Basic Design Goals and Philosophy          

The boats which use Sunhawk techniques have sail areas greatly in excess of normal designs and thus are capable of unusually high speeds.  This makes them fun and exciting for use in sailing games such as sailball and sailing frisbee - the intended uses for this technology.  The speed is particularly impressive at low to medium winds.  At high wind speeds the design emphases stability. 

Background

Countering heeling has been a challenge for designers of high performance sailboats for centuries.  The traditional approach with large monohulls has been to use a heavy weight on the keel.  For dinghies, normally heeling is countered by the skipper or crew hiking out to windward.  Catamarans separate their hulls, and when sailing on one hull, there is a long lever arm and thus righting moment to oppose heeling.  However, there are disadvantages to all previous approaches, and all are limited in their ability to compensate for heeling in very high winds.  Also, in many cases anti-heeling techniques optimized for a particular wind condition work poorly for another. 

The Sunhawk approach uses a different solution to the heeling problem, the use of negative and positive lifting hydrofoils on windward and leeway sides of a boat.  Of course, it, too, requires balancing advantages and disadvantages of design features and making judicious trade-offs; however, frequently it provides overall superior performance to classic approaches.

Fundamental Concepts

It is difficult to design a sailboat which performs well in all wind conditions and points of sail because aerodynamic and hydrodynamic forces vary as the square of speed.  The Sunhawk family of products is intended for use over a range of apparent wind velocities from 2 to 20 knots.  Thus these forces can vary by 100 to 1.  The Sunhawk technique is more flexible than the traditional methods used on monohulls and catamarans.  The keel of a monohull and the distance between hulls of a catamaran must be designed to accommodate the maximum wind speed, and both features can be a detriment at low speeds where less anti-heeling is needed.  But, in the Sunhawk design the anti-heeling righting forces increase as higher winds generate faster boat speeds.  Also righting forces can be adjusted by varying how far the hydrofoils are pushed down into the water. 

Balance of Forces and Moments

During constant boat and wind speeds and directions, all the forces on the boat and their moments must be balanced [1.4]. Thus the forward component of the aerodynamic force on the sail must equal the hydrodynamic drag of the submerged parts of the boat; the sidewise force on the sail and the leeway force must cancel each other; and the heeling moment on the sail must be balanced by the moments of the foils, the skipper hiking out, etc. 

Analysis

Fundamental Assumptions

1. The goals of the sailball field are set at right angles to the true wind direction. 

2. 2.It is assumed that true wind speed is equal to the boat speed when the true wind is a right angles to the boat direction, and this is the case at all wind/boat speeds.
   

This assumption is based on an analysis of the Tornado catamaran[6.0].  The Sunhawk14SS is expected to behave like a cross between and monohull and a catamaran since it carries an unusually large and tall sail, has a planing hull, and rides partly on the outwardly curving hydrofoils on the leeward side, all of which produce boat speeds in excess of those usually experienced with monohulls.

3. The sailball game will not generally be played in apparent winds above 20 knots,

Overall Performance, Apparent Wind and Leeway

This analysis is based on those contained in Marchaj and Fossati.  The extent possible variable nomenclature conforms to that of these authors.

A sailboat is driven forward at a velocity of VS  by a wind VT.  This causes the sail to experience an apparent wind of VA,  which is at an angle β to the boat’s motion, which is the result of the true wind and the headwind VHD  produced by boat motion.  In the case being analyzed since the true wind and boat speed are equal, this angle is 45º.  The sail is set and a trim angle of δ m, the angle between the center line of the boat and the chord of the sail. 

