Marine Investigation Report M10F0003

The Transportation Safety Board of Canada (TSB) investigated this occurrence for the purpose of advancing transportation safety. It is not the function of the Board to assign fault or determine civil or criminal liability.

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Knockdown and capsizing of the sail training yacht Concordia
300 miles SSE off Rio de Janeiro, Brazil
17 February 2010

Introduction

On 17 February 2010, at approximately 1423, the sail training yacht Concordia was knocked down and capsized after encountering a squall off the coast of Brazil. All 64 crew, faculty, and students abandoned the vessel into liferafts. They were rescued 2 days later by 2 merchant vessels and taken to Rio de Janeiro, Brazil.

The Concordia's stability was evaluated for wind and heel scenarios considered to be representative of those experienced around the time of the occurrence. This information was then analyzed to determine the range of wind speeds which could have induced the behaviour observed onboard the Concordia during the occurrence.

Description of the vessel

The sail training yacht Concordia was built in Poland as a steel–hulled barquentine (see Photo 1). As such, the vessel was rigged with three masts: a square–rigged foremast, and fore–and–aft–rigged main and mizzen masts. The vessel could set four jibs forward and five square sails on the foremast. Between the main and foremast, the vessel could set three staysails; both the main and mizzen masts had gaff topsails and a main and mizzen sail, respectively. (Refer to Appendix A for sail plan.)

Photo 1. Concordia (Credit: Matt Jacques Photography)

Photo 1. Concordia (Credit: Matt Jacques Photography)

The vessel had three decks. The lowest deck comprised the engine room, fuel tanks, fresh water and ballast tanks, laundry facilities, and stores. The accommodation deck housed the cabins for crew, faculty and students, a captain's lounge aft and port side forward seminar room. On the main deck were two deckhouses. The wheelhouse, chartroom, radio room, and classroom were located in the aft deckhouse. The forward deckhouse contained the galley, pantry, and mess (this was used as a second classroom). Both deckhouses had escape hatches along the centreline in the deck head and weathertight doors leading to the main deck. Entrance to the paint and bosun lockers was via centerline hatches on the forward part of the main deck. The vessel's gangway was stowed overhead, supported on either end by brackets on the main mast and the wheelhouse. (Refer to Appendix B for general arrangement plan)

Environmental information and corresponding ship behaviour

Refer to the occurrence report for complete history of the voyage and weather and forecast information.

To enable analysis of the Concordia's stability prior to and during the occurrence, it was necessary to reconcile, as closely as possible, the available environmental information and the corresponding ship behaviour. As a result, information regarding ship heading and speed, true wind direction and speed, apparent wind direction and speed, and ship heel angle were compiled for 5 representative timeframes:

  • the first hour of the watch;
  • the hour or so preceeding the occurrence where the OOW was alone in the wheelhouse;
  • the 2 to 3 minute period prior to the occurrence;
  • the initiation of the knockdown; and
  • immediately after the knockdown, with the vessel on her beam ends.

Where specific items of information were not known or were unclear, approximations or calculations were made, based on assumptions consistent with the known information. For a summary of this information, refer to Appendix C. For information about the calculation method, refer to the section entitled “Wind Heeling”.

Basic data

Plans

The following plans, which were prepared by the shipyard in 1990, were made available to the TSB by the vessel's owner:

  • Lines Plan
  • General Arrangement Plan
  • Tank Plan
  • Sail Plan
  • Rigging Plan
  • Engine Room Arrangement Plan

Stability information booklet

The stability information booklet for the vessel was prepared by the shipyard in 1992. The calculations and information presented in the book were intended to satisfy criteria from the following two sources:

  • Polish Register of Shipping publication No 29/P “Guidelines for Sailing Vessels Stability Calculation and Evaluation”; and
  • British Department of Transport “The Safety of Sail Training Ships – A Code of Practice”, London 1990

The booklet was approved by Lloyd's as being, “in an approved form in accordance with the terms of Chapter I General and Regulation 10(2) of Annex I of the International Convention on Load Lines 1966” on 16 June 1993 and contains a variety of information including:

  • Details of the arrangement of solid ballast
  • Lightship data, including the inclining test report (24 Feb 1992)
  • Position of draft marks
  • Sail areas and centres
  • Information on downflooding points and immersion angles
  • Notes on Stability for the Guidance of the Master
  • Tank Capacities Table
  • Intact Stability (Righting Arm Curves) at Different Loading Conditions
  • Inclining Test Report
  • Hydrostatic and Cross Curve Tables

Using this basic data, a computer model of the hull form and tanks of the vessel was developed and validated for use in further calculations.

Occurrence loaded condition

The investigation determined that, at the time of the occurrence (approx 1422, 17 February 2010), fluid levels in the various tanks were approximately as follows:

Total Tank Capacity and Estimated Levels at the Time of the Occurrence
Tank Approximate Total
Capacity (m3)
Occurence (m3)
Water ballast 24.5 Empty 1
Potable water 37.2 29
Fuel 48.8 16
Lube oil 0.58 0.5
Black water 5.8 3
Grey water 2.7 0.76
Bilge   Dry
Oil water 1.2 Empty

Estimated change in lightship weight and centre of gravity

The investigation determined that modifications to the vessel since its launch affecting the vessel's lightship displacement or centre of gravity were few and included:

  • the relocation of the battery locker from a location on the weather deck below the wheelhouse to a location on the top of the aft deckhouse;
  • the addition of a small hydraulic pump in the engine room;
  • the addition of lifejacket stowage on the tops of the forward and aft deckhouses; and
  • modifications to some of the square sails which would have changed their shape and reduced their area by a small amount.

At the time of departure from Recife (1400, 8 February 2010), Concordia's drafts were approximately 3.8 m forward and 4.0 m aft, corresponding to a total displacement of approximately 450 t. Having estimated the fuel consumption and other changes in fluids and consummables over the course of the voyage (9 days) and then reconciling this with the departure displacement, the vessels lightship displacement and vertical centre of gravity (VCG) at the time of the occurrence were estimated as follows:

Table 1. Estimated change in lightship
  Stability Booklet (1993) Occurrence (2010) Change
Lightship (t) 379.10 382.20 0.82 %
VCG (m above BL) 5.05 5.10 %

Occurrence righting arm curve

The hydrostatics and righting arms (RA) for the vessel, in its loaded condition at the time of the occurrence, were developed. Note that the effect of water entering the deckhouses via the open doors (for details of these, see section on downflooding points below) was modelled by eliminating the buoyancy contribution of the relevant space at angles beyond that which immersed their door – the forward deckhouse was neglected after about 58 degrees and the aft deckhouse after about 88 degrees – thereby reducing the righting arms beyond those angles. A summary of these results is given in Figure 1 below. (Refer to Appendix D for further details)

Figure 1. Righting arm (RA) curve in occurrence condition.

Figure 1. Righting arm (RA) curve in occurrence condition.

Note that, based on information available to the investigation regarding the distribution of liquid tank loads, it is estimated that the vessel would have developed a list to port of about 3.5 degrees by the time of the occurrence. Considering that vessels under sail are constantly heeling, the presence of such a list would not likely have been noticed by those onboard.

