J Mar Sci Technol (2001) 6:31-41 Journal of _
liarine Science
and TiElwIiif
©SNAJ 2001Development of a single-handed hydrofoil sailing catamarae
Y A S U H I K O INUKAI^'^, KOUTAROU HORIUCHI^, T A K E S H I K I N O S H I T A \ HIROMASA K A N O U ^ , and H I R O S H I ITAKURAI
'Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan ^ Japan Solar- and Human-Powered Boat Association, Shizuoka, Japan
^Ishikawajima-Harima Heavy Industries, Yokohama, Japan
Abstract A new, high-speed, recreational dinghy has been developed. It is a catamaran with submerged hydrofoils, which allow the crew to control the trim and heel balances. The two hulls are allowed to rotate about a main beam.The hydrofoils, which are attached below each hull, change the angle of attack independently, and the difference between the lift forces act-ing on each hydrofoil makes the catamaran stable. The stabil-ity of the boat is examined by numerical calculations and one-third scale model tests.
Key words Sailing catamaran • Hydrofoil
Introduction
Sailing and windsurfing are very enjoyable recreations. Sailing dinghies are much slower than sailboards. A standard dinghy sails at 6 or 7 knots i n a w i n d of 10m/s, whereas a sailboard moves at more than 20 knots in the same wind. I f a recreational dinghy could sail at more than 20 knots and can be carried on top of a car like a sailboard i t would be very popular.
Wave resistance prevents conventionally shaped yachts f r o m sailing at high speed. One way to overcome this limitation is to l i f t the hull above the water surface won a hydrofoil, either submerged or piercing the surface. A surface-piercing boat with a hydrofoil can balance automatically by adjusting the area of the hydrofoil. However, such a boat is apt to be heavy, the hydrofoils are inefficient, and the influence of the waves causes serious problems.
O n the other hand, a boat with submerged foils is hardly affected by the waves, but i t is difficult to main-tain the t r i m and heel balance. I n particular, a sailing boat changes its heel moment dramatically at high speed. Therefore, a sailing boat with a submerged f o i l has not been practical i n the past. I t is, however, more attractive as a recreational sailing boat than one with a surface-piercing f o i l , because a fast light boat can be designed which uses the hydrofoil efficiently.
I n this work, we developed a new kind of high-speed sailing boat with submerged foils, which has good t r i m and heel balance. The stability of the boat is examined in this study using numerical calculations and model tests.
Design of the boat
We designed the boat shown i n Fig. 1.^ The design concepts, the system of controlling the t r i m and heel balance, and the shape of the hull were decided i n the manner described below.
Concept of the boat
We considered a recreational dinghy with the following characteristics: it should be able to take o f f at normal wind speeds (about 5m/s); it should sail at more than 20 knots i n a strong wind (over 8m/s); an amateur sailor should easily be able to sail alone; i t should be possible to carry i t on top of a car (i.e., maximum length 4.5m); the crew should be able to move about on the deck to balance the boat.
Address correspondence to: T. Kinoshita (kinoshit@iis.u-tokyo.ac.jp)
Received: September 14, 2000 / Accepted: July 3, 2001
System of controllmg the attitude of the boat
As mentioned above, this refers to the system of con-trolling the heel moment and height of the boat above the water.
Fig. 1. The basic concept of the boat
Fig. 2. The general arrangement of Avocet
System of controlling the heel moment. The heel mo-ment of a conventionally shaped boat is controhed by changes to the center of gravity and the buoyancy, but this is not possible f o r a hydrofoil boat. We then con-sidered the controls oi Avocet, which was developed by Greg Ketterman f o r an attempt on the sailing speed record.2
Figure 2 shows the general arrangement of Avocet, which is a trimaran with submerged foils. I t is character-ized by two large plates like surfboards, which are set up on both sides of the main huU and allowed to rotate about a main pipe of aluminum. Submerged hydrofoils are attached below each plate. When Avocet sails i n a strong wind and the load on the leeward plate becomes heavier, the connecting beam of both plates is twisted, so that the angle of attack of the hydrofoil below the leeward plate becomes larger and the l i f t force i n -creases. Conversely, the l i f t force acting on the hydro-f o i l below the windward plate decreases owing to the smaUer angle o f attack.
