5.1 Background to the Problem.

It is clear from "Sail Balance, a New Rule of Thumb" by Austin Farrar, published by RINA in 1990, and other literature on the subject of balancing the longitudinal hydrodynamic and aerodynamic centres, that there is no agreed method for determining the correct balance. Certain methods will work well for certain types of craft and for certain designers. It seems that most designers use a data base of similar well balanced past designs to determine the balance for a new design.

This method only works well if a new design is a development of similar old designs and data about these designs is accessible. Unfortunately the author does not have a large data base of past designs and experience to help.

5.2 Factors Affecting Balance

The following factors will affect the balance of a sailing craft:

· angle of trim of the hull
· angle of heel
· hull shape below the water line
· speed of the hull
· leeway angle
· hull shape above the water line
· keel position
· sail configuration
· sail profile
· mast step position
· sail twist
· mast rake
· sail camber

This subject is clearly complicated and it is therefore no surprise that the problem is normally solved using a rule of thumb.

The aim of the following exercise is to balance the boat when sailing to windward in most wind strengths. Other points of sailing shall be ignored as sail balance is most important when sailing on a close hauled course.

To make a reasonably accurate prediction of the best mast step and dagger board position the factors affecting balance must be discussed and understood before a rule of thumb can be developed. Data from the Aussie Axeman design shall be analysed and then used to find a suitable position for the WSH mast step and dagger board.

Angle of Heel

The angle of heel of the boat has a very large effect on the balance. In general, if the boat is balanced when upright it will experience weather helm when heeled to leeward and lee helm when heeled to windward. That is to say, when the boat heels to leeward it will want to turn into the wind and vice versa. This is due to two factors.

1 As the craft heels the underwater water planes become asymmetrical. They then can behave like an asymmetrical foil section, and produce yawing moments.

2 When the hull is upright the driving force from the sail and the resistance from the hull are along the same vertical plane. When the boat heels the two opposing forces are separated and form a yawing moment.

Hull shape below the water line

The underwater shape of the WSH design is likely to be much more directionally stable with heel than the Axeman design. This is because of its deep U sections aft, unlike the flat bottomed transom form of the Axeman. Transom forms change their water line sections more with heel than canoe bodies.

A Moth will normally be sailed with no angle of heel. In strong winds the boat will be heeled to windward to increase righting moment and decreases sail heeling moment. (See chapter 2.) This will produce a yawing moment steering the boat away from the wind.

The CLR Position

The centre of lateral resistance is the combined dynamic centre of pressure of the underwater hull and dagger board surfaces. This centre is hard to pin point and it moves with heel, angle of trim, headway and angle of leeway.

The CLR position will probably be governed more by the dagger board position than the underwater profile of the hull, because it produces a large proportion of the lift opposing leeway. It is therefore important to be very cautious of a calculated solution that predicts that the dagger board should be placed a large distance away from the existing balanced designs position.

There will also be a centre of lateral resistance associated with the hull and rigging above the water line. In general this is ignored as its effect on the balance is very small.

The CE Position

The centre of effort is the combined centre of pressure of the sails. In the case of the Moth there is only one sail. This centre will move along the length of the waterline with mast rake, sail camber, sail profile and twist.

Mast Rake

Clearly if the mast pivots at its step and is raked aft it will move the centre of effort aft. As discussed in chapter 4.6 the WSH design should be balanced with the mast raked at 5° . In very strong winds the mast will be raked as far back as possible. This will introduce a large amount of weather helm. Twisting the sail is very useful in strong winds not only does it depower the rig (see chapter 4.3 ) but it also moves the centre of effort forward which helps to reduce the weather helm.

Weather helm can also be offset against the lee helm produced by heeling the boat to windward. The sailor will have to judge the best mast rake, sail twist and angle of heel for the given wind strength to maintain good control and speed.

5.3 Rule of Thumb for Balancing International Moths

The author offers the following rule of thumb which is similar to Austin Farrar's "New Rule of Thumb". Austin Farrar's new rule worked well in his paper, but he applied it to keel boats heeled to leeward by 20° .

The author's rule which is to be applied to Moths shall only be validated or proven inaccurate following extensive analysis on many Moth designs. At this stage in the project such analysis is unfortunately impossible due to lack of time.

Determining the CLR

This method does not define the actual centre of lateral resistance but a centroid of the underwater area, which is analogous to the neutral axis.

The underwater shape of the hull and dagger board are traced and then cut out in card. The card is then balanced on an edge that is perpendicular to the static loaded water line. This finds the centroid of the area of the underwater surfaces.

Determining the CE

The centre of effort is found by balancing a card cut-out of the sail profile on a pin. Again this finds the centroid of area. Its position along the water line length is then measured. Note: a correction for mast rake must be done. The two different sail profiles and their centroids are shown in figures 5.1 and 5.2.

The distance between the two centroids is then defined as the lead. If the WSH design has the same lead value as the balanced Aussie Axeman then it too shall be assumed to be balanced.

Axeman data

2° of mast rake
CE from mast = 0.68 m ( see figure 5.1 )
CE from mast step = 0.76 m ( using trig relationships )
Mast step at x = 0.57 m
CE at x = -0.2 m
CLR at x = 0.12
Dagger board position at x = -0.028 m
Lead = 0.32 m ( = 9.6 % of waterline length.)

WSH data

CLR at x = -0.043 m
Dagger board at x= -0.043 m
5° of mast rake
CE from mast = 0.7 m ( see figure 5.2 )
CE from mast step = 0.91 m ( using trig relationships )
Lead = 0.32 m
CE at x = -0.043 - 0.32 = -0.363 m
Mast step position at x = -0.363 + 0.91 = 0.55 m

5.4 Sail Balance Conclusions

Two achieve the same good balance as an Axeman with 2° of mast rake the WSH design with 5° of mast rake must move the dagger board aft by 1.5 cm and the mast step aft by 2 cm.

The under water surface of the WSH design is far larger than the Axeman due to its narrow deep U sections. There may therefore be an opportunity to reduce the dagger board size and hence its resistance. Reduction in dagger board size will not change the calculated balance very much as the area of the dagger board is close to the pivot.

The dagger board and mast step are not moved very much away from the Axeman positions. This is encouraging as large position changes would throw suspicion on the method of balancing the design.