Figure 2, below compares the Concordia's righting arm curve at the time of the occurrence with two examples from the vessel's stability booklet – the arrival with short sail condition and the departure basic sail condition – as well as a theoretical occurrence condition, assuming that the deckhouses had been secured weathertight. It can be seen that, from an overall perspective, the loading of the vessel (and the resulting righting arm curve) closely resembled the approved arrival condition from the stability booklet. The obvious deterioration of the righting arms resulting from the lack of buoyancy contribution of the deckhouses is discussed further in a later section.

Figure 2.Comparison of righting arm curves.

Figure 1.Comparison of righting arm curves.

Hull and deckhouse openeings

The investigation determined that there were numerous openings in the weather deck and deckhouses which were open at the time of the occurrence and which would serve as points of entry for seawater when immersed (see Photo 2). The angles of immersion of some of these openings were calculated as follows:

Table 2. Hull and Deckhouse Openings
Description Angle of Immersion
(degree)
Galley Door (forward deckhouse, port side) 56.5
Mess Door (forward deckhouse, port side) 58.4
Sanitary Exhaust Vent (forward deckhouse, port side) note 65.0
Radio Room Window (aft deckhouse, port side) 68.6
Wheelhouse Door (aft deckhouse, port side) 74.2
Chart Room Interior Door 87.9
Engine Exhaust (top of mizzen mast) note 91.7
Engine Room Skylight (fwd of wheelhouse, offset to stbd) note 100.5
Mess Stairway (inside fwd deckhouse) note 116.5

note Immersion of these openings would lead to downflooding of the hull.

Photo 2. Some critical port side openings. From forward to aft: mess room door, galley door, sanitary exhaust vent, engine room skylight, and wheelhouse door

Photo 2. Some critical port side openings. From forward to aft: mess room door, galley door, sanitary exhaust vent, engine room skylight, and wheelhouse door

In addition to the aforementioned, there were also vents on the forward main deck leading to the paint and bosun lockers, as well as intake and exhaust vents to the engine room and steering gear compartment and an aft stairway leading to the 'tween deck accommodation spaces, located inside the aft deckhouse. Although all these openings were fitted with a means of closure or protection2, at the time of the occurrence they were open. It should be noted that the righting arms and immersion angles determined by the computer model do not reflect the negative effect on the righting arm curve of water flooding the spaces below the main deck as the downflooding openings were immersed.

Wind heeling

Wind heeling arm curve – horizontal wind

The heeling moment exerted on a sailing vessel by a horizontal wind is proportional to, among other factors, the area of the surface exposed to the wind and the velocity of the apparent wind squared. As the vessel heels between upright (0 degrees) and 90 degrees, this moment has been found to decrease according to the following relationship3:

(1) WHMθ = WHM0 × cos1.3θ where,
WHMθ = heeling moment at a given angle, θ
WHM0 = heeling moment at upright (0 degrees)

Furthermore, just as a vessel's righting ability, due to buoyancy, is described by the righting moment (RM) at a given angle of heel,

(2) RM θ ∝ Displacement × RA θ,

the heeling effect of wind can be described by the heeling moment as follows:

(3) WHM θ ∝ Displacement × WHA θ

We also know that, when sailing in wind, a vessel will heel to an angle where the righting moment and heeling moment are equivalent, in other words, where RA θ = WHA θ so that:

(4) WHM θ ∝ Displacement × WHA θ

It follows therefore, that if the RA curve for the vessel is known, the heeling moment being applied by the wind can be determined for any observed angle of heel (up to 90 degrees). Using equation (1) above, we can then work backwards to calculate the heeling moment that was exerted on the vessel when it was upright (refer also to Figure 3 below):

(5) WHA 0 = RAθ ⁄ cos 1.3 θ where,

WHA 0 = the wind heeling arm associated with the wind heeling moment which, when applied to the upright vessel, would result in the vessel heeling to an angle, θ

Figure 3.Example wind heeling arm (WHA) curve resulting in steady heel angle of about 18.5 degrees.

Figure 3. Example wind heeling arm (WHA) curve resulting in steady heel angle of about 18.5 degrees.

Estimated wind speed

Prior to the occurrence, the vessel's sail plan was reduced in anticipation of strong winds (Beaufort force 7 or 8) which were forecast for later in the day. The resulting sail plan, which used approximately 45 % of available sail area, consisted of the following sails (refer to Appendix E):

  • Inner Jib
  • Fore Staysail
  • Fore Upper Topsail
  • Fore Lower Topsail
  • Main Staysail
  • Main Sail
  • Mizzen (reefed)

Knowing the details of the sail plan, the apparent wind speeds corresponding to various upright wind heeling arms were then calculated (results are given in Table 3 and Figure 4 below; refer also to Appendix F) using the following equation:

(6) WHM 0 = 0.5 ρ v2 (As hs Cs + Ah hh Ch) where,
  • ρ = density of air
  • v = apparent wind speed
  • As = sail area
  • hs = height of the centroid of the sail plan above the half draft
  • Cs = sail heel force coefficient4; assumed to vary between 1.0 and 2.0 in this instance
  • Ah = profile area of hull and superstructures above the waterline
  • hh = height of the centroid of the hull and superstructures above the half draft
  • Ch = hull heel force coefficient; assumed to be 1.
Table 3. Apparent wind speed versus wind heel angle
Steady Wind
Heel Angle (deg)
Apparent Wind Speed (knots) Notes
CS = 2 CS = 1
3.5 0 0  
8.5 10.4 13.9  
13.5 14.6 19.6  
18.5 17.8 23.9  
23.5 20.5 27.5  
28.5 23.0 30.9  
28.9 23.2 31.1 main deck edge immersed
33.5 25.4 34.0  
38.5 26.9 36.0 approximate angle of maximum righting arm
43.5 27.6 37.0 deck rail at midship immersed (41 deg)
48.5 27.6 37.0  
53.5 27.1 36.3  
56.5 26.6 35.7 galley door immersed
58.5 26.4 35.4 mess door immersed
63.4 25.3 34.0 bridge deck edge immersed;
sanitary exhaust vent immersed (65 deg)
68.5 26.7 35.8 radio room window immersed
73.5 37.1 49.8 port wheelhouse door immersed (74.2 deg)
78.5 51.1 68.4  
83.5 64.1 85.9  
88.5 119.8 160.5 crew evacuate wheelhouse

Figure 4. Apparent Wind Speed versus Heel Angle
Figure 4. Apparent Wind Speed versus Heel Angle 

As indicated by Table 3 and Figure 4, the same apparent wind speed (in the range of approximately 27 to 37 knots) would result in a range of steady wind heel angles – anywhere from approximately 38 to 68 degrees. In other words, as the apparent wind increases from 0 to a value between 27 and 37 knots, there would be a steady increase in the resultant wind heel angle up to about 38 degrees. However, an increase in wind beyond this point would result in a much greater response, heeling the ship to almost 70 degrees. This result can be seen more clearly by superimposing the wind heeling arm curve on the vessel's righting arm curve, as shown in Figure 5 below, which demontrates that there is no clear intersection of the 2 curves until an angle of approximately 70 degrees.

It can also be seen in Figure 4 that to induce wind heel angles beyond 70 degrees or so, the necessary apparent wind speeds increase significantly to the point where winds in excess of 100 knots would be required to knock the vessel down to an angle in the range of 90 degrees.

