top of page

## Theory

This page provides a summary of the principles underlying the WindFly Rig. Some simplifications have been made in the summary, a more rigorous analysis is provided in the documents available on the download page.

#### No heel

No heel

(successfully tested)

A short mast supports one end of the boom. The boom is free to rise and fall about the top of the mast. The mast is positioned on a base unit which allows the mast (and the boom which it supports) to rotate around the longitudinal axis of the mast.

The kite lines pass three times between the base of the mast and the third point of the boom. From the third point the kite lines continue to the end of the boom and then to the kite.

The lengths of the mast and boom are chosen so that two similar triangles formed by:

1. The top of the mast, the bottom of the mast, and the third point of the boom, and

2. The top of the mast, the centre of the keel, and the end of the boom.

Therefore the triple set of lines passing between the base of the mast and the third point of the boom are always parallel to the line passing from the centre of the keel to the end of the boom.

To maintain equilibrium of the boom, the triple set of lines passing between the base of the mast and the third point of the boom must be parallel to the  lines passing from the end of the boom to the kite . The boom automatically rises and falls to maintain equilibrium as the kite moves.  Therefore, the line of action of the kite lines always passes through the centre of the keel and, since the line of action of the kite lines always passes through the centre of the keel, no heeling moment is applied to the boat by the kite.

As the kite moves around the boat the mast and boom automatically rotate to track the kite so that the boom is always aligned towards the kite.

#### No leeway

No leeway

(successfully tested)

If the WindFly Rig is mounted at the stern of the boat the keel and rudder can be combined into one, or two, 'keel-rudder(s)' which is (are) used to steer the boat and also resist the sideways component of the kite load.

The centre of lift of a symmetrical foil is located 25% of the chord length behind the leading edge. If the WindFly Rig is mounted above the quarter point of the 'keel-rudder', the 'keel-rudder' rotates until the sideways force of the kite is balanced by the lift provided by the 'keel-rudder': the 'keel-rudder' adjusts automatically to offset the sideways component of the kite load.

Therefore leeway of the boat is not required to generate the lateral load to balance the sideways fore of the wind.

Of course this only works if the boat is moving fast enough for the 'keel-rudder' to generate enough lift to balance the kite load. Unless the boat has steerage way the stern will tend to swing round to follow the kite.

To prevent the stern swinging after the kite, the kite lines can be run through a guide at the bow so that the bow follows the kite until steerage way has been built up and the lines can be released from the guide. Typically the bow guide will be used during launch and retrieval of the kite when the kite is likely to be flown at low elevation for sustained periods.

Kites generally form less efficient aerofoils than conventional sail rigs. Therefore kite boats do not typically point as close to the wind as conventional sail boats. However, the maths indicates that if the WindFly Rig is mounted so that leeway is avoided the boat will be able to achieve a course as close to the wind as can be achieved by a traditional sail boat.

#### Placement of the WindFly Rig on the boat

Placement

(successfully tested)

To avoid making the vessel turn, the WindFly Rig should be placed above the centre of lateral resistance.

For a displacement hull which pushes through the water the WindFly Rig may be located above a keel (or 'keel-rudder') which is placed anywhere along the length of the hull. It may be practical to place the WindFly Rig towards the bow to avoid complications when the speed is too low to provide steerage way.

For faster boats which plane (skim across the  top of the water), the bow sometimes leaves the water surface. The WindFly Rig should be located so far back on the boat that the hull below the WindFly Rig never lifts clear of the water. This can be achieved by fixing the WindFly Rig to the stern of the boat, in the location where the outboard motor would traditionally be placed.

Planing - 1

#### Planing or semi-planing - With a simple keel-rudder

(not yet tested)

As a boat travels through water, water is moved to make way for the hull.  As the water is moved it is accelerated .  A force is applied by the hull to accelerate the water and an equal and opposite force is applied by the water on the hull.  At high speed and with suitable hull geometry this hydrodynamic force is sufficient to support the boat.  When this happens the boat is planing. Part of the hydrodynamic force provides lift N to the hull and part of the hydrodynamic force provides drag R which resists movement of the hull.

The hydrodynamic lift and drag vary as the boat speed and trim angle vary. In a conventional analysis of a planing motor boat moments are taken about the point P where the drive force F from the propeller intersects the hydrodynamic lift N. The trim angle adjusts until the moment from the drag R is balanced by the moment due to the self weight W of the boat so that

aR = bW.

The same theory that is used for analysis of a  boat using the WindFly Rig. However, the weight of the vessel and the position of the centre of gravity are modified to take account of the vertical component of the kite load, Fz. If the WindFly Rig is placed at the stern of the boat the modified weight U acts further forward on the boat than the true self weight W does. Now the trim angle adjusts until the moment from the drag R is balanced by the moment due to the modified weight U of the boat so that aR = cU.