Avocet uses this difference in l i f t forces between the two hydrofoils to control the heel balance.
- pivot The surface water p ^ i - - , , ^ / arm planing plate \ V stmt ^ ^ - h y d r o f o i l
Fig. 3. Equipment to control the height above the water of a human-powered vehicle
We apphed the principle of this system to control the heel balance to a catamaran i n which each hull, func-tioning as one of the large plates, can rotate about the main beam.
System of controlling the height of the boat above the water. I n the field of human powered vehicles, many boats w i t h submerged hydrofoils have recently ap-peared i n Japan.3 These boats use the simple equipment shown i n Fig. 3 to control the height above the water. I n this system, the angle of attack of the hydrofoil changes depending on the position of the hull, so that the plan-ing plate always follows the water surface, and the planing plate, strut, and hydrofoil can rotate about the pivot. Therefore, by adjusting the angle o f attack of the hydrofoil automatically, the hull can control its height above the water.
We adopted this equipment f o r our boat because it has been confirmed that a human-powered vehicle with this equipment can run stably on still water at least.
Generally, a boat with submerged hydrofoils, which has pivoted foils such as those shown i n Fig. 3 i n the f r o n t and fixed foils at the rear, takes off in the following way. A t flrst, the f o r e f o i l has a large angle of attack because the planing plate floats over the water. A s the boat begins to run, the bow rises up and the attack angle of the rear foils becomes larger. Then, the h f t force acting on the rear foils increases and the t a ü rises up. The boat keeps running i n f o ü - b o r n e mode as the l i f t force acting on the rear f o i l balances the one acting on the fore f o i l .
Shape ofthe boat
Arrangement of hydrofoils. The boat is designed as a catamaran with a single sail. A l t h o u g h Avocet is a trimaran with two sails, we considered i t to be too large for a pleasure boat. Each huh of the catamaran has a pivoted f o r e - f o i l which controls the height of the huU above the water, and a fixed rear-foil which supports
Y. Inukai et al.: Single-handed hydrofoil catamaran
Fig. 4. The arrangement of beams in the torsional boat
most of the weight of the boat. The struts of the fore-foil also function as a rudder.
Area of hydrofoils. Generally, a boat with a large f o i l takes off quickly, but when it is foil-borne its speed gets slower. Therefore, the hydrofoil of a human-powered vehicle usually has small hydrofoils in order to r u n faster when it is f o ü - b o r n e . However, we designed this boat with foils which were as large as possible so that the boat could take off quickly and remain stable i n a variety of sea conditions, because a large thrust is avail-able in a strong wind in the case of a sailing boat but not in a human-powered boat. I n particular, the fore f o i l needs to have a large area i n order to avoid pitch poll, which means that the bow submerges suddenly in blow. Thus, we referred to the area of the hydrofoils of Cogito, a human-powered catamaran with submerged hydrofoils developed by Yamaha^ (Hamamatsu, Japan), and decided that the area of the main foils of the boat should be twice the size of those in Cogito, and the area of the fore foils of the boat should be four times the size of those i n Cogito (here, the area of the hydrofoil is a nondimensional number)
Beam. We designed the beams as shown in Fig. 4 to |)roduce a torsional catamaran. Each huh of the catama-ran rotates about the fore beam (main beam), which is connected to each hull. The rear beam pierce the huh only through an inner bracket so as not to disturb the rotation.
Sail We used windsurfing sails because the boat needs a good performance at high speed.
For Cogito, the required thrust is estimated to be about 10% of the total boat weight, and the boat speed needed f o r take-off is estimated to be about 4 m/s. Therefore the necessary sail area f o r a boat whose weight is about U O k g (boat 50kg + crew 60kg) to take
33 Table 1. The principle parameters of the boat
Length and width 4.5m X 1.6m Hydrofoil area Main foil 0.08m2x2
Fore foil 0.04 m^ x 2
Sail • Its for windsurfing
Sail area 6 m'
Total weight 110kg
(boat 50 kg + crew 60 kg)
off in a beam wind of 5 m/s is estimated to be about 6 m^, which is the average sail area f o r windsurfing. Table 1 gives the principal parameters of the boat.
