wave piercing hull catamaran

What Is a Wave Piercing Hull?

Last Updated by

Daniel Wade

August 30, 2022

Plenty of different sailboats allow you to experience life on the sea. One design that can improve your experience is a wave piercing hull.

Some hull designs are catered to certain outcomes, with many of them being debatable. How is a wave piercing hull different from a conventional hull?

A wave piercing hull does exactly what the name suggests, as it helps cut through waves due to its fine bow and reduced buoyancy. Traditional bows will ride a wave, whereas a wave piercing hull slices right through. The rounded bottom and sharp top of the hull give a boat this unique ability.

While wave piercing hulls benefit from cutting through waves, it does not reduce the ability to stay dry. The main focus of this hull design is to maintain forward speed through a wave, so you will be soaked in the process.

According to experienced sailors, some love to use boats with wave piercing hulls since they have minimal resistance through waves. However, this is debatable for sailors that want a smoother ride.

Table of contents

‍ Positives to a Wave Piercing Hull

Wave piercing hulls are either loved or hated by sailors, but it all boils down to how you want to sail. Depending on your sailing goals, you need to understand that there are many options available to reach those goals.

There are a handful of positives to consider in a wave piercing hull. There are variations of a wave piercing hull, such as an axe-bow or reverse hull, that have slightly different characteristics and can provide positives to sailors.

For example, an axe-bow is meant to help the crew be more comfortable and is better suited for medium or larger waves. The boat size, for this type of wave piercing hull variation, is best for smaller vessels. A reverse hull is another name for a wave piercing hull.

Unique Design

In comparison to a traditional bow on a boat, the wave piercing hull offers a longer waterline length. These boats will submerge in the water during rough conditions, but the top of the bow provides an increase in downforce and allows for buoyancy.

The design also allows it to reduce pitching motion, which is when a boat rides a wave and then drops when the wave is going down. This means a smoother ride all around if you are able to cut through a wave, but arguably a wet one.

Wave piercing hulls are a bit slower and do not accelerate as fast as traditional hulls. However, they are likely to remain at a constant speed since they can cut through waves and help you save on fuel.

This can help, in some situations, remain at high speeds in some cruisers or catamarans. In some smaller vessels, this also has a better effect.

The larger the boat, the better, when it comes to the boat’s ability to cut through the waves. The long length will actually cut through waves a little more effectively than smaller vessels.

Reliable in Rough Conditions

When wind and waves are becoming increasingly dangerous, a wave piercing hull could provide a smoother ride. Depending on the situation, you could potentially make the ride more manageable with this type of hull cutting through rough waters.

Since these designs are fairly sleek and slender, it is easier to turn the boat at a higher speed. If you are in a catamaran, this will likely not be the case since that design is much different even with two hulls. No matter what the marine environment is throwing at you, a wave piercing hull can help dramatically in rough waters.

Compared to other traditional hulls, these offer less vibration and noise. When cutting through a wave, you are likely going to feel more than just some vibration, but the overall comfort is much different than a traditional hull.

Drawbacks to Wave Piercing Hulls

Not everyone enjoys a wave piercing hull and that is perfectly fine. Every sailor is going to have their preferences, especially with the traditional boats being the most common.

You could argue that these boats are an acquired taste and need some experience to perform confidently in them. There are definitely some negatives to look at before you decide to purchase one.

Since you are cutting through a wave instead of riding it, there will be water everywhere. On a racer or cruiser, it might not be that big of a deal since they usually experience a lot of water anyway, but on a catamaran, this might not be favorable.

As mentioned, you are not riding a wave’s pitch and are cutting through the water. If you are doing any long trips, this might be undesirable.

If you were to ask an experienced sailor which they would prefer, being dry and safe would be the universal answer all the way around. However, that does not stop many sailors from enjoying the benefits of a wave piercing hull.

Potential Dangers on Deck

Since the deck is constantly wet, this could cause some issues walking around or trying to remain stable on your feet. The slippery surface is one hazard to deal with, which seems to be something sailors are just going to have to deal with.

The other issue is that if you have guests or your crew walking around while you are trying to cut through a wave, they are at risk of being swept off of the deck. If the wave is strong enough, it could potentially push someone off of the deck.

It does not appear to be a friendly environment to be in when waters become rough, especially when the front of the boat is going down into the water. This could also increase the risk of the boat capsizing if mishandled.

Motion and Pitch

If you are used to being on a boat that follows a wave’s pitch, then you are not going to find that here. Following a wave’s contour is not what these hulls are designed to do.

In some instances, too long of a bow might create too much yawing motion or side to side movement. This all depends on how you encounter the wave, but the boat might not be desirable for some sailors.

This will be a new feeling if you are used to riding a wave’s pitch and might even create seasickness for some sailors or their crew. If possible, you might want to experience a ride on one yourself before committing to one.

What to Expect with a Wave Piercing Hull

Out of all of the pros and cons of a wave piercing hull, it is up to the individual sailor on what they could do with or without. Depending on your desired sailing experience, this type of hull could work in your favor.

If you are trying to optimize the best resistance for waves, then a wave piercing hull is a proven design to help combat pitch. Keep in mind that you are going to be wet, essentially the entire time you are on the boat.

You would likely need to utilize clothing fit for wet conditions and quality shoes to help remain stable. You also might want to plan out your trip for shorter stops to make sure you are not overwhelmed in the process.

One of the best things you can do is take a ride on someone else’s wave piercing hull boat and get a good feel for what is going on. This way you can try it and work any issues out so to speak before you decide to buy a boat with this hull design.

Keep in mind that the perfect bow is not going to exist, so take into account what you want to accomplish. Compared to a traditional hull, this could potentially be the hull design for you if you are up for te challenge.

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Saint John Paul II High Speed Wave Piercing Catamaran

Saint John Paul II is a high-speed vehicle passenger (RoPax) ferry built by Incat Tasmania shipyard in Hobart, Australia, for Virtu Ferries, a Maltese ferry services operator. It is the world’s second biggest catamaran to operate at more than 70km/h.

Vessel Type

High-speed catamaran ferry

Virtu Ferries

Incat Tasmania

Construction Started

February 2019

Length Overall

A contract worth approximately $80m for the design and construction of the ferry was awarded to Incat Tasmania by Virtu Ferries in October 2016. The planning and design phase of the project lasted for approximately one year.

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Construction on the ship began in 2017 and its launching ceremony was held in December 2018. The ship was delivered in February 2019.

The wave-piercing catamaran joins Virtu Ferries’ existing fleet of 14 high-speed craft. It allows the company to provide year-round fast-ferry services between Malta and Sicily in the Mediterranean Sea basin with increased reliability and passenger comfort.

Saint John Paul II catamaran design

Saint John Paul II features a wave-piercing catamaran hull structure with two slender hulls built using welded and bonded aluminium. The hulls are connected by a bridging section. A wave-piercing type bow is installed in the centre line to provide increased speed and a comfortable voyage at sea.

The high-speed catamaran is built in line with the standards of DNV-GL classification society. Design techniques and safety features of the ferry are designed in compliance with International Code of Safety for High Speed Craft (HSC) 2000 adopted by the International Maritime Organization (IMO).

The ferry complies with the requirements of Italian Port State and is registered under Malta Flag following the receipt of necessary approvals.

With a dead weight of 1,000t, the vessel can carry up to 900 passengers. The overall length and breadths of the vessel are 110.6m and 28.2m respectively.

Deck details of Saint John Paul II

The high-speed wave-piercing catamaran vessel is equipped with two passenger decks, containing four lounges.

The interior is designed to offer three classes of seating with economy, VIP, and business class. It incorporates 996 indoor passenger seats and 138 outdoor passenger seats.

The garage deck of the ferry can accommodate up to 23 heavy commercial trailers / 167 cars / 490 truck lane metres.

Up to two rigid hulled boats are carried at the stern of the ship to for transportation at sea. The boats are launched or retrieved using a crane.

Operation and control of the vessel are performed from the wheelhouse located amid ships. Marine radars and communication systems are fitted atop the wheelhouse to ensure safe operation of the ferry.

Large windows on the passenger deck and bridge areas provide an unobstructed view of the sea.

Propulsion details

The Saint John Paul II RoPax ferry is powered by four MTU 20V 8000 series diesel engines, each generating an output power of 9,100kW.

The vessel’s propulsion system comprises four Wärtsilä LJX 1500 SRI modular waterjets, which ensure fast and reliable operation of the ferry by providing a 10% reduction in weight and improved fuel efficiency.

The high-speed wave-piercing catamaran is installed with a Lipstronic control system, also developed by Wärtsilä, for controlling vessel speed, relative load, pitch and rotations per minute (rpm).

Saint John Paul II performance

Virtu Ferries’ new wave-piercing catamaran has a service speed of 38k. The ferry is capable of completing its journey from Malta and Sicily in approximately 90 minutes.

The ship’s slender demi-hulls provide low wave-making resistance and high transverse stability.

Contractors involved

Incat Tasmania awarded a contract to Wärtsilä in April 2017 for the supply of water jet cutters.

Australian company Revolution Design provided design and architectural solutions for Virtu Ferries’ new RoPax ferry (hull number 089). The ship’s design was also supported by Seaspeed Marine Consulting.