Figure 5. WHA curve coincidence with RA curve for winds approximately 27 to 37 knots

Figure 5. WHA curve coincidence with RA curve for winds approximately 27 to 37 knots

Wind heeling arm curve – wind inclined from the horizontal

The heeling effect of wind inclined from the horizontal, such as in a downburst, 5 may be estimated by shifting the heeling arm curve for a horizontal wind, as described in the previous section, to the right on the x–axis. For example, to look at the effect of winds inclined to 45° from the horizontal, the horizontal wind heeling arm curve can be shifted 45° to the right.

Figure 6 demonstrates this effect on the Concordia's righting ability. First, it is assumed that the vessel is heeled to an angle around 28° due to a horizontal wind. According to the relationship between apparent wind speed and heel angle shown in Appendix G, horizontal winds of between 23 and 31 knots would be sufficient to induce this heel angle. Then, the heeling arm curve is shifted 30° to the right, assuming the winds have shifted to 30° from the horizontal. As can be seen in Figure 6, the vessel's righting ability would be completely overcome by this combination of wind speed and inclination.

Figure 6. Wind heeling arm curve for wind inclined 30° from the horizontal

Figure 5. Wind heeling arm curve for wind inclined 30° from the horizontal

The knockdown

Heeling in horizontal winds

Observations indicate that, during the hour or so preceeding the occurrence, the Concordia was sailing with a heel angle of approximately 10 degrees. 6 Furthermore, based on the information gathered regarding vessel course and speed as well as wind speed and direction during this period, it was found that apparent winds of 18 knots from just aft the vessel's beam were representative of the conditions during this timeframe.Using the righting arm curve derived for the vessel at the time of the occurrence, in addition to equations (5) and (6) described previously, it was calculated that apparent winds ranging in speed from 12 to 16 knots would have been required to heel the vessel to this angle. The discrepancy between the observed and calculated wind speed values is likely due in large part to differences between the assumed and actual efficiency of the sails 7 as well as the difficulties inherent in determining which wind and heel observations may be considered as representative of the naturally fluctuating conditions during such a prolonged period of time. Figure 7 below describes these parameters and illustrates the likely stability condition for the vessel during that period.

Figure 7. Wind heeling arm calculated based on 10 degrees mean heel angle

Figure 7. Wind heeling arm calculated based on 10 degrees mean heel angle

For a two to three minute period prior to the occurrence, the apparent wind speed and the vessel's heel angle were observed to increase to approximately 23 knots and 23 degrees, respectively. Using a similar process as described above, it was calculated that apparent winds ranging in speed from 20 to 28 knots would be required to induce a heel angle of 23 degrees. This represents an increase in apparent wind speed of approximately 5 knots over the value estimated for the hour before. This increase in wind speed was likely associated with the onset of the squall which had been approaching the vessel from a direction broad off the starboard bow.

The improved agreement between the observed and calculated wind speed values indicates a more fitting approximation of the sail efficiency. This more fitting approximation is likely linked to the change in apparent wind angle, as well as an improvement to the quality of data available to the investigation during this time period. Figure 8 below describes the stability condition for the vessel during that period, based on these parameters.

Figure 8. Wind heeling arms calculated based on 23 degrees mean heel angle

Figure 8. Wind heeling arms calculated based on 23 degrees mean heel angle

Beyond this point, the apparent wind speed began to increase and the angle began to decrease, indicating that the apparent wind was shifting forward , or backing. In response, the Concordia began to heel further.

There were no further definitive observations of vessel heel angle and corresponding wind speed, but when the Concordia had reached over 88° the anemometer was climbing through 30 knots. 8 Calculation results indicate that, from the previously observed 23 knots, an increase in apparent wind speed to between 27 and 37 knots could have been sufficient to cause the vessel to heel to an angle of about 38 degrees. This represents an increase in wind speed of only between 4 and 14 knots over the previous observation. No further increase in wind speed would then have been necessary; having reached this critical point, the vessel would continue to heel to an angle approaching 70 degrees (see Figure 9).

Figure 9. Wind heeling arms calculated for the occurrence

Figure 9. Wind heeling arms calculated for the occurrence

Figure 9 indicates that, although the vessel would theoretically take up a steady heel angle of almost 70 degrees in such winds, water would have begun entering at various critical points before that angle – first, via the open doors in the forward deckhouse (56.5 degrees), then shortly thereafter via the sanitary exhaust vent which was just aft of that (65 degrees). With all doors on the port, or lee, side as well as the ventilators and engine room skylight in the open position at the time of the knockdown, there was nothing to prevent or mitigate the downflooding that followed, progressing until the vessel ultimately lost all stability, rolled over and capsized. The vessel's ability to recover would have been further hindered by the weight of water entrained in the sails as they submerged in addition to the shifting of weights/equipment which may have occurred.

Photo 3. Port deck edge immersed at 29 degrees.)

Photo 8. Rebuilt VIA GM F40PH-2D locomotive (source: TSB)

Heeling in winds inclined from the horizontal

The Concordia's righting ability was further evaluated to determine the impact to the vessel if it had been struck by winds that were inclined from the horizontal. As demonstrated by the graph in Figure 6, an increase in apparent wind speed to between 23 and 31 knots would have been sufficient to heel the vessel to about 28 degrees. This is an increase of between 0 and 8 knots over the last observed wind speed before the knockdown of 23 knots. From this point, an inclination of those winds to approximately 30 degrees from the horizontal (due to the downflow winds associated with the squall moving over the vessel) would have been sufficient to completely overcome the righting ability of the vessel.

Although the righting arm curve indicates that, theoretically, the vessel would experience negative, or capsizing, moments once at 90 degrees of heel, the capsize (which occurred some minutes later) may have be been delayed by the damping effect of sails and rigging as they dipped in the water and the initial buoyancy of the deckhouses (until such time as they flooded through the open doors).

Influence of water ballast

At the time of the occurrence the Concordia was not loaded with water ballast, whereas all the typical loading conditions presented in Concordia's stability booklet included some amount – 20.8 tonnes in the departure conditions and 26.2 tonnes in the arrival conditions. Figure 10 below provides a comparison of the righting arm curve for the vessel in its occurrence condition (with no water ballast) and a hypothetical condition comprised of the occurrence loading but with the addition of water ballast as indicated by the departure conditions in the stability booklet. Two example righting arm curves from the stability booklet are also shown. This comparison demonstrates that while the overall righting ability is somewhat reduced in the absence of the water ballast, this reduction is small and the occurrence righting arm curve closely resembled the approved arrival condition from the stability booklet. As such, the guidance information contained in the Concordia's stability booklet was relevant at the time of the occurrence.

Figure 10. Comparison of occurrence righting arm curves with and without water ballast

Figure 10.  Comparison of occurrence righting arm curves with and without water ballast

Further calculations were performed to estimate the range of wind speed that would induce the vessel response that was likely experienced during the occurrence, as previously described. These results indicate that, with approximately 20 tonnes of added water ballast, apparent wind speeds from 30 to 41 knots could have heeled the vessel to approximately 60 degrees (see Figure 11 and Appendix G). In the occurrence condition (with no water ballast) the wind speed required for this type of heeling in horizontal wind was determined to be in the range of 27 to 37 knots. Thus, the results above indicate the wind speed required increased by only 4 knots and remain consistent with the range of wind speeds observed around the time of the occurrence.