Numerical calculations
We calculated the static equilibrium and the dynamic stabihty of the boat when i t is foil-borne.'» As the inhial values of trim and heel and the initial angle of attack of the hydrofoils f o r iterative calculations, the results of the model tests were applied.
Coordinate system
We defined a body-fixed system, o-xyz, as foUows. The origin is located i n the middle of the main beam. The X-axis is taken i n the direction of the line that connects the middle of the rear beam and the origin, and the y-axis is taken in the direction of the main beam. Furthermore, to describe the motions of the plan-ing plate, fore strut, and fore hydrofoil around the pivot, we defined the fore-foil fixed system as that i n which the origin is located at the pivot (p), the plane o^f-x^jy^j is parallel with the plane o-xy of the body-fixed system, and the plane o^j-x^jZ^j coincides with the plane of the fore strut. The subscript indicates which side the pivot is located on: j = 1 denotes the system on the starboard side, while ƒ = 2 denotes the system on the port side.
Coefficient of torsional rigidity,
Each hull of the boat rotates independently about the main beam. T o describe the torsion of the boat (the rotation of the boat around the main beam), the coeffi-cient of torsional rigidity, K^, is defined by the equation
M b , - M , , = /^„-77 (1) where M^, is the moment of the right hull about the
main beam, Mb, is the moment of the left hull about the main beam, and r\ is the torsional angle of the boat (i.e., the angle between the main beam and the rear beam). Here, i t should be noted that 7C„ is a dimensional coeffi-cient with units of kg-mVs^. 7C„ - 0 means that both hulls
rotate independently, and /C„ = oo means that the boat is rigid and cannot rotate about the main beam.
Assumptions used in the analysis
The numerical calculations have been done with the foUowing assumptions:
— the surface of the water is flat;
— both hulls are located above the water and the hy-drodynamic forces act only on the planing plates, struts, and hydrofoUs;
— the aerodynamic force acting on the crew and the boat are ignored;
— cavitation and ventUation do not occur;
— the hydrodynamic force acting on the hydrofoils is in a quasisteady state;
— the rotation of the hulls about the main beam does not influence the rotation of the fore foils about the pivots;
— when the boat saUs in a steady state, the planing plates always follow the water surface, and the state i n which the planing plates do not touch the water surface is regarded as being unstable;
— the wash of the f r o n t foUs has no influence on the main foils.
Performance tests on the hydrofoil
I n order to obtain the coefficients of the hydrodynamic forces acting on the hydrofoils and the planing plates, we carried out force measurement on the hydrofoils and the planing plates on a one-third scale model i n a water channel, and compared the results w i t h the values given by Wadlin's formulae (Eqs. 2 and 3 ) , " which estimate the l i f t force and drag force of a hydrofoil, including the effect of the free surface.
üf^nA da nA + ao{l + T:)
where
( 2 )
and is the three-dimensional h f t coefficient, ƒ is the depth at one-quarter of the chord length, A is the aspect ratio, c is the average chord length of the f o i l , a^ is the graduation of the two-dimensional l i f t coefficient, r a correction factor f o r the foil form,« and a is the angle of attack.
CV ' ^DO + ^L3
nA . W 2
-(3)
where C^^ is the three-dimensional drag coefficient, t / i s the boat speed, CDO is the drag coefficient of the f o i l f o r m
: 2 C ^ - ^ l - f 1.2 -i-60
Q is the coefficient of skin friction of a plate (= 0.455/ (log,oRe)2-5s), t is the thickness of a f o i l . Re is the Reynolds number (= Uciv), v i s the kinetic viscosity.
