The aerodynamics of sails

8

110'1.

1963

TRAINING CENTER FOR EXPERIMENTAL ·AERODYNAMICS

TECHNICAL MEMORANDUM 16

THE AERODYNAMICS OF SAILS

by

Adrian MILLWARD

RHODE-SAINT-GENESE, BELGIUM May 1963

{'

I

.'

THE AERODYNAMICS OF SAILS

by

Adrian Millward, B.Sc. Robert Blackburn Memorial Fellow

and student at TCEA, 1962-63

Lecture given at TCEA

Notation

1. Introdu.ction 1

2. History 1

3. The Aerodynamic and Hydrodynamic Prob1em 2

4. Conve.ntiona1 Sai1s 5

4.1 Forces 5

4.2 Wind Tunnel Prob1ems 5

4.3 Aerofoil Cross Section 6

4.4 Aspect Ratio 9

4.5 Out1ine of the Sail 10

4.6 Interaction of the Sails 11

4.7 Airflow 12 4.8 Conclusions 13 5. Wingsails 14 5.1 General 14 5.2 Canoe Wlngsail 15 5.3 Norwegian Wingsail 15 5.4 B1ackburn Wingsai1 16 5.5 Conclusions 17 References 18

A CD C H C HW CL Cp CR C RW

Cv

C VW F H F HW FR F RW FV FVW KH K~ KR K RW

~

KVW MH M HW M R M RW MV

Wetted area of hull at rest

Drag coefficient relative to wind Aerodynamic side force coefficient Hydrodynamic side force coefficient Lift coefficient relative to wind Pressure coefficient

Thrust coefficient

Horizontal water resistance coefficient Vertical aerodynamic coefficient

Vertical hydrodynamic coefficient Aerodynamic side force

Hydrodynamic side force Thrust force

Hydrodynamic resistance Vertical aerodynamic force Verticalhydrodynamic force

Aerodynamic trimming coefficient Hydrodynamic trimming coefficient Aerodynamic heeling coefficient Hydrodynamic heeling coefficient Aerodynamic yawing coefficient

Hydrodynamic yawing coefficient Aerodynamic trimming moment

Hydrodynamic trimming moment Aerodynamic heeling moment Hydrodynamic heeling moment

NOTATION (continued)

MVW Hydrodynamic yawing moment

P Characteristic length of sailplan Q Characteristic length of hull S Sail area

VA Apparent wind speed V

MG Yacht's speed to windward V

s

Yacht's water speed V

T True wind speed

~ Setting angle between sails a

M lncidence of mainsail to apparent wind aR Rudder angle

a

Apparent wind angle to course Y Course angle to true wind

À Leeway angle

PA Density of air Pw Density of water

~ Angle of sail to course

e

Angle of heel

A considerab1e amount of research has been done on the design of boat hu11s, 1arge1y of an ad hoc nature, put very 1ittle research has been done on sails. The 1ittle that is known was done main1y between the two wars in both Germany and the U.S.A. In the last few years a serious

attack on the problem has been started in the United Kingdom at Southampton University.

A sai1 can be considered as a thin aerofoil mounted in a vertical plane and therefore some useful comparisons can be made with aeroplane wings provided the differences are also remembered. The main differences are that a sail is a very thin flexible aerofoil, possibly porous, and works in a non-uniform velocity field. The non-uniform velocity field is

due to the boundary 1ayer formed over the sea which is about 10 metres thick. The velocity distribution is further modified by the presence of the hu1l.

A know1edge of some sailing terminology wou1d be useful to an aeronautica1 engineer and fig 1 shows a simple sailing boat with various parts of the sails and rigging labelled. In fig 2 are shown the courses which a boat can sail relative to the wind and the names applied to them.

2. History

The use of sails is considerab1y younger than the use of boats and seems to have started in Egypt where a light but steady wind blows up the Nile. The Egyptians found that by stretching a large mat across the

Jboat perpendicular to the wind they could proceed .up river without using their oars. A typical Egyptian ship is shown in fig 3. Sails, however, remained on1y an auxi1iary souree of power unti1 ab out 300 AD because they could only be used with a following wind.

