Part 2 – Motion at Sea

General Principles of Motion

Fig. 1 shows the 6 ways in which a vessel can move in a seaway. Comfort at sea will depend on how large these movements are, the frequency of movement and the accelerations. Slow movements can be less disturbing to crew than fast movements and high acceleration will cause discomfort and sometimes injury.

Safety is connected to sea kindliness, since a vessel that is easy on the crew will result in less fatigue and hence leave the crew more alert and energetic should a difficult situation arise.

The primary considerations are – how does the vessel get induced to move and how is that movement damped or controlled.

The main design aims for easy motion at sea are:

1. Reduce accelerations.
2. Increase inertia or resistance to movement, both fore and aft to resist pitching, and sideways to reduce roll.
3. Increase damping.
4. Increase the period of roll or pitch. i.e slow the movement down.

The study of these effects in the following discussion shows that with careful attention to the relationship between weight distribution and hull form, we can achieve a vessel that is seakindly and fuel efficient. The trimaran configuration has exceptionally good damping of movement thereby creating a vessel that is very seakindly, both at rest and powering through waves.

Rolling

Roll accelerations are well documented as being the primary culprit that induces seasickness. All vessels are partly or only stabilised by the shape of the hull. In order to achieve fuel efficiency the trend is towards longer narrower hulls. In a monohull as the hull is narrowed the vessel becomes more prone to rolling and in all cases some means of roll damping is added to reduce this effect. A mathematical analysis of the hull forms in Fig. 2 shows that the LDL hull shape will have the least resistance to roll of the five hull forms. The catamaran and the trimaran have the highest, and although the trimaran has less of the outer hulls in the water than the catamaran, the wide beam gives the same or higher righting moment and hence the same or higher resistance to roll as the catamaran.

Conventional monohull yacht design theory states that ….”in general we observe that while greater beam will provide less roll angle, greater beam will also provide much more harsh, rapid, aggressive roll accelerations. Other factors being equal, stiffness (initial stability) varies as the cube of the beam. In other words, small changes in beam have a dramatic effect. We conclude from this that widening the water plane (increasing beam) will increase stiffness, but will at the same time reduce comfort and degrade seakindliness.” Michael Kasten 2012.

In a monohull this is true, but in a trimaran provided the outriggers are immersed to the correct depth, the wider beam does decrease roll angle but does not create worse roll accelerations. In fact the opposite is true. The very high initial righting moment in a catamaran and trimaran of the Adastra type has a huge effect in damping roll. This has been proven by many sea miles covered in large catamarans, and in the case of Adastra in radio controlled model testing in waves and now in the full sized vessel. The owner of Adastra describes the motion as stately, and “like an old transcontinental steam train”. Basically a small slow easy movement from side to side.

This is caused by the hulls of a catamaran and a trimaran reacting to waves in a completely different way to a monohull.

Monohulls in Roll

The reason that a vessel will roll is that a varying force is being applied to the hull side by the passing waves. Fig. 3 shows three different positions of a LDL monohull in relation to the wave fronts. If the pressure from the waves was fixed then the boat would roll to a fixed angle of heel and stop there. However the diagram shows that the pressure changes constantly. Therefore the boat will roll back and forth in an attempt to stabilise itself in relation to the changing force on the side of the hull. This causes the vessel to roll.

 

The photographs above show a typical low displacement to length ratio (LDL) monohull shape and the Palmer Johnson outrigger stabilised monohull (PJ 42m Supersport) side by side. Both vessels have a main hull length to beam ratio of 7, and it is clear that the outriggers on the PJ Supersport will reduce rolling, as the LDL hull on its own has very low resistance to rolling. In the standard LDL underwater hydraulic wing stabilisers have to be added, or a Gyroscopic system is required. These boats will still roll to some extent depending on the added damping system.

Catamarans in Roll

Catamarans have very high roll moment of inertia because most of the weight is concentrated in the hull. The theory behind why this reduces roll will be discussed later in this chapter. The high volume of the hulls and the high inertia prevent any significant roll. However, the varying loads on the two hulls does create sway. There can also be a sense of dipping the bow as the overall buoyancy of the platform changes. So the boat does not go through the water as if there are no waves, but the effect is different and rolling is virtually eliminated.