The wind produces a force on the sail which can be resolved into two forces, one driving the boat forward, FR, and the other, FH, which causes it to try to slide sideways at the leeway angle, λ, and heel. The daggerboard produces a force, FS, to oppose the sideways motion and the curved hydrofoils of the Sunhawk apparatus produces windward and leeward forces, LFTHW and LFTHL, which oppose the heeling motion along with the skipper hiking out.  The action of the daggerboard produces in the leeway angle, the horizontal attack angle.  The forward performance of the boat can be viewed as resulting from the wind on the sail at the trim angle and the water impinging on the daggerboard at the leeway angle.  At a constant wind velocity and in the absence of any action by the skipper, the above water and below water forces and moments will balance each other, and the boat will continue on its course in the same direction and at constant speed.

Forces, Drags and Centers

An object forced through a fluid can generate various kinds of drag forces - skin friction, induced, and form (sometimes called “displacement,” “hull” or “wave”).  These forces can be viewed as originating at points - center of force on a sail, center of buoyancy on a hull, etc.  The forces can result in linear motion, e.g. sway, surge,  and heave, or rotational motion e.g. pitch, roll, and yaw.  The forces are defined in a cartesian coordinate system: x = direction of boat motion, perhaps across the page from right to left; y = direction into the page; and z = direction up from the surface of the water, up the page. 

All forces are derived from the force of the wind on the sail.  The object of the design is to idealize the useful forces, such as the forward force or the anti-heeling force, and the minimize the detrimental forces such as induced drag of a foil or the skin friction of a hull.  In the case of the Sunhawk technology, the objective is maximum speed at low and moderate wind speeds and optimum stability and safety at high speeds.  The objective for a racing boat, cruising boat or speed sailing boat is usually different.

In this analysis it is assumed that the boat is always approximately upright windward to leeward and forward to aft.  It is assumed that this disposition is effected in part by the position of the skipper.  However, since a small amount o heel can improve anti-heeling moment with little adverse effect on driving force, it may not always be desirable to sail perfectly upright.

Calculation of the Heeling Force

The first step in designing the anti-heeling apparatus is to determine force produced by the sail.  The heeling force can be determined from this, and using the sail plan, the center of force can be identified.  The the moment of the sail can then be calculated.  The Sunfish anti-heeling apparatus must be designed to produce a hydrodynamic moment which counters all or an appropriate amount of the heeling moment, taking into consideration the righting moments associated with the position of the crew and possibly the righting moment of the hull.  Throughout the process the drags of all aerodynamic and hydrodynamic drags must be minimized.

The formula for the total force, or lift, generated by a foil, aero or hydro, which is moving relative to a fluid, is [3.0]

Lift = C*π *ρ*V²*A*sin(T),        (1)                 (the asterisk, *, is the multiplication sign)

in which

C = a lift constant including the effects of aspect ratio, camber, turbulence, conversion of units (if needed), etc.,

ρ = density of the fluid,

V = speed of the fluid,

A = area of the foil, and

T = attack angle.

Rather than go through the calculation here a software program on the internet can be used to determine the characteristics, i.e., forces, moments, etc., of a sailboat. This software assumes a mainsail in the form of a right triangle so the dimensions of the Sunfish sail must be altered slightly to convert from the lateen form to a triangle.  The area of the triangle encompassing the sail for a SunhawkSS14 is 142 ft^2.  The long side of the triangle is 22.75 ft.  For the purposes of the software the short side of an equivalent triangle would then be 2*(142/22.75), or 12.48 ft.  Since the curved hydrofoils have a center of rotation at deck level and a radius of 2 feet, the sail on the boom must be about 2 ft 2 inches (2.1666 ft) above deck level so that the boom cannot not impinge on the hydrofoils.  The design philosophy calls for calculating the sail forces and moments for the case where the true wind is at right angles to the boat motion, and, as stated before, we assume equal wind speed and boat speed so the angle of the apparent wind to the direction of  travel is 45º. 

Thus the values of the  variables to be inserted in the software are:

P, main luff = 6.93 meters

E, main foot = 3.8 meters

BAS, distance from deck to foot = .66 meters

AWS, apparent wind speed = 5.14 meters/sec

AWA, apparent wind angle = 45º

The output of the software predicts:

Mainsail area = 167 ft^2     Note the difference between this value and the triangular area of 142 ft^2 is presumed to be a measure of the curvature of the roach and the camber of the sail.