The first improvement was made in China where the sai1 was turned fore and aft and stiffened so tHat the boat could be sailed at an acute

angle to the wind. Unfortunately the Chinese made no further advances and the junk shown in fig 4 has remained basically unchanged ever since.

The Arabs who traded with the Chinese borrowed the fore and aft rig and af ter modifying it to the form shown in fig 5 brought it to Europe where it has developed into the sailing rigs of today (figs 6

&

7).

3. The Aerodynamic and Hydrodynamic Problem

The velocities in the horizontal plane, which will be cal led the Geometry Field, are illustrated in fig 8. It can be seen that V

MG, the speed made good to windward, which is the major criterion of windward performance, is dependent on the true wind speed. It is convenient to take

the ratio VMG/V

T and the course angle Y and express them in terms of the apparent wind speed VA' the boatls speed V

s

'

and the apparent wind angleS which are all quantities that apparently might be easily measured at sea. Thus

(1)

siny sin

a

(2)

Provided V

T is taken as the wind speed relative to the water, thus taking into account any tide effect, a complete solution can be found in the Geometry Field by a knowledge of VA' V S and S. lJnfortunately S , which

includes the leeway angley, is difficult to measure with any accuracy because of the effect of the huil. For this reason the results obtained by the now defunct Yacht Research Council are somewhat suspect.

hydrodynamic forces and their relative positions. Davidson referred the forces to axes parallel and perpendicular to the boat's course. This is convenient when considering the water forces such as in a tank test but for the wind forces it must be remembered that the hull is inclined to the apparent wind or to the tunnel axis at an angle (

a-À)

.

Also when a yacht heels over, the sailplan develops both dihedral and sweepback. It would therefore seem more convenient to refer the forces to a system of "body axes" Ox, Oy, Oz with their origin at some fixed point such as the inter-section of the mast and the deck. The aerodynamic forces would then be represented by forces FR' FR' FV with moments M

R, MH' MV causing the yacht to heel, trim by the head and yaw respective1y. The hydrodynamic forces wou1d similar1y be represented by forces F

RW' FHW' FVW and moments MRW'

M_{RW ' MVW}

U~der steady sai1ing conditions

FR + F _RW = 0 M _R +M _RW = 0

FR + FHW 0 and M_R +M _RW 0

F + F = 0 _MV +M = 0

V VW VW

The moments and forces may be expressed in terms of the coefficients as in conventional aerodynamics CR FR KR M R

=

_{/ 2} = ₂

1 2 P AV A S 1/2 PAV A PS for the sail

and

F

RW MRW

C

RW = 1/2 PWV_S 2 A KRW = 1/2 P WV S 2AQ for the hull

where PA and Pw are the air and water densities respectively, S the sail area, A the wetted area of the hull at rest, and Pand Q are characteristic lengths of the sail plan and hull respectively. However, since P W = 835 PA' the equations can be simp1ified to

835

w(::f

-- C _ _ R = C RW - C _{. H} - - = C HW - C _ _ V C VW (3)

and

(4)

Thus in addition to equation (1) there are six relationships between V

s

and VA in terms of force and moment coefficients to be satisfied. The complete determination of the wind forces and moments to which the coefficients relate requires a knowledge of the angle of heel S ,

the angleS between V S and VA' the incidence of the sailplan a

M, the setting angle between the two sails aF and upon the magnitude of VA. Thus in the aerodynamic field alone there are 5 independent and 6 dependent variables.

Similarly in the hydrodynamic field there are 3 forces and 3 moments which are dependent on S, À , V

_s

and the rudder angle aR' Further-more the effect of trim although probably negligible in the aerodynamic field is quite important in the hydrûdynamic field. Therefore there are also 5 independent and 6 dependent variables in this field.

Some simplifications may reasonably be made:

-a) Vertical components are likely to be small and opposed. b) Trimming moments are assumed small, especially as they may

be balanced by crew movement in many boats.

c) Yawing moments and rudder angle may be disregarded since in a weIl balanced boat neither occurs to a significant extent. d) Variations in sail shape, which affect the sail coefficients,

may be neglected.

Thus only thirteen variables remain and are shown in fig 10. For dinghies and multihulled boats which are not allowed to heel, the heel angle S and the heeling moments may be neglected, leaving 10 variables.