cr = A A + 12 U A A' . ( f ^ + 4
Figures 5 and 6 show the l i f t and drag coefficients plotted against the angle of attack of the main f o i l and the fore f o i l when the flow velocity is 0.6m/s. I t was
Y. Inukai et al.: Single-lianded hydrofoil catamaran 35 U g o to O O 4=; 4 ^ -0:5- ..Of,:-0 angle of attack (deg)
..0
Fig. 5. Lift coefficient vs. angle of attack of the main foil and the fore foil. Solid diamonds, main foil (measured); open
dia-monds, main foil (Eq. 2); solid triangles, fore foil (measured); open triangles, fore foil (Eq. 2)
Ü
Angle of attack, a.pi.te (deg)
Fig. 7. Lift coefficient vs. the angle of attack of the planing plate. Solid squares, measured; Ime, Eq. 5
Q U o o —955— n i 3 A .•'A n 1 ^ V * A U. i - J n 1 U. i A A > - • • e - ' 0 5 10 Angle of attack (deg)
15 20
Fig. 6. Drag coefficient vs. angle of attack of the main foil and the fore foil. Solid diamonds, main foil (measured); open
diamonds, main foil (Eq. 3); heavy broken line, main foil (Eq.
4); solid triangles, fore foil (measured); open triangles, fore foil (Eq. 3)
f o u n d that the experimental values of the l i f t coeffi-cients of both foils correspond very well with the theoretical values. However, Fig. 6 shows that the ex-perimental values of the drag coefficient of the main f o i l are greater than the theoretical values. We then applied E q . 4, i n which C^^ is larger than i n E q . 3, to the calcu-lation of the drag coefficient of the main f o i l .
^ D 3 ~ ^DO + 1-36C^3
8;r nA
(4) W e also measured the resistance of a full-scaled planing plate (Figs. 7 and 8). We applied the approximations in
0.3
I
0.25 y 0.2 a o 0.158
0.05 LJ ^ 5 10 • 15 Angle of attack, apj^te (deg)20
Fig. 8. Drag coefficient vs. the angle of attack of the planing plate. Solid squares, measured; line, Eq. 6
Eqs. 5 and 6 to the calculations i n relation to the planing plate.
Qpiate = 2.86ap„j, (5)
C n p „ „ = 0.016+ 0.38Cip„„. (6)
where Qpiate is the l i f t coefficient of a planing plate,
Copiate is the drag coefficient of a planing plate, and c^.^,^ is the angle of attack of a planing plate.
Static equilibrium
We assumed that the boat has nine degrees of freedom (six of them being about the origin of the body-fixed system, the rotations of the fore hydrofoils on both sides about the pivots, and the rotation of each huh) and solved the equations of these nine dimensions i n terms of static equilibrium.
The l i f t forces and drag forces induced by the foils, struts, and planing plates were found by assigning coefficients derived f r o m Eqs. 2-6. The l i f t and drag coefficients on the sail were taken f r o m the literature."
4.5 6.5 8.5 10.5 12.5 14.5 Vrw (m/s)
Fig. 9. Boat speed, U, vs. the real wind speed, at 7f„ = 0kg-mW 12 10
1
5.5 6 6.5 Vrw (m/s) 7.5Fig. 11. The boat speed, f/m/s, vs. the real wind speed, V^ml s, atX„ = 50000kg-m%2 _ 4 bo OJ I 0 - 4
\
1 8a.-
1 2 1 4 1 Vrw (m/s)Fig. 10. The torsional angle of the boat, 7;°, and the angle of attack of the main windward foil, a°ai„i, vs. the real wind speed, K„m/s, at = Okg-m'/s'
Sailing conditions at various velocities of the reed wind. Figure 9 shows the boats speed in the x-direction, U m/s, plotted against the real wind speed,
ni/s, at = Okg-mVs^. We made the following assumptions:
— the boat sails w i t h a beam wind;
— the crew is in the most exposed position on the deck in the x-direction, and i n the middle of the deck i n the ^'-direction.
The boat sails at a speed of 20 knots at V,,, - 8.5m/s, and with a speed of 35 knots at y^iv = 15 m/s according to the calculations. Figure 10 shows the torsional angle of the boat, r\°, and the angle of attack of the main wind-ward f o i l , a°^aini (subscript 1 indicates the windwind-ward f o i l ) , plotted against at / f „ = Okg-m^/s^. I n a strong wind (Fj„ > 8 m/s), the boat is twisted and the angle of attack of the main windward f o i l , a5^ai„i, becomes nega-tive. W i t h a negative lifting force acting on the main
<
4 3 2 1 0 -1 -2\
i 5 5 f ) 6 5\
7 5 ki
i Vrw(in/s)Fig. 12. The wetted area of the windward planing plate, ^piaieini''10-^> vs. the real wind speed, F,„in/s, at /C„ = 500dOKg-mVs'
windward f o i l against the greater heel moment caused by the wind, the boat can maintain static balance re-gardless of the velocity of the real wind.
