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Water world of human powered racing boats “Hull design approach for Waterbikes”

By: Leo de Vries, M.Sc.

Webmaster, World of Waterbiking - www.waterbiking.org Senior member of Delft Waterbike Technology (DWT)

Project Manager, Centre for Mechanical and Maritime Structures (CMC), TNO, The Netherlands

1 Introduction Six metres of experiment length, with a need for human powered speed. Human Powered boats in Europe are mostly called “waterbikes”. Teams from different countries build them in order to meet every year and compete with one another during waterbike championships to see who is the best. Because of the limited size of these vessels there is a tremendous advantage of being able to afford experimental design variations at high risk. This is what makes waterbikes interesting to learn from. Not only from a biking point of view but especially from a shipbuilders point of view. Designing for a waterbike championship means that the performance of the boat and its human power supply are optimal. The main objective is: Hull design for maximum cruising speed and a high top speed. The different conceptual design solutions involved reflect diversity in operational performance, resulting into sub-optimal design solutions in order to meet the main objective. It was discovered that little is available in literature involving waterbikes. This article describes a hull design approach by showing the influences of four different hull design solutions. Moreover, the influences upon the main objective, sailing speed, are being discussed. After the hull design solutions, results are being evaluated by comparison of high speed and long distance speed performances, followed by a discussion. Generalised standard commercial waterbike In general, when waterbikes are being mentioned, it involves commercial waterbikes with a limited sailing performance and ergonomics for the cyclists. Mostly, one aspect of commercial waterbikes is very good. It is its robustness. Is design for robustness contradictive to design for a good performance? The answer should be no, if challenging its design freedom. However, two boundary conditions are decisive: protection of the propulsion unit and a good stability against list. These two conditions are well met when a catamaran configuration with a pedal wheel propulsion system is chosen. Figure 1.1 shows an example of such a design.

Figure 1.1 Illustrative example of a generalised standard commercial waterbike

Some designs are quite similar to the generalised standard commercial waterbikes. The differences in main dimensions and details have a huge impact in the overall performance. Figure 1.2 shows an example of such a similar concept.

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Figure 1.2 “5 vor 12” from waterbike team Flensburg University, Germany

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

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:

Distance Hull speed Elapsed time 100 metres 4 – 6 m/s (14 – 22 km/h) 17 – 25 sec 10 kilometres 2 – 3 m/s (7 – 11 km/h) 55 – 85 min

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. 1 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.

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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.

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Ship speed [m/s]

Hul

l Res

ista

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[N]

A

L/D=0L/D=0.3

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:

LgvFn ⋅= / 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:

3/1/VL 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

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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:

4>stern

s

gz

v Eq. 2.3

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

sternsternstern AgzF ρ21= Eq. 2.4

With: vs = design speed zstern = dept at stern Astern = Stern area below waterline g = gravity acceleration = 9.8 m/s2 ρ = 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 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.

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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, CF • Spray resistance, Cspray • Induced resistance, Cinduce • Wave resistance, Cwave

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The total resistance can be expressed by:

waveinducesprayFD CCCCC +++= 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:

2)2(Re)/(075.0 −= LOGCF Eq. 2.6 With:

6188.1/Re −= Evc 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]:

369.4

)03.0036.0(

−

−=

E

Cct

CF

spray Eq. 2.7

With: CF = 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]:

AR

2

⋅=

πL

induceKC

C 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 CL = lift force AR = aspect ratio of the wing foil

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

)2

(2 22

2

FhExp

Fc

CC L

wave−= Eq. 2.9

With: CL = 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.

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Hul

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Hydrofoilflight elevation energy

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.

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effect of weight reduction

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]:

3/2∇PA

Eq. 2.10

With: Ap = 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

2.2 Propulsion power When designing a hull, minimum resistance is the prime focus for waterbikes. Designing a hull for minimum resistance however, depends on the sailing speed under which the performance should be best. Design speed is related to hull resistance, depending on the available propulsion power and efficiency loss. Therefore it begins with starting from the available propulsion power.

