful. We'll look at that in a moment.


As a ship moves in the water, it creates standing waves that oppose its movement. This effect increases dramatically in full-formed hulls at a Froude number of about 0.35, which corresponds to a speed-length ratio (see below for definition) of slightly less than 1.20 (this is due to a rapid increase of resistance due to the transverse wave train). When the Froude Number grows to ~0.40 (speed-length ratio about 1.35), the wave-making resistance increases further due the divergent wave train. This trend of increase in wave-making resistance continues up to a Froude Number of about 0.45 (speed-length ratio about 1.50) and does not reach its maximum until a Froude number of about 0.50 (speed-length ratio about 1.70).

This very sharp rise in resistance at around a speed-length ratio of 1.3 to 1.5 probably seemed insurmountable in early sailing ships and so became an apparent barrier. This leads to the concept of 'hull speed'.





Hull speed can be calculated by the following formula:





  is the length of the waterline in feet, and


   is the hull speed of the vessel in knots.


The constant may be given as 1.34 to 1.51 knot·ft −½ in imperial units (depending on the source), or 4.50 to 5.07 km·h−1·m-½ in metric units.


The ratio of speed to     is often called the "speed-length ratio", even though it's a ratio of speed to the square root of length.



Wave making resistance depends dramatically on the general proportions and shape of the hull: modern displacement designs that can easily exceed their 'hull speed' without planing include hulls with very fine ends, long hulls with relatively narrow beam and wave-piercing designs. These benefits are commonly realised by some canoes, competitive rowing boats, catamarans, fast ferries and other commercial, fishing and military vessels based on such concepts.

Vessel weight is also a critical consideration: it affects wave amplitude, and therefore the energy transferred to the wave for a given hull length.

Heavy boats with hulls designed for planing generally cannot exceed hull speed without planing. Light, narrow boats with hulls not designed for planing can easily exceed hull speed without planing; indeed, the unfavorable amplification of wave height due to constructive interference diminishes as speed increases above hull speed. For example, world-class racing kayaks can exceed hull speed by more than 100%, even though they do not plane. Semi-displacement hulls are usually intermediate between these two extremes.





The Froude number (Fr) is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be defined as the ratio of a body's inertia to gravitational forces. In fluid mechanics, the Froude number is used to determine the resistance of a partially submerged object moving through water, and permits the comparison of objects of different sizes. Named after William Froude, the Froude number is based on the speed–length ratio as defined by him.




where v is a characteristic velocity, and c is a characteristic water wave propagation velocity. The Froude number is thus analogous to the Mach number. The greater the Froude number, the greater the resistance.





In open channel flows, Bélanger (1828) introduced first the ratio of the flow velocity to the square root of the gravity acceleration times the flow depth. When the ratio was less than unity, the flow behaved like a fluvial motion (i.e., subcritical flow), and like a torrential flow motion when the ratio was greater than unity.

Quantifying resistance of floating objects is generally credited to William Froude, who used a series of scale models to measure the resistance each model offered when towed at a given speed. Froude's observations led him to derive the Wave-Line Theory which first described the resistance of a shape as being a function of the waves caused by varying pressures around the hull as it moves through the water. The naval constructor Ferdinand Reech had put forward the concept in 1852 for testing ships and propellers. Speed/length ratio was originally defined by Froude in his Law of Comparison in 1868 in dimensional terms as:

Speed - Length - Ration calculation


v = speed in knots
LWL = length of waterline in feet

The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did. In France, it is sometimes called Reech–Froude number after Ferdinand Reech.





For a ship, the Froude number is defined as:


where v is the velocity of the ship, g is the acceleration due to gravity, and L is the length of the ship at the water line level, or
Lwl in some notations. It is an important parameter with respect to the ship's drag, or resistance, including the wave making resistance. Note that the Froude number used for ships, by convention, is the square root of the Froude number as defined above.




The Froude number is used to compare the wave making resistance between bodies of various sizes and shapes.

In free-surface flow, the nature of the flow (supercritical or subcritical) depends upon whether the Froude number is greater than or less than unity. You can easily see the line of "critical" flow in you kitchen or bathroom sink. Leave it un-plugged and let the faucet run. Near the place where the stream of water hits the sink, the flow is supercritical. It 'hugs' the surface and moves fast. On the outer edge of the flow pattern the flow is subcritical. This flow is thicker and moves more slowly. The boundary between the two areas is called a "hydraulic jump". That's where the flow is just critical and Froude number is equal to 1.0.

The Froude number has been used to study trends in animal locomotion in order to better understand why animals use different gait patterns as well as to form hypotheses about the gaits of extinct species.

Froude number scaling is frequently used in construction of dynamically similar free-flying models in which lift = weight. Since these models oppose gravity, their linear accelerations at model scale match those of full-size aircraft.



Blackcurrant 1  |  Blackcurrant 2  |  Catamaran  Hull Design  Drag  |  SWASH  |  SWATH  |  Trimaran





In fluid dynamics, drag (sometimes called air resistance or fluid resistance) refers to forces which act on a solid object in the direction of the relative fluid flow velocity. Unlike other resistive forces, such as dry friction, which is nearly independent of velocity, drag forces depend on velocity.


Drag forces always decrease fluid velocity relative to the solid object in the fluid's path.