If the WindFly Rig is fixed to the stern the kite load reduces the trim angle relative to that of a boat with a conventional propeller drive. The following steps can be taken to mitigate this effect:

• The centre of mass may be placed further aft than it would be for a motor boat.

• The kite may be flown at a low angle, close to the water, to limit the vertical component of the kite load.

• A more slender (longer, narrower) hull may be used. This limits the effect of movements in the position of the hydrodynamic lift N. While a longer hull increases the resistance it improves sea keeping and can provide an efficient ‘high speed displacement’ (or ‘semi-planing’) hull for operation with Froude numbers in the range 0.4 to 1.1.

When a boat is planing the hull skims over the top of the water instead of pushing through the water.

The combined assembly of WindFly Rig and 'keel-rudder' may be mounted in place of the outboard engine on commercially available 'off the shelf' boats. The boat will plane at a lower trim angle than with a conventional outboard engine.

#### Planing - With a keel-rudder and hydrofoil

Planing - 2

(not yet tested)

A hydrofoil can be placed below the WindFly Rig to pull downwards to balance the component of the kite load that acts upwards along the axis of the mast. In this arrangement the WindFly Rig rises and falls to change the angle of incidence of the hydrofoil until the hydrofoil load balances the component of the kite load acting along the mast.

The rig can be mounted on the transom at a level and angle so that the drive force from the kite acts along the same line as the drive force from the propeller would act.

The combined assembly of WindFly Rig, 'keel-rudder' and hydrofoil may be mounted in place of the outboard engine on commercially available 'off the shelf' boats.

#### Planing - The Length / Displacement ratio

Planing - 3

(established theory)

Resistance on planing hulls falls very quickly as the Length / Displacement Ratio increases from 5.2 to 6.9.

A Length / Displacement Ratio greater than 5.7 is generally considered desirable for a planing hull.

Using a traditional sail rig, it is very difficult to build standard yachts with a Length / Displacement Ratio larger than about 5.2, therefore the vast majority of yachts are unable to plane reliably and are therefore unable to achieve speeds corresponding to a Froude number greater than around 0.45.

Due to the reduction in ballast, standard yachts using the WindFly Rig will typically have a Length / Displacement Ratio in the range of 6 to 7. Yachts using the WindFly Rig are therefore able to plane reliably when there is sufficient wind.

_________________________________________________

• The Length / Displacement Ratio is the water line length (m) divided by the cube root of the displacement (m3).

#### Kite control

Kite control

(successfully tested)

The majority of the kite load is carried by the central 'drive lines'. The two outer lines - 'control lines' - are lightly loaded and are used to steer the kite and adjust the power of the kite.

After passing three times between the third point of the boom and the base of the mast the 'drive lines' can stop at the base of the mast. The 'control lines' may continue through the mast base unit to the cockpit where the crew manually adjust the 'control lines' to control the kite.

Alternatively the 'control lines' may also terminate at the base of the mast. In this case the 'control lines' pass through pulleys on the boom and 'crew lines' connected to the pulleys pass through the mast base unit to the cockpit where the crew manually adjust the 'crew lines' to alter the length of the 'control lines' and so control the kite.

This arrangement allows the kite to be controlled as the length of the kite lines is altered.

The WindFly Rig rotates around the axis of the mast to follow the kite. The 'crew lies' - or the 'control lines' - may be passed over / under each other to avoid the lines becoming crossed as the mast rotates.

(successfully tested)

In gusts the wind speed increases causing a sudden increase in the load on wind powered drive elements – sailing boats are heeled over and may broach, kite boats are  accelerated and may be lifted clear of the water. The effect is particularly applicable to kite boats: the airspeed and therefore the lift (drive force) vary as the kite is flown faster or slower, this effect may amplify a change in wind speed leading to an even greater increase in the drive force during a gust. In addition a kite may move quickly from the ‘edge of the window’ to the ‘power zone’ leading to a rapid and severe increase in the kite load. If the boat is lifted clear of the water it may not land upright, or may break up on impact with the water. It is impractical to design the kite, rigging, attachment system and boat strongly enough to take the potential increase in the kite load without breaking.

The WindFly Rig includes an arrangement that limits the maximum load which can be developed by the kite:

• As the kite lines pass three times between the third point of the boom and the base of the mast the lines pass around a pulley at the base of the mast.

• The pulley is held in place by a line which is connected to a spring. A traction gas spring is used so that the spring has zero extension up to the selected load and then extends rapidly if further load is applied.

• A 'load limiter line' is also connected to the spring. The 'load limiter line' passes through a pulley system to amplify the extension of the spring. The 'load limiter line' then continues up the mast and along the boom.