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Influence of an active T-foil on motions and passenger comfort of a large high-speed wave-piercing catamaran based on sea trials

Original article
Open access
Published: 03 March 2022
Volume 27 , pages 856–872, ( 2022 )

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You have full access to this open access article

Chun-Yu Lau ORCID: orcid.org/0000-0003-0150-3809 1 ,
Jason Ali-Lavroff 1 ,
Damien S. Holloway 1 ,
Babak Shabani 1 ,
Javad A. Mehr 1 &
Giles Thomas 2

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T-foil and stern tabs were installed on a wave-piercing catamaran (Incat Tasmania Hull 061) to improve ship motions and passenger comfort. More than 40 total effective hours of sea trials were conducted by the US Navy in 2004, encountering sea states 4–5 in the Atlantic Ocean near the United Kingdom. In this paper the influence of a ride-control system (RCS) on the heave and pitch response amplitude operator (RAO) of the full-scale high-speed catamaran was investigated using the sea trial data. The reduction in motion sickness incidence (MSI) was estimated in order to examine the effectiveness of the RCS in improving passenger comfort. With the existing control algorithm, the vertical accelerations were found to be best controlled by the active T-foil working together with the active stern tabs, while the pitch RAO was mainly mitigated by deploying only the stern tabs. About a 23% reduction was observed in the peak heave RAO with deployment of an active T-foil. The MSI can be reduced by up to 23% with respect to the cases with stern tabs only, depending on the encountered wave conditions, based on ISO recommendation for MSI calculation of a 2-h seaway passage.

Numerical investigation on added resistance and motions of a high-speed trimaran equipped with T-foil and stern flap in regular head and oblique waves for varying wave steepness

Yunbo Li, Ang Li, … Kun Dai

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1 Introduction

1.1 background.

Roll-on–roll-off (Ro–Ro) vessels have an important role in maritime transportation due to their ability to carry large number of passengers, cargo, and vehicles. In 2019, Ro–Ro vessels contributed 72% of the total 2.2 million vessels that called into the main ports in the European Union [ 1 ], i.e. that embarked, disembarked or handled freight. The increasing demand for high-speed transportation has pushed the evolution of Ro–Ro ferries towards larger capacity and higher speed. In the family of high-speed large Ro–Ro vessels, the catamaran is often a popular choice, owing to its large deck area, low wave-making resistance and high transverse stability [ 2 , 3 ].

It is essential to understand the motions of a vessel encountering waves to determine its operability or seaworthiness. The response amplitude operator (RAO) is the prevailing indicator of the vessel response in waves of different frequencies, despite that the vessel response is somewhat non-linear. Fang et al. [ 4 , 5 ] investigated the heave and pitch RAOs for three catamarans in regular waves from Fr = 0.3–0.5, to validate the motion predictions from two numerical potential theories. Similarly, Tezdogan et al. [ 6 ] used three different numerical methods, namely conventional strip theory, high-speed theory without hull interaction, and high-speed with hull interaction, to generate RAOs and analyse vessel operability. These numerical results were compared to the experimental data collected from a 151 m Ro–Ro catamaran ferry travelling at 20 knots. The authors found that in most cases, the estimates of the conventional strip theory were aligned well with the measured results. Their analysis also extended to the prediction of Motion Sickness Incidence (MSI) and operability envelopes based on the seasonal wave scatter diagrams.

1.2 Wave-piercing catamarans (WPCs)

To push the speed limit and operability in rough seas, wave-piercing catamaran’s (WPC) were developed from the conventional catamaran hull form, with addition of piercing bow edges on the demi-hull to reduce wave response [ 8 ], and a centre bow to provide reserve buoyancy and minimise deck diving [ 9 ]. Figure 1 shows the distinctive centre bow on the WPC ‘HSV-2 Swift’ with this vessel being central to the work presented in this paper.

98 m Incat Tasmania Hull 061 WPC showing prominent wave-piercing centre bow [ 7 ]

There is a wide range of research papers that report on the frequency dependent motions of WPCs in waves, including slamming and seakeeping performance [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. According to Fang and Chan [ 20 ], WPCs show excellent seakeeping characteristic relative to conventional catamarans in oblique sea, based on model test and numerical results of a 41 m WPC at 20 knots. As a leader in the design and manufacture of aluminium WPCs, Incat Tasmania constantly seeks the most optimised and refined system that can be used to further enhance the operability of their design through the installation of ride-control systems (RCS) and centre bow [ 7 , 11 , 13 , 17 , 20 , 21 , 22 , 23 , 24 ].

The RCS fitted on Incat Tasmania vessels generally consists of a single retractable T-foil at the aft end of the centre bow and two transom mounted trim tabs, as shown in Fig. 2 . The T-foil on the vessel ‘HSV-2 Swift’ has two adjustable angles, which are strut angle and flap angle. When encountering high sea states, the RCS provides counter control forces to mitigate the motions, specifically heave, pitch, and roll. In contrast, when the vessel is travelling in calm water, the T-foil can be retracted above the water surface to minimise the hydro-resistance and improve the fuel efficiency.

Incat Hull 061—HSV-2 swift ride-control surface locations [ 25 ]

1.3 Ride-control system algorithms

The individual hydraulic mechanisms of each control surfaces allow the RCS to react actively upon encountering a wave train. AlaviMehr et al. [ 26 ] performed a comprehensive analysis on the capability of the RCS, by measuring the heave and pitch response on a 2.5 m model of a 112 m WPC that was excited by deflecting the T-foil and the stern tabs separately. Used to validate theoretical calculations, their study on the RCS control responses provided a sound foundation for optimisation of the control algorithms. In following research [ 27 ] in 2017, the influence of different control algorithms (listed in Table 1 ) on WPC motions was investigated. In terms of the slew rate, each algorithm can be categorised as linear (the control surfaces deflect linearly following the vessel motions’ rate and remain within their maximum range of physical movement) and non-linear control (the control surfaces move at maximum slew rate between their extreme positions, thus generating maximum control force at all times). They reported that the non-linear pitch control algorithm can significantly reduce the peak pitch motion by up to 70% in 60 mm (2.7 m full scale) regular head waves, and by 50% in 90 mm (4 m full scale) regular head waves.

Smith [ 28 ] identified the algorithm applied to the sea trials on HSV-2 Swift to be pitch damping on the T-foil strut angle, and the stern tabs were always controlled by 60% pitch damping and 40% roll damping. However, as will be discussed, the characteristics of both pitch damping and stiffness are expected to be observed in the motion response, due to the phase lag between control surfaces deflection and pitch motion.

1.4 Motion response of WPC fitted with RCS

AlaviMehr et al. [ 27 ] also investigated the phase lag between control surfaces deflections, the wave profile, and the motions. Through tank tests on the 2.5 m model in regular waves, they concluded that the control force of the pitch damping algorithm can be represented by a combination of pitch damping and stiffness control, due to the phase lag between the demand for each control surfaces deflection and its response. Unsurprisingly, this phase lag was found to be much more significant at higher frequencies than at lower frequencies, according to AlaviMehr et al. [ 29 ], and the phase lag was found to fluctuate over a range of 90° regardless of the type of surface or control method [ 27 ]. This observation from the model test is also seen in the full-scale sea trial data that will be discussed in the present study (see Sect. 3.3).

In 2004, the US Navy conducted a comprehensive suite of sea trials on a 98 m WPC, HSV-2 Swift, to assess its seakeeping and structural capability [ 30 ]. During the sea trials, two methods of activation of the RCS were used: T-foil with stern tabs, and stern tabs alone—thus, the effectiveness of an active T-foil could be assessed from the sea trials data. Bachman [ 30 ] linked the activation of the T-foil to the reduction of pitch angle Root Mean Square (RMS) as well as heave RMS throughout all headings at high speeds.

Jacobi et al. [ 31 ] further investigated the same dataset by applying RAO analysis, which investigated the frequency and wave spectrum dependent motions, instead of time-averaging the motions into a simple RMS. They reported a 20% reduction in the maximum heave RAO by deploying an active T-foil when the vessel travelled at 30 knots. They also found that the effect on the pitch RAO of activating the T-foil was insignificant in both full-scale data and the prediction of the two-dimensional green function time-domain strip theory (BEAMSEA) developed by Holloway and Davis [ 32 , 33 , 34 ]. They suggested that due to the reduced distance between the T-foil and centre of mass of the vessel, the main contributor to pitch motion reduction at high speed was the trim tabs at the transom rather than the T-foil. However, another reason is suggested in Sect. 3.3 of the present study.

Recently, Davis [ 35 ] expanded the test conditions applied to the BEAMSEA model to assess the motion of WPC fitted with RCS. He included the various combinations of active or passive T-foil deployment, algorithm, and slew rate of the RCS at high speed (Fr = 0.64). It was similarly observed that in regular waves the pitch motion can be controlled with active stern tabs alone, while heave can only be well controlled with the T-foil deployment. He also further noted that the reduction in RAO was highly dependent on the maximum control slew rate, as well as the application of non-linear control terms. These findings agreed with the towing tank result of AlaviMehr et al. [ 27 ].

1.5 Motion sickness incidence of WPC

As studied in the pioneering work on motion sickness of O’Hanlon and McCauley [ 36 ], motion sickness is caused predominantly by vertical accelerations. Therefore, the ability of RCS to reduce vessel responses in waves is of significant benefit in the development of high-speed light-craft including WPCs.

To quantify the influence of vessel motions on passenger comfort, the Motion Sickness Incidence (MSI) metric was proposed, defined as the percentage of unacclimatised subjects who would experience sickness for a given duration of exposure to motions. O’Hanlon and McCauley [ 36 ] suggested that MSI is a function of frequency and amplitude of vertical acceleration. Their study found that ordinary humans are sensitive to sinusoidal accelerations at a frequency in the vicinity of 0.2 Hz. The research was later continued by McCauley et al. [ 37 ] wherein an empirical model for MSI under conditions including pitching and rolling motions was investigated. However, it was found that the angular motion had no significant effect on MSI.