Another observation is that, with water ballast added, the range of angles where the righting arms and heeling arms coincide was approximately 45 to 60 degrees, compared to 38 to 68 degrees without water ballast. Although somewhat reduced compared to the occurrence condition without ballast water, the theoretical knockdown angle would still have been sufficient to immerse the portside doors of the deckhouse, thereby setting into motion the ingress of water which ultimately caused the vessel to roll over, capsize and sink.

While this comparison indicates that the Concordia's resistance to knockdown on the day of the occurrence would have been somewhat improved had the vessel been loaded with water ballast, it is unlikely that this improvement would have had a significant impact on the sequence of events.

Figure 11. Wind heeling arms calculated for the occurrence condition with the addition of water ballast.

Figure 11.  Wind heeling arms calculated for the occurrence condition with the addition of water ballast.

Influence of list angle

As noted previously, information gathered during the investigation indicates that it is likely that the Concordia was experiencing a list of approximately 3.5 degrees at the time of the occurrence due to unsymmetrical liquid loads onboard. After applying a hypothetical correction to the righting arm curve so as to eliminate this list, further wind heeling calculations were performed to examine the influence of this parameter on the range of wind speed that would induce the vessel response that was likely experienced during the occurrence.

These results are illustrated in Figure 12 below and Appendix H. From these it can be seen that, apparent wind speeds from 29 to 39 knots could have heeled the vessel to approximately 66 degrees. In the occurrence condition (with 3.5 degree list) the wind speed required for this type of heeling in horizontal wind was determined to be in the range of 27 to 37 knots. Thus, the results above indicate the wind speed required increased by only 2 knots and remain consistent with the range of wind speeds observed around the time of the occurrence.

Another observation is that, with the list corrected, the range of angles where the righting arms and heeling arms coincide was approximately 42 to 66 degrees, compared to 38 to 68 degrees in the occurrence condition. Although somewhat reduced compared to the occurrence condition without ballast water, the theoretical knockdown angle would still have been sufficient to immerse the portside doors of the deckhouse, thereby setting into motion the ingress of water which ultimately caused the vessel to roll over, capsize and sink.

While this comparison indicates that the Concordia's resistance to knockdown on the day of the occurrence would have been somewhat improved had the vessel been loaded symmetrically and the list removed, it is unlikely that this improvement would have had a significant impact on the sequence of events.

Figure 12. Wind heeling arms calculated with list corrected.

Figure 12. Wind heeling arms calculated with list corrected.

Weathertight integrity

Although the Concordia was equipped with weathertight protection for all means of access to spaces below the weather deck (such as doors and hatches)—in addition to closing appliances for all ventilators leading to below deck spaces—not all of these had been secured prior to the knockdown. The investigation was not able to confirm if the windows on the portside of the aft deckhouse had been properly secured when they were closed against the oncoming rain, or whether they failed after the vessel was knocked down; however, information gathered during the investigation indicates that water may have entered via that route as well.

Figure 13 below, compares the righting arm curve of the Concordia with the two deckhouses secured, and therefore contributing buoyancy to the vessel, with that of the vessel at the time of the occurrence, which considers their buoyancy only until such point as the open doors became submerged. From this, it can be seen that, in addition to the obvious advantages of preventing water ingress, the righting ability of Concordia is substantially improved when the deckhouses are assumed to be secured weathertight. From this, it can be concluded that, with prompt action from the crew – to release sails and start the engine, for example – the vessel would have been more likely to recover from the excessive heeling.

Figure 13.Comparison of RA curves with/without deckhouses.

Figure 13.Comparison of RA curves with/without deckhouses.

This lack of advance preparation by the crew to fully secure the vessel against water entry ahead of the approaching squall not only permitted the ingress of water into the hull, but it also so deteriorated righting ability that the likelihood of the vessel recovering from the knockdown was significantly reduced. As a result, the downflooding progressed, causing the loss of stability until the vessel ultimately capsized.

Conclusions

  1. The comparison of known parameters of wind and ship behaviour with calculated ones, demonstrated that the theory regarding ship response to wind can be used to provide an explanation of and offer insight into the behaviour of the Concordia at the time of the occurrence.
  2. Over the period of approximately 1 hour before the occurrence, the observed increase in apparent wind speed of about 5 knots (from 18 to 23 knots) would have been sufficient to increase the ship's heel angle to the observed 23 degrees;
  3. From the heel angle of approximately 23 degrees, which was sustained for 2 to 3 minutes, a further increase in apparent wind speed to between 27 and 37 knots would have been sufficient to cause the vessel to heel to an angle approaching 70 degrees. If the vessel were affected by winds inclined from the horizontal (such as in the downdraft from a squall) the initial horizontal wind speed could have been reduced to between 23 and 31 knots.
  4. The increases in apparent wind speed referred to above were the likely result of changes in true wind speed (increases) and direction as it backed towards the southwest, as forecast, and as a result of the approaching squall with an associated downburst.
  5. As the vessel heeled, downflooding would have commenced via open doors and ventilators, precluding any possibility of the vessel righting itself, until it ultimately lost all stability and capsized.
  6. At the time of the occurrence, the vessel was not loaded with water ballast and other liquid loads were asymmetrical such that the vessel had likely developed a list of 3.5 degrees. While these factors reduced the Concordia's resistance to wind heeling somewhat, it is unlikely that this played any role in the sequence of events on the day of the occurrence.

Appendices

Appendix A – Sail plan

Appendix A - Sail Plan

Appendix B – General arrangement

Appendix B – General arrangement

Appendix C – Environmental and ship behaviour information

Explanation of terms used in the table:

  • Investigation info: provides the range of values obtained during the investigation (example: wind speed 20–24 knots)
  • Approximation: refers to a single value representative of the corresponding investigation info (example: wind speed = 22 knots)
Environmental and Ship Behaviour Information
Time Period (Approx) Ship Speed /Heading True Wind Apparent Wind Heel Notes

1200 to 1300

Master goes below at 1300;
OOW alone on bridge

Investigation Info: 5.5 knots @ 220°

Approximation:
5.5 knots @ 220°

Investigation Info: Force 5 /lower Force 6 @ 1 or 2 points W of N

Approximation:
20 knots @ 345°

Investigation Info:
15 to 18 knots @ Broad Reach

Derived Using Approximations of Ship and True Wind Info:
 17.4 knots @ 110°

Investigation Info:
5°

Calculated range of apparent wind speed for this heel is 6 to 8 knots
  • Vessel had been experiencing small squalls during the previous 2 days
  • Earlier in the morning the sail plan had been reduced in anticipation of Force 7/8 conditions forecast for later that day
  • Sails trimmed for broad reach – square sails braced one point forward; mainsail and reefed mizzen sheeted out to maximum
  • Wind had been backing (shifting forward) the previous days and was expected to continue to do so; squalls anticipated.