Sailing conditions at various torsional rigidities, K„. Figure 11 shows U plotted against at K„ = 50000kg-m%^. The boat cannot maintain static balance at > 7 m/s according to this calculation. The assump-tions of the wind direction and the crew position are the same as i n the previous section.
Figure 12 shows the wetted area of the windward planing plate, Apiaj^im^-lO-^ (the subscript 1 indicates the windward planing plate), plotted against at = 50000kg-mW. The wetted area of the windward plan-ing plate, A p i j i e i , approaches 0 near = 7m/s. This suggests that the windward planing plate cannot follow the water surface at Vj„ > 7 m/s and the boat loses static equilibrium.
Figure 13 shows the maximum value of K„ at which the boat can maintain static equilibrium against y,„. We
-Y. Inukai et al.: Single-handed hydrofoil catamaran 37
200000 160000
s
120000 to 80000 40000 » 5 7 9 11 13 15 17 Vrw(m/s)Fig. 13. The maximum value of /C„ at which the boat can maintain static equilibrium
15
10
0) - aI
-10
u
—u
— 1 60
8 •^ t
2— 41
—r
61
J— 8 2ratio of the designed sail area
Fig. 14. The boat speed, U(m/s), and the torsional angle of the boat, 7]°, with the various area of sail, at K„ = Ofks-mVs'), V = 8(m/s)
15
10
03 0)5
Cr-0
E ,-5
-10
... u
... u
) Q1 5
J ! 2ratio of the designed area of the hydrofoils Fig. 15. The boat speed, U(m/s), and the torsional angle of the boat, 7?°, with the various area of both main and fore foils at K = O(kg-mVs'), l / „ = 8(m/s) w .2 0 "o 0 CD
1
-:r— ^ 7 5-\
0."5-\
).25 1.2 - 1 -C ).4 - ( 0 ).2 0 * - 1\
).25 0.5 the c r e w position in t h e X direction (m)Fig. 16. The position of the crew needed to maintain static equilibrium at various values of the coefficient of the torsional rigidity. Circles, = 0; diamonds, 7^„ = 20000; triangles, K„ = 40000; stippled squares, = 60000; stars, = 80000
now move the crew to the optimum position with each value o f i n order to maintain static equihbrium f o r as long as possible. The boat remains i n static balance at K „ < 7m/s regardless of the size of K„. However, when is greater, the boat cannot maintain static balance at large values of K^. For example, a boat w i t h K„ = 80000kg-m%2 cannot maintain static balance at = 9 m/s.
Thus, we can see that i t is very important f o r the value of K„ to be small f r o m the point of view of the static equilibrium of the boat.
Sailing conditions with various areas of sad and hydrofoils. Figures 14 and 15 show the boat speed, Um/s, with various areas of the sail and hydrofoil, i n the x-direction at K„ = Okg-mVs^, T/„ = 8m/s. Here, the value on the X-axis i n these figures indicates the ratio of the sail or the hydrofoil area to the original design shown in Table 1. Figure 14 shows the effects of changing the
area of the sail but not of the hydrofoils, and Fig. 15 shows the effects of changing the area of the hydrofoils but not o f the sail. F r o m Fig. 14, i t can be seen that with a larger sail the speed does not necessarily increase i n relation to the increased area of the sail, and the tor-sional angle of the boat gets larger. This suggests that a boat with a large sail cannot sail efficiently because of a large heel moment. Figure 15 shows that a boat with larger hydrofoils gets slower and the torsional angle is reduced.
The movement range ofthe crew with various values of K„. Figure 16 shovv's the movement range of the crew for various values of K„ at y „ = 8m/s. The area plotted i n the figure represents the deck. A t lower values of K^, the boat can maintain balance when i t is foil-borne if the crew moves diagonally across the deck at the angle shown. This suggests that the torsional boat is easy to handle.