Moving diagonally to the direction of the waves, the catamaranÕs two hulls are crossing the wave face at different times. This means that the motion of the catamaran can be more complex due to the period of the lifting force varying in an irregular manner.

Each hull length to beam ratio 10. Wavelength 12.5 m. Wave height 1.5 m. The sideloads on both hulls are large, varying, and are different on each hull.

Trimarans in Roll In earlier versions of the power trimaran concept like Earthrace and Cable & Wireless, the outriggers were designed to skim the water. This reduced drag by about 8% compared to the position of the outriggers on Adastra. However the problem with having very low initial stability is that when a wave lifts the windward outrigger the downwind one has to sink to the depth required to counteract the lift on the opposite side of the vessel. If the outrigger is just touching the water it will sink very rapidly and then slow very suddenly as it picks up buoyancy. The image below shows how the outriggers of Cable & Wireless skim the surface, and hence how easily the boat will roll with high accelerations.

Adastra on the other hand has both outriggers firmly in the water. As a wave lifts the windward hull, the opposite outrigger picks up buoyancy immediately and damps the roll. This is the same roll damping effect that is used in the PJ Supersport, except in Adastra the outriggers are 14 meters apart as opposed to 7.5 m, and are higher volume and more deeply immersed.

 

Another difference between Cable & Wireless and Adastra is that Adastra’s outriggers are longer and have more overall volume lower to the water which has a further damping effect on rolling.

 

Comparing the PJ Supersport to Adastra in the above picture, with both boats at similar scale, it is obvious that the outriggers placed at 7 metres from the centre will have a massive effect in roll damping. Note that the main hull of Adastra with a length/beam ratio of 17 has no inherent stability. Not having to design the main hull with the constraints of creating stability from the hull form, allows us to design a hull that is optimised to reduce pitching, heave and yaw.

Fig. 6 shows how the wave pressures affect the main hull and the outriggers. Although there is a varying force on the three hulls, the forces on the outriggers are much lower than the main hull. The larger lateral pressure on the main hull is not enough to cause the boat to roll provided the outriggers are immersed to the correct depth and have the correct volume. It can also be seen from the diagram that the effect of varying force on the hulls will be virtually eliminated compared to a catamaran. With the long thin hull, directional stability is excellent and the boat will not have the same uneven motion that can occur in a catamaran.

Effect of Inertia on Roll

The next important element is inertia. This is the vessel’s inherent ability to resist movement and, rather like a flywheel, it is dependent on the weight relative to the centre of rotation. If the weight is concentrated at the perimeter it will be hard to get moving and then equally can be hard to stop once it is going. The rate at which a vessel begins to roll and then stops rolling is therefore highly dependent on the vessel’s weight distribution and beam. While the hull form dominates the reaction of the vessel to the waves, the distribution of the vessel’s mass has a very significant effect on the momentum and accelerations as the boat responds to the effect of the interaction between the hull/s and the waves. The roll moment of inertia is a measure of the vessel’s resistance to rolling. The higher the roll moment of inertia, the more the vessel will resist rolling and the more slowly it will return from movement to a neutral state. Moment of inertia is calculated using the square of the distance between the resisting mass and the centre of rotation (C of R.). The effect of the square rule is that weights far from the centre of rotation have significantly more effect in increasing the moment of inertia than those close to the C of R.

One way of increasing the inertia in a monohull is to raise the Vertical Centre of Gravity (VCG), but as previously explained this can only be done to a limited degree in an LDL because the vessel will not pass the required stability requirements of the classification societies if the VCG is too high. On a trimaran we prefer to keep the VCG low as it means a smaller and lower volume outrigger is required to achieve stability in waves. The total volume of the outer hull is determined by the lift required when the hull is following the face of a steep breaking wave. It can be reduced as the VCG is lowered and the beam is increased. The smaller the outriggers the less they will drive the pitching or yawing motion of the vessel which is discussed later in this article.

