Summary

In this discussion about delta-shaped and related sails, experiences with prototype sails are described first. The sails have a forgiving nature, providing significant lift as well as propulsion when sailing off the wind, and produce a relatively small heeling force. The results of a numerical simulation carried out by Adam Ryan are then summarised. In a discussion about the aerodynamics of sails (and wings) that have a conical or truncated conical form, it is hypothesised that vortex production from the tip of the sail is minimised by the curvature of the upper part of the sail to windward, by sweepback, and by washout. It appears that delta-shaped sails are particularly effective because of the way they manage airflow across them in three dimensions.

Definition

A delta-shaped sail has a highly-raked (ie: 40º or more from the vertical) leading edge supported either by a spar or a stay, a foot that is approximately parallel to the surface of the water, and a trailing edge that is approximately vertical.

There are several traditional sailing rigs that carry delta-shaped sails, for example the Lateen and Crab-Claw. A proportion of Jibs, Genoas, and Asymmetric Spinnakers could also be considered within the category of delta-shaped sails as broadly defined above. There are other rigs that carry sails conforming partially to the conical geometry of delta-shaped sails, for example Lug, Junk, Gaff, and Transition rigs – these will be referred to in this discussion as truncated deltas.

Introduction

The inspiration for this investigation into delta-shaped sails came from watching films of Australian 18-foot skiffs (‘Awesome Aussie Skiffs’ 1 and 2). These lightweight boats carry a crew of three who can trapeze out from the extensive wings on each side of the boat and carry a proportionately large sail area. In suitable conditions the Aussie skiffs are capable of planing on most points of sail. Sailing downwind, the crew hoists a large asymmetric spinnaker supported from a forestay and the craft follows a rapid zig-zag downwind course gybing from tack to tack. From viewing the films, it became clear that the spinnaker – in addition to generating considerable forward power - also generates lift, holding the bow of the craft up out of the water and reducing the risk of nose-diving into the back of a wave in front.

Figure 1:
Idea for Concept Boat
competition entry

Test rig

To test the performance of this sail before continuing further with the design concept, I made a test rig for a Fireball dinghy. The spar carrying the sail was made from aluminium tubing bent into a curve and stiffened with spiral layers of carbon tape embedded in epoxy resin. The A-frame was made from aluminium tubing and supported from an aluminium cross-tube at the stern of the dinghy. The sail was cut from an existing Fireball sail and a mast sleeve added along the new leading edge. The curve of the leading edge of the sail exactly matched the curve of the spar so that when it was rigged in still air it hung flat below the spar without any built-in camber. Three horizontal battens were added. These were made from tapered carbon-fibre tubes (fishing rods) which narrowed towards the leading edge. The main sheet was attached to the clew of the sail and acted around a rope traveller tied to the ends of the cross-tube. This arrangement allowed trimming tension to be applied to the sail both downwards and backwards.

Figure 2: Sail filling and lifting due to airflow across it

Onshore with the rig aligned appropriately towards the wind, it was clear that the unrestrained sail had a tendency to billow to the side and lift up (Figure 2). As it billowed, curvatures appeared both from front to back across the sail (horizontal camber) and from top to bottom (vertical camber). As a consequence of the curvature of the mast, the more the originally flat sail moved out to the side, the greater this ‘ballooning’ effect became. This can best be understood by thinking about the situation where the sail has lifted until it is flying almost horizontally alongside the spar. In this position, looked at from above, the spar appears straight and the curved leading edge of the sail has to conform with it. This results in slackening of the cloth between the mid region of the spar and the foot of the sail, encouraging cambers to form. This adaptive change in the sail from being relatively flat when sailing close-hauled to being more curved when sailing off the wind contributed to its effectiveness.

Figure 3: Sailing upwind

Figure 4: Sailing off the wind

On the water, the rig performed well (Figures 3 and 4). The spar and A-frame provided a stable, interference-free support for the sail. Compared with more conventional rigs, the low aspect-ratio sail with its correspondingly low centre of effort reduced the capsizing moment produced by gusts and stronger winds, giving the dinghy a more stable feel. In conditions ranging from Force 2 to Force 4 it was relatively easy to set a course and maintain it, and the sail seemed tolerant of sheeting angles. The dinghy could be sailed on all the usual points of sail, although it was noticeably slower on a dead run downwind, particularly in lighter winds. This was probably due to the reduced area presented to the wind by the fully-sheeted out sail. Under these conditions most of the wider aft parts of the sail were flying out almost horizontally to the side of the upper third of the spar, and the wind was being directed forward mainly onto the narrower, more vertical part of the sail near the bow.

