Stability of big sailing vessels


If going to sea under sails it is necessary always to bear in mind that all forces that work on the sails relate to the squared velocity of the apparent wind. If the wind gains force (aka speed) the aerodynamic forces grow even faster and are liable to become means of disaster. Masts that carry a huge area of sail may break, the ship heels over more and more and she might even capsize. The latter being most dangerous as the capsizing of a sailing vessel in most cases happens within seconds and there is a great chance that she will go down together with the entire crew.
There is a simple method to achieve more safety: reducing of sails in relation to the speed of the wind. That means reefing or taking away sails to reduce the sail area or de-powering sails by bracing (or sheeting) them less sharply. As a rule reducing the sails starts from the mast tops down to the deck thus not only reducing the all-over sail area but also moving the centre of windage more down and thus reducing the heeling moment of the wind in the sails.

On the MIR there are 5 standard variants which will be chosen accordingly to the wind velocity:

Sails set  Up to ... app. Wind [kt]  Sail area [m2]  Height [m] centre of windage above keel
all sails  <15   2881 30.97
without royals, flying jib  15 2359 28.97
as before without t’gallants, upper layer of staysails, outer jib, mizzen   17 1704 25.6
as before without courses, lowest layer staysails 20 980 29.31
only with lower topsails 23 459 26.14
under bare poles (no sails set) >30 920 15.98


Additionally to these the figures the windage of the hull and the bare rigging (see last row of the table) must be taken into account and the moment added to moment from the sails.

Whether the forces of the wind in the sails lead to more speed or to more heel is a matter of the aerodynamic forces in the sail. Without going to much into detail here it can be said that the heeling moment has it's maximum on close-hauled courses where the wind not pushes the ship but the aerodynamic forces suck her into a direction rectangular to the yard arm that means on closed-hauled courses approx. 60° leeward of the bow. Thus you receive a heeling moment which results of the wind force times the sail area working (both sails and hull) times the height of the centre of windage (minus middle draught) squared times the cosinus of the heeling angle.

Mheel = ( Fhull + Fsail ) x ( Zwindage – T/2) x cos Θ

with

Fhull + Fsail  = Cy  x ρ/2 x W² (Asail + Ahull) x cos Θ

Mheel = heeling moment
Fhull + Fsail    = wind forces on sails and hull (and standing rigging)
Zwindage = Height of the centre of windage
T = middle draught
Θ = heeling angle
Cy = aerodynamic coefficent (roughly 1.3)
ρ = barometrical air pressure
W = velocity of the apparent wind
Asail + Ahull x cos Θ  = working area of sails and hull

The next question is now what does this heeling moment with our ship? For this we must understand what actually is stability.

Under stability we understand the ability of the ship to return into an upright position after a disturbance (e.g. squalls, high waves, steering errors). This works trough the equilibrium of the forces of gravity (the weight of the ship) and buoyancy (the weight of the water displaced by the ship).

Now keep in mind that a big tall ship is not a yacht and does not behave like a yacht. While on yachts the centre of gravity is normally at or near the keel and thus always below the centre of buoyancy, a tall ship is – despite being fitted with a keel – a cargo ship with sails and thus behaves like a cargo ship. That means that the centre of gravity is always situated higher than the centre of buoyancy and she is liable to capsizing like a dinghy if we do not treat her with the necessary care.

To make the fun complete different than on cargo ships where once the cargo is lashed and given that there are no changes in the ballasting the centre of gravity remains in one place for the durance of the voyage, it can move on sailing ships due to the weight of the sails set or dowsed and the relatively large number of crew on board moving around. Send 100 cadets aloft to furl sails and you have moved 6 tons 30 m up and 20 m out from the centre line...

But let’s return to the wind force in the sails. It attacks in the centre of windage and heels the ship around a point above the keel called the metacentric height. On one side of it act the heeling forces as seen in the equation above and on the other side we have the righting forces from the hull. Without wind those would act to return the ship into an upright position but now the wind forces are counteracting this and so the righting moments (Mstatic) will only work up to an equilibrium with the heeling moments from the wind (Mheel). You now achieve a new “zero-position” into which the ship wants to return due to her buoyancy. That means the ship sails with a certain heel angle and the waves will make her roll from this position on. E.g. this can mean that in a heeling angle of 15° starboard she will actually roll from 5° port to 35° starboard where a cargo ship of the same size would roll from 20° port to 20° starboard.