A similar result was found by Lawther and Griffin [ 38 ], in which they quantified the MSI with the translational and rotational motions based on experimental data. The correlation between motion sickness and the acceleration time histories was analysed, and a strong connection was found between MSI and vertical motion, influenced by both magnitude and duration of exposure, while the angular accelerations were not found to be significant in inducing motion sickness. MSI has been widely applied for passenger comfort research [ 35 , 39 , 40 , 41 ], and it has also been included in the ISO standard 2631-1 since 1997, which was reviewed recently in 2021 [ 42 ].

The MSIs during a 60-min journey on a WPC travelling at 40 knots under various ride-control condition were predicted by Davis [ 35 ] using the BEAMSEA code [ 34 ]. He found that MSI is highly dependent on the encountered significant wave height and the longitudinal location within the vessel. He also suggested that by deploying a T-foil and stern tabs with a pitch damping control mode, the MSI for 90-min exposure duration can be reduced by up to 23% compared to a bare hull.

The reduction of RAO due to RCS activation in those seakeeping trials will be investigated in this paper. Since there were two states of the RCS in the sea trials, (T-foil with stern tabs, and stern tabs only) the influence of T-foil deployment on the motions will be discussed in this paper.

To further investigate the effect of T-foil activation on the passenger comfort, i.e. the difference between MSI with stern tabs only, and with both T-foil and stern tabs, on a full-scale WPC (HSV-2 Swift), the remainder of this paper will present analyses of sea trials data using a linear regression model. The reductions in MSI due to T-foil deployment for a 120-min journey will be predicted under different significant wave height, encountered peak wave frequency and speed conditions. The MSI in the HSV-2 Swift passenger cabin will also be predicted and plotted in the form of a 3D surface, with the aim of demonstrating the influence of the longitudinal and transverse location on the passenger comfort in oblique seas.

2 HSV-2 swift sea trials and data collection

2.1 hsv-2 swift.

High-speed vessel 2 swift (HSV-2 swift) is a large wave-piercing catamaran (WPC). These vessels provide fast, efficient, and economical sea transportation for both commercial and military use [ 9 , 27 , 43 ]. The RCS actively controls the hull motions during voyage, and are customised to suit the needs of each WPC. HSV-2 Swift RCS includes a retractable T-foil with strut and flap control at the aft of the centre bow, and two individual controlled stern trim tabs. The T-foil provides vertical forces to counter heave and pitch motions. Two trim tabs at the demi-hull stern generate a lift force at the transom to maintain the desired vessel dynamic trim, and to reduce pitch and heave. The stern tabs can also counterbalance roll motion when they are operated differentially.

Full-scale sea trials datasets were acquired on the HSV-2 Swift wave piercing catamaran, shown in Fig. 3 , which was built by Incat Tasmania. Details of the trials and data acquisition will be discussed in the next section. The main particulars of the vessel are shown in Table 2 .

98m Incat Tasmania aluminium high-speed wave-piercing catamaran HSV-2 Swift [ 7 ]

2.2 Sea trials and data acquisition

The sea trials were performed in the North Atlantic Ocean, near the coasts of Norway and the United Kingdom, in the northern summer of 2004. To examine the operability and structural response of the vessel, the trials were conducted in moderate to rough seas, which is generally more severe than the wave environment experienced on a typical route of a commercial Ro–Ro ferry in service. Specifically, the highest encountered significant wave height ( H s ) was 3.7 m (Douglas sea state 5), and the average encountered H s was about 2.2 m (Douglas sea state 4).

The trials consisted of 21 octagons, each encountering a different combination of significant wave height, wave spectrum, vessel speed and state of deployment of the T-foil. In general, every octagon included at least five legs, which comprised the five headings of head seas, bow-quartering seas, beam seas, stern-quartering seas, and following seas, as shown in Fig. 4 . Around half of the octagons were completed by manoeuvring to port by 45°, while the rest were completed by turning to starboard.

Typical sea trial manoeuvre pattern

The typical procedure of the sea trials started with the visual observation of the wave direction. The dominant wave direction was recorded, as well as secondary waves and swell if they existed. Then HSV-2 Swift was turned to head seas and maintained speed and heading until steady, and then all the instruments on board started recording. The heading was adjusted 45º to port or starboard and testing continued for another leg of the trial. Generally, the speed and course were maintained for 20 min in head-sea case, 30 min in beam-sea case, and 40 min in following-sea case, to encounter more waves for maintaining statistical accuracy. After five (or sometimes all eight) legs of the sea trial were completed, the data collection under this particular sea state, speed and T-foil deployment was considered to be complete [ 30 ]. More than 40 h of data were measured throughout the sea trials undertaken specifically by the Naval Surface Warfare Centre Carderock Division (NSWCCD).

To acquire motion and wave data from the vessel HSV-2, instrumentation including accelerometers and a wave height radar were installed. Four three-axis accelerometers were located on the centreline at the bow, bridge, Longitudinal Centre of Gravity (LCG) and flight deck. All the accelerometers were sampled at 100 Hz. This sampling frequency was appropriate since the frequencies of interest for motion and excitation were below 1 Hz. Pitch and Roll were also recorded at the LCG using inclinometers [ 30 , 44 ].

To enable comparison of runs in similar sea states, the significant wave height ( H s ) (defined as $Hs=4\sqrt{{m}_{0}}$ , where m 0 is the area under the encountered wave height spectrum) was evaluated. The encountered wave environment was monitored by the wave height meter WM-2, designed by the Tsurumi Seiki Co., Ltd. (TSK). It was installed at the bow to sample the wave profile before the water surface interacted with the hull. This microwave Doppler radar was engineered to measure the wave height from an unstable platform, such as a ship, with relative displacement compensation [ 45 ].

2.3 Method of data analysis

To investigate the hull motions when encountering waves, and hence to identify the influence of the RCS on motions and passenger comfort, vertical and angular motion of the vessel were examined. The analysis started with the heave motions (based on measured vertical acceleration) at the LCG, and these were extrapolated throughout the passenger cabin using the angular motions, to obtain the MSI distribution across the cabin. Lastly, dimensionless acceleration along the hull was analysed to yield a comprehensive understanding on the distribution of motions and MSI, as shown in Fig. 5 .

Flow chart of data analysis in the present study

Since the hull response is frequency dependent, most of the data processing and analysing were conducted in the frequency domain. To obtain a smoothed power spectrum density (PSD) for the encountered wave height, Welch’s method with 8000-sample Blackman–Harris windowing (50% overlap) was applied, employing the fast Fourier transform (FFT). The Blackman–Harris window was chosen due to its ability to detect nearby frequencies of vastly different amplitudes [ 46 , 47 ].

The heave RAO is defined as the square-root of the ratio between the heave and wave height PSDs, like Eq. 1 , while the angular (roll and pitch) RAOs depend on the wave slope spectrum rather than the wave height, as shown in Eq. 2 .

The encountered wave slope power spectrum of the n th sine wave in irregular waves is calculated as ${\alpha }_{n}={k}_{n}{\varsigma }_{n}$ , where ${\alpha }_{n}$ is the n th wave slope, ${k}_{n}$ is the n th wave number, and ${\varsigma }_{n}$ is the n th wave amplitude. In the sea trials location, the minimum water depth was about 130 m [ 48 ], which means it could be considered deep water for the waves shorter than 260 m [ 49 ]. In deep water, ${k}_{n}={\omega }_{n}^{2}/g$ , where ${\omega }_{n}$ is the n th wave frequency and g is gravitational acceleration. Therefore, the wave slope PSD can be estimated by Eq. 3 for at least ${\omega }_{n}>0.5$ rad/s approximately in the shallowest locations.

The dimensionless wave encounter frequency ${\varpi }_{\mathrm{e}}^{*}$ is ${\varpi }_{\mathrm{e}}^{*}=2\pi {f}_{\mathrm{e}}\sqrt{{L}_{\mathrm{WL}}/g}$ , where the encounter frequency ${f}_{\mathrm{e}}$ is in Hz and L WL is the water-line length.

According to ISO-2631-1 [ 42 ], MSI can be estimated by $\mathrm{MSI}={K}_{\mathrm{m}}{a}_{\mathrm{w}}\sqrt{{T}_{\mathrm{e}}}$ , where ${K}_{\mathrm{m}}$ is the constant 1/3, suggested by the ISO for a mixed population of unadapted males and females; ${a}_{\mathrm{w}}$ is the root mean square of frequency-weighted (Fig. 6 ) vertical acceleration, ${a}_{\mathrm{w}}={[\sum_{i}{\left({W}_{i}{a}_{i}\right)}^{2}]}^{0.5}$ ; and ${T}_{\mathrm{e}}$ is the exposure time in seconds.

Frequency weighting of motion sickness incidence evaluation [ 42 ]

A spatial shift method for time-domain vertical accelerations has been used for the HSV-2 Swift dataset to estimate the MSI distribution in the passenger cabin, and is verified in Sect. 3.6 . The time-domain vertical acceleration translation at any point in the cabin can be written as Eq. 4 .

where ${X}_{\mathrm{CA}}$ is the longitudinal distance between the LCG and the prediction location C ; ${X}_{\mathrm{BA}}$ is the longitudinal distance between the location of a second accelerometer at B and the LCG; and ${Y}_{\mathrm{C}}$ is the transverse distance between the prediction location and the LCG.