To learn more about the airflow across and behind the sail, woollen tell-tales were attached in a grid-like pattern across both surfaces of the sail and streamers attached to the trailing edge at the top of the sail and at batten locations. It could be seen that on the windward side of the sail, the airflow in the vicinity of the surface was being deviated somewhat upwards as it passed from leading to trailing edges. The streamer at the top of the sail streamed smoothly behind with very little fluttering compared with the streamer at the foot of the sail.

Modifications to the rig concept

With the experience gained from the test rig, it was possible to return to the design of the rig for Concept Boat competition entry. To enhance the downwind capability in light airs, I decided to have a double-skinned sail that could be opened out like a spinnaker when required, doubling its area (Figure 5, a). On other points of sail, the two laminae of the sail would remain together (Figure 5, b).

Figure 5: Different rig configurations – a) sailing downwind with sail laminae separated, b) normal sailing with laminae together, c) sail reefed and A-frame feet moved forwards to lower spar and bring sail foot close to hull

This double-layered approach opened a new possibility for reefing. The batten layout was changed – a lower batten was positioned along the foot of each sail lamina, and then an upper batten was positioned from the front lower tip of each lamina obliquely across the sail to the mid-point of the trailing edge. For reefing, the lower segment of each lamina could then be folded up in between the two laminae and fixed in position so that the upper batten becomes the new sail foot. The sheet for the sail would then be moved to eyelets adjacent to the ends of the upper battens. The sail, now halved in area, could be used either in its normal position to give greater headroom for those on board, or lowered for high-wind use by sliding the feet of the A-frame forwards along the side tubes until the new foot of the sail is close to the board (Figure 5, c).

Figure 6: Flèche going upwind
with the sail laminae together

Figure 7: Flèche going down wind
with the sail laminae separated

Prototype Flèche

A prototype Flèche was made. Initial test sailings indicated that a rigid traveller across the stern was needed for the main sheet, but in general the concept worked well (Figure 6). Sailing downwind with the two sail laminae separated proved to be effective (Figure 7).

Numerical study of the Flèche rig

Adam Ryan, a student studying for a sports science degree at the University of Plymouth, modelled the properties of the Flèche rig using computational fluid dynamics (CFD). CFD is a method that employs the equations of fluid mechanics to describe a flow field on and around a surface. By numerically modelling the shape being studied and placing it within a defined fluid domain, the flow field characteristics can be calculated. To simplify the calculations, the leading edge spar, battens, changing sail shapes under load, and the relationship of the sail with the hull were not modelled, so the results have to be interpreted with this in mind.

Figure 8: Movement of the centre of effort at
different angles of incidence (from Ryan 2007)

The simulated sail was studied at different angles of incidence to the airflow from 5º to 40º. The sail produced a maximum C_L (coefficient of lift) at around 30º, beyond which the sail stalled and the C_L rapidly dropped off whilst the C_D (coefficient of drag) increased. In terms of the greatest lift to drag ratio, the most efficient angle of operation was 15º. The centre of effort was at its lowest at 5° incidence and then steadily rose up and aft on the sail until 25° was reached (Figure 8). At higher angles of attack the centre of effort dropped back down again and forward. The largest heeling moment was produced at 30° incidence.

At smaller angles of incidence, the simulated Flèche sail produced more drag than Bermudan rigs, but performed more efficiently than them at higher angles of incidence. The low-aspect ratio (0.7) Flèche stalled at 31º compared with 14° and 25° for Bermudan rigs with aspect ratios of 6 and 1.5 respectively. However, compared with figures published for the Crab-Claw rig, the Flèche rig was relatively inefficient.

Computed streamlines illustrated the airflow around the sail (Figure 9). The streamlines showed good attachment up to an incidence of 30°, after which detachment began. Although the release of air at the top of the sail was clean, a large vortex was formed at the foot of the sail at higher angles of incidence as air spilled from the higher pressure windward side to the lower pressure leeward side.

Figure 9: Streamlines with the sail set at 5º (above)
 and 35º (below) to the airflow (from Ryan, 2007)

Vortex formation at the foot of the Flèche sail became particularly marked at high angles of incidence. The vortex increases the drag of the sail and reduces its efficiency. To simplify the calculations, the interaction of the sail with the hull and water surface was not included. If the gap between sail and hull can be minimised or - ideally - closed, then vortex formation could be inhibited or prevented. (This is sometimes known as the ‘end-plate’ effect. In the 1980s windsurfers began to take advantage of the improvement in performance that can be gained by ‘closing the gap’. They achieved this by altering the cut of the lower part of the sail and by adjusting the rake of the rig in use in order to close the gap.) The Flèche sail has been shaped with the aim of keeping this gap as narrow as possible, but in practice the size of the gap changes as the sail is trimmed according to the course being sailed.