0.5 0 -0.5 -1 -1.5 - 2 1 1 1 Kn=0(kgm2/s2) -=-Kn=10000(kgm2/s2) Kn=0(kgm2/s2) -=-Kn=10000(kgm2/s2) ?..,_ ) 1 1 1 i 15 •'• V r w (m/s)
Fig. 17. Parts of the roots of Eq. 7 vs. the real wind speed, K„,m/s
Pulley block
Fig. 18. The test equipment
when i t was hull-borne, which is difficult to estimate by calculations.
Dynamic stability
Ciiaracteristic equatioti. The dynamic stabihty of the boat is estimated by examining smah displacements away f r o m static equihbrium. We assumed that the crew could control the yaw motion, i.e., the rotation around the z-axis of the body-fixed system, by steering w i t h the rudder. Hence, terms relating to yaw motion are ig-nored. The corresponding homogeneous f o r m of the equation of motion is taken, and the unknowns («, V,. . . ) are replaced by (u^e'^, v^e^,. . . ) , which leads to the characteristic equation
-f + . . . a„i = 0 (7)
The boat is regarded as stable when the real parts of all the roots of E q . 7 are negative or zero.
Results. Figure 17 shows the real parts of the roots of Eq. 7 plotted against K „ at = 0 and 10000 ( k g - m W ) . Here, to avoid confusion i n the figure, only the solutions which change the sign of the real part i n different condi-tions are shown. We can see that the boat is unstable in a weak wind immediately after taking o f f f r o m the water, but after that the boat sails stably as far as it is considered to be quasisteady.
Thus, we find that i t is very important f o r the hull to be able to twist f r o m the point of view both of static equilibrium and dynamic stability. I t also shows that the boat can saU at high speeds in a wide range of wind speeds.
Model tests
The stability of the boat was confirmed by the calcula-tions given above. We also carried out towing tests on still water and i n waves, and sailing tests on the sea. We examined whether the model actually runs stably and at the same time we observed the behavior of the boat
Towing tank tests on still water
We carried out the towing tests on a model without a sail i n the towing tank of the Institute of Industrial Science, University of Tokyo (1.85m x 20m x l m ) , to observe the behavior of the model when it was hull-borne, and to find the inhial angle of attack and poshion of the hydrofoils f o r it to be able to take o f f with the lowest possible thrust.
We made a one-fifth-scale model and a one-third-scale model. W e used the smaller model f o r the initial tests because the effectivè length of the tank, about 10 m , was too short f o r us to use the larger one. W e used the larger one f o r the sailing tests because the smaller one could not carry the large servomotors which are needed f o r sailing tests. We also carried out towing tests on fhe larger model.
The test equipment is shown i n Fig. 18. Three strung puUeys were arranged at each end and at the center. The plummet strung on the center pulley gave the model thrust and balanced the resistance of the model. The velocity of the model was measured by counting the number of revolutions of the center pulley w i t h a speed indicator designed f o r a bicycle (Cat Eye Co. L t d , Cateye Astrale, Osaka, Japan). The angle of the fohs was measured by an angle gauge. The t r i m angle of the hull was measured by eye.
We found that these were differences i n the perfor-mances of the one-third-scale model and the one-fifth-scale model. This is beheved to be because the Reynolds numbers of the models are different, and the hydrofoils of the one-fifth-scale model are too small to be shaped precisely. When adjusting the hydrofohs, we relied mainly on the results f r o m the one-third-scale model because the performance of this hydrofoil had been confirmed by the tests.
I n Figs. 19-21, the boat speed has been converted to that of a full-scale boat, and the boat's resistance is shown as a ratio of the boat's weight. Figures 19-21
Y. Inukai et al,: Single-handed hydrofoil catamaran 39 CD
I
28 24 20 16 12 8 4 01
Xa*' / 0 1 2 3 4 5 Boat speed (m/s)Fig. 19. The resistance vs. the boat speed with various upper-limit angles of the fore foil. The upper upper-limits of the angle of the fore foil were: diamonds, 2°; squares, 4°; triangles, 6°; crosses, 8°. The initial angle of attack of the main foil was 0°. The burden of the fore foil was 30%
24
g
20
16
Or;
cq12
CO • i-H8
GO CO p<4
0
i
\
r0 1 2 3 4 5
Boat speed (m/s)
Fig. 20. The resistance vs. the boat speed with various initial angles of attack of the main foU. The initial angles of attack of the main foil were: diamonds, 0°; squares, 1.5°; triangles, 3°;
crosses, 4.5°. The upper limit of the angle of the fore foil was
6°. The burden of the fore foil was 20%
show the results f o r the one-fifth-scale model only, because the one-third-scale model without optimum adjustment often reached the end of the tank while stih accelerating and without taking off. Therefore its true velocity could not be measured, although with optimum adjustment true velocity could be measured without incident.