Since the superstructure of the vessel was isolated from the hull to enhance passenger comfort, the vibration measured on the superstructure, i.e. at the bridge, was found to be slightly lower than the value estimated from accelerations measured on the hull substructure, but a uniform scaling of 0.95 applied to accelerations measured on the substructure was found to give excellent agreement across the full frequency range of interest. Therefore, to fully simulate the environment in the passenger cabin, which is within the superstructure, this adjustment was used. Further details can be found in Sect. 3.6.

3 Results and discussion

3.1 time record of sea trial data.

Figure 7 shows typical time traces of HSV-2 Swift sea trials data for a short segment of two corresponding runs with deployed and retracted T-foil. Both datasets were recorded in a 2.2 m significant wave height in head seas at 35 knots. Normalised, instantaneous wave elevation at the bow, heave displacement at the LCG, and angular displacements and their rates are shown in the plots. A zero-phase noise filter (4 th -order Butterworth cut off at 0.5 Hz) was applied to all data in these plots. Records such as these provide crucial information on the external excitation and how the vessel responds. A phase lag was noticed between waves at the bow and motion at the LCG, but since the motion analysis in this study focuses on comparing the real part of the FFT, the phase shift due to wave measurement location makes no difference.

Normalised ship motion and ride-control activity recorded during trials of HSV-2 98m Incat wave piercing catamaran in head seas with a 2.2 m significant wave height at a speed of 35 knots a T-foil deployed with stern tabs b Stern tabs only

The activity of the T-foil and stern tabs can be observed in the plots on the left-hand side of Fig. 7 . It should be noted that the stern tabs still actively counter pitch and roll motion, even with the T-foil retracted, as shown on the plots on right-hand side of Fig. 7 . According to the work of Smith [ 28 ], and the time records used in this study, it has been found that the T-foil strut angle was controlled by a pitch damping algorithm, while the control gain for the stern tabs was set to 60% pitch damping and 40% roll damping. There was no observable relationship between T-foil flap angle and vessel motions or rates in time domain, as Smith [ 28 ] also suggested, therefore the applied algorithm cannot be identified solely by the time record.

3.2 Influence of T-foil deployment on vessel motions at different speeds

The motions analysis in this study focuses on heave and pitch motions, since according to ISO-2631-1 [ 42 ], motion sickness primarily depends on the vertical acceleration in the environment. Considering further that, based on the study of Jacobi et al. [ 31 ], the WPC motions are most significant in head seas, this part of the analysis concentrates on the heave and pitch RAOs in head seas.

To understand the vessel response at various frequencies and speeds, with and without the T-foil, the RAOs have been evaluated in head seas at three speeds: 20 knots, 30 knots, and 35 knots. Figure 8 shows a measured sample of the encountered wave height spectrum at 30 knots in head seas, along with the corresponding encountered JONSWAP spectrum that was generated using the measured significant wave height (2.24 m) and peak wave frequency (1.04 rad/s or ${\omega }_{\mathrm{e}}^{*} \sim 3.0$ ), and with gamma = 2.0. It was found that the measured encountered peak wave frequencies were quite consistent at different speeds. The average peak frequencies were 1.02, 1.00, and 1.04 rad/s at 20, 30, and 35 knots, respectively.

Measured encountered wave spectrum at 30 knots with JONSWAP spectrum (gamma = 2.0)

Figure 9 a, b show the RAOs for HSV-2 Swift encountering seas with a significant wave height of about 1.8 m at 20 knots. There is little difference between results with the T-foil deployed or retracted, for both heave and pitch RAOs. This was expected since the lift force generated by the T-foil is a function of the vessel speed, higher speed generating higher lift. Therefore, the ability of RCS is limited at low speeds.

Response amplitude operators with T-foil and without T-foil of a wave piercing catamaran in head seas a heave at 20 knots b pitch at 20 knots c heave at 30 knots d pitch at 30 knots e heave at 35 knots f pitch at 35 knots. For comparison note that the results of Davis in e and f were for a slightly different hull form with a length of 106 m and at a speed of 40 knots

The RAOs at 30 knots were evaluated (Fig. 9 c, d) and compared with the work of Jacobi et al. [ 31 ], and show very high agreement. The data with and without T-foil were measured at H s = 2.7 m and 2.3 m, respectively.

At first, the authors expected the heave and pitch RAOs to approach unity at low frequencies, i.e. ~ 0.1 Hz or ${\omega }_{\mathrm{e}}^{*}=2.0$ , since the ship motion is dominated by the hydrostatic term in long waves. However, this was not the case for the pitch RAO. According to the strip theory proposed by Salvesen et al. [ 50 ], the governing equation of pitch motion consists of added-mass and damping terms, which included $1/{\omega }^{2}$ in their coefficients. Thus, it often predicts that the pitch changes rapidly at low frequencies, and tends to zero at extra low frequencies, e.g. < 0.1 Hz or ${\omega }_{\mathrm{e}}^{*}<2.0$ [ 33 ]. One must also bear in mind that because stern tabs were always active in both cases, the RAOs were not reflecting the response of the bare hull.

The lower pitch RAOs at low frequency were consistent with the pitch stiffness ride-control evaluation in Davis’s work [ 35 ]. Although we identified in the previous section that this WPC probably utilised damping control in its RCS, the resultant force of the control surfaces will in practice appear as a combination of damping and stiffness due to the phase lag between the stern tabs deflection and vessel [ 27 ]. Thus, the pitch RAO for the case of tabs only is closer to 1 at low frequencies due to the effective pitch stiffness ride control by the stern tabs.

Consider now these results in the context of the ISO MSI frequency weighting, which reaches its maximum at ~ 0.17 Hz or ${\omega }_{\mathrm{e}}^{*} \sim 3.3$ . At this frequency, the heave RAO reduced by ~ 30% on deployment of the active T-foil, a notable improvement compared with 20 knots, which can be explained by the higher speed generating larger lift. Similar observation is also noted near the catamaran’s first rigid body natural frequency at ${\omega }_{\mathrm{e}}^{*} \sim 4.5$ , where the heave RAO reduced by ~ 20% with deployment of the T-foil. Indeed, the most effective frequency range of the T-foil for reducing heave at 30 knots is $3\le {\omega }_{\mathrm{e}}^{*}\le 5$ . The motions at high frequency, i.e. above ~ 0.33 Hz or ${\omega }_{\mathrm{e}}^{*}=6.5$ , tend to zero as expected, as the vessel becomes much longer than the waves.

The RAOs at 35 knots (Fr = 0.60; H s = 2.2 m) are plotted in Fig. 9 e, f, along with numerical results predicted by Davis [ 35 ] using the BEAMSEA code [ 32 , 33 , 34 ]. Davis compared the effect of the T-foil and tabs to the case of stern tabs only, using different RCS algorithms, for a 106 m WPC travelling at 40 knots (Fr = 0.64) in 3 m head seas. Plotted in this figure are Davis’s results for pitch damping and pitch stiffness algorithms. Although the conditions between the sea trials and numerical simulations were not identical, the results demonstrate the same nature of motion reduction on deployment of the T-foil.

Comparing the peak heave RAOs with deployment of the T-foil, we see about 23% reduction in the sea trials, consistent with a predicted ~ 20% in the work of Davis [ 35 ] with the RCS used in a pitch damping mode, and about 40% when using pitch stiffness control. More broadly, the T-foil produced significant reduction in heave RAO for all frequencies ${\omega }_{\mathrm{e}}^{*}\ge 4.0$ at high speed in both sea trials and numerical analysis. The most effective frequency range of the T-foil in reducing heave RAO was $4\le {\omega }_{\mathrm{e}}^{*}\le 6$ at 35 knots, compared with $3\le {\omega }_{\mathrm{e}}^{*}\le 5$ at 30 knots.

In contrast, the influence of the bow-mounted T-foil on pitch was not as significant as for heave, even though the T-foil was in pitch control. This is aligned with the work of Davis [ 35 ], in which pitch motion was well controlled by stern tabs only.

It is interesting that again the pitch RAOs obtained from the sea trials were generally below 1.0 at low frequencies, regardless of the T-foil deployment, in contrast to the pitch damping algorithm results modelled using BEAMSEA, which starts at ~ 1.0, but in agreement with the modelled pitch stiffness algorithm results, which start at ~ 0.7. This implies that there was at least a component of pitch stiffness control, at least at low frequencies, in the sea trials.

Finally, the results from BEAMSEA appear to be shifted to the right, which may in part be because the simulations were not based on exactly the same hull form or Froude number.

3.3 An explanation for the difference between the RCS control algorithm and the control outcomes

It was noted in the preceding section that the sea trials data exhibited characteristics of pitch stiffness control, although the RCS was presumably configured to a pitch damping control mode. The possible reason is that there will inevitably be a lag in the RCS due to its own system inertia, and any such lag will manifest itself as a control based on an integrated form of the intended motion input. For example, since displacements lag velocities, ideal control forces based on velocities (i.e. damping) will in practice contain a small component based on displacements (i.e. stiffness). This has also been noted by AlaviMehr et al. [ 27 ].