Sail Drive, FR = 53 lbs

Sail heeling force, FH  = 92 lbs

Heeling moment = 893 ft-lb

Leeway, λ = 3.4º  Note:  Calculation of the leeway angle requires knowledge of daggerboard characteristics which are not inputted.  It is not know what assumptions have been made for this calculation.

Drive to heeling moment ratio = 1.43

Driving force coefficient = 0.824

Center of effort height % of rig height = 39%

Depowering factor = 1

Heeling force coefficient = 1.608

Rig Aspect ratio = 3.7

Lift coefficient = 1.72

Drag coefficient  = 0.554

These values result in:

Ratio of Lift coefficient to drag coefficient = 3.1

Ratio of driving force to heeling force = 0.58

Calculation of Performance of the Hydrofoils

From the performance of sail it is possible to determine the performances required of the hydrofoils and daggerboard.  This will depend not only on the results above but assumptions such as the maximum wind speed to account for, the weight of the crew and how far they hike out, the amount of lift allowable for the lee hydrofoil, the performance desired when close hauled, and allowable stresses on the righting apparatus, etc.  After the needed performance is determined the curvature, length, width, thickness and attack angle of the hydrofoils can be determined.  Along with this the characteristics of the daggerboard must be defined.

The hydrofoil analysis starts by determining the righting moments needed.  Two situations are analyzed - 10 knot apparent wind at 45º, the design median, and 20 knot wind at 45º, the upper end of the design wind range.  The righting moments for these two situations are 893 ft-lbs and 3593 ft-lbs. 

Assumption 1 - the crew weighs 200  lbs., consisting of either an adult skipper at 200 lbs. or two kids each weighing 100 lbs.

Assumption 2 - The crew does not hike out beyond the gunwale.  This give the crew that opportunity to hike out further to right the boat when a puff hits, and the increased wind has not yet translated into the increased boat speed necessary for the hydrofoils to oppose heeling.

Assumption 3 - The maximum amount of uncompensated lift allowable for the leeward hydrofoil is half the combined weights of the boat (150 lbs) and the crew (200 lbs) or 175 pounds.  If the windward hydrofoil produces negative lift, the lift of the leeward hydrofoil can increase above this limit.  The object of this situation is to lift the boat to reduce form and skin friction drags and facilitate planing without causing the boat to lift so high that it becomes unstable.

The 10 knot apparent wind condition:

The gunwale of a Sunfish is approximately 2 feet from the center line of the boat.  Thus a 200 pound crew generates 400 ft-lbs of righting moment, leaving 493 ft-lbs needed from the hydrofoils.  The midpoint of a fully extended curved hydrofoil is 3.25 ft from the center line of the boat.  Thus to completely provide for the addition moment, the lee hydrofoil must generate 152 pounds of lift.

The 20 knot apparent wind condition:

For this situation, the windward and leeward hydrofoil must make up the difference between the sum of the moments of the crew and the lee hydrofoil, or 2700 ft-lbs.  Adding equal amounts to each hydrofoil resuts in 1350 ft-lbs for the windward foil and 1843 for the lee foil. .   The lee moment must produce 567 pounds of force when the hydrofoil is fully extended.  The hydrofoil is 0.8 ft (9.5 in) wide and the submerged horizontal length is 2 ft so the area is 1.58 ft^2.  From this the needed attack angle can be computed. 

LFTHW = Kh* VS* VS* AH*sint,

                                                    in which Kh = π*ρ* CFkfs* CFkfs = 17.4,

                                                                                          VS   =  20*0.707 = 14.14 knots,

                                                                             LFTHW is negative lift.

Since at small angles the sine of the angle is equal to the angle in radians,

t = (360/2 π) 567/(17.4*14.14*14.14*1.58) = 57.3*567/5497 = 5.9 degrees.