Upper limit of the rotational angle of the fore foil The rotation of the fore f o i l must be limited to the correct range i n order to take off with the lowest thrust. We examined the resistance against the velocity of the model with various upper-limit angles of the fore f o i l (Fig. 19). I n all eases, the lower limit was set at - 2 ° .
I t was observed that the model w i t h a smah upper-limit angle could not take off quickly, while the model with a large angle experienced much more resistance.
I n the one-third-scale model, the best upper-limit angle of the fore f o i l is about 9°, which is estimated to correspond to the angle of attack f o r the maximum l i f t coefficient according to the performance tests on the fore f o i l .
Initial angle of attack of the main foil We examined the resistance in relation to the velocity of the model with various initial angles of attack of the main f o i l (Fig. 20). I t was observed that the model w i t h a smah angle cannot take o f f quickly, while the model with a large angle cannot take up the bow.
I n the one-third-scale model, the best initial attack angle of the main f o i l is about 3°, which was estimated
by calculating the maximum value of Q J / C D J according to the performance tests on the main f o i l .
Position of the main foil The behavior of the model before taking o f f strongly depends on the relative posi-tions of the main f o i l and the fore f o i l and the center of gravity. Having a longer distance between the main f o ü and the center of gravity means that the burden of the fore f o ü gets larger, and a shorter distance means that burden of the fore f o i l gets smaller. We examined the resistance i n relation to the boat's speed with various positions of the main foü. The position of the f o r e f o ü was fixed (Fig. 21). I t was observed that the model with a large fore f o i l burden could not take off quickly, while the model with a too small burden could not take o f f stably.
I n the one-third-scale model, we found that the proper ratio of the burden of the fore f o i l against the total weight of the model was 20%.
Resistance-velocity curve. The peak of the resistance-velocity curve appears just before take-off because the t r i m angle of the model is at the maximum value.
Towing tank tests in waves
We then examined the behavior of the model without a sail i n waves at various values of K^. The test was carried out i n the towing tank of the Department of Environ-mental and Ocean Engineering, University of Tokyo. The model was towed at a speed of 2.5 m/s (the
conver-24
0 1 2 3 4 5
Boat speed (m/s)
Fig. 21. Resistance vs. speed in various positions of the main foil. The burden of the fore foil was: diamonds, 15%; squares, 20%; triangles, 25%; crosses, 30%. The upper-hmit angle of the fore foil was 6°. The initial angle of the main foil was 3°
Table 2. The dynamic stabihty of the 1/3-scaled model towed at 2.5nr/s in the waves /C„ (kg-m%2) Wave 2 Wave 4 0 O O 20 O O 255 O X 3000 X X X{m) ƒƒ„ (mm) Wave 2 0.6 60 Wave 4 1.2 60
sion velocity to a full-size boat is about 4.3m/s). The model was connected to a fishing rod held by a man on the towing carriage. He moved transversely on the towing carriage to duplicate obhque waves.
When the model is towed i n head waves, it runs stably for aU values of /C„, but when i t is towed i n oblique waves, models with larger /C„ values are unstable. Table 2 shows the experimental results. (The values of 0, 20, 255, 3000kg.m%2 i n Table 2 correspond to 0, 1620, 20655, 243000kgm2/s2 in the actual ship.)
We observed that a model with a large value can not constantly follow the water surface when the differ-ences i n the relative motions of each h y d r o f o ü to the wave elevations become larger.