More specifically, factors contributing to the control lag include: 1. control surface mass inertia; 2. hydraulic system response time; 3. maximum slew rate; and 4. inertia of the water surrounding the control surface. According to the model test result of AlaviMehr et al. [ 27 ], the phase lead of the T-foil to pitch motion was 60°, while the phase lag of tabs to pitch motion was 120° at ${\omega }_{\mathrm{e}}^{*}$ = 2, at a speed of Fr = 0.6 in the pitch damping control mode. The phase lag or lead for a corresponding 2.5 m WPC scale model in regular waves was extracted from Fig. 10 and is summarised in Table 3 [ 27 ].

Phase lag of a T-foil b stern tabs deflection relative to pitch motion on a 2.5 m model-scale WPC at Fr = 0.61 and 90 mm wave height [ 27 ]

The resultant ratio of damping to stiffness input in the control algorithm can be estimated by analysing the phase lag. Since pitch rate leads pitch angle by 90º, the ratio of damping to stiffness can be determined by calculating the zero-crossing timing of the deflections separately. For example, at the frequency ${\omega }_{\mathrm{e}}^{*}$ = 2, the T-foil and tabs deflect with a phase lag of 30º relative to the pitch rate. So the resultant damping to stiffness ratio can be estimated as 2:1 as shown in the Eq. 5 .

Since the phase lag changes across the frequency spectrum, the effective RCS algorithm, i.e. ratio of pitch damping to stiffness input, is influenced by ${\omega }_{\mathrm{e}}^{*}$ , even though the programmed control algorithm remains unchanged.

The estimated resultant algorithms at high and low encounter frequencies are given in Table 4 , showing that the resultant ratio not only varies with frequency, but also depends on the control surface. Although the exact phase lag of the vessel HSV-2 Swift was not able to be extracted from the sea trials data, the phase lag recorded by another WPC model with similar hull and RCS were analysed for reference.

Based on these estimates of the resultant algorithm ratio, the control algorithm applied to the RCS may benefit from phase compensation to minimise the vessel motions, suggesting that further reduction in hull response may be possible by fine-tuning the algorithm.

3.4 Motion sickness incidence in head seas

Motion sickness incidence (MSI) is calculated from the acceleration measured at the LCG, using the method in ISO-2631-1 [ 42 ], and are for 2 h exposure, unless otherwise stated.

To interpolate the head seas MSI value for different speeds and wave heights, a linear regression was fitted, which is visualised in Fig. 11 a along with the raw MSI data. The sea trials data were segmented into 10-min windows, with 50% overlap, to reduce the random error from each sea trail run. Based on 59 observations in head seas, the linear model obtained coefficient of determination ( R 2 ) = 0.981, and adjusted R 2 = 0.978, which indicate it is representative without overfitting.

a 3D plot of MSI with T-foil and tabs deployed (small, black markers), and with stern tabs only (large, red markers) in head seas b 3D plot of MSI percentage reduction due to T-foil deployment in head seas

According to the regression, the MSI value is highly dependent on the speed of the vessel ( p = 6.2 × 10 –20 ), significant wave height ( p = 5.7 × 10 –8 ), and peak encountered wave frequency ( p = 0.0001). The influence of T-foil deployment on MSI can clearly be identified by comparing the cases of T-foil with tabs, and stern tabs only.

Unsurprisingly, the effectiveness of the T-foil in reducing MSI increased with speed, as shown in Fig. 11 b, with MSI reduced by up to 23% at 35 knots and at mid sea state (~ 1.6 m wave height). Although the MSI reduction was understandably slightly reduced in higher seas due to the larger denominator, about 15% was still achieved at the highest significant wave height at 35 knots. On the other hand, the effectiveness of an active T-foil at 20 knots is unclear, which aligns with the previous vertical motion findings.

Analysing the fitted regression more closely, we find that the ability of the T-foil deployment to reduce MSI in head seas is most strongly influenced by the vessel speed ( p = 3.8 × 10 –12 ), followed by a minimal dependence on peak encountered wave frequency ( p = 0.58), with the wave height ( p = 0.68) having no significant effect.

The conclusion is that deploying the T-foil with active stern tabs can always improve passenger comfort regardless of the H s or wave frequency if the speed is over 20 knots. On the other hand, wave height and frequency are critical factors for the MSI in head seas, so the ability of the T-foil to reduce MSI independently of the wave spectrum is an important finding.

3.5 MSI at different headings

Figure 12 shows the influence of headings on the MSI calculated at the LCG at 35 knots based on sea trials data. MSI has been normalised by dividing the maximum value for improved illustration. As expected, the highest average MSI can be found in head seas, and the average MSIs declined as the encountered waves approach the stern. There is an outlier in bow-quartering seas, because the encountered peak wave frequency experienced in this run was 0.18 Hz, which is very close to the most sensitive frequency (0.17 Hz) for MSI according to ISO-2631-1 [ 42 ]. Excluding the outlier, the MSI in bow-quartering seas was generally only half of the head seas MSI, while beam and other headings only experienced less than a quarter of the head seas MSI.

Normalised MSI in different headings in sea trials at 35 knots, groups by significant wave height and T-foil activation (Port mirrored to starboard)

The cases of tabs with T-foil deployed, and stern tabs only, are also indicated in the plot by colour. However, in spite of over 40 h of full-scale data, comprising over 150 runs, no firm conclusions about the effect of T-foil deployment in oblique seas can be drawn from these trials due to the large number of variables.

3.6 MSI throughout the passenger cabin

As the purpose of MSI assessment is to provide insight into the reaction of a mixed, unadapted population to periodic motion [ 42 ], it is more meaningful to compute the MSI at different locations in the passenger cabin, rather than just on the vehicle deck or at the LCG.

There were four accelerometers installed on board during the sea trial, but none of them was in the passenger cabin. Thus, in the present study the vertical accelerations were extrapolated to different locations on board, as described in the Sect. 2.3. To confirm the validity of the extrapolation, estimated and measured vertical accelerations at the bridge in the time domain are plotted in Fig. 13 a with a ~ 0.95 factor correction, showing no observable difference. Across all runs, and at all instrumented locations other than the LCG (i.e. bow, bridge, and flight deck), excellent agreement in the RMS acceleration is further demonstrated in Fig. 13 b in more than 700 observations.

Comparison of estimated and measured vertical accelerations: a a time-domain sample at the bridge b RMS from different runs at the various accelerometer locations on the vessel

By this method, the distribution of normalised MSI inside the passenger cabin was evaluated. The X (longitudinal) and Y (transverse) coordinates were based on the HSV-2 Swift general arrangement, and the Z (vertical) coordinate was set to 0.7 m above the deck level. The X = 0 m is set at the stern, while Y = 0 m is set at the centreline of the vessel. In the case of 2.3 m bow-quartering sea at 30 knots with the T-foil, chosen because it demonstrates the MSI distribution in oblique headings at high speed, the highest MSI can be found at the corner of the cabin facing the encountered waves, i.e. starboard fore, as shown in Fig. 14 a. It was unsurprising to see the other fore corner also experiencing relatively strong MSI, while the aft of the vessel was least affected by the motion.

98m WPC passenger cabin: a MSI distribution b MSI percentage reduction with deployment of the active T-foil (in addition to stern tabs) at 30 knots with significant wave height of 2.2–2.3 m in an oblique sea (Port mirrored to starboard for valid comparison)

Figure 14 b shows the percentage reduction in MSI on deployment of the active T-foil, by comparing the data in Fig. 14 a with a T-foil retracted case (30 knots bow-quartering sea, H s = 2.2 m). This was about 10% on average, and up to 14%. The reduction at the stern was higher than at the bow, which was not expected because the T-foil was fitted towards the bow, close to 80% of the water-line length from the transom and very close to the forward limit of the passenger cabin. But if we consider the fact that the influence of T-foil on heave RAO was much more significant than on the pitch RAO, it was reasonable to find that MSI reduced overall instead of mainly at the bow. Relatedly, the smaller percentage reduction at the bow than at the stern can be explained by the larger denominator, since the absolute MSI reduction was similar regardless of the longitudinal location.

3.7 Dimensionless vertical acceleration along vessel length

The purpose of this section is to better understand how the RCS influences the MSI, though looking at vertical accelerations as a function of both position and frequency. The vertical accelerations thus contain information that is lost in RAOs and MSI since (1) while heave and pitch RAOs describe the vessel motions as functions of frequency, they only indirectly provide information about the spatial distribution of vertical accelerations (and only if the relative phase is known); (2) on the other hand, while MSI provides this spatial information, it reduces data to a single value for each location, losing information about the frequency dependence of the motions—in particular, one loses information about whether conditions at the ship’s resonant frequency, or at frequency of peak human sensitivity, or indeed other frequencies, have had more influence on the outcomes.

To visualise more clearly how the active T-foil reduces MSI, dimensionless vertical accelerations are plotted along the length of the vessel at representative frequencies. The local vertical acceleration amplitude is computed by multiplying the local heave RAO by ${{\omega }_{\mathrm{e}}^{*}}^{2}$ , where the local heave RAO is extrapolated from the heave RAOs at four different longitudinal locations. The evaluation method for the heave RAOs is described in Sect. 2.3, with the addition that the power spectra were smoothed using a window of 6000 samples to provide a representative acceleration for analysis.

