Chapter 12 The geometry of the Bermuda rig as it is used in model
yachting
The sheeting mechanism
The Bermuda rig is shown in Picture 12-1. It is the rig most commonly used in model yachting. It has a main sail and a fore sail. The main sail is mounted on the mast being attached by rings of some sort at the luff. The foot of the main sail is attached to the main sail boom which swings on a goose neck. The fore sail is attached at its foot to a boom that is either pivoted at its forward end or on a swivel at some point along the boom. The luff of the fore sail is attached in some way to the fore stay. A mechanical system of sheeting is used to adjust the two sails. In a model yacht it would be desirable to have a sheeting system which made it possible to set the sails in the best positions for any point of sailing.[1] In practice, even when the class rules permit the use of two winches, most opt for only one winch. This winch operates though a very simple system of cords and pulleys that is not necessarily amenable to the fine adjustment that would be needed for the sails to be set to their best positions at all points of sailing. However, given the simplicity of the system, we can look at its geometry to find out what is possible and then use the outcome in conjunction with the Hele-Shaw equipment to attempt to optimise the rig and its sheeting.
We need a clear idea of the system that we are thinking about. The pictures are of a metre boat.
Picture 12-2 shows the deck mounted
sheeting system on a metre boat. The travel of the sheeting is between two
pulleys fixed to the deck. The sheeting cord runs round these two pulleys and
the two reels of the drum on the winch. The loop is closed by a short spring
that takes up changes in length of the cord as it winds off one reel and on to
the other. Two more cords are attached to the appropriate end of the sheeting
cord and these pass through two more pulleys in the triple block near to the
mast. One then goes via the sheeting post to operate the main sail boom and the
other goes through an eye on the deck to control the fore sail.
Picture 12-3 shows the rig sheeted in. Note that the eye on the main boom passes over the top of the sheeting post. If the eye on the boom is at any other radius the sheeting cord will be angled and an unnecessary load will be applied to the winch. Picture 12-4 shows the rig sheeted out. By the design of this sheeting mechanism the two sheeting cords travel the same distance between the positions shown in these two pictures. It seems to me that a study of the sheeting mechanism for a Metre boat is likely to be of use to more readers than any other class and is easily transferable so I have analysed that.
The winch
Most yachts are fitted with drum type winches like the one shown above. Commonly such winches can rotate by up to 5 turns for the full throw of the transmitter stick. This can be reduced either at the winch or through the transmitter if ATV is fitted. There is a compromise to be made. The work required from the winch when sheeting in fully in heavy weather is the same regardless of the number of turns that the winch makes. If it makes only two turns the current drain must be twice that for the same winch set up to sheet in during four turns. This may well exceed the specification of the winch. The resolution of the winch is not so good for two turns as for four but four turns takes twice as long as two turns. There is an optimum number of turns and commonly this is three turns taking about three seconds. The manufacturers of winches will specify how many turns of the winch drum gives the best compromise between speed of the winch and power demand during sheeting. This has an influence on the set-up of our rigs.
The requirements of the rig.
We have yet to look at the sails to see what relationship between the sail angles might be best for all points of sailing. However one might expect that we need to have the same relationship for all three of the suits of sails that are permitted on a one metre boat. Most designers would aim to use the most simple set-up and then the critical dimension is the distance from the fore sail swivel to the sheeting eye on the boom of the third (smallest) suit. As we shall see this determines the position of the sheeting eye for the main sail as well. It also adds another significant factor to the compromise to be made for the winch.
Sheeting the fore sail
Let us start with the fore sail.
Diagram 12-5 shows a typical arrangement of a fore sail. It is the only
arrangement permitted for Metre boats. The boom is attached to the deck through
a swivel and the fore stay and the leech line are attached to some point up the
mast. If the tension in the fore stay is increased so also is the tension in
the leech line. Adjustment of the length of the leech line will alter the
distance between the head of the sail and the clew and so alter the set of the
sail. In windy conditions the sail tends to fill and, if the tension in the
forestay is insufficient, the leech line will go slack and the shape of the
sail go out of control. In order to avoid this and, for the tension in the fore
stay not to be excessive, the distance from the swivel to the forestay must be
as large as is practicable. However there is a contrary requirement. The sail swings
about an axis through the swivel and the mast fixing and the sail will only set
quickly during a tack if the force on it is far enough aft of the axis to have
a useful moment arm. This sets a limit to the rearward position of the swivel
that turns out to be about 25% of the length of the foot of the sail.