So let’s find out about the righting moment (Mstatic). A first estimate on it can be done by calculation the distance between the centre of gravity (G) and the metacentre (M), the so called GM. If you imagine a triangle spanning between G, M and the centre of buoyancy (B) you will easily understand that a righting lever between B and G can only work satisfactorily if GM has a minimum length.

Unfortunately the metacentre is only static in small heeling angles (up to 15°). If the ship heels further it moves upwards and to windward. To make things still calculable all big ships have tables where the distance of the metacentre from the keel is listed. If we now want to find out about the righting moment our ship has to return into an upright position under the given circumstances we need to calculate the righting lever between the centre of gravity (G) and the centre of buoyancy (B), which also moves due to the form of the hull. (B is always in the centre of the submerged space of the hull.) This righting lever GZ is a function of the heeling angle and the distance between the centre of gravity and the keel. If calculating this for different heeling angles you receive a characteristic curve which represents the intact stability of the vessel.

GZ = (KN – KG) x sin Θ

Mstatic = GZ x Dg

With
GZ = righting lever between G and the horizontal component of B (Z)
KN = distance between the keel and the vertical component of the metacentre (N)
Dg = weight of the ship

As for cargo ships there exist certain limits in which this static stability must be. As for sailing ships these limits do not work. Remember, she does not return to an upright position after a disturbance, but to the “zero-position” which belongs to the heeling forces of the wind in the rigging which depends on the sail area and angle of attack which you have in that very moment. Therefore there must be an added safety range. While on cargo ships the margin of stability (where there is still a positive righting lever) is normally 60° on sailing ships the minimum should be 90°. On MIR it is 110°.

To find out how much heel the ship will have under the influence of a certain wind impact both equations – the righting moment Mstatic and the heeling moment of the wind Mheel  -  must be compared. This is normallyy done by calculating the work needed to heel and right the ship for certain heel angles and drawing the curves into one diagram. At the point where the curves cut each other you can read the angle of heel that belongs to this wind impact.

Another important figure is the heeling angle where the righting lever is maximal. It normally represents the angle when the edge of the deck comes to water. On MIR with a freeboard of 4.6 m this happens only near 60° and with her having all openings in the deck near the ship’s middle her righting lever still grows after this until 90°.

But this is all blind theory. In the famous cases of capsizing of tall ships in the past (ALBATROSS, MARQUES, PRIDE OF BALTIMORE, NIOBE, PAMIR) hatches or companionways were wide open at the time of the incident and downflooding happened. So keep in mind that the deck-to-water angle is the critical point and set your sails always so that in case of an unexpected squall laying you over no water will enter the inside of your ship. Reduce the sail area at the moment when you think of it. Don’t wait for a moment that might suit better (e.g. at the change of watches) and never assume deteriorating weather to get better after a short while. Always expect the worst.

Sails set   Wind necessary to heel MIR to 45° [m/s]
all sails 14.0
without royals, flying jib  15.8
as before without t’gallants, upper layer of staysails, outer jib, mizzen 19.1
as before without courses, lowest layer staysails 22.0
only with lower topsails 29.0
under bare poles (no sails set) 42.0
 

Yet there is another way to reduce the impact of the wind forces on the heeling of our ship. If you feel you cannot reduce the sail area any more, e.g. if otherwise you would loose steerage way or you have already taken away all sails and she is still heeling. Remember, all forces are relative to the squared velocity of the apparent wind. The apparent wind consists of 2 vectors: the true wind and the negative vector of your own speed. If beating against the wind both add. So if you bear off you will diminish the apparent wind by the rate of your own speed. In the extreme this will mean running before bare poles. In how far this is practicable – that is another question which will be discussed in the chapter about bad weather strategies.

this page was added 10/07

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