The dimensionless vertical acceleration distributions at speeds of 20, 30 and 35 knots are plotted in Figs. 15 , 16 and 17 , respectively. Each figure is split into four sub-plots: low frequency; the frequency of the maximum of the MSI weighting curve; the ship’s first rigid body resonance; and a representative high frequency. Low frequency, here ~ 0.1 Hz or ${\omega }_{\mathrm{e}}^{*}$ = 2.0, demonstrates the hull response in long waves; ~ 0.17 Hz or ${\omega }_{\mathrm{e}}^{*}=3.3$ is crucial for understanding the passenger comfort; the hull natural frequency, ~ 0.23 Hz or ${\omega }_{\mathrm{e}}^{*}=4.5$ , represents the largest motions of the vessel; and finally, motions are examined at a higher frequency where they are still significant, in this case ~ 0.33 Hz or ${\omega }_{\mathrm{e}}^{*}=6.5$ . It is noted that the ${{\omega }_{\mathrm{e}}^{*}}^{2}$ multiplier in the acceleration expression contributes to the non-trivial significance of the high frequencies relative to low in the MSI calculations, so the importance of the ${\omega }_{\mathrm{e}}^{*}=6.5$ should not be underestimated.

Dimensionless vertical acceleration along the length of vessel at a speed of 20 knots in head seas

Dimensionless vertical acceleration along the length of vessel at a speed of 30 knots in head seas

Dimensionless vertical acceleration along the length of vessel at a speed of 35 knots in head seas

At 20 knots (Fig. 15 ), there was no significant reduction in local motions at any point caused by the T-foil, regardless of the encountered frequency. This agreed with previous finding in relation to RAOs and MSI, and was again expected because of the lower lift force of the T-foil and/or tabs generated at low speed.

At 30 knots (Fig. 16 ), the heave acceleration reduction upon activation of the T-foil can be observed quite strongly at ${\omega }_{\mathrm{e}}^{*}$ = 4.5, and to a lesser extent at ${\omega }_{\mathrm{e}}^{*}$ = 3.3. At the LCG (~ 40% LWL), about 21% reduction at ${\omega }_{\mathrm{e}}^{*}$ = 3.3 was recorded, which is consistent with the MSI reduction prediction shown in Fig. 11 b. A similar reduction can also be observed at ${\omega }_{\mathrm{e}}^{*}$ = 4.5, but at this frequency the T-foil activity was able to limit the heave motion throughout the whole vessel.

Figure 17 shows the heave acceleration at 35 knots. At low frequency and at ${\omega }_{\mathrm{e}}^{*}$ = 3.3 there was again very limited vertical acceleration reduction on deploying the T-foil. The ${\omega }_{\mathrm{e}}^{*}$ = 3.3 result was not expected, since the percentage reduction of MSI reached about 20% in Fig. 11 b. Nevertheless, it could be explained by the effective motion reduction frequency range of the T-foil ( $4\le {\omega }_{\mathrm{e}}^{*}\le 6$ ) discussed earlier with reference to Fig. 9 e. Moreover, consistent with the Fig. 9 e results, at the two higher frequencies ( ${\omega }_{\mathrm{e}}^{*}$ = 4.5 and ${\omega }_{\mathrm{e}}^{*}$ = 6.5), the dimensionless vertical acceleration was again significantly reduced over the whole ship length on deployment of the active T-foil.

Amongst all cases discussed, the highest heave reduction (~ 35%) consistent over the whole vessel is found at 35 knots at ${\omega }_{\mathrm{e}}^{*}$ = 6.5, followed by ${\omega }_{\mathrm{e}}^{*}$ = 4.5 at the same speed (~ 23%). This demonstrates the ability of the active T-foil to control global vertical acceleration over the whole ship at high-speed.

Overall, the highest vertical acceleration is found at the bow, while the lowest is generally near the LCG, which agrees with the MSI distribution shown in Fig. 14 a as well as the observation made by Davis [ 35 ] of MSI changes along hull. Furthermore, at ${\omega }_{\mathrm{e}}^{*}$ = 2.0, the dimensionless vertical accelerations remained very low regardless of the speed. The acceleration amplitude was again lower at ${\omega }_{\mathrm{e}}^{*}$ = 6.5, though still significant. At ${\omega }_{\mathrm{e}}^{*}$ = 3.3 and ${\omega }_{\mathrm{e}}^{*}$ = 4.5, the influence of T-foil deployment was a function of both vessel speed and encounter frequency—at higher velocity, the effective range of motion reduction tended to shift toward higher frequencies.

4 Conclusions

To investigate the contribution of deploying an active T-foil on vessel motion control and passenger comfort, sea trial records for a 98m piercing-wave catamaran, HSV-2 Swift, were analysed. This study not only provide insight of full-scale WPC motion in random waves, but also demonstrate some new characteristics that have not been discussed in existing model tests and numerical analyses. The Incat Tasmania catamaran was equipped with a retractable T-foil located aft of the centre bow, and two trim tabs fitted at the stern of the two demi-hulls. Throughout the sea trials, the stern tabs were always actively used to counterbalance the pitch and roll motion in damping control, while the T-foil could be deployed or retracted. Thus, the influence of the active T-foil deployment with assistance of stern tabs was evaluated in this study.

Heave and pitch motion response amplitude operators (RAOs) were calculated and compared with previous studies and analytical predictions. The RAOs at 20–35 knots in head seas showed that, compared with active stern tabs only, the combination of T-foil and stern tabs can effectively reduce the heave peak RAO by about 23% when the forward speed was greater than 20 knots, but there was no significant decrement in pitch RAO observed with deployment of the T-foil, regardless of forward speed. Comparing the heave RAOs at 30 and 35 knots in random seas, the effective frequency range of the T-foil was noted to shift upwards from $3\le {\omega }_{\mathrm{e}}^{*}\le 5$ to $4\le {\omega }_{\mathrm{e}}^{*}\le 6$ .

The RAO plots showed evidence that the effective Ride-Control System (RCS) algorithm was a combination of damping and stiffness control, which was attributed to the phase lag between the demanded control surface deflections and the actual control forces. Further investigating the phase lag, the resultant damping and stiffness ratio was estimated, along with the effect of encounter frequency and control surface type. That suggested that vessel motions might be further reduced with adjustments to the control set-up.

A linear regression was fitted to generalise the effect of T-foil deployment on 2-h motion sickness incidence (MSI). Like the RAO, a reduction of MSI in head seas due to the T-foil was only observed when the vessel was travelling faster than 20 knots. The MSI decrease was up to about 23% at 35 knots, and around 15% on average, but depended on the speed and wave height.

The influence of heading on MSI at high speed was also examined and visualised in a polar plot. In general, it was clear that the MSI was highest when the vessel encountered head seas, while the MSI was halved in bow-quartering seas. The MSI further reduced as the heading approached the stern: in beam seas and following seas, the values reduced to less than a quarter of the head seas MSI.

To better understand the environment to which passengers were exposed, MSI on the passenger deck was also assessed. The motions experienced at the centre of the stern was the lowest in the entire cabin, and further benefited by up to 14% MSI reduction with the T-foil deployment.

The dimensionless vertical acceleration along the vessel length at specific frequencies was evaluated to highlight the connection between vertical heave motion and MSI. In short, the accelerations were consistent with the heave RAO and MSI, e.g. the T-foil decreased the heave acceleration by about 20% when the vessel speed was above 20 knots. As with heave displacement, the effective frequency range of the T-foil for vertical acceleration reduction shifted to higher frequencies when the speed increased, i.e. from $3\le {\omega }_{\mathrm{e}}^{*}\le 5$ at 30 knots to $4\le {\omega }_{\mathrm{e}}^{*}\le 6$ at 35 knots. This shift to higher frequencies affected the ability of T-foil deployment to control hull motions and improve passenger comfort due to the system inertia.

Finally, the sea trials demonstrated fair agreement with previous towing tank studies and numerical calculations. Nevertheless, the measured dataset also showed some unique characteristics that had not previously been fully understood, such as that the resultant control was a combination of stiffness and damping modes, and the shift of the T-foil effective frequencies range and their influences.

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Shabani B, Lavroff J, Davis MR, Holloway DS, Thomas GA (2019) Slam loads and pressures acting on high-speed wave-piercing catamarans in regular waves. Mar Struct 66:136–153. https://doi.org/10.1016/j.marstruc.2019.03.007

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Acknowledgements

The authors thank Incat Tasmania Pty Ltd and Revolution Design Pty Ltd, especially Dr. Jason McVicar, for their support towards this research work. Naval Surface Warfare Center, Carderock Division (NSWCCD) is also acknowledged for providing access to data collected from sea trials on HSV-2 Swift. The Australian Research Council (ARC) is also gratefully acknowledged in supporting this work thru Linkage Grant LP 1701000555.

Open Access funding enabled and organized by CAUL and its Member Institutions.

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Chun-Yu Lau, Jason Ali-Lavroff, Damien S. Holloway, Babak Shabani & Javad A. Mehr

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Correspondence to Chun-Yu Lau .

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About this article

Lau, CY., Ali-Lavroff, J., Holloway, D.S. et al. Influence of an active T-foil on motions and passenger comfort of a large high-speed wave-piercing catamaran based on sea trials. J Mar Sci Technol 27 , 856–872 (2022). https://doi.org/10.1007/s00773-022-00876-8

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Published : 03 March 2022

Issue Date : June 2022

DOI : https://doi.org/10.1007/s00773-022-00876-8

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Boat of the Week: This Wave-Piercing 75-Foot Explorer Yacht Is Designed to Dominate Stormy Seas

With her wave-piercing hull and bulletproof windshield, "enmer" takes on the roughest waters and still works as a stylish, comfy cruiser., howard walker, howard walker's most recent stories.

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This 75-foot yacht was designed to travel in the roughest seas

It’s a boater’s worst nightmare. Howling 40-knot winds churning-up near-vertical 20-feet walls of frothing sea. Add to the maelstrom a vicious rip-tide, horizontal rain and menacing coal-black skies. Definitely not a good day for a cocktail cruise around the bay.