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The power that humans can provide depends on a lot of factors: body shape, age, training, pedal revolutions per minute, leg position, etc. Figure 2.9 shows an indication of human power over time. Measurements [4] were carried out on a home trainer in a laying configuration. The persons involved had ages of about 25 years and from Holland (where everybody has a bike). It is expected that reducing the laying angle gives some increase of power over time. This is due to the fact that blood supply towards the legs improves. Bikes on flat roads can go faster when the biker is laying extremely backward and the air resistance reduces drastically. In case of boats, speeds are much lower and the influence on air resistance is less, but not negligible. In many cases a laying configuration is also preferred because of ship stability behaviour against heeling.

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Time [min]

Hum

an p

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[W]

well trained male

good trained male

used to biking male

untrained female

Figure 2.9 Human power versus time, measured on a home trainer in a laying configuration

It also appears that the rates per minute preferred by humans in order to supply power vary in relation to the time period that power has to be provided along a range of 60 to 110 rates per minute. Figure 2.10 gives an impression of the average cycling rates per minute for humans [4].

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[rpm

]

average for humans

Figure 2.10 Cycling rates per minute, preferred by humans for their power supply

2.3 Hull resistance With the power supply being available, as indicated in the previous paragraph, energy to overcome the hull resistance for moving forward can be provided. In Figure 2.11, the different resistance characteristics are shown for the hull types being considered. The characteristics are an indication for waterbikes, carrying 2 persons with a boat length of 6 meters. They depend on main dimensions, hull shape, trim and weight of the waterbike. For the hydrofoil, the

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wings and struts are included. Appendages such as rudders and propulsion shafts are considered as having minor influences and being equal for all configurations. L/B is the length versus beam ratio of the different hull types. The hydrofoil consists out of a slender mono-hull with side hulls and a large wing amid ship. From the resistance characteristics, the hull energy can be derived, Figure 2.12.

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[N] Slender mono-hull,

L/B=12

Catamaran, L/B=14

Hydrofoil

Planing hull(estimate), L/B<5

indicative

Figure 2.11 Indications of ship resistance versus ship speed, 4 hull types

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Slender mono-hull, L/B=12

Catamaran, L/B=14

Hydrofoil

Planing hull(estimate), L/B<5

indicative

Figure 2.12 Indications of hull energy versus ship speed, 4 hull types

3 Results By deriving the available power supply by a human from Figure 2.9, and transferring this towards the hull energy presented in Figure 2.12, the instantaneous speed can be determined for each hull type. By integrating the speed over time, the distance being passed can be calculated. Figure 3.1 shows the required time to sail distances beyond 10 kilometres. Figure 3.2 gives an indication of the energy consumption in relation to the distance. Again the figures are shown for a short distance scale up-to 100 metres, referring to Figure 3.3and Figure 3.4. The figures that are presented show ideal estimates of waterbike performances and energy consumptions. In practice, a considerable amount of energy is lost when transferring human power into ship speed. Elements that introduce energy loss/consumption are:

• Additional water resistance of appendages such as rudders and propulsion shafts; • Additional wave resistance due to undesired longitudinal trim of the hulls;

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• Mechanical losses of the shafts, chains and gears of the propulsion unit; • Propeller / peddle wheel losses; • Air and wave resistance due to weather conditions on channels and lakes; • Take-off energy to get airborne in case of hydrofoils • Stabilizer losses in case of active stability control of unstable waterbikes and hydrofoils

Therefore the results being presented are only useful for a comparison purpose between different hull type performances related to the human power supply. Efficiency losses can vary significantly between different waterbike propulsion designs and their manufacturing.