The problem of solution is therefore quite formidable even when the aerodynamic coefficients are well known, which is unfortunately not the case;

for conventional sails and then to a much les ser extent for a more uncon-ventional form of sail.

4. Conventional Sails

4.1 Forces

A wind tunnel balance will give values of lift and drag coefficients. It is not ilDmediately obvious what these signify in the case of sails and

they are therefore normally resolved into coefficients CR and C

H as shown

in fig 11. For maximum sailing speed it can be written that equation (5)

should be a maximum.

(5 )

(6)

This can be obtained either numerically or graphically but it is a lengthy process when found for all points of sailing.

Typical curves of the variation of lift and drag coefficients

with incidence are shown in fig 12. It can be shown that when sailing close

to the wind high LID ratio is important whereas downwind high CD is

predominant. It is interesting to note that a sa~l appears to stall at

about 30° to 40°, and that it is operated in this region when reaching.

4.2 Wind Tunnel Problems

The determination of sail forces in a wind tunnel causes some difficulty, not only because of the number of variables involved, but because accurate model representation is difficult. Most models to date have been made of sheet metal since the use of cloth sails for even

moderately small sizes has only recently become possible. Further a model

needs to be capable of being heeled about an axis making an angle (f3 -À )

and a1so the hu11 inf1uence on the sai1s need to be investigated and represented in wind tunnel tests.

4.3 Aerofoi1 Cross Section

A sai1 bears a simi1arity to the wings of ear1y aircraft because

both have on1y one canvas surface partia11y stiffened with wood. A sai1 is basica11y a 10w-speed infinite1y thin aerofoi1 with the two drawbacks that it is both f1exib1e and porous, a1though the latter is probab1y

insignificant with modern synthetic materials.

It seems reasonab1e that an arched sail will give more thrust than a flat sail but it is more difficu1t to decide exact1y how much arching wi1l give the optimum thrust, and a1so at what distance a10ng the

chord 1ine the position of maximum arch shou1d beo The amount of arching mayalso have to be changed according to the weather conditions since the

true wind speed may vary from zero to about forty feet per second. The

same true wind speed wi11 a1so give a different apparent wind speed over

the sai1 according to the course being sailed. Ideal1y therefore the arching of the sai1 may have to be changed even during the course of a race.

A series of tests was made by Eiffe1 using tin wings to determine the characteristics of surfaces with different amounts of arching. Fig 13 shows the resu1ts he obtained for a flat p1ate and three arched surfaces with a wind speed of 10

mIs.

The resu1ts are p10tted as they were obtained from the lift and drag ba1ance, but the forward thrust and side thrust may be obtained by the methods mentioned in &ection 4.1. It wou1d seem that section C has

the best characteristics but it is on1y the best when reaching or running.

Section B wou1d be the best for windward conditions and since this is of ten

the most important point of sai1ing, section B would be the best compromise. A considerab1e advantage wou1d, however, be gained if the section shape

could be altered easily.

The shape taken up by a two dimensional sail has been calculated by Thwaites, assuming that the luff and leach were a fixed distance apart. It should be remembered that because a sail is flexible neither the shape

nor the loading can be specified in advance since they are interdependent.

His solution shows that the point of maximum camber is a little forward of mid-chord at high incidences, moving aft to the mid-chord point as the

incidence decreases. Experimental confirmation of the calculation was

provided by Tanner.

Thwaites' two dimensional sail did not, however, include a mast. This could considerably influence the flow and therefore the optimum

position for the maximum camber. Some experimental results of interest

were obtained by Junkers who tested some models of sails in a wind tunnel

at Dessau in 1923. He tried five models in which the sail had a constant

angle of incidence all the way up the mast and three more models which had a decreasing angle of incidence towards the tip corresponding more closely to real sails. The cross-sectional shapes and results obtained are shown in fig 14.

All the sails were triangular in outline but each had a different cross-sectional shape and the details are:

Model I had a moderate arch, a decreasing angle of incidence towards the tip and also a gap between the mast and the sail to simulate a sail which is only laced to the mast.

