What is a Semi-Swath and does it really exist?

To understand what a semi-swath is, we need to define a Swath. A Swath is a Small Waterplane Area Twin Hull: S.W.A.T.H. and it has very exact hydrodynamic meaning. The clue is the S.W.A. part of the acronym. The Small Waterplane Area – is a hull from that has a very low waterplane area. For any floating body it has 6 degrees of freedom – translation and/or rotation about an axis. So what does this mean? Well if we look at the equation of motion of a floating body we have (in words):

Inertia moment + Damping Moment + Restoring Moment = Wave Excitation.

If this equation is set to zero we can calculate the natural period of motion of the floating body. The “first order” in this equation is the Restoring Moment. This is a force x lever or more simply the displacement (buoyancy) x GZ, as this is the righting moment. This righting moment recovers the floating body – vessel – from its disturb position back to its equilibrium.

And for any floating body only the motions of: heave, roll and pitch have restoring forces. And the restoring force of any vessel has the waterplane area at the core of the calculation. Why is this??.. well we know that ship motions are calculated as follows:

Rolling Period                  T = 2π.kxx / √(g.GMT)

Pitching Period                 T = 2π.kyy / √(g.GML)

Heaving Period                 T = 2π. √(ρ.?) / (g.AW)

So, we can see that for Rolling, it is proportional to the GM – transversely, and for Pitching to the GM – longitudinally and in Heave to the WPA. How do we calculate the GM, from the BM of the vessel & the BM is dictated by the “I” the waterplane inertia or simply its waterplane area (WPA) and heave is of course directly proportional the WPA. And looking at these equations, simply put, the smaller the WPA the longer the natural periods of motion.

A hull form that has a period of motion that is far enough away from the encounter period of waves that pass it by, is less likely to be “excited” (resonance) by the wave and yield a much lower response as a result. A hull form that has a natural period of say 5 seconds, and if stationary and experiences waves passing by with each wave having a period of 5 seconds, the natural period of motion = the exciting motion = resonance. Yet if the same hull form has a natural period of say 10 seconds = minimal motions because the natural period does not equal the encounter period. So, the objective is to move the natural period of motion away from the encounter period of the wave, i.e. longer periods of motion.

And we know that the accelerations that are experienced owing to the vessel in a sea state can be calculated knowing that acg = we2.z, 

Which means the encounter period squared times the amplitude of the motion. The goal being to reduce the encounter period and the amplitude of the resonance as this leads to lower vertical accelerations. As a simple example the stationary vessel, a period of T = 10 seconds is -> we = 0.632 = 0.39rads, whereas a period of encounter that is a quarter at T = 2.5 seconds is we = 2.512 = 6.32rads, which is 16 times greater, i.e. 16 times higher accelerations. Which in simple words means, as each event is experienced in less and less time between each event, the accelerations experienced increases. Clearly demonstrating the link between encounter period and accelerations experienced. Therefore, increasing the time between each event (increasing the natural periods of motion), for a given constant wave amplitude, leads to lowering the vertical accelerations. This is the basic hydrodynamic reason of why a Swath hull form exhibits exceptionally superior seakeeping. With much longer natural periods of motions, the time between each encounter increases, which significantly reduces accelerations.

Why is all the technical stuff above important? It goes to the heart of understanding what a small waterplane does hydrodynamically and why hydrodynamically there is no such thing as a semi-swath.

So, take any typical CTV of 24m. If we assume that the stern has either 1 or 2 smaller waterjets, we can assume a typical width of around 2.0m. And then assume say 2/3rd of the length of say 16m makes a simple rectangle shape of 32m2, and then assume a simple triangle to the bow gives an area of 8m2. This gives a WPA of 40m2 per hull or a total of 80m2. The displacement of this typ 24m CTV is in the order of 70 tonne.

The measure of a Swath hydrodynamically is a measure if its restoring force, or rather, lack of restoring force, as the vessel is ‘tender’. There is a non-dimensionalised ratio called the waterplane to displacement ratio that is a means to determine if the hull form has a low waterplane area - low restoring force – to be called a real swath. It is simply the WPA/(displacement)2/3 and must be less than a value of 2.0. The closer to a value of unity 1.0 is the measure of a true Swath. Therefore a mid-range value of say 1.50 is considered to be more true swath like, whereas above 1.50 less true swath like.

So the example 24m Catamaran CTV its ratio is = 80/(70)0.666 = 4.71, which is way over.

If we wanted to make this 24m Cat CTV a more Swath like we can rearrange this ratio using a value of 1.5 to obtain the displacements on its existing WPA, the displacement would be 390 tonnes!

Ok, if we try changing the WPA and keeping the displacement the same, the WPA reduces to 25m2 total or 12.5m2 per hull. This is more than 3 times less than its original hull. This means a hull width of around 600mm. Not enough to fit an engine or waterjet in!

Now, if we wanted a semi-swath hull form, the ratio needs to be in the 2.0-2.5 range. So running the same numbers again, using the upper value of 2.5 the displacement would be 181 tonnes, which is more than twice its existing displacement. If we reduce the WPA this becomes 42m2 or roughly 21m2 per hull. This equates to roughly a hull of 1.05m wide.

So if the hull is roughly 1.05m wide at the extreme, what would be the draft to carry this displacement? This works out around 5.0m draft.

Therefore, to answer the simple question of is there such a thing as a semi-swath, can be answered by, How many 24m catamaran CTVs of 180 tonne or 1.05m wide hull sitting on a 5.0m draft are there? There are designs that “look” like a Swath in profile by adding a lower tube with narrow waterline bow, but does this underwater “torpedo tube bow” and the hull displace more than twice the vessel without one, as demonstrated by the hydrodynamic facts noted above…no! Well, what about their drafts, do they have drafts of 5.0m, again… no!

So, as noted, when looking at the facts, hydrodynamically there is no such thing as a semi-swath, perhaps these attempts should more correctly be called semi-catamarans.

The results of a semi-swath hull form compared to a conventional catamaran from the simplified calculations noted above are shown below for guidance:-