• At the end of the boom two pulleys are fixed to the end of the 'load limiter line'. The two 'control lines' pass through these pulleys.

When the selected maximum kite load is exceeded the spring extends. The 'load limiter line' therefore extends which moves the pulleys at the end of the boom. This increases the length of the 'control lines' and depowers the kite. This arrangement allows the control lines to be used to control the kite as the spring extends to depower the kite.

Lines tensioner

#### Lines tensioner & storage

(tested, principles proved but difficult to de-bug)

Kites do not fly reliably at low airspeed. Apart from when the wind is just not strong enough, there are various other occasions when low airspeed is encountered:

• When the kite is overflown it drifts back, stalled and windless, until it is can re-engage. This may happen even when the true wind speed is significantly greater than the minimum airspeed required.

• In downwind sailing the boat may over take the kite.

• When the wind is gusty there may be periods when the actual wind speed is less than the required minimum airspeed.

When the airspeed falls too low the kite lines go slack and it becomes impossible to control the kite.

The WindFly Rig includes a lines tensioner which avoids these problems:

• From the base of the mast the lines continue to a drum which is mounted on the rear side of the mast.

• The drum is connected to a motor spring which applies a constant torque to the drum.

• In normal use the kite load is sufficient to unwind the lines off the drum. However if the lines become slack the motor spring rotates the drum and draws the lines to maintain a minimum tension in the lines.

• The lines are paid out again once the kite is flying properly again.

• The drum provides a line storage system when the kite is not in use.

In conjunction with the arrangements for kite control and load limiting described above, this system allows the kite to be controlled using the crew lines as the kite lines are taken in and paid out. If a small kite is used a lock may be provided on the drum to prevent the lines being taken in when the kite load is small.

#### Automatic kite control

Automatic control

(not yet tested)

For automatic control of the kite the crew line running to the lower corner of the kite is connected to a boom line. The remaining crew line is set to a fixed length and therefore maintains the upper control line at constant length.

The boom line runs from the crew line to the free end of the boom. The lengths of the boom line and crew lines are set so that when the kite is at the target height and power the two control lines are of equal length.

If the kite descends below the target height the boom lowers. The boom line pays out the crew line and lengthens the lower control line. As a result the kite turns and climbs back towards the target height.

If the kite ascends above the target height the boom rises. The boom line pulls the crew line and shortens the lower control line. As a result the kite turns and descends back towards the target height.

#### Offset boom self-weight

Boom weight

(successfully tested)

The self weight of the boom causes the boom to fall. The kite has to fly higher to lift the boom, this affects the alignment of the kite lines which causes the line of action of the kite lines to miss the centre of the keel which introduces a heeling moment.

The WindFly Rig includes a spring which balances the self weight of the boom. The spring allows the boom to operate as a spring balanced cantilever so that the kite lines do not have to support the boom: the alignment of the kite lines is therefore unaffected by the weight of the boom and the line of action of the kite lines always passes through the centre of the keel so that the boat does not heel.

Raising foils

#### Raising the foils

(successfully tested)

An uphaul and bungee downhaul can be used to raise and lower the foil(s). This is the same arrangement as is typically used to raise and lower rudders on sailing dinghys. The arrangement allows the foil(s) to rise to pass over obstructions that are hit.

Steering

#### Steering

(successfully tested)

A tiller can be used to steer the boat.

If two keel-rudders are used the tiller pintle is placed at the midpoint of the line that connects the pintles of the two 'keel-rudders'. This ensures that the distance between the stern of the tiller and the 'keel-rudders' remains constant as the tiller and the 'keel-rudders' rotate, a fixed length linkage can be used to connect the end of the tiller to each of the ‘keel-rudders’ so that all turn together.

Quick release

#### Quick release

(successfully tested)

Kite surfing equipment now includes an emergency quick release to allow the kite surfer to separate himself or herself from the kite. The same principle is adopted for the WindFly Rig, a quick release system allows the kite and WindFly Rig to be jettisoned in an emergency.

As with kitesurfing equipment a tiered release system is provided.

• If the 'crew lines' are released the kite is fully depowered. This will be sufficient in most emergency situations.

• A hook knife should be carried by the crew so that the lines can be cut to release the kite.

• Quick release brackets are provided at all points where the rig is connected to the boat. One handle is pulled to release all of the quick release brackets, this separates the kite and the WindFly Rig from the boat.

Self righting

#### Self righting capability

(established theory)

Since no heeling moment is applied to be boat a narrower hull can be used for displacement craft. This makes it easier to achieve a high angle of vanishing stability and a small or zero negative area on the static stability curve, both of which improve the self righting capability.

________________________________________________

• The angle of vanishing stability is the maximum angle of roll from which the boat will return to upright in calm water.

bottom of page