Model 11 was similar to Model lexcept that the slit between the mast and the sail was closed. The lift-drag curve shows that this was a

considerable improvement.

Model 111 was similar to the previous two but the mast was faired

into the sail to give a more streamlined shape. As might be expected this

sail was a great improvement on the previous two models.

incidence all the way up the mast. It had only a slightly arched surface resulting in very poor lift.

Model V represented sails in which the leach was flat or even sagged to leeward. The extremely unfavourable curve obtained shows how useless this sail shape would beo

Model VI was similar to Model I, with the difference that it had a uniform angle of incidence and the point of maximum arch was aft of the mid-chord position. The greatly improved characteristics of the model can be attributed mainly to the uniform angle of incidence.

Model VII was similar to Model VI but with the mast faired into the sail in a similar manner to Model 11, with a corresponding improvement.

Finally Model VIII was tried. It differed from Model VII only in the position of the maximum camber which was moved to the mid-chord position. The model stal led at a lower lift value than Model VII but had a bet ter

lift-drag ratio.

In conjunction with Junker's experiments the results of pressure plotting on a full-size sail by Warner and Ober, and also on a model by

,

Southampton University, are of interest. A typical pressure distribution on a simple sail is shown in fig 15. It is noticeable that the high negative pressure peak obtained on a wing is absent. Warner and Ober found this peak present on the jib and therefore attributed the loss to the effect of the mast. Tanner however has shown that such waveness in

pressure distribution will theoretically occur on a very thin aerofoil within a limited range of incidence and curvature, which could explain why the

effect was not found on the jib or on the head of the main sail.

It is suggested therefore, using the results so far available that the cross-section of a sail should be a circular arc with a camber of about 1/13. The mast should be faired into the sail if possible and the sail should be set at a uniform angle of incidence to the apparent wind.

leach. The .unfavourable lift-drag curve obtained explains why the leach of most sails is stiffened with battens. It has been suggested that battens extending completely across the sail in the chordwise direct ion would

further improve the performance of the sail, and this is now allowed on catamarans and a few other classes of boats. A simple experiment was done to demonstrate first the effectiveness of a curved surface and then the further advantage gained by stiffening it in a chordwise direct ion. Three gliders were made, one with

a

flat wing, one with a loose curved surface, and the third with a stiffened arched surface. Each glider was towed up on the end of a thin line and the greatest angle of elevation each achieved was noted. The results, shown pictorially in fig 16 indicate the superiority

of a stiffened arched surface.

4.4 Aspect Ratio

The cross-sectional shape has now been suggested, but the aspect ratio and the outline of the sail are still undecided. A high aspect ratio would conform to aircraft practice and would have the advantage that the sail would be less likely to be blanketed by other boats and obstacles, and also could use the increased wind speed higher up, due to being further out of the boundary layer formed near the water. Unfortunately as the aspect ratio increases so the cent re of pressure moves further up the mast. This affe cts the stability of the boat which is limited by the beam and the righting moment of the crew or keel.

Morwood has produced some results of the effect of aspect ratio. These are in the form of thrust and side force coefficients, parallel and perpendicular to the course of the boat respectively, and he also brought in the speed of the boat by using a speed ratio given by the ratio of the boat speed to wind speed. Ris graphs show curves for speed ratios of 0 and 1 corresponding to strong and light winds. In fig 17 the thrust coefficient is plotted against aspect ratio with the apparent wind 40°

from the course being sailed. The curves show that an aspect ratio of 6 would be best, while fig 18, which shows the side force ~oefficient under the same conditions, indicates that any aspect ratio greater than three would have the same side force coefficient.

Figure 19, however, shows the variation of thrust coefficient with aspact ratio when the apparent wind is 1200

off the course. Although an aspect ratio of 6 is best for light winds, a much lower aspect ratio seems better for strong winds. Unfortunately no corresponding side force coefficients were given for fig 19. Morwood's resu~ts appear to have been derived from experimental data but no further details were given.