In a trimaran like Adastra we placed generators and engines for back up propulsion, and for maneuvering in the outer hulls. These weights are 7 m from the centerline and therefore create very high roll moments of inertia. A further benefit is that the generators are kept separate from the main hull and living areas. A weight positioned 7 metres from the centre of rotation has a roll moment of inertia of 49/14 = 3.5 times the roll moment of inertia of the same mass at 3.75 metres from the centre of rotation, as in the PJ 42m Supersport LDL monohull. It is not surprising then that we find that Adastra extremely stable at anchor.

In a catamaran most of the weight is in the two hulls, and so this type of vessel has a very high roll moment of inertia and is very resistant to roll accelerations. The effect of this is that the catamaran is very stable in long wavelengths where the hull will follow the wave face in a gentle manner while the monohull will always roll to some degree. Adastra will also follow the wave face in a similar manner to the catamaran without the complex swaying movement as described in the section above on catamarans in roll.

Pitching

The next most important movement in causing uncomfortable motion is pitching. This is where the vessel is rocking in the fore and aft direction. High accelerations and large movements in this direction can be very disturbing and in extreme cases can cause injury due to the high G forces that can be generated.

In a similar way to the factors that cause and control roll, in pitching the hull form reacting to the wave movement along the hull or hulls is the primary factor inducing the motion. The displacement of the vessel and the distance of the centre of gravity from the centre of rotation (C of R) will be the main factor in creating damping. The volume of the forward part of the vessel and its relationship to the volume aft will also pay a part in damping pitching.

Effect of Inertia on Pitching

The pitch moment of inertia is the sum of the moments of inertia of all the weights in the vessel x the square of the distance of each weight from the C of R.

It is a common misconception that a vessel will pitch either around the centre of Gravity (C of G) or the centre of the waterplane area. A fairly simple calculation of the relationship of forward momentum and rotational momentum as a vessel accelerates shows that the centre of rotation moves aft from the centre of the waterplane area, and eventually ends up about a quarter of the waterline length forward of the stern.

It is clear then from the diagram in Fig.7 that concentrating some weight in the vessel further forward will increase the lever arm of the pitch moment of inertia, and since that effect is proportional to the square of the distance between the C of R and each weight, the effect of pitch damping can be quite dramatic. This approach has been proven on the sea trials of Adastra at full size. It is possible sometimes to create a resonant pitching frequency in the vessel that can match the frequency of the wave fronts, and then the boat will pitch more. This can be controlled by moving weight if necessary. In the case of Adastra we have fuel tanks distributed along the bottom of the hull with a capacity of about twice the normal full fuel load. This means that weight (fuel) can be moved along the hull fore and aft to create optimum trim and/or pitching control.

The Effect of Hull Shape and Position on Pitching

In the case of a trimaran it might seem sensible to put the outriggers right at the aft end of the vessel so that the effect of the two outer hulls pitching forces are completely damped by the inertia of the main hull. The picture below shows the approach taken in the Earthrace design of pulling all the weight aft, including the engines. We believe that this will cause the boat to pitch more than it would if the outriggers, accommodation, wing beams and engines were further forward.

We have found that the correct size outriggers do not have the power to make the vessel pitch even if placed further forward. This means that the outriggers can be placed to create maximum stability, and further away from the C of R thereby increasing the pitch moment of inertia of the vessel.

The image below shows the bow of Adastra”s outrigger and it is visibly obvious that the upward lift of the bow will have little effect on the pitching of the main hull. This can also be shown mathematically.

Catamaran and Adastra outrigger bow on view.

The catamaran on the other hand has two bows which are more buoyant than the single bow of the trimaran as the length to beam ratio of the trimaran is in the range of 17 to 20 as opposed to 10 for both of the catamaran hulls.

In the image below it is again visibly clear that the very long thin main hull bow of Adastra will cut through the waves rather than lift upwards. The amount of lift induced by the bows will be significantly less than any of the vessels shown.