This was the punishing sea-trial inflicted on the newly christened Enmer , a no-nonsense 75-foot XSV20 explorer yacht, before being delivered to her new owner, French billionaire and passionate yachtsman Jack Setton.

Even the delivery was extreme. Before Monsieur Setton was handed the keys, Enmer went on a 2,500-mile, high-speed blast from builder Safehaven Marine’s yard in Cork, Ireland, to her new slip in ritzy Porto Cervo, Sardinia.

With a hull more common on offshore pilot boats than motor yachts , the XSV20 blasts through big waves rather than stumbling over them. Courtesy Edmiston Yachts

Now, after more than a year of cruising the Med and Caribbean, Setton has decided to sell the military-grade Enmer – the name is French for “At Sea,” with an asking price of about $2.35 million. “It’s time for me to lose a lot of money, which I seem to do regularly with my boats, and let someone else enjoy her,” Setton told Robb Report .

Setton’s past acquisitions have included the rugged 194-foot expedition yacht Senses , the 60-foot high-performance sailing yacht Ciao Gianni , named after his close friend, the late Fiat boss Gianni Agnelli, and the record-shattering 110-foot “Maxi” catamaran Swift . After his last “project,” the converted 105-foot Texas commercial fishing boat Pink Shrimp, which Setton transformed it into a luxurious world traveler, the Frenchman went looking for something equally rugged, but faster.

Setton found it in the XSV20, with an innovative, wave-piercing hull, thundering 51-mph top speed and go-anywhere capability. “I’ve always loved boats that look rugged on the outside but are comfortable inside—boats with no frills that I know will get the job done,” he says.

The pilothouse is no-nonsense, with shock-absorbing seats and an inch-thick ballistics-glass windshield that is shatterproof. Courtesy Edmiston

The serial yacht owner worked with Safehaven to fine-tune the design, installing twin 1,150-hp Cat C18s hooked-up to waterjets. For Setton, the goal was less complexity, easier maintenance and better low-speed maneuverability. Those factors were important since it would be primarily Setton and his girlfriend who would cruise on the boat.

What didn’t change was the XSV20’s unique hull design. It starts as a carbon fiber and Kevlar-reinforced mono hull with a knife-like, wave-piercing bow. This then flows back into a deep-V mid-section, then seamlessly transitions into twin, catamaran-style hulls. He used inch-thick ballistic glass for the forward windows to provide extra protection for the wheelhouse.

Not a fan of boats that careen over waves, Setton designed a unique ballasting system. “It keeps the nose down, so the boat acts like a submarine, punching straight through the waves,” he says. “We experienced some bad conditions in the Med and it took everything incredibly well.”

The wave-piercing hull is a unique design for a motoryacht but serves the owner’s passion for going mano-a-mano with big ocean swells. Courtesy Edmiston

Though fast, Setton prefers to run at slower speeds. “Yes, she’ll get up to 51 mph but she’s a lot happier at 40,” he says. Come down to 30 mph and she’ll cover over 600 nautical miles without refueling. You have a lot of performance and range.”

The interior was designed to be simple, yet comfortable enough for long cruises. Below decks, there’s a master suite, a guest cabin and crew quarters in the bow. When the seas turn gnarly, the pilothouse features four SHOXS commercial-grade, shock-absorbing helm and passenger seats for safety and comfort.

Setton thinks the next owner will either be someone looking for a boat to turn heads cruising into St. Tropez or an experienced sailor looking for adventures. “I need someone who is as passionate about the boat as I am,” he says. “I admit that I have turned down buyers in the past who didn’t understand what my boats were about. I’m optimistic I’ll find the right person.”

At rest, Enmer has a handsome profile, along with an exposed upper helm and open rear deck for relaxing in the sunshine. Courtesy Edmiston

Enmer , currently moored in the South of France, is listed with Edmiston and judel/vrolijk & co. Here’s a video of the yacht in action.

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Moscow Muled

Best virgin moscow mule recipe.

Nov 30, 2019

Wherever there are great cocktail recipes, there are equally fabulous mocktail recipes for those of us who enjoy all the style and taste of cocktails without liquor. In this post, we reveal the best recipe for the Virgin Moscow Mule on the internet! Let's get started!

Introduction

A cocktail is essentially a blend of two or more ingredients of which at least one is alcoholic. As of late, cocktails are getting more inventive with upwards of four and five ingredients.

The Moscow Mule keeps it classically simple with only three ingredients that most of us already have at home. Vodka, ginger beer, and lime juice.

The intense burn of the ginger beer blended with the refreshing sourness of lime juice delights the palate and warms you right up from the first sip.

There are a multitude of practical reasons for choosing a mocktail over a cocktail.

This could include health concerns and diet practices. Or, maybe you're the designated driver and don't want to miss out on a fun night with your social group.

Whatever the reason, mocktails make sure no one is left out.

Most will say that a mocktail is simply a recipe for any cocktail sans the alcoholic ingredient(s), but we're going to show you fantastic ways to enjoy a Virgin Moscow Mule without sacrificing flavor or taste.

Ingredients:

Sparkling Water
Fresh limes
Ginger beer
Simple syrup

Instructions:

You can either muddle a couple of fresh limes or use freshly squeezed lime juice. We won't tell if you decide to do both ;)
Next, combine your favorite sparkling water and a splash of ginger beer
Add a serving of simple syrup (1 part water, 1 part sugar)
Stir. If you have a shaker on hand, you can also shake the combined ingredients together, but be cautious when pouring as the turbulence may have created a little extra fizz from the sparkling water.
Pour over ice

With this excellent non-alcoholic version of the Moscow Mule, you can have guilt-free seconds or even thirds!

Moscow Muled copper mugs filled with clear liquid ice cubs and lime slices

Health Benefits

Typically, in every 6 oz serving of the traditional Moscow Mule cocktail there are approximately 180 to 200 calories.

One fantastic upside of making a Moscow Mule mocktail is that with the extraction of vodka (say 1.5 oz) you can eliminate around 96 calories, meaning that a typical 6 oz serving is approximately 100 calories or less!

Layers of Flavors

one whole ginger beside four sliced ginger

Now that we've laid the foundations, it's time to explore the variations and wonderful layers we can add to perfect our Virgin Moscow Mule. With these alterations, your mocktails are sure to be enjoyed by all!

In addition to following the preparation of the basic recipe noted above, we suggest adding a few slices of fresh ginger to the mix.

To fully extract the flavors of the ginger, consider muddling it with your limes. Be careful to strain afterward, unless you want to be sucking up bits of ginger through your straw and set your mouth ablaze!

Coupled with the ginger beer, this is sure to amplify the smoldering tones of the original cocktail's taste.

Be sure to use ginger beer and not ginger ale. Most commercially sold ginger beer, though fermented, is alcohol-free. It differs from ginger ale in the way it is manufactured. The intensity of ginger essence in ginger ale isn’t comparable to that of the essence in ginger beer.

So, if you decide to replace ginger beer with ginger ale, you’ll be disappointed at the silenced flavors of ginger in your drink. Essentially, what you’d be drinking wouldn’t be a Moscow Mule at all.

Take it from us, use ginger beer!

If you would rather direct your variations or additions towards the sweet and fruity citrus flavors of your Virgin Mule, you can switch out the simple syrup for a fruit-flavored syrup.

Use a lime-flavored syrup if you would like to stay true to the original characteristics of the classic Moscow Mule.

If you're looking to put a spin on your virgin mule, don't be afraid to try any berry-flavored syrup for an extra layer of fruity goodness.

Sugar-Free Options

Not everyone is a fan of sugar and all things sweet. With this modification, the recipe can accommodate those of us who are patrolling our sugar intake due to dieting and/or health concerns.

More specifically, if you're counting calories or looking to steer clear of sugar all together, you can modify the Virgin Mule recipe by using sugar-free syrup.

With 8 grams of sugar in one tablespoon of conventional syrup, the sugar-free option is a great way to go. A couple of dollops of the sugar-free syrup is a guilt-free way to enjoy the sweetness of this mocktail without the guilt.

Depending on your location and accessibility, you may or may not find brands of sugar-free syrup. All the merrier if you can!

If you can’t find sugar-free syrup, another option is to use flavored sparkling water to add some additional flavour to your mocktail. Some brands of flavored sparkling water are sold in tasty flavors with no sugar, no sweeteners, and no calories. Furthermore, the carbonation in sparkling water will augment the invigorating fizz of the ginger beer. Win-win-win!

Serving Time

Just because we've decided to forego the alcohol component doesn't mean we're also forsaking presentation. We 're all about balance in life as well as in mocktails. So, if one component of the drink has been removed, another must be added!

And what better place to embellish then in the presentation?

It's no secret that the Moscow Mule is served in a copper mug . There are a variety of reasons why, and one of them is that copper is trusted to maintain a cooler temperature. In addition, the copper adds a "zing" to the flavor of the cocktail with each sip.

Whatever the reason, we can't deny that a Moscow Mule served in a copper mug just looks and feels right. The same is to be said for a Virgin Mule.

Besides, if we’re talking about looks, no one has to know you’re drinking a mocktail if you don’t want them to. The copper mug will keep your secret!

In lieu of serving your Virgin Mule in a copper mug, you can serve it in any bar glass. With so many types and shapes of cocktail glasses, there really is no reason why you couldn't enjoy your mocktail in a highball, an old fashion glass, or even a martini glass.