There are several ways in which the gap might be effectively closed when using a Flèche-type rig out on the water. One way would be to trim the sail to the course required, and then slide the feet of the A-frame forwards to lower the spar supporting the sail until the foot of the sail is as close to the hull as possible. The A-frame can then be locked in this position until the next change of direction. Another way would be to close the gap with cloth extending from the foot of the sail to an attachment along the midline of the hull. There would need to be some way of adjusting the amount of cloth made available to accommodate changes in sail trim, so perhaps a spring-loaded conical roller could be arranged along the midline to take up any slack in the gap-closing cloth.

Rather than aiming to close the gap, it may be possible to reduce vortex formation by adopting the strategy of the Crab-Claw rig, using the vortex-inhibiting qualities of a concave leech and a sweptback tip at the bottom of the sail as well as at the top.

Key characteristics of delta-shaped sails

These studies involving full-sized prototypes and computational modelling have shown that delta-shaped sails have several characteristic properties:

  since they have a lower aspect ratio than most other sailing rigs, they have a correspondingly lower centre of effort which in turn results in a lower heeling moment for a given sail area (other conditions being equal)

  they can operate more effectively at higher angles of incidence than other sails and have a delayed stall. This makes them tolerant in use

  other than when sailing close-hauled, the delta-shaped sails produce a significant amount of upwards-directed lift in addition to forward propulsion

  tip vortices are minimised, although a large vortex develops at the foot of the sail if it is not close enough to the hull or water to enjoy an endplate effect.

Aerodynamics of delta-shaped sails

It is interesting to consider the aerodynamics of delta-shaped sails and the related truncated-delta forms. I have come to the belief that the tolerant, efficient nature of these sails is due to the way that they guide the airflow across their surfaces and then release it cleanly from the trailing edge, particularly at the tip. These sail forms, and also certain wing forms found both in nature and in certain types of aircraft, have in common a conical geometry, and this results in several desirable properties. As a consequence of their overall 3-D form, conically-shaped sails seem able to manage the airflow smoothly across both windward and leeward surfaces. With their swept, slightly washed-out tips, and with the upper parts of the sail curving to windward, they appear to have an ability to suppress drag-inducing tip vortices.

Figure 10: The form of an early hang glider wing

It is helpful to consider the geometry of early hang gliders. The concept for these fabric wings was first patented in 1951 by Frances Rogallo (Messenger and Pearson, 1978). Each wing consisted of a conical billow of cloth supported by the sweptback leading edge and the midline fuselage tube (Figure 10). The longitudinal axis of each billow halves the angle between the leading edge and midline, converging on each side towards the nose of the glider. Different parts of the wing have different angles of incidence in relation to the approaching airflow, the regions close to the midline having a more positive angle of incidence, and the regions towards the wing tip having reduced angles of incidence. (This is sometimes referred to as ‘washout’. It is comparable to ‘twist’ in the upper parts of a sail.)

This simple geometry provides stability around all three major axes (pitch, yaw, and roll). Thus, if the wing is perturbed in flight, it will automatically dampen the perturbation and return to stable flight. (Stability is enhanced by placing the pilot below the wing and thus lowering the overall centre of gravity to give added pendulum stability. The more recent hang gliders have reduced sweepback and double-skinned wings that have a thicker aerofoil section to improve performance.)

It is immediately apparent that there is a kinship between the arrangement of early designs for a hang glider wing and the delta-shaped sails being discussed here. Although the wing most usually operates in a more horizontal position, and the sail more vertically so that the aerodynamic vectors are arranged differently, nonetheless it is probable that patterns of airflow across their surfaces are comparable. Furthermore, the inherent stability of this conical form may also contribute to the good-natured feel of delta-shaped sails, a point that was touched upon in the discussion of Lewis (2003).

Figure 11: The variable conical geometry of a bird’s wing –
the axes (pink) of the joints at the elbows and wrist
are principally normal to the imaginary conical surface
shown in blue. As the wing flexes and extends,
this conical form is maintained

The wings of birds that are efficient gliders generally have washout (increasingly negative angle of incidence) towards the tip, and the tip is commonly directed downwards (anhedral) and backwards (sweep). This was first noted by the pioneer of flight Otto Lilienthal (1889). During development of the Transition Rig (Dryden, 2004), my studies of bird wings (for example: those of the gull) indicated that their wings also conformed to a conical geometry (Figure 11). Thus they can be considered as truncated deltas, conforming to part of a conical surface. I found that in general the axes of the wing joints were set normal to such a surface (plus or minus a limited range of movement for control during flight), allowing the conical form to be maintained as the wing flexed, extended, and folded (Figure 11).