1300–1415

Hour or so prior to occurrence – OOW in charge of watch

Investigation Info: 5.5 knots @ 200 to 220°

Approximation:
5.5 knots @ 210°

Investigation Info: Force 5; wind direction not known

Approximation:
 20 knots @ 320°

* See notes

Investigation Info:
Up to 20 knots @ 80 to 90 deg

Derived Info:
18.8 knots @ 94.1°

Investigation Info:
10°

Calculated range of apparent wind speed for this heel is 12 to 16 knots
  • Main staysail sheeted in and yards braced another point (now 2 points forward); this indicates that apparent wind had actually shifted forward
  • Squall approaching on radar, broad off starboard bow, 1 ½ to 2 miles away
  • Note that heel angle has increased significantly over previous hour despite minimal change in apparent wind speed. This may be accounted for by the shift in wind direction or inaccuracies related to the estimation of the heel angles experienced.

Appendix C - Environmental and Ship Behaviour Information

1420

2 to 3 minutes – Student takes video 57 sec) showing conditions on deck and some still photos

Approximation:
9 knots @ 210°

Approximation:
25 knots @ 320°

Investigation Info:
23 knots

Derived Using Approximations for Ship and True Wind Info:
23.5 knots @ 88.9°

* See notes

Investigation Info:
23° min

Calculated range of apparent wind speed for this heel is 20 to 28 knots

* See notes
  • Analysis of video footage determined that the minimum angle of inclination of the vessel which could be discerned from the video was 23 degrees. [See photo, below]
  • Video shows inner jib with leading edge full but trailing edge flapping; likely due to blanketing effect of forestaysail. Main staysail and main also appear full, indicating a likely apparent wind angle at least at the beam or aft of that
  • Square sails full, indicating likely apparent wind angle at least at the beam or aft of that [see photo below]

Appendix C - Environmental and Ship Behaviour Information
Appendix C - Environmental and Ship Behaviour Information
Photo credit: Erica Trimble

Appendix C - Environmental and Ship Behaviour Information
Photo credit: Erica Trimble

1423

Start of Capsize
Approximation:
9 knots @ 210°
Approximation:
28 knots @ 310°

Investigation Info: Wind speed starts to increase (climbing to 27 knots) and apparent angle decreases

Derived Using Approximations for Ship and True Wind Info:
27.9 knots @ 81.5°

* See notes.

Investigation Info:
Vessel starts to heel; motion is essentially continuous

Calculated range of apparent wind speed for heel from 38 to 68° is 27 to 37 knots
  • As vessel heels, port lookout moves to bridge door to express concern; at this point vessel would have been heeled to about 63.5° as bridge deck port side is just going underwater.
  • Information obtained during the investigation indicated that winds did not reach a level that caused concern or made it impossible to remain standing upright on deck. Considering these factors and the calculations it is unlikely that the winds would have been much in excess of 40 knots.
  • The 2/O observed the anemometer (30 knots from 120–150 degrees) when the vessel was heeled by about 88 degrees. It should be noted that the anemometer is not considered reliable at this angle and also that the vessel may have turned in response to the port helm.

Appendix C - Environmental and Ship Behaviour Information

Vessel on Beam Ends

Approximation:
0 knots @ 210°

* See Notes
Approximation:
28 knots @ 310°

Investigation Info: 30 knots @ 120 to 150 degrees

Derived Using Approximations for Ship and True Wind Info:
28 knots @ 100 deg

* See Notes

Calculated:
 > 88°

Based on fact that port bridge door frame was underwater and port radar was about to submerge.
  • Reliability of anemometer reading is questionable because of large vessel heel angle.
  • Helm had been given hard to port; therefore, change in apparent wind angle could be attributed in part to vessel bearing off.

Appendix D – Stability calculation results

Concordia - Occurrence Condition
Hull model includes main hull, aft deckhouse and forward deckhouse

Appendix D - Hull model includes main hull, aft deckhouse and forward deckhouse



Appendix D - Hull model includes main hull, aft deckhouse and forward deckhouse

Fluid Legend
Fluid Name Legend Weight
(MT)
Load %
FRESH WATER 28.27 83.79%
DIESEL OIL 14.69 37.23%
BW 3.00 54.00%
DW .76 70.00%
SO .45 78.00%

Drafts below are actually given at the fwd and aft draft marks:

Floating Status
Draft FP 3.582 m Heel port 3.57 deg. GM(Solid) 0.744 m
Draft MS 3.830 m Equil Yes F/S Corr. 0.023 m
Draft AP 4.078 m Wind Off GM(Fluid) 0.721 m
Trim aft 0.496/30.300 Wave No KMt 5.610 m
LCG 17.339f m VCG 4.867 m TPcm 2.52
Displacement 441.97 MT WaterSpgr 1.025    
Loading Summary
Item Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
Light Ship 0.00 0.000 0.000 0.000
Deadweight 441.97 17.339f 0.047p 4.867
Displacement 441.97 17.339f 0.047p 4.867
Fixed Weight Status
Item Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
LIGHT SHIP 0.00 0.000 0.000 0.000
CREW AND EFFECTS 8.00 19.500f 0.000 6.000u
LIGHTSHIP 2010 WITH SAILS SET 382.20 17.260f 0.000 5.100u
LUBE OIL 0.50 8.400f 0.000 5.000u
PROVISIONS 4.10 22.800f 0.000 2.900u
Total Fixed: 394.80 17.352f 0.000 5.095u

Tank Status

SALT WATER
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO14–WB.C 1.025          
NO1–WB.C 1.025          
NO21–WB.C 1.025          
NO22–WB.P 1.025          
NO23–WB.S 1.025          
NO2–WB.C 1.025          
FRESH WATER
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO3–FW.P 1.000 98.00% 11.64 22.092f 3.165p 3.279
NO4–FW.S 1.000 98.00% 11.64 22.101f 3.150s 3.280
NO5–FW.P 1.000 50.00% 4.99 16.702f 3.183p 2.761
Subtotals:   83.79% 28.27 21.143f 0.568p 3.188
DIESEL OIL
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO10–DO.P 0.850 52.00% 0.85 8.573f 2.834p 3.009
NO11–DO.S 0.850 37.00% 3.40 10.921f 2.991s 2.798
NO12–DO.P 0.850 45.00% 3.39 5.132f 1.444p 3.164
NO13–DO.S 0.850          
NO18–DO.C 0.850 78.00% 0.66 11.751f 0.003p 0.390
NO19–SUMP.C 0.850 78.00% 0.42 10.502f 0.003p 0.390
NO6–DO.S 0.850 40.00% 3.40 16.698f 3.088s 2.658
NO9–DO.P 0.850 70.00% 2.57 9.909f 3.214p 3.215
Subtotals:   37.23% 14.69 10.631f 0.346s 2.758
BW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO7–SEWAGE.P 1.000 54.00% 3.00 13.513f 3.192p 2.819
Subtotals:   54.00% 3.00  13.513f 3.192p 2.819
OW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO16–WELL.C 1.000          
NO20–WELL.C 1.000          
NO8–BILGE.S 1.000          
DW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO15–DRAIN.C 1.000 70.00% 0.76 16.747f 0.005p 0.350
Subtotals:   70.00% 0.76 16.747f 0.005p 0.350
SO
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO17–SLUDGE.C 0.850 78.00% 0.45 13.000f 0.004p 0.390
Subtotals:   78.00% 0.45 13.000f 0.004p 0.390
All Tanks
  Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
Totals:   42.83% 47.17 17.236f 0.436p 2.958
Displacer Status
Item Status Spgr Displ
(MT)
LCB
(m)
TCB
(m)
VCB
(m)
Eff
/Perm
HULL.C Intact 1.025 441.97 17.304f 0.180p 2.739 1.000
SubTotals:     441.97 17.304f 0.180p 2.739  