It should be noted that the hydrofoils curve outward.  This is opposite of the approach used on most boats, but the outward curvature increases the hydrofoil’s lever arm when countering heel, which increases the righting moment.  Outward curvature has been tried on trimarans, but it was found that the effect of leeway angle negated some of the effect of hydrofoil lift.  In these trimarans, the hydrofoils are used for both leeway control and lift.  In the Sunhawk14, a separate daggerboard does most of the leeway function.  In order to minimized the problem identified with catamarans, the Sunhawk14 hydrofoils are set at the leeway angle.

The Sunhawk technology results in boats which have similarities to both planing monohulls and catamarans.  Generally boat speeds of monohulls are less than the true wind speed in moderate airs, and high performance catamarans achieve speeds higher than true wind speed [1.2]. 

In this simple analysis it is intended that the anti-heeling forces cause the boat to sail perfectly upright in all wind conditions.

Calculation of the aero and hydrodynamics forces and moments of even the simplest sailboats is a difficult task.  Many of the fundamentals can be found in Marchaj’s books,  Aero-Hydrodynamics of Sailing and his preceding book Sailing Theory and Practice.  More advanced treatment can be found in Fossati’s Aero-Hydrodynamics and the Performance of Sailing Yachts.  Since the object of the Sunhawk technology is to keep the sailboat upright, the simpler force and moment diagrams on page 10 of the second Marchaj book are used rather than the more generalized ones which account for a heeling angle.

The forces and moments are summarized in the page on Aero and Hydro Dynamic Forces and Moments on this site.

Settings of the Hydrofoils

There is a hydrofoil holder on each side of the boat.  Each holder allows at least two positions for its hydrofoil, including one for positive lift and one for negative lift. 

There are a great many possible ways of setting  the hydrofoils, depending on weather and sea conditions and the skipper’s preferences.  Normally two hydrofoils are used, one to windward and one to leeward; however, there are situations in which only one is used.  A hydrofoil can be totally or partially immersed, and the windward and leeward depth settings can be different.

For most Sunhawk equipped boats, heeling is countered by both the hydrofoils and lateral position of the hiking  crew.  Because hiking out does not generate drag, but the hydrofoils do, as a general rule, as wind speed increases anti-heeling is provided first by the crew and then supplemented by the hydrofoils.  Also the hydrofoils are not lowered any further than is necessary to achieve the desired purpose so drags are minimized.

On a run both hydrofoils can be fully withdrawn.

The hydrofoil setting determines not only the attack angle of the hydrofoil but the leeway angle.  Thus if the windward hydrofoil is set for positive lift in hopes of further reducing the apparent weight of the boat, it will be set at the wrong leeway angle and will not perform as desired.  It is, however, possible to design the hydrofoil holders to allow alternative leeway angles.  However, such designs would require total removal of the hydrofoil from the holder when tacking which increases the chance of losing control of the hydrofoil.

Total Hydrod Foil Area for Optimum Leeway

Immersed area of Sunfish daggerboard = 30.125X9.5 = 286 in^2 less the little missing curved area at the tip, and the area of the sail is 75 ft^2.  Area of sail for the SS14 = 142 ft^2.  The foil area to sail area for a Sunfish is 2/75 = 2.67%. (Foil to sail ratio is normally about 4% (1.3 Sail area to dagger board area ratio)) Nominal foil area needed is thus .0267*142 = 3.79 ft^2, or 3.79x144 = 545.76 in^2 .  Additional area needed from is 3.79 - 2 = 1.79 ft^2, which would require an additional 1.79x144/9.5 = 27” more daggerboard length, but only 15 inches more is used because if 27” were added, it would extend to far down to be conveniently withdrawn when running. It is important that the depth of immersion of the hydrofoils is small compared that of the daggerboard since the hydrofoils are curved out (see Ketterman’s senior project).