Ideal time records, good trained males(no efficiency losses)

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time

[min

] slender mono-hull

Catamaran

Hydrofoil

planing hull

Figure 3.1 Elapsed time versus long distance (beyond 10km) for different hull types

Ideal energy consumption, good trained males(no efficiency losses)

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Distance [m]

Tota

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cons

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slender mono-hull

Catamaran

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planing hull

Figure 3.2 Energy consumption versus long distances (beyond 10km) for different hull types

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Ideal time records(no efficiency losses)

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Distance [m]

tim

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ec]

slender mono-hull

Catamaran

Hydrofoil

planing hull

planing, welltrained males

Figure 3.3 Elapsed time versus short distances (100m) for different hull types

Ideal energy consumption(no efficiency losses)

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planing, welltrained males

Figure 3.4 Energy consumption versus short distances (100m) for different hull types

When comparing the different hull types in relation to their long distance and short distance performance, the following conclusions can be made:

• Long distance performance. In case of a long distance sailing of 10 kilometres, the best performing hull types are slender mono-hulls and catamarans. Hydrofoils show less good performance because they cannot manage to continue flying. Being afloat, they have to cope with hull resistance and wing resistance. Planing hulls perform poor due to the fact that they are not planing and because they have a large wave resistance in comparison to the other hull types.

• Short distance performance. In case of a short distance race of 100 metres, hydrofoils are the most fast. Their hull is lifted out of the water and the wing underwater makes it possible to sail efficiently at high speeds2. Planing hulls can be fast, if enough power is supplied and planing mode is guaranteed for the whole distance. Figure 3.3and Figure 3.4 show the curves for a planing mode with well-trained males pushing the pedals. After 70 metres the required time to overlap distance increase drastically. Also the required energy increases at the same moment. In planing mode, the required energy is about equal to slender mono-hulls and catamarans. In case of not planing, the required total energy consumption is larger. Well-trained males consume even more energy than good trained males due to the fact that the well tained mails sail with a speed closer to the resistance hump.

2 With this comparison it is assumed that the hydrofoil is already airborne before start. In case of starting at zero-speed, the performance in terms of time becomes less. The amount of energy required increases slightly.

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Also it can be concluded that the performance of catamarans and slender mono-hulls is about similar. Figure 3.5 shows an exciting competition between slender mono-hull Macbath from Delft Waterbike Technology and catamaran l’Ordegno from Triëste Waterbike Team, at the International Waterbike Regatta 2002 in Genoa, Italy.

Figure 3.5 Competition between slender mono-hull Macbath (close) and catamaran l’Ordegno (far)

4 Discussion Designing a waterbike that performs well at high-speed during a 100 meters sprint, a long distance of 10 kilometres is quite a challenge. Not a single hull configuration performs best for both distances and a multiplicity of design constraints and uncertainties of theoretical models result in multiple iterations and attempts. The propulsion power is limited to the leg power of the sportsmen that are pushing the pedals. Besides that, all energy losses result into reduction of speed. And because the torque that occurs in the propulsion shaft can sometimes be larger than in a car, a reliable structural design of the propulsion unit with low friction is inevitable. Transferring the human energy towards the hull energy includes energy losses. Underestimating these losses is one of the main reasons why waterbike designs do not perform as expected. Other causes are: Exceeding of the total waterbike design weight, excessive backward trim of the hull at high sailing speeds and poor ergonomics due to excessive laying position backward. Looking at the diversity of conceptual designs of waterbikes it is shown that there is not a single concept that performs best overall. It is always a combination of design choices that make the difference.

5 References [1] Ir. J.Pinkster,

“MT113, Ship Design IV”, University of Delft, 1994 [2] Ir. Raven,

“User guide CATRES”, version 3 report no X.47142-2-RF, MARIN Wageningen, Oktober 1988 [4] Different authors DWT,

“Flying Delft Blue”, internal technical report about development of hydrofoil “Flying Colours”, Delft Waterbike Technology (DWT), The Netherlands, 1991

[3] Different authors DWT, “Het project Nederwood”, internal technical report about development of planing hull Nederwood, Delft Waterbike Technology (DWT), The Netherlands, July 1996

[4] Different authors DWT, “Page”, Internal technical report about development of slender mono-hull “Macbath”, Delft Waterbike Technology (DWT), The Netherlands, July 1997

[5] Walree, F. van, Resistance Prediction Method for Hydrofoil Craft, Laboratorium van scheepsbouwkunde TH Delft, rapport no. 690-S 1985

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