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• 1 Introduction
• 2 Hull design approach
  • 2.1 Hull configurations
    • 2.1.1 Slender mono-hull
    • 2.1.2 Catamaran
    • 2.1.3 Hydrofoil
    • 2.1.4 Planing hull
  • 2.2 Propulsion power
  • 2.3 Hull resistance
• 3 Results
• 4 Discussion & References

2 Hull design approach 

The design approach involves hull design, human power supply, propulsion system and structural design. It focuses on the implications towards: top speed and cruising speed. Manoeuvrability and towing force are not being considered in the scope of this paper.

The boundary conditions that are taken into account are as follows:

• Propulsion by two persons who only use their feet
• Maximum length of the boat: 6.00 meter¹
• Breadth minor to length

The majority of the European two persons waterbikes do not exceed a length of 6 metres. Reason for this is the fact that longer boats are not allowed at the International Waterbike Regatta. This regatta is a European student championship.

Within these boundary conditions, there is a large freedom of conceptual solutions. Within the scope of this paper, examples are being taken from different European teams over the past ten years.

There is a huge diversity in hull configurations. Mono-hulls, twin-hulls, triple-hulls, Small Water plane Area Twin Hulls (SWATH) and Hydrofoils appeal at the starting lines of human powered boat championships. This indicates that, apparently, there is not an obvious single ideal design that meets the full main objective.

Four different hull types are being considered: Slender mono-hull, catamaran, hydrofoil and planning hull.

When considering the design of the hull for speed, two sailing conditions are relevant:

1. Maximum top speed at the maximum power supply with a target distance of 100 metres.
2. Maximum cruising speed at the maximum continuous power supply with a target distance of 10 kilometres.

Indication of hull speed ranges, for good performing waterbikes:

Table 1 Indication of time records, measured at championships in Europe

World and European championships and record attempts require starting with the bow point behind the starting line at zero speed. However, some waterbike championships allow approaching the starting line with speed at the 100 kilometres. This results into time differences in the order of 2 seconds.

2.1 Hull configurations

Some general aspects can be taken into account for design considerations of the different hull types. The next paragraphs give an explanation of the individual hull type resistance characteristics and the design influences upon them. 

2.1.1 Slender mono-hull

Slender mono-hulls have a low resistance at lower ship speeds, i.e. below 3 m/s. The main reason for this is the fact that at low speeds, friction is the dominant resistance factor while the wave resistance is low. Because mono-hulls have a small wet surface, in comparison to the other hull types, their resistance is the lowest at low speeds.

Figure 2.1 Ship resistance versus ship speed for a slender mono-hull type

When slender mono-hulls increase their speed, they start to go planing. In Figure 2.12, planing starts beyond 4 m/s. A transition of semi-planing to planing occurs between 4 to 6 m/s. This can be expressed in a non-dimensional parameter, the Froude number:

Eq. 2.1
With:

• v= ship speed [m/s]
• g = gravity acceleration = 9.8 m/s2
• L = ship waterline length [m]

Transition of semi-planing occurs between Froude number between 0.5 and 0.7 for slender mono-hulls. Also shown in the figure are ratios for lift versus displacement, (L/D) ratios. Sailing as a displacement vessel the L/D-ratio is equal to zero. When planning, lift is being generated and the L/D-ratio can reach up to a maximum of about 0.3 for slender mono-hulls. A great advantage of slender mono-hulls is the fact that the resistance hump towards planing is very low in comparison with other hull types. Catamarans, consisting of two extreme slender hulls also have this benefit. Besides the L/B-ratio to express the slenderness, another ratio can be defined between length and displacement:

Eq. 2.2
With:

• L = ship waterline length [m]
• V = displacement volume [m3]

Slender mono-hull waterbikes can have very extreme values, reaching up-to a L/V1/3-ratio of 22. At such slender ratios, main attempt is to design very fine bowlines. One should keep in mind however that the bow wave generation could become critical. This means that the wave initiation of the front bow is to low, resulting into a wave resistance increase of the overall hull. In order to avoid this, at lease 10% of the ship-volume should remain in the front part beyond 1/3 of the ship length.

The aft of the ship is also an important part, influencing the resistance. By designing a flat stern, the ship can be virtually enlarged, affecting the wave resistance positively. In order to guarantee a smooth flow behind the ship, the draft of the aft ship can be estimated, using the empirical formulas of Raven [2]: Clearance of the stern with a smooth flow can be created if:

Eq. 2.3

Estimated resistance force when the flat stern is clear from the water:

Eq. 2.4
With:

• vs = design speed
• z_stern = dept at stern
• A_stern = Stern area below waterline
• g = gravity acceleration = 9.8 m/s2
• r = mass density of water = 1000 kg/m3

Figure 2.2 Slender mono-hull Macbath from Delft Waterbike Technology, The Netherlands, Genova 2002

Stability of slender mono-hulls is minimal in general. This affects the performance during manoeuvring such as slalom trials. When steep corners are taken, weight can be used to compensate low stability. A stable rudder control is important. A large advantage is the small wet area.
In case of high waterbike sea states, i.e. significant wave heights Hs in the order of 0.12 metres (3-4 Bft on large channels, wave period Ts=1.4 sec, wave length Lw 2 metres) waves from behind is a severe problem. Slender Mono-hulls show the most capsizing of all hull types during championships.
In case of extreme slender mono-hulls, such as in a tri-maran configuration where two small side hulls provide additional stability, waves from the front can result into green water, demanding to lower speed significantly.