Figure 12: Hypothesis: tip-vortices produced by different
wing configurations – straight wings produce large vortices (left);
anhedral wings produce smaller vortices (second left);
sweptback anhedral wings produce smaller vortices still;
sweptback anhedral wings with washout produce
minimal tip-vortices (right)

Figure 13: Hypothesis: tip-vortices produced by different sailing rig
configurations – a vertical wing sail (back left) produces a large vortex;
a vertical wingsail that curves to windward produces a smaller vortex
(second from left); a wingsail that both curves to windward
and is also sweptback has a reduced tip-vortex (third from left);
a wingsail that is curved to windward, is sweptback,
and twists so that the tip is at a reduced angle of incidence
in relation to the apparent wind has the smallest tip-vortex,
and hence, drag (right)

There has been a continuing discussion about the Crab-Claw rig. In most respects, the Crab-Claw conforms to the definition given above for delta-shaped sails, the main difference being that the longitudinal axis of the rig can be tilted to different angles in the vertical plane according to the course being sailed. This means that the foot of the sail is not always parallel with the surface of the sea. Marchaj (1996) presented evidence from wind tunnel tests of models that the Crab-Claw was much more efficient than more commonly used rigs such as the Bermudan, particularly at high angles of incidence. He suggested that this was due to the formation of leading edge vortices on the leeward side of the sail which increased the lift being generated, rather like the wing of Concorde when flying at slow speed and a high angle of incidence. More recently, Slotboom (2005a, 2005b) has questioned this analysis and proposes that the efficiency of the Crab-Claw is due to optimal camber and angle of incidence of the sail in its different positions.

On the basis of my experience with delta-shaped sails and the foregoing discussion, I would add that the Crab-Claw rig probably generates minimal tip vortices both at the top of the sail and the clew, and that this contributes to the rig’s efficiency. The numerical simulation of the Flèche rig by Ryan (2007) did indeed show vortex generation along the foot of the sail that became more marked with increasing angles of incidence, and this may lend support to the view of Marchaj (1996) with regard to leading edge vortices, but the simulation showed that vortex production resulted in a rapid increase in drag as the sail approached the stall, so it seems unlikely that this mechanism accounts for the overall efficiency of the Crab-Claw rig.

Conclusion

It has been recognised for a long time that delta-shaped and truncated delta sails possess many admirable properties. For example they are efficient, forgiving, have a low centre of effort and thus are less likely to produce capsize, produce lift as well as propulsion, and can be supported by masts and spars that are not unduly stressed due to the low aspect ratio. Prototypes and simulations of the Flèche rig have given a little more insight into the aerodynamics of delta-shaped sails, and have drawn attention to the way that tip vortices may be minimised by this configuration. These sails have an effective way of managing airflow across them in 3-dimensions (Figure 14), and are worthy of further investigation.

Figure 14: A delta-shaped sail (back right) and two truncated deltas –
the Transition Rig (front left) and Junk Rig (mid position).
The airflow across the delta-shaped sail
is suggested by streamlines

References

‘Awesome Aussie Skiffs’ (1 and 2) Ronstan. Australia: Front Lawn Productions (videos).

Dryden, R. (2004) Transition sailing rig. Catalyst, 18, 14-20 (October).

Lewis, O.T. (2003) A search for effectiveness. Catalyst, 11, 7-8 (January).

Lilienthal, O. (1889) Birdflight as the basis of aviation. Hummelstown, A: Markowski International Publishers (reprinted in 2001).

Marchaj, C.A. (1996) Sail performance: theory and practice. London: Adlard Coles Nautical.

Messenger, K., and Pearson, R. (1978) Birdmen: A guide to hang gliding. London: Corgi Books (pvii).

Ryan, A.J. (2007) A study into the efficiency of the Flèche sail design, with use of computational fluid dynamics. Thesis, University of Plymouth (April, 55 pp).

Slotboom, B. (2005a) A new analysis of the Pacific Crab Claw rig. Catalyst, 22, 15-17 (October).

Slotboom, B. (2005b) Delta sail in a “wind tunnel”. http://www.multihull.de/technik/t-slotboom_gb.htm (downloaded 14/01/2005).