Whatever you have on hand should work just fine!

Garnish Like a Pro

Add a lime wedge to the rim and voila!

Want to take things up a notch? Drag the lime wedge along the rim of your glass, allowing the citrus to coat the edge. Turn your glass upside down into a plate of salt or sugar.

Extra points for presentation and added flavor with every sip!

For herb garnishes, clap your choice of herbs between your hands to bruise it lightly and release its essential oils and aroma. Mint works great!

And here's an extra tip. If you have them, sprinkle a few pomegranate seeds on the surface of your drink! However, be careful if drinking with a straw as those little seeds will get sucked right up! It’s also a beautiful addition to your Virgin Mule, as you can see in the photo below.

Moscow Muled copper mug filled with liquid cranberries and sliced lime

We hope this article has been useful in helping to introduce you to the Virgin Moscow Mule! The Moscow Mule is an incredibly versatile drink, so don't hesitate to let your creativity push you to experiment with new variations. And, if you want to take your presentation and style up a notch, make sure to equip your kitchen bar with a few copper mugs !

Did You Enjoy This Article?

Thank you for reading! If you enjoyed this article, you might also like the following articles: Top 7 Tennessee Mule Recipes and Top 6 Gin-Gin and Gin Mule Recipes

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INCAT HULL 095 / 35m Wave Piercing Catamaran

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COMMENTS

Wave-piercing hull
A wave-piercing boat hull has a very fine bow, with reduced buoyancy in the forward portions. When a wave is encountered, the lack of buoyancy means the hull pierces through the water rather than riding over the top, resulting in a smoother ride than traditional designs, and in diminished mechanical stress on the vessel. It also reduces a boat's wave-making resistance.
What Is a Wave Piercing Hull?
A wave piercing hull does exactly what the name suggests, as it helps cut through waves due to its fine bow and reduced buoyancy. Traditional bows will ride a wave, whereas a wave piercing hull slices right through. The rounded bottom and sharp top of the hull give a boat this unique ability. While wave piercing hulls benefit from cutting ...
A Look at Wave-piercing Bows on Multihulls
May 21, 2015. There are several reasons why reverse bows—also called wave-piercing—have become more popular of late. Probably the most valid of these is the claim (and generally accepted fact) that such a bow form reduces pitching, which is not only uncomfortable, but also slows the boat. Pitching is aggravated when a conventional bow picks ...
Wave-Piercing Bows
Wave-piercing bows - or reverse or hammerhead bows are part of today's cutting edge naval architecture and the latest thinking in catamaran go fast comfort. ... this buoyancy and lift are achieved by making the hull fuller down low. On some wave piercing designs, the hull is wider at the waterline than at the deck, especially near the bow ...
PDF Chapter 8 Wave-Piercing Vessels
with conventional catamarans, so the waterline entrance angle at the bow is smaller than that on a high-speed catamaran. Figure 8.4 shows a typical relation between the unit power P=v s∇ and volumetric Froude number Fig. 8.2 Wave-piercing bow in action - US Navy HSV-2 - Incat Hull 050 8.2 Features of Wave-Piercing Vessels 339
Hydrodynamic and Structural Investigations of Catamaran Design
The semi-SWATH type has a type of hull that can occur a smaller increase from the buoyancy force to the front of the vertical hull. Then the INCAT wave-piercing catamaran hull design was found a b a b 98 Rizki Ispramudita Julianto et al. / Procedia Structural Integrity 27 (2020) 93â€"1006 Julianto et al. / Structural Integrity Procedia 00 ...
Wave-Piercing Vessels
Zhao L-E et al (1995) Investigation on performances and hull form design of wave piercing catamaran (in Chinese). In: Symposium on seminar of ship resistance and performance. Google Scholar Rong H-Z (2002) Application of linearized theory of wave resistance to HACAT, SWATH and wave piercing catamaran (in Chinese).
Saint John Paul II High Speed Wave Piercing Catamaran
Saint John Paul II features a wave-piercing catamaran hull structure with two slender hulls built using welded and bonded aluminium. The hulls are connected by a bridging section. A wave-piercing type bow is installed in the centre line to provide increased speed and a comfortable voyage at sea. The high-speed catamaran is built in line with ...
Incat
Hull 077 was towed 8 km from Incat's shipyard to Sullivans Cove before finishing work was done on site. In addition to ferry berths, the pier hosts a restaurant, a cafe and a number of stalls. ... In the "Length / class" field of the table WPC means the vessel is a wave piercing catamaran. The three K class vessels were a low profile design ...
Wave Piercing Catamaran
The traditional catamaran, developed over the centuries by South Pacific cultures, is a fast, stable, two-hulled boat, but on choppy seas it gives a rough ride. In 1984 New Zealand-born Phil Hercus successfully combined the strength and speed of the catamaran with a wave-piercing hull design called SWATH (Small Waterplane Area Twin Hull).
Influence of an active T-foil on motions and passenger ...
T-foil and stern tabs were installed on a wave-piercing catamaran (Incat Tasmania Hull 061) to improve ship motions and passenger comfort. More than 40 total effective hours of sea trials were conducted by the US Navy in 2004, encountering sea states 4-5 in the Atlantic Ocean near the United Kingdom. In this paper the influence of a ride-control system (RCS) on the heave and pitch response ...
(PDF) CENTREBOW DESIGN FOR WAVE-PIERCING CATAMRANS
T-foil and stern tabs were installed on a wave-piercing catamaran (Incat Tasmania Hull 061) to improve ship motions and passenger comfort. More than 40 total effective hours of sea trials were ...
Wave impact loads on wave-piercing catamarans
Wave slamming is investigated for the 112 m INCAT wave-piercer catamaran with reference to experimental work conducted at full scale, numerical computation by CFD and FEA and testing at model scale using a 2.5 m segmented hydro-elastic model.The segmented model was tested in regular head seas to investigate the magnitude and location of the dynamic wave slam force and slam induced hull bending ...
Boat of the Week: This Wave-Piercing 75-Foot Explorer Yacht Is Designed
It starts as a carbon fiber and Kevlar-reinforced mono hull with a knife-like, wave-piercing bow. This then flows back into a deep-V mid-section, then seamlessly transitions into twin, catamaran ...
Incat Hull 091 / 111 Metre Wave Piercing Catamaran
incat hull 091 / 111 metre wave piercing catamaran. volcan de tagoro has entered service in the canary islands. download specs. download ga. image gallery. video gallery. download brochure. media release. incat hull 091: vessel type: 111 metre wave piercing catamaran. trading name: volcan de tagoro. operator: naviera armas sa. region: europe ...
72ft Wave Piercing Hull Design
www.floethyachts.comThis is a 72ft wave piercing catamaran hull design. Please visit out factory to see the real boat. To be launched 2017
Custom Wave Piercing Catamaran boats for sale
2003 Custom Wave Piercing Catamaran. US$1,850,000. ↓ Price Drop. ASIAMARINE in Phuket | Phuket, Thailand. Request Info. <. 1. >. * Price displayed is based on today's currency conversion rate of the listed sales price.
2003 Custom Wave Piercing Catamaran Power Catamaran for sale
Description. 2003 Custom Wave Piercing Catamaran. A custom build and designed Wave Piercing Catamaran, this vessel is a strong, robust expedition motor yacht designed to cross oceans that does not sacrifice comfort for functionality. Guest cabins are roomy; the vessel features 2 double cabin and 1 twin cabin with en suite bathrooms and ...
PDF Comparison of Standing and Travelling Wave Operations for a ...
range both Standing(SW) and Travelling Wave (TW) oper-ations are possible. For comparison, rf parameters for TW Disk Loaded Waveguide (DLW) as well as for SW Coupled Cells Structures (CCS) have been optimized at an operat-ing frequency of 1300 MHz in a wide range of cells di-mensions. General properties for the two operating modes
Radio Moscow: circa 1968
Radio Moscow: circa 1968. February 11, 2014. Many thanks to David Firth, who is kindly sharing shortwave radio recordings he made on his reel-to-reel recording equipment in the late 1960's. Firth is uncovering and digitizing these recordings as time allows. We are grateful for this recording of Radio Moscow, which Firth recorded in 1968.
Best Virgin Moscow Mule Recipe
Fresh limes. Ginger beer. Simple syrup. Instructions: You can either muddle a couple of fresh limes or use freshly squeezed lime juice. We won't tell if you decide to do both ;) Next, combine your favorite sparkling water and a splash of ginger beer. Add a serving of simple syrup (1 part water, 1 part sugar) Stir.
INCAT HULL 095 / 35m Wave Piercing Catamaran
INCAT HULL 095 / 35m Wave Piercing Catamaran. Incat Hull 095 has been delivered to Port Phillip Ferries. DOWNLOAD SPECS. DOWNLOAD GA. IMAGE GALLERY. VIDEO GALLERY. DOWNLOAD BROCHURE. MEDIA RELEASE. INCAT HULL 095: VESSEL TYPE: 35m Wave Piercing Catamaran. TRADING NAME: GEELONG FLYER. OPERATOR: PORT PHILLIP FERRIES. REGION: AUSTRALIA. ROUTE ...
Moscow Navigator
We specialize in private and customer-tailored tours for individuals and groups. Moscow Tours. Business trips to Moscow. Eco-tours, hikings in Moscow region. Trips to the towns of the Golden Ring of Russia. MoscowNavigator International Travel Club. St. Petersburg tours. Tour options include: Moscow tours in 1 day/2days/3days (Red Square tour ...