Critical point
Name L,T,V (m) Height (m)
(1) Galley Door 21.000f, 2.890p, 6.900 2.911
Freeboard Status
Location
(m)
To Deck
(m)
To Margin
(m)
42.500f 4.568 4.568
40.000f 4.112 4.112
38.000f 3.812 3.812
36.000f 3.579 3.579
35.000f 3.466 3.466
34.000f 3.343 3.343
30.500f 2.992 2.992
26.500f 2.639 2.639
23.000f 2.373 2.373
19.000f 2.125 2.125
15.000f 1.992 1.992
11.500f 1.947 1.947
7.500f 1.926 1.926
4.000f 1.955 1.955
2.000f 1.992 1.992
1.990f 1.992 1.992
0.000 2.033 2.033
2.500a 2.105 2.105
3.470a 2.133 2.133

Least freeboard is 1.926 m at 7.500f
Least freeboard (to margin line) is 1.926 m at 7.500f

Hull Data (with appendages)

Baseline Draft: 3.582 at 34.500f, 4.078 at 4.200f
Trim: aft 0.496/30.300 
Heel: port 3.57 deg.

DIMENSIONS

Length Overall: 45.970 m   LBP: 30.300 m      Beam: 9.440 m      BWL: 9.203 m
Volume: 431.187 m3      Displacement: 441.969 MT

COEFFICIENTS

Prismatic: 0.743      Block: 0.375      Midship: 0.505      Waterplane: 0.883

RATIOS

Length/Beam: 4.870      Displacement/length: 442.775      Beam/Depth: 2.292
MT/ cm Immersion: 2.525

AREAS

Waterplane: 246.308 m2      Wetted Surface: 393.937 m2
Under Water Lateral Plane: 125.473 m2      Above Water Lateral Plane: 190.469 m2

CENTROIDS (Meters)

Buoyancy: LCB = 17.304 fwd       TCB =0.180 port       VCB = 2.739
Flotation: LCF = 16.835 fwd
Under Water LP: 17.588 fwd of Origin, 1.821 below waterline.
Above Water LP: 18.576 fwd of Origin, 2.315 above waterline.

Note: Coefficients calculated based on length of 30.300 m

Righting Arms vs. Heel

Righting Arms vs Heel Angle
Heel Angle
(deg)
Trim Angle
(deg)
Origin Depth
(m)
Righting Arm
(m)
Area
(m–Rad)
Critical Pt Height
(m)
Freeboard Height
(m)
Notes
3.57p 0.94a 4.139 0.000 0.000 2.911 (1) 1.926 Equil
8.57p 0.90a 4.074 0.063 0.003 2.646 (1) 1.543  
13.57p 0.83a 3.957 0.122 0.011 2.375 (1) 1.144  
18.57p 0.73a 3.787 0.175 0.024 2.101 (1) 0.756  
23.57p 0.61a 3.565 0.222 0.041 1.828 (1) 0.381  
28.57p 0.47a 3.295 0.265 0.062 1.557 (1) 0.022  
28.88p 0.46a 3.276 0.268 0.064 1.540 (1) 0.000 Deck Imm.
33.57p 0.33a 2.984 0.300 0.087 1.289 (1) −0.333  
38.57p 0.24a 2.738 0.310 0.114 1.017 (1) −0.683  
43.57p 0.11a 2.309 0.297 0.141 0.739 (1) −1.028  
48.57p 0.01a 1.948 0.264 0.165 0.454 (1) −1.366  
53.57p 0.07f 1.579 0.220 0.186 0.166 (1) −1.696  
56.49p 0.12f 1.358 0.194 0.197 −0.001 (1) −1.881 CrtPt
58.57p 0.14f 1.198 0.177 0.204 −0.119 (1) −2.010  
63.57p 0.21f 0.804 0.148 0.218 −0.396 (1) −2.313  
68.57p 0.23f 0.410 0.164 0.231 −0.665 (1) −2.594  
73.57p 0.24f 0.024 0.277 0.250 −0.932 (1) −2.860  
78.57p 0.31f −0.408 0.356 0.277 −1.170 (1) −3.080  
83.57p 0.38f −0.882 0.337 0.308 −1.358 (1) −3.235  
88.57p 0.44f −1.353 0.296 0.336 −1.525 (1) −3.355  
93.57p 0.48f −1.817 0.242 0.360 −1.672 (1) −3.447  
98.57p 0.50f −2.270 0.179 0.378 −1.798 (1) −3.517  
103.57p 0.50f −2.709 0.111 0.391 −1.901 (1) −3.551  
108.57p 0.48f −3.129 0.042 0.398 −1.982 (1) −3.549  
111.65p 0.46f −3.380 0.000 0.399 −2.021 (1) −3.532 RaZero
113.57p 0.45f −3.531 −0.026 0.398 −2.041 (1) −3.514  
118.57p 0.41f −3.912 −0.089 0.393 −2.077 (1) −3.443  
123.57p 0.35f −4.266 −0.140  0.383 −2.085 (1) −3.341  
Critical point
Name L,T,V (m) Height (m)
(1)   Galley Door 21.000f, 2.890p, 6.900 2.911

Appendix D - Righting Arms vs. Heel (image 1)

Limit Report
Limit Min/Max Actual Margin Pass
(1) Absolute Angle at Crit. >0.00 deg 56.49 56.49 Yes
(2) Absolute Angle at Deck Immersion >0.00 deg 28.88 28.88 Yes

Concordia – Occurrence Condition
Hull model includes main hull and aft deckhouse only

Appendix D - Hull model includes main hull and aft deckhouse only

Appendix D - Hull model includes main hull and aft deckhouse only
Fluid Legend
Fluid Name Legend Weight Load%
FRESH WATER   28.27 83.79%
DIESEL OIL   14.69 37.23%
BW   3.00 54.00%
DW   .76 70.00%
SO   .45 78.00%

Drafts below are actually given at the fwd and aft draft marks:

Floating Status
Draft FP 3.582 m Heel  port 3.57 deg. GM(Solid) 0.744 m
Draft MS 3.830 m Equil Yes F/S Corr. 0.023 m
Draft AP 4.078 m Wind  Off GM(Fluid) 0.721 m
Trim aft 0.496/30.300 Wave No KMt 5.610 m
LCG 17.339f m VCG 4.867 m TPcm 2.52
Displacement 441.97 MT WaterSpgr  1.025    
Loading Summary
Item Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
Light Ship 0.00 0.000 0.000 0.000
Deadweight 441.97 17.339f 0.047p 4.867
Displacement 441.97 17.339f 0.047p 4.867
Fixed Weight Status
Item Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
LIGHT SHIP 0.00 0.000 0.000 0.000
CREW AND EFFECTS 8.00 19.500f 0.000 6.000u
LIGHTSHIP 2010 WITH SAILS SET 382.20 17.260f 0.000 5.100u
LUBE OIL 0.50 8.400f 0.000 5.000u
PROVISIONS 4.10 22.800f 0.000 2.900u
Total Fixed: 394.80 17.352f 0.000 5.095u