Types of drag are generally divided into the following categories:-

* parasitic drag, which consists of:

* form drag,
* skin friction,
* interference drag,
* lift-induced drag, and
* wave drag (aerodynamics) or wave resistance (ship hydrodynamics).

The phrase parasitic drag is mainly used in aerodynamics, since for lifting wings drag is in general small compared to lift. For flow around bluff bodies, drag is most often dominating, and then the qualifier "parasitic" is meaningless. Form drag, skin friction and interference drag on bluff bodies are not coined as being elements of "parasitic drag", but directly as elements of drag.

Further, lift-induced drag is only relevant in the design of either semi-planing or planing hulls.


Wave drag occurs when a hull is moving through a freely-moving fluid surface with surface waves radiating from the hull.

Drag depends on the properties of the fluid and on the size, shape, and speed of the hull. One way to express this is by means of the drag equation:




FD is the drag force,
ρ   is the density of the fluid,
v    is the speed of the object relative to the fluid,
A    is the cross-sectional area, and
Cd is the drag coefficient – a dimensionless number. 

The drag coefficient depends on the shape of the object and on the Reynolds number:



where D is some characteristic diameter or linear dimension and ν is the kinematic viscosity of the fluid (equal to the viscosity μ divided by the density). At low Reynolds number, the drag coefficient is asymptotically proportional to the inverse of the Reynolds number, which means that the drag is proportional to the speed. At high Reynolds number, the drag coefficient is more or less constant. The graph to the right shows how the drag coefficient varies with Reynolds number for the case of a sphere.

For high velocities (or more precisely, at high Reynolds number) drag will vary as the square of velocity. Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half the coefficient of drag multiplied by the fluid mass density, the cross sectional area of the specified item, and the square of the velocity.

Wind resistance is a layman's term for drag. Its use is usually used in a relative sense (e.g. a badminton shuttlecock has more wind resistance than a squash ball).




The power required to overcome the aerodynamic drag is given by:



Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power. It's important to value the rolling resistance in relation to the drag force.



Shape and flow



















In physics and fluid mechanics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. 

Laminar boundary layers can be loosely classified according to their structure and the circumstances under which they are created. The thin shear layer which develops on an oscillating body is an example of a Stokes boundary layer, while the Blasius boundary layer refers to the well-known similarity solution near an attached flat plate held in an oncoming unidirectional flow. When a fluid rotates and viscous forces are balanced by the Coriolis effect (rather than convective inertia), an Ekman layer forms. In the theory of heat transfer, a thermal boundary layer occurs. A surface can have multiple types of boundary layer simultaneously.

For ships, unlike aircraft, one deals with incompressible flows, where change in water density is negligible (a pressure rise close to 1000kPa leads to a change of only 2–3 kg/m3). This field of fluid dynamics is called hydrodynamics. A ship engineer designs for hydrodynamics first, and for strength only later. The boundary layer development, breakdown, and separation become critical because the high viscosity of water produces high shear stresses. Another consequence of high viscosity is the slip stream effect, in which the ship moves like a spear tearing through a sponge at high velocity.


One way of reducing a vessels skin friction (and to some extent form) drag, is to introduce air bubbles at bounding surface, so reducing viscosity.




Time Elapsed: 21 DAYS: 06 HOURS: 50 MINUTES: 17 SECONDS
Distance from Rhode Island 674.3 mi    Distance to Spain 2740 mi
Distance traveled by Scout 915.7 mi     Velocity 3.5 mi hr

CURRENT STATUS: N 43° 6’ 7.27”  W 58° 11’ 45.64”  Compass 102° Waypoint 99° CoG 66°




Visit the Scout website at






Following on from the Scout Atlantic bash in 2013, in 2020, a team comprising Promare, IBM, and many other technology partners, decided to attempt to cross the Atlantic against the prevailing winds and currents. They set out to build a 100ft craft named Mayflower Autonomous Ship (MAS) for launch and an attempt, aiming for the 400th anniversary of the Pilgrim Fathers journey starting on the 6th of September 1620.


They never made that date, partly due to Covid 19, but did manage to get a hull in the water for the ceremonies in Plymouth, Devon in 2020. On the 15th June 2021, the unmanned craft departed from Plymouth in England, aiming for Plymouth, Massachusetts, USA. You can follow the journey on their blog:





Mayflower Autonomous Ship MAS 400 IBM and Promare Atlantic unmanned attempt 15 June 2021



MAS 400 - The fully autonomous trimaran Setting off from Plymouth, England on the 15th June 2021. There are solar panels, that presumably add to the diesel-electric setup. The idea is to be COLREGs compliant with a self learning program, as such vessels build a database. Much the same as with the current bevy of self-driving robotaxis and robotracks. The question is therefore, will ships beat trucks to the autonomous punch?







LINKS - busy shipping lanes
UK Winds , Sailflow Winds , Met Office Rain & Wind

World Sea conditions, Temperatures & Sunshine or for expected wave heights

Scout on Facebook





This website is Copyright © 2013 Bluebird Marine Systems Ltd.   The names Bluebird™, Bluefish™, Solar Navigator™,Blueplanet Ecostar BE3™, Utopia Tristar™ and the blue bird and fish in flight logos are trademarks. The color blue is an essential element of the marks. All other trademarks are hereby acknowledged.


  Bluebird trademark legend, blue bird in flight logoBluefish flying fish autonomous robotic ships navigation system