We have already noted that the geometry must
be based on the length of the boom on the fore sail of the third suit. The
class rules for metre boats allow a length of 11.75² for the foot of the fore
sail. We know that the swivel will have to be attached at about 25% of the
length of the foot from the luff attachment that means at about 3² from
the end of the boom. This leaves us with a maximum distance between the swivel
and the sheeting eye (I shall call this distance the sheeting arm) of 8.75²
which means that allowing for a clew fitting we must think of 8², or
perhaps less, as a typical length.
Diagram 12-6
shows the sheeting mechanism of the fore sail boom. I have supposed that when
it is sheeted in the boom makes an angle of 20° and when it is sheeted out an
angle of 85°.
The sheeting cord has an initial length of ABi and a final length of ABo. If we let
the distance between the swivel and A, the sheeting eye on the deck, be equal
to the sheeting arm of 8²
the length from A to Bi can be found using the cosine rule.[2]
It is 2.78².
The same trigonometrical expression can be used to plot the increase in the
boom angle as the distance AB changes from ABi to ABo
This is graph 12-7. It is almost a straight line and it shows that the sheeting cord will have to be let out by a total of 8² to sheet out from 20° to 85°.
It is tempting to think that the shape of the
graph can be altered by moving the sheeting eye on the deck nearer to the
swivel. This can be checked. If the swivel is given the letter S then we can
plot graphs for different values of S-A. If this length is given values of, 7², 7.5², 8² and
9² and
Graphs 12-8 are the result. Clearly the graphs are all the same shape and
merely alter the length of cord to be sheeted out to produce the same change of
angle. The mechanism is not sensitive to the length S-A.. However this is
useful to know when locating the sheeting eye to be fixed to the fore deck.
We must be careful with this. When the fore sail is sheeted in the best position for the sheeting eye on the fore deck is when it puts the sheeting cord at right angles to the boom. This gives the lowest force on the winch. If the sheeting eye on the deck is moved backwards or forwards the force on the winch increases because of the angle of the cord.
Sheeting the main sail
Now we can move to the main sail boom. Of
necessity the sheeting travel is also 8² and this must change the angle
of the boom from 0°
(or just a few degrees) to say 85°.
Diagram 12-9 shows the arrangements for the main sail sheeting. C is the
sheeting post on the deck, D is the sheeting eye on the boom. For the correct
length of the sheeting arm the sheeting travel of 8² will let out the boom
from Di,
which is coincident with C, to Do. The sheeting arm can be calculated and it will be 5.9² say
6².
Then we can plot a graph relating the travel of the sheeting and the angle of
the main boom and the resulting graph is Graph 12-10. This too is very nearly
straight.
Sheeting the sails together
Now
if we plot a graph showing both sails on the same axes we shall see what is
possible. Graph 12-11 shows the angles that the two booms make for any sheeting
position. Both booms sheet out to 85°.
Small alterations of the two sheeting arms will alter the crossover point but
this graph is really the only sheeting geometry that we can have. By and large
this seems to be very promising and, in my view, better than we might have
expected.
This result clears the way for us to look at more flow patterns in the Hele-Shaw rig and in the next chapter this graph is used to give possible combinations of angles for the sails in the Hele-Shaw equipment.
Selecting a drum size for the winch
We now know that, for a sheeting arm on the fore sail of the third suit of 8² the travel of the sheeting will be about 8². If the winch is to make three turns its maximum diameter will be 0.85² and a little less depending on the diameter of the sheeting cord. The sheeting arm for the main sail is 6² which some might regard as being on the low side. However there is no escaping this unless provision is made to adjust the position of the sheeting eye on the main sail boom and the travel.
Position of the sheeting eye on the fore deck
As the sheeting arms for all three rigs is the same the sheeting eye on the boom of the fore sail of the top rig will be well forward of the eye on the third suit. This suggests the use of three sheeting eyes on the deck. Graph 12-8 tells us that we can manage with one that is centrally placed and in practice the angle of the sheeting cord when the fore sail is sheeted in will not be excessive.