The curves indicate that a sail with an aspect ratio of 6 would be the best compromise, especially since the sail is rarely used to its full extent in strong winds. Dr. Ljungström came to a similar conclusion and built a boat with a single high aspect ratio sail, shown in fig 20, which he sailed during the Clyde International Fortnight in 1938. The mast was not stayed and could be rotated to reef the sail. The sail also had a loose foot to allow good arching all the way down. The sail was not stiffened in any way and there was no jib with the result that the boat did not perform so weIl close to the wind but in other respects the rig was very satisfactory.

There are two main rigs for sailingboats, the Bermuda and gaff rigs, shown in fig 21. The Bermuda rig gives a higher. aspect ratio for the same sail area than the gaff rig which also has the disadvantage, as shown by Professor Junkers, that the gaff sags to leeward, thus decreasing the angle of incidence at the head of the sail.

4.5

.Outline of the Sail

The Bermuda sail is triangular in outline, although on more modern boats there is a noticeable curve on the leach of the sail. Simple aerodynamic theory proves that an elliptical wirtg plan gives the greatest lift and lowest induced drag 80 that a similar shape would seem best for a

sail plan. A similar result has been deduced by other yachtsmen, not from aerodynamic principles, but from comparison with the wings of those birds which have to glide for long periods. As a result a few rigs have been produced with the tip of the mast pulled aft, as shown in fig 22.

Only the mainsail however was considered, and the presence of the jib completely ignored. A better solution might be obtained if the whole sail plan were elliptical or a close approximation and would then perhaps be as shown in fig 23. No account however has been taken of the effect of the gap between the boom and the huil. The structural problems

involved in producing such a mast tip would be considerable.

4.6 ·. Int~raction of the Sails

Manfred Curry and also Warner and Ober investigated the air flow around a mainsail both with and without a jib. As can be seen from figs 24 and 25 the air flow is much smoother with a jib in position. The jib works in a similar manner to a leading edge slot and once this has been realised many improvements can be suggested for the design of the jib. On an ordinary boat the jib extends to between half way and two thirds of the way up the mainsail. This results in an irregular air flow over the upper part of the sail and a considerable improvement could be made by having a tàller jib.

Force measurements show that the maximum lift-drag ratio of about 4.4 obtained on a mainsail by itself was increased to about 6.5 when a large overlapping jib was used.

Figure 26 shows how the air flow is affected when as so of ten happens the jib is cut with too much arching or is hauled in too close to the mainsail. Therefore the jib should be made with just a little arching, and adequate provision made to allow the jib to the correct~y positioned.

Comparison with a leàding edge slot shows th at the jib is unfavourably placed to produce the best effect on the mainsail and a

comparison with tests on aerofoils suggests that the chord of the jib should be one third of the size of the mainsail chord, and its leach should be on the quarter chord line of the mainsail. The tests also indicate t~at the luff of the jib is too far to leeward so th at a consid-erable improvement could be made if the jib could be traversed sideways to bring it more into the position shown in fig 27.

It is more awkward to gain appreciably from the interaction of the sails when the wind is directly astern of the boat. The usual method of sailing is to spread the sails nearly at right ang1es to the boat as shown in fig 28.

It has been suggested, however, that if the mast could be made strong enough not to need shrouds as supports it w0uld be possible to let the sail further out and thus make it become an aerofoil again. However, the shape of the lift and drag curves make this impractical.

4.7 Air Flow

The air flow over the lee side of the sails has already been shown in figs 24 and 25. Manfred Curry also investigated the air flow over the weather side of the mainsail and was surprised to find that the air flow direct ion at the front of the sail was forwards. The sail he used, illustrated in fig 29, had a gap between the mast and the luff of the sail, with the resuit that the air escaped from the weather side into the low pressure region on the lee side of the sail. Warner and Ober, however, did not find this flow because their yach~ had a more modern rig in which the Iuff of the sail was securely fastened to the mast.

Similarly, the air was found to flow under the boom into the low pressure region. Warner and Ober tested a model sail in the wind tunnel and found that by placing a piece of material between the boom and the floor of the tunnel this air flow was eliminated. From an aerodynamic point of view, stopping the vortex forming under the boom increases the

aspect ratio. It was therefore expected that the lift coefficient would increase, but rather surprisingly it was found that the lift was slightly decreased but with a larger decrease in drag. In practice it is not possible to join the boom to the hull. However, in conjunction with the idea of fully - battened sails, mentioned when considering the cross-sec-tional shape of the sail, it might be possible to restrict the flow under the boom as shown in fig 30 and would also allow the sail to be arched right down to the boom. This idea has been tested by Millward and was found to give slightly better results. However,the validity of the result is questtonable since the improvement was small and possibly outweighed by the inaccuracies of the equipment available for the test.