2.1.2 Catamaran

In comparison with slender mono-hulls, the resistance hump towards planing is much lower for a catamaran, taking into account the fact that 2 hulls are included, Figure 2.3. Also shown in the figure is an indication of the ratios for lift versus displacement, (L/D) ratios. Resistance and L/D ratio are given for 2 hulls. Since the hulls are very slender, the order of L/B=20, little up-to no dynamic lift is being generated.
Although the friction of the two hulls is larger than in case of one hull, acceleration towards top speeds goes very smooth. This makes catamarans very safe to develop from a design point of view. Slender mono-hulls are more critical than catamarans when it comes to design errors and inaccurate estimates of longitudinal trim at high speeds. Nevertheless, low resistance can only be reached with a good hull design.

Figure 2.3 Ship resistance versus ship speed for a catamaran type

Sailing boats are able to lift out one of the hulls, resulting into further increase of sailing speed. Unfortunately this phenomenon does not occur in case of waterbikes. Therefore comparison of waterbikes and sailing boats is poor in case of a catamaran configuration.

Formulas presented for the slender mono-hull are applicable for catamarans also. The distance between the two hulls does not depend on the minimum required stability but on the wave interaction between the hulls. It is worth analysing the wave patterns in relation to the distance between them.

Figure 2.4 Catamaran hull design KATastroph from Duisburg waterbike team, Germany, Flensburg 2003

2.1.3 Hydrofoil

Hydrofoils are mostly erected from a slender mono-hull with side hulls or a catamaran. Besides the hulls, a wing is constructed below the waterline. For efficiency reasons the main foil is always fully submerged, carrying a weight between 80% and 100% of the total waterbike weight.

When designing the foils for generating lift, balance between the lift and weight of the waterbike is the prime focus. A difficult choice however, is the design speed. When designing a high cruising speed in the flight mode, take off out of the water can become difficult. Due to the hull resistance while afloat, limited speed and thus the foils can generate limited lift.

The lift and drag forces of the wing foil can be derived from NACA profiles. Besides the drag force of the wing foil profile, 4 other resistance components can be identified [4]:

• Friction force, C_F
• Spray resistance, Cspray
• Induced resistance, Cinduce
• Wave resistance, Cwave

The total resistance can be expressed by:

Eq. 2.5

Friction can be derived from the ITTC-friction line, where the number of Reynolds (Re) is related to the chord of the wing foil:

Eq. 2.6
With:

• v = ship speed
• c = chord of the wing foil

The spray resistance is mostly determined on an empirical basis, depending on profile thickness, nose shape, thickness/chord ratio. An example of spray resistance prediction can be found in [5]:

Eq. 2.7
With:

• C_F = Friction force
• t = wing foil thickness
• c = wing foil chord

In general, the spray resistance is low in case of waterbike designs

The induced resistance for an elliptical wing can be calculated by [4]:

Eq. 2.8
With:

• K = correction factor due to the effects of the air media above the wing [4] 
  • K = 1.5 when h/b = 0.1
  • K = 1.2 when h/b = 0.3
  • K = 1 when h/b = 1
• h = wing depth
• b = wing span
• C_L = lift force
• AR = aspect ratio of the wing foil

Wave resistance can be calculated for h/c>1 by using the following equation [4]:

Eq. 2.9
With:

• C_L = lift force
• F = Froude number
• c = chord of the foil
• h = wing depth

Figure 2.5 shows the hull resistance energy versus the ship speed for a hydrofoil. Besides the hull energy, the energy to elevate out of the water is required in case of the hydrofoil. Another 200 up-to 400 W is needed for lifting a hull with a total weight of about 250 kg out of the water into flight mode.

Figure 2.5 Hull energy versus ship speed for a hydrofoil type

The steering foil carries a weight between 20% and 0% of the total waterbike weight. In order to come out of the water, a steering foil at the front side of the hull seems to be very affective. When steering the front foil up, an upward force is being generated, helping the hull moving upwards. In case of a steering foil at the rear side of the hull, a down force is being generated when lifting the hull out of the water, influencing the take of in a negative manner.
On the other hand, elevation control with a steering foil at the back is much more stable than a steering foil on the front. Therefore, when a front foil is being used, an active control is required in order to fly with a constant elevation above the water. By using a floater that follows the waterline, the angle of the steering foil can be controlled.

Figure 2.6 Waterbike Hydrofoils, the Af Chapman II, Chalmers University, Sweden at the front, ~ 1995

2.1.4 Planing hull

Fully Planing hulls are not applied for waterbike designs. Major difficulty is the transition from displacement mode (low speed) to planing mode (high speed). Figure 2.7 shows an estimate of the hull resistance versus ship speed for a planing hull. The feasibility of passing the resistance hump is uncertain. However, if the hump can be passed, significant reduction of resistance at higher speeds can be gained.
For planing hulls, weight reduction has a large influence on the resistance hump. The effect of weight reduction is significant.

Figure 2.7 Ship resistance versus ship speed for a planing hull type

Another important influence on the resistance curve is the longitudinal trim of the hull. The trim should be acceptable for three stages:

1. Low speed, long distance cruising;
2. Going into planing mode 
3. Planing

An important design parameter is the ratio between planing area and displacement [3]:

Eq. 2.10
With:

• A_p = planing area 
• = displacement of the non-planing hull

This ratio lays in the order of 9, in case of L/B=6 as for the Nederwood from Delft Waterbike Technology, Figure 2.8.
The deadrise, i.e. V-shape of the hull can be low, since sea keeping behaviour does not have to be accounted for in principle.

Figure 2.8 Planing-hull design Nederwood, Delft Waterbike Technology, The Netherlands, Berlin 2004

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