The other factor of induced motion in pitching is the way the wave will lift the stern. So even if the bows of the vessel are lengthened and made narrow, the stern could have too much volume and hence lift the aft end of the vessel and dip the bow. Therefore it is essential to keep the centre of gravity far enough forward to allow the stern to work with the bow to reduce rather than increase pitching.

The long thin main hull of Adastra has the least tendency to lift in a wave of any vessel because of the relatively thin sections forward and aft. In seas with a wavelength up to approximately 70% of the waterline length and a typical maximum height 3 metres she will slice straight through the waves with very little pitching. The outrigger volume is balanced so that they are just large enough to create sufficient roll stability but slender enough to cut through the waves and thereby induce very little pitching motion into the boat. As the wavelengths get longer she will start to follow the wave surface, but with an easy motion which can be further controlled by choosing the best speed and angle to the waves for the conditions.

The image below shows how large the bows of a semi displacement vessel are compared to the LDL, the catamaran and the trimaran. The reason that this does not cause as much pitching as would appear to be the case from the hull form, is because the pitching moment of inertia is high, and the large weight of the vessel damps the movement.

Heaving

If we refer to the bow on views of the vessels in the previous sections, it will be visually apparent that the hull of Adastra, with the near vertical hull sides and very narrow long thin shape will be lifted by the waves the least of any hull shown. This can be shown mathematically by calculating the rate of increase of volume with hull immersion, and comparing that for different vessels. But the mathematics only shows what the images reveal.

The narrow beam of the main hull will allow waves to rise further up the hull sides without lifting the vessel. Wider hull vessels will heave much more than thin hulls. In heavier wider hulls some of the effect of heave will be counteracted by the forward momentum and this will reduce heave, but in a relatively light vessel like Adastra the long thin hull and the forward momentum combined will control heave.

Surge

Surging is the tendency of the vessel to accelerate and decelerate fore and aft. In order to achieve fuel efficiency the vessel needs to be as light as possible. As the boat becomes lighter its ability to drive through waves without decelerating decreases. By making the hull very long and thin, this effect is reduced. Thereby reducing surge to a minimum.

Yaw

A long thin hull with a skeg aft has very good directional stability. This will reduce yawing to a minimum. The most serious form of yawing is broaching. Broaching is caused by the pressure on the bow slowing the boat, while at the same time the overtaking wave pushes the stern around from aft. The long thin bow of the trimaran cuts more easily through the water reducing this breaking effect on the bow. The lower drag of the hull allows it to move more easily forwards as the wave pushes from aft, and the long hull will track in a straight line down the wave face. This effect has been proven many times in large racing multihulls.

Swaying

The movement of Adastra sideways in waves will be similar to a long narrow monohull vessel. In normal conditions swaying will not be a significant cause of discomfort in either of these types of vessel. In large breaking waves the ability of the vessel to drift sideways when struck by a breaking crest can be an important factor in dissipating the energy of the wave impact.

Inertia of forward movement

With all vessels the effect of forward movement has a gyroscopic effect (like riding a bicycle), and that creates more inertia and reduces sudden accelerations. Due to all of the points discussed so far Adastra is more easily driven than the other vessels considered in this article, so she can move faster through waves than vessels with a wider hull. This enables her to use inertia created by forward momentum to dampen induced accelerations still further, and gives the captain of the vessel a wider range of speeds to choose in order to achieve minimum pitching.

Conclusion

The search for greater fuel efficiency appears to be limited in the monohull form by the difficulty of creating a seakindly vessel with narrow beam. The solution to use small outriggers to reduce roll on a LDL monohull, still does not make the vessel as efficient as a power trimaran.

Power trimarans can be made to be very seakindly, provided the full benefits inherent in the three hull configuration are taken into account at the design stage, and careful attention is paid to the effect of mass distribution and hull shape on the inertias and driving forces induced by waves.

Very different hull forms are possible in a trimaran compared to monohulls which creates new possibilities for efficiency and comfort at sea.

Adastra has proven to be extraordinarily fuel efficient and in the words of her owners is also proving to be “a good sea boat, and a joy to be aboard”.