4.8 C.onclusions

Several improvements have been suggested even from the little data available, although structural considerations may not allow some of them to be used. It is suggested that the following improvements could be made.

1. The cross-sectional shape should have an arch of approximately 1/13 with the maximum arch at the half chorda

2. The sail should have a uniform angle of incidence to the apparent wind all the way up the mast.

3. The mast should be faired into the sail.

4. Full length battens would be an improvement on the short battens at present in use.

5. An aspect ratio of 6 would be the best compromise for normal weather conditions.

6. The jib should extend as far up the mast as pbssible to give the full "leading edge slot" effect.

7. The jib should be able to be traversed sideways into the correct position for the optimum effect on the air flow over the mainsail.

A considerable amount of research is needed before any definite

conclusions can be reached. It is unfortunate that the only official body

in England, the Yacht Research Council, formed to promote research into hulis, sails and fittings, died through lack of support from the yacht

building industry. Siffiilarly Southampton University who are now doing

considerable work in both sails and hulis, although they have gained considerahle support from the United States have received little support from the British yachting industry.

It is interesting to note that the huIl of 'Sceptre', the 1958 America's Cup challenger was partly tank tested but no research was done on the sails at all!

5 Wingsails

5.1 General

In more recent years many people have become intereste-d in improving yacht performance and there have been attempts to use aircraft practice in providing the thrust for the boat instead of using the more conventional sail. For convenience these devices wil 1 be cal led wingsails.

Most wingsails have been designed and built on an amateur basis and therefore they range from the freaks to the few which are based on

sound principles. Before describing three wingsails it would be useful to

summarise the differences between anormal sail and a wingsail.

Information is readily available on the lift and drag coefficients of standard aerofoils, although mostly at Reynolds numbers considerably above those encountered in sailing. However, as has been shown previously, there is little information available on sails. It is possible to conclude

however that:

-1. The lift coefficient of a sail is about the same as for a cambered aerofoil.

2. The drag of a sail even when not flapping is considerably higher than that of an aerofoil. At low lift coefficients which involves allowing the sail to flap, the comparison is

even more in favour of the aerofoil.

It should be remembered that the criterion for maximum performance of a boat varies with wind speed for any form of sail power. For example at low wind speeds when the heeling moment can be balanced, maximum lift is required for beating into the wind. However, at high wind speeds the requirement changes to minimum drag, because the heeling moment due to the full lift force becomes too large. It is in these circumstances that a conventional sail has to be allowed to flap causing a further increase in drag, assuming that the same sail area is retained.

A boat also has to be able to sail with the wind on either side of the boat and therefore on either side of the sail, so that a cambered aerofoil, unless using some complicated mechanism for reversing the camber, becomes impracticable. This results in thechoice of a symmetrical section aerofoil.

5.2 Canoe Wingsail

The wingsail shown in fig 31 was made for a 10 sq.m. canoe. The wingsail was mounted on a pivot allowing it to rotate through 3600 _{but was}

maoually set at an incidence to the wind.

Little sailing experience was gained with this sail because the whole performance was rather alarming for the helmsman except in very light winds.

5.3 Norwegian Wingsail

The wingsail shown in fig 32 is of a considerably more sophisticated design than the previous one although built many years before it. The

provided with a tailplane. The tailplane angle was controlled by the

helmsman and th~s enabled the main aerofoil to be set automatically to any desired incidence to the wind irrespective of the direct ion of the boat. A mass balance was provided forward of the leading edge.

This wingsail performed very satisfactorily but was unfortunately

destroyed before it could be further improved.

5.4 Blackburn Wingsail

This wingsail is a logical progression from the two previously described and may indeed have been influenced by them. As can be seen in fig 33 it consisted of a rectangular wing with a 25% chord plain flap. A smaller aerofoil was mounted behind as a tailplane. Both aerofoils were of NACA 0015 cross-sectional profile. The whole assembly was freely pivoted on a stub mast with control cables leading from the helmsman's position in the boat to the flap and tailplane.