Sailing test
We carried out the sailing test of the one-third-scale model at Hamana Lake. We operated the model w i t h three servomotors (for the rudder, the saü, and a weight
Fig. 22. The one-third-scale model foil-borne in a wind of 5¬ 6 m/s on Hamana Lake
balancer instead of a crew) f r o m a motorboat which ran beside the model. The rotation of the model was set up to be free. The wind speed was measured with a wind-speed indicator Kestrel 2000 (Nielsen-Kellerman, Chester, U S A ) .
We observed that the model saüed stably i n a wind of 5-6 m/s. Figure 22 shows the foil-borne model.
We found that the model ran stably when foil-borne, even i n waves, as each huh rotated about the main beam. W h ü e hull-borne, the weight balancer moved to balance the boat against the heel moment.
Conclusions
We have designed a new type of sailing catamaran. Submerged hydrofoils are used to l i f t the huUs o f f the water to reduce the resistance. We confirmed that the system, i n which each hull is allowed to rotate about a main beam, functions efficiently when the heel moment is controhed. The stabihty of the boat was examined by numerical calculations and model tests. I t was con-firmed that the boat is remarkably stable under the design conditions.
Revised particulars
Finally, we revised the principal parameters, as shown i n Table 3, to satisfy the initial design concept in which the boat can take o f f in a slight wind of about 5 m/s and run at 20 knots i n a wind of 8-lOm/s. We estimated that the thrust required at take-off is 10% of the total weight of the boat as reported f o r Cogito, but i t was found that the one-third-scale model actually needs a thrust of 17.5% of the total weight of the boat (19% f o r the
Y. Inukai et al.: Single-handed hydrofoil catamaran Table 3. Revised principal parameters
Length and width 4.5 m X 1,76 m
Hydrofoil area
Main foil 0.124 m' X 2
Fore foil 0.062 m' X 2
Sail For windsurfing
Sail area 8.4m2 Total weight 115kg (= boat 55 kg + crew 60 kg) 10 12 Vrw (m/s) 14 16
Fig. 23. The boat speeds, U, of the original and revised boats vs. the real wind speed, V^„. Diamonds, revised; circles, original
one-fifth-scale model) at take-off according to the tow-ing tests. Although i t is expected that the influence of the laminar boundary layer on the prototype would be less than on the model (e.g., CDQ i n E q . 3 f o r the proto-type is less than f o r the model: C^o (protoproto-type)/Cj3o (one-third-scale model) = 0.82 at the boat's take-off speed), and the resistance of the prototype would thus decrease, the required thrust at take-off is expected to be larger than the initial estimation because of such details as strut splay.
41
Therefore, so that the prototype could take o f f i n a lighter wind, we enlarged the area of ah the fohs without changing the aspect ratio (span/chord). We make the span of the main foils l m (the span of the original boat was 0.8m). We also enlarged the area of sah, because the boat's speed could decrease with a larger f o i l area, as shown in Fig. 15. We used a sah of 8Am^ area i n order to sail at 20 knots in a wind of about 9m/s. Furthermore, in order to avoid increasing the torsional angle of the boat with the larger sah area, as shown i n Fig. 14, and make the sah inefflcient, we increased the width of the deck. We increased the width between the centers of each huh to 1.76 m to hold the torsional angle of the boat within 1° when taking off. The boat speed plotted against the real wind speed after the revisions is shown in Fig. 23. I t was found that the revised boat can saü when foil-borne i n a lighter wind than can the original boat.
References
1, Horiuchi K (1998) The concept of a fast sailing ship Twin Ducks (in Japanese), J Sailing Yacht Res Assoc 13
2, Kubota H (1996) Fast boat with 19,45 knots (in Japanese), J Human-Powered Veh Assoc 14
3, Yanagihara H (1994) Introduction of human-powered vehicle Cogito (in Japanese), J Human-Powered Veh Assoc 1
4, Masuyama Y (1983) Research on a sailing boat with hydrofoils (in Japanese). Doctoral thesis. University of Osaka
5, Wadlin K L , Shuford CL, McGehee JR (1955) Theoretical and experimental investigation of the lift and drag characteristics of hydrofoils at subcritical and supercritical speeds, NACA Rep 1232 6, Hoerner SF (1956) Fluid-dynamic lift. Iloerner üuid dynamics,
Brick Town, N,J,
7, Glauert H (1926) The elements of aerofoil and airscrew theory. Cambridge University Press, London