Tank Status

SALT WATER
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO14–WB.C 1.025          
NO1–WB.C 1.025          
NO21–WB.C 1.025          
NO22–WB.P 1.025          
NO23–WB.S 1.025          
NO2–WB.C 1.025          
FRESH WATER
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO3–FW.P 1.000 98.00% 11.64 22.092f 3.165p 3.279
NO4–FW.S 1.000 98.00% 11.64 22.101f 3.150s 3.280
NO5–FW.P 1.000 50.00% 4.99 16.702f 3.183p 2.761
Subtotals:   83.79% 28.27 21.143f 0.568p 3.188
DIESEL OIL
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO10–DO.P 0.850 52.00% 0.85 8.573f 2.834p 3.009
NO11–DO.S 0.850 37.00% 3.40 10.921f 2.991s 2.798
NO12–DO.P 0.850 45.00° 3.39 5.132f 1.444p 3.164
NO13–DO.S 0.850          
NO18–DO.C 0.850 78.00% 0.66 11.751f 0.003p 0.390
NO19–SUMP.C 0.850 78.00% 0.42 10.502f 0.003p 0.390
NO6–DO.S 0.850 40.00% 3.40 16.698f 3.088s 2.658
NO9–DO.P 0.850 70.00% 2.57 9.909f 3.214p 3.215
Subtotals:   37.23% 14.69 10.631f 0.346s 2.758
BW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO7–SEWAGE.P 1.000 54.00% 3.00 13.513f 3.192p 2.819
Subtotals:   54.00% 3.00 13.513f 3.192p 2.819
OW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO16–WELL.C 1.000          
NO20–WELL.C 1.000          
NO8–BILGE.S 1.000          
DW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO15–DRAIN.C 1.000 70.00% 0.76 16.747f 0.005p 0.350
Subtotals:   70.00% 0.76 16.747f 0.005p 0.350
SO
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO17–SLUDGE.C 0.850 78.00% 0.45 13.000f 0.004p 0.390
Subtotals:   78.00% 0.45 13.000f 0.004p 0.390
All Tanks
  Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
Totals:   42.83% 47.17 17.236f 0.436p 2.958
Displacer Status
Item Status Spgr Displ
(MT)
LCB
(m)
TCB
(m)
VCB
(m)
Eff
/Perm
HULL.C Intact 1.025 441.97 17.304f 0.180p 2.739 1.000
SubTotals:     441.97 17.304f 0.180p 2.739  
Critical point
Name L,T,V (m) Height (m)
(1)   Chart Room Door 9.500f, 1.420p, 7.680 3.592
Freeboard Status
Location
(m)
To Deck
(m)
To Margin
(m)
42.500f 4.568 4.568
40.000f 4.112 4.112
38.000f 3.812 3.812
36.000f 3.579 3.579
35.000f 3.466 3.466
34.000f 3.343 3.343
30.500f 2.992 2.992
26.500f 2.639 2.639
23.000f 2.373 2.373
19.000f 2.125 2.125
15.000f 1.992 1.992
11.500f 1.947 1.947
7.500f 1.926 1.926
4.000f 1.955 1.955
2.000f 1.992 1.992
1.990f 1.992 1.992
0.000 2.033 2.033
2.500a 2.105 2.105
3.470a 2.133 2.133

Least freeboard is 1.926 m at 7.500f
Least freeboard (to margin line) is 1.926 m at 7.500f

Hull Data (with appendages)

Baseline Draft: 3.582 at 34.500f, 4.078 at 4.200f
Trim: aft 0.496/30.300 
Heel: port 3.57 deg.

DIMENSIONS

Length Overall: 45.970 m   LBP: 30.300 m      Beam: 9.440 m       BWL: 9.203 m
Volume: 431.187 m3      Displacement: 441.969 MT

COEFFICIENTS

Prismatic: 0.743      Block: 0.375      Midship: 0.505      Waterplane: 0.883

RATIOS

Length/Beam: 4.870      Displacement/length: 442.775      Beam/Depth: 2.292
MT/ cm Immersion: 2.525

AREAS

Waterplane: 246.308 m2      Wetted Surface: 393.938 m2
Under Water Lateral Plane: 125.473 m2      Above Water Lateral Plane: 164.266 m2

CENTROIDS (Meters)

Buoyancy: LCB = 17.304 fwd       TCB =0.180 port       VCB = 2.739
Flotation: LCF = 16.835 fwd
Under Water LP: 17.588 fwd of Origin, 1.821 below waterline.
Above Water LP: 17.721 fwd of Origin, 2.035 above waterline.

Note: Coefficients calculated based on length of 30.300 m

Righting Arms vs. Heel

Righting Arms vs Heel Angle
Heel Angle
(deg)
Trim Angle
(deg)
Origin Depth
(m)
Righting Arm
(m)
Area
(m–Rad)
Critical Pt Height
(m)
Freeboard Height
(m)
Notes
3.57p 0.94a 4.139 0.000 0.000 3.592 (1) 1.926  
8.57p 0.90a 4.074 0.063 0.003 3.456 (1) 1.543  
13.57p 0.83a 3.957 0.122 0.011 3.312 (1) 1.144  
18.57p 0.73a 3.787 0.175 0.024 3.162 (1) 0.756  
23.57p 0.61a 3.565 0.222 0.041 3.008 (1) 0.381  
28.57p 0.48a 3.295 0.265 0.062 2.850 (1) 0.022  
28.88p 0.46a 3.276 0.268 0.064 2.840 (1) 0.000 Deck Imm.
33.57p 0.33a 2.984 0.300 0.087 2.685 (1) −0.333  
37.97p 0.23a 2.695 0.310  0.111 2.524 (1) −0.641 MaxRa
38.57p 0.21a 2.654 0.310 0.114 2.500 (1) −0.683  
43.57p 0.11a 2.308 0.297 0.141 2.295 (1) −1.028  
48.57p 0.01a 1.949 0.264 0.165 2.070 (1) −1.366  
53.57p 0.07f 1.579 0.220 0.186 1.827 (1) −1.696  
58.57p 0.15f 1.199 0.174 0.204 1.570 (1) −2.011  
63.57p 0.23f 0.806 0.133 0.217 1.303 (1) −2.322  
68.57p 0.30f 0.414 0.114 0.228 1.021 (1) −2.619  
73.57p 0.40f 0.025 0.158 0.239 0.719 (1) −2.914  
78.57p 0.57f −0.406 0.188 0.254 0.441 (1) −3.171   
83.57p 0.76f −0.879 0.141 0.269 0.202 (1) −3.363  
87.92p 0.89f −1.289 0.080 0.278 0.000 (1) −3.513 CrtPt
88.57p 0.91f −1.349 0.071 0.279 −0.030 (1) −3.534  
93.10p 1.01f −1.767 0.000 0.281 −0.234 (1) −3.662 RaZero
93.57p 1.02f −1.810 −0.007 0.281 −0.255 (1) −3.673  
98.57p 1.11f −2.259 −0.088 0.277 −0.473 (1) −3.775  
103.57p 1.18f −2.694 −0.172 0.266 −0.684 (1) −3.841  
Critical point
Name L,T,V m Height m
(1)   Chart Room Door 9.500f, 1.420p, 7.680 3.592

Appendix D - Righting Arms vs. Heel (image 2)