The full flap angle 'is used for maximum speed except when the heeling moment becomes too great in high winds. The flap angle can then be progressively reduced until in very strong winds or when maneouvering in çonfined spaces only the symmetrical aerofoil is used. The tailplane is again merely used to set the aerofoil at an incidence to the wind.

The construct ion was similar to model aircraft practice. The ribs and spans were made of I millimetre plywood reinforeed with square section hardwood. The leading edges were plywood but the rest of the skin was muslin. The whole skin was sprayed with several coats of dope.

It was unfortunate that the testing programme had to be hurried since high winds prevented calibration tests being do ne on dry land. It was soon found 00 the water that the tailplane was not powerful e~ough to hold the main aerofoil at any given incidence to the wind. The incidence control therefore had to be done manually which was not very satisfactory. Another problem was that any small disturbance of the boat caused an

incidence change on the aerofoil, the whole system rapidly becoming unstable.

A mass balance and a larger tailplane were added, shown dotted

in fig 33. A further test showed some improvement. Unfortunately no

more tests were carried out because of the close of the sailing season.

~ome useful information was however obtained. The main conclusion was that even assuming the aerodynamic controls could be made to work

properly the wingsail would be much bet ter for experimental purposes if mounted on a more stable boat such as a catamaran.

5.5 Conclusion

It seems that a wingsail could be made to work satisfactorily, especially if used on a catamaran or similar boat, where the greater weight and moment of inertia of a wingsail would not be so noticeable. Such a large fragile structure is awkward to store when not in use and difficult to erect, particularly in windy conditions. A wingsail does, however, give a very fine control of thrust and can easily be used to send

the boat in reverse. However, whether a wingsail will eventually show any

advantages compared with improved versions of more conventional sails is somewhat doubtful.

REFERENCES

1. T. Tanner "A Survey of Yacht Research at Southampton University" -Roya1 Aeronautica1 Society Journa1 - Volume 66, N° 622, October 1962.

2. A. Millward "The Aerodynamics of Sails (with particular reference to dinghies)" - Roya1 Aeronautica1 Society Journa1 - Volume 66, N° 624, December 1962.

3. T. Tanner "The Forces on a Yacht's Sai1" - Royal Aeronautica1 Socie.ty Journa1 - October 1930.

4. B. Thwaites "The Aerodynamic Theory of Sai1s - I Two-dimensional Sails" Proceedings of the Roya1 Society - A Volume 261, 1961.

5. E.P. Warner

&

S. Ober "The Aerodynamics of Yacht Sails" - Society of Nava1 Architects and Marine Engineers - November 1925.

6. A. Millward "Some Wind Tunnel Measurements on Yacht Sails" - unpublished.

HEAO

LUFF

FOOT

TACK

f

1-

.-l ~ \ _BOOM

I

FIG.l

.

THE PARTS OF A SAILING

BOAT

TRUE' WIND TRUE WIND

1

1

~

~EACHING

!

RUNNING

FIG.2.

THE COURSES OF

A

Windward

~

V

MG

=

Speed to

y

=

Course Angle

B

=

Apparent Wind Angle

FIG.

8

VELOCITIES IN THE GEOMETRY FIELD.

F

RW FHW

F

H

=

Aerodynamic Side Force FR

=

Thrust Force

FV

=

Vertical Aerodynamic Force

I='H

F

HW

=

Hydrodynamic Side Force F

RW

=

Hydrodynamic Resistance

- - FftW _FyW

₌

Yertical Hydrodynamic Force Y

S

=

Yacht's Water Speed

F~w Y

A

=

Apparent Wind Yelocity

CL C -D CR C_H z VA y E. V_{s VA} V_s VA 6, a, _{aM' aF} À, a fl _{CR' CH' KR CRW ' CHW ' KRW}

-FIG. 10 A SUMMARY OF THE VARIABLES INVOLVED.

Measured Lift Coefficient

Measured Drag Coefficient Thrust Coefficient

Aerodynamic Side Force

Apparent Wind Velocity

Course Ang1e

Ang1e of Sai1 to Course

FIG. 11 RESOLUTION OF WIND TUNNEL FORCES.

I-r

1-0

o-a

UFT & nRAC

COE.FFIC.IEJolT'S 0-4 0-4 oot o _{o 40 f,Q 00} AHGLE. OF INClllE.NCE.

FIG. 12 TYPICAL CURVES OF LIFT AND DRAG

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WIND 10 M,/! EC. 002

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I D. ARCHING /27 _~----~

FIG.13. LIFT -DRAG CURVES FOR UNIFORMLY ARCHED SURFACES

LIFT KG. a b 4 , . / ... / " 0 - - -1- _ _ __ -1

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_{- - v} • I 1 Ó DRAG KG . ~O II~ III~ TWISTEO IV ---- --~ V ~,...---_{- ---0 VII . .r __ ~} VI~YIIJ~ NO TWIST

FIG.14. LlFT-DRAG CURVES FOR DIFFERENT CROSS SECT/ONAL SHAPES

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CR 0-4 0-2 0-0 -!.1, h I 4 b q ASPECT RATIO

FIG.1? THE EFFECT OF ASPECT RATIO

ON THRUST COEFFICIEN T C H o WIND AT 40i - I

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Yb

4 b ASPEC r RATIO Cl

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FIG .18. THE EFFEC TOF ASPEC TO RATIO

QlII SlOf FORCE COEFFICIEN T

2-0 I-b 1-2 CR o·a 0'" o WIN AT I o· !4. ~ Eo Cl ASPECT RATIO

FIG.19. THE EFFECT OF ASPECT RATIO

----

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FIG.20. OR. LJUNGSTRÖMS HIGH

ASPECT RATIO RIG

FIG.22 . SEMI-ELLIPTIC

MAINSAIL

FIG.21. ILLUSTRATION OF BERMUDA

& GAFF RIGS

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FIG. 2 6 . AIRFLOW WI

TH

BAD JIB

- WITH JIS

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FIG.27. AIRFLOW

WITH TRAVERSABLE

FIG

.

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.

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Aerodynamics

I • MILLWARD A.

made with aeroplane wings provided the differ

-THE AERODYNAMICS OF SAILS

11. TCEA TM 16 ences are a150 remembered.

May 1963 _{A knowledge of some sailing terminology would}

be useful to an aeronautical engineer.

A considerable amount of

re-search has been done on the design of boat hulls, but very

little research has been done on sails. A sail can be considered

as a thin aerofoil mounted in a vertical plane and therefore

some useful comparisons can be

TCEA TM 16

I

Training Center for Experimentall Aerodynamics

I • MILLWARD A.

made with aeroplane wings provided the differ-THE AERODYNAMICS OF SAILS

11. TCEA TM 16 ences are also remembered.

May 1963. _{A knowledge of some sailing terminology would}

be useful to an aeronautical engineer.

A _{considerable amount of}

re-search has been done on the design of boat hulls, but very

little research has been done on sails. A sail can be considered

as a thin aerofoil mounted in a vertical plane and therefore

some useful comparisons can be

Aerodynamics

THE AERODYNAMICS OF SAILS May 1963

A considerable amount of

re-search has been done on the design of boat hulls, but very little research has been done on sails. A sail can be constdered as a thin aerofoil mounted in a vertical plane and therefore

some useful comparisons can be

I. MILLWARD A.

11. TCEA TM 16

made with aeroplane wings provided the differ

-ences are a180 remembered.

A knowledge of some sailing terminology would

be useful to an aeronautical engineer.

''---

=ft

~IT=C=EA==T=M=1=6================::::;:1 ==========~II

I

Training Center for Experimentall Aerodynamics

THE AERODYNAMICS OF SAILS May 1963.

A considerable amount of

re-search has been done on the design of boat hulls, but very little research has been done on sails. A sail can be considered as a thin aerofoil mounted in a vertical plane and therefore

Some useful comparlsons can be

I. MILLWARD A.

made with aeroplane wings provided the

differ-11. TCEA TM 16 Ilences are also remembered.

A knowledge of some sailing terminology would