Limit Report
Limit Min/Max Actual Margin Pass
(1) Absolute Angle at Crit. >0.00 deg <N/A> <N/A> <N/A>
(2) Absolute Angle at Deck Immersion >0.00 deg <N/A> <N/A> <N/A>

Concordia – Occurrence Condition
Hull model includes main hull only

Appendix D - Hull model includes main hull only

Appendix D - Hull model includes main hull only

Fluid Legend
Fluid Name Legend Weight Load%
FRESH WATER   28.27 83.79%
DIESEL OIL   14.69 37.23%
BW   3.00 54.00%
DW   .76 70.00%
SO   .45 78.00%

Drafts below are actually given at the fwd and aft draft marks:

Floating Status
Draft FP 3.582 m Heel  port 3.57 deg. GM(Solid) 0.744 m
Draft MS 3.830 m Equil Yes F/S Corr. 0.023 m
Draft AP 4.078 m Wind  Off GM(Fluid) 0.721 m
Trim aft 0.496/30.300 Wave No KMt 5.610 m
LCG 17.339f m VCG 4.867 m TPcm 2.52
Displacement 441.97 MT WaterSpgr  1.025    
Loading Summary
Item Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
Light Ship 0.00 0.000 0.000 0.000
Deadweight 441.97 17.339f 0.047p 4.867
Displacement 441.97 17.339f 0.047p 4.867
Fixed Weight Status
Item Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
LIGHT SHIP 0.00 0.000 0.000 0.000
CREW AND EFFECTS 8.00 19.500f 0.000 6.000u
LIGHTSHIP 2010 WITH SAILS SET 382.20 17.260f 0.000 5.100u
LUBE OIL 0.50 8.400f 0.000 5.000u
PROVISIONS 4.10 22.800f 0.000 2.900u
Total Fixed: 394.80 17.352f 0.000 5.095u

Tank Status

SALT WATER
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO14-WB.C 1.025          
NO1-WB.C 1.025          
NO21-WB.C 1.025          
NO22-WB.P 1.025          
NO23-WB.S 1.025          
NO2-WB.C 1.025          
FRESH WATER
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO3-FW.P 1.000 98.00% 11.64 22.092f 3.165p 3.279
NO4-FW.S 1.000 98.00% 11.64 22.101f 3.150s 3.280
NO5-FW.P 1.000 50.00% 4.99 16.702f 3.183p 2.761
Subtotals:   83.79% 28.27 21.143f 0.568p 3.188
DIESEL OIL
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO10-DO.P 0.850 52.00% 0.85 8.573f 2.834p 3.009
NO11-DO.S 0.850 37.00% 3.40 10.921f 2.991s 2.798
NO12-DO.P 0.850 45.00% 3.39 5.132f 1.444p 3.164
NO13-DO.S 0.850          
NO18-DO.C 0.850 78.00% 0.66 11.751f 0.003p 0.390
NO19-SUMP.C 0.850 78.00% 0.42 10.502f 0.003p 0.390
NO6-DO.S 0.850 40.00% 3.40 16.698f 3.088s 2.658
NO9-DO.P 0.850 70.00% 2.57 9.909f 3.214p 3.215
Subtotals:   37.23% 14.69 10.631f 0.346s 2.758
BW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO7-SEWAGE.P 1.000 54.00% 3.00 13.513f 3.192p 2.819
Subtotals:   54.00% 3.00 13.513f 3.192p 2.819
OW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO16-WELL.C 1.000          
NO20-WELL.C 1.000          
NO8-BILGE.S 1.000          
DW
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO15-DRAIN.C 1.000 70.00% 0.76 16.747f 0.005p 0.350
Subtotals:   70.00% 0.76 16.747f 0.005p 0.350
SO
Tank Name Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
NO17-SLUDGE.C 0.850 78.00% 0.45 13.000f 0.004p 0.390
Subtotals:   78.00% 0.45 13.000f 0.004p 0.390
All Tanks
  Spgr Load
(%)
Weight
(MT)
LCG
(m)
TCG
(m)
VCG
(m)
Totals:   42.83% 47.17 17.236f 0.436p 2.958
Displacer Status
Item Status Spgr Displ
(MT)
LCB
(m)
TCB
(m)
VCB
(m)
Eff
/Perm
HULL.C Intact 1.025 441.97 17.304f 0.180p 2.739 1.000
SubTotals:     441.97 17.304f 0.180p 2.739  
Critical point
Name L,T,V (m) Height (m)
(1)   Top of Fore Mast 28.200f, 0.000, 39.000 35.242
Freeboard Status
Location
(m)
To Deck
(m)
To Margin
(m)
42.500f 4.568 4.568
40.000f 4.112 4.112
38.000f 3.812 3.812
36.000f 3.579 3.579
35.000f 3.466 3.466
34.000f 3.343 3.343
30.500f 2.992 2.992
26.500f 2.639 2.639
23.000f 2.373 2.373
19.000f 2.125 2.125
15.000f 1.992 1.992
11.500f 1.947 1.947
7.500f 1.926 1.926
4.000f 1.955 1.955
2.000f 1.992 1.992
1.990f 1.992 1.992
0.000 2.033 2.033
2.500a 2.105 2.105
3.470a 2.133 2.133

Least freeboard is 1.926 m at 7.500f
Least freeboard (to margin line) is 1.926 m at 7.500f

Hull Data (with appendages)

Baseline Draft: 3.582 at 34.500f, 4.078 at 4.200f
Trim: aft 0.496/30.300 
Heel: port 3.57 deg.

DIMENSIONS

Length Overall: 45.970 m   LBP: 30.300 m      Beam: 9.440 m      BWL: 9.203 m
Volume: 431.187 m3      Displacement: 441.969 MT

COEFFICIENTS

Prismatic: 0.743      Block: 0.375      Midship: 0.505      Waterplane: 0.883

RATIOS

Length/Beam: 4.870      Displacement/length: 442.775      Beam/Depth: 2.292
MT/ cm Immersion: 2.525

AREAS

Waterplane: 246.308 m2      Wetted Surface: 393.937 m2
Under Water Lateral Plane: 125.473 m2      Above Water Lateral Plane: 133.116 m2

CENTROIDS (Meters)

Buoyancy: LCB = 17.304 fwd       TCB =0.180 port       VCB = 2.739
Flotation: LCF = 16.835 fwd
Under Water LP: 17.588 fwd of Origin, 1.821 below waterline.
Above Water LP: 20.443 fwd of Origin, 1.680 above waterline.

Note: Coefficients calculated based on length of 30.300 m

Righting Arms vs. Heel

Righting Arms vs Heel Angle
Heel Angle
(deg)
Trim Angle
(deg)
Origin Depth
(m)
Righting Arm
(m)
Area
(m-Rad)
Critical Pt Height
(m)
Freeboard Height
(m)
Notes
3.57p 0.94a 4.139 0.000 0.000 35.242 (1) 1.926 Equil
8.57p 0.90a 4.074 0.063 0.003 34.927 (1) 1.543  
13.57p 0.83a 3.957 0.122 0.011 34.358 (1) 1.144  
18.57p 0.73a 3.787 0.175 0.024 33.540 (1) 0.756  
23.57p 0.61a 3.565 0.222 0.041 32.480 (1) 0.381  
28.57p 0.47a 3.295 0.265 0.062 31.189 (1) 0.022  
28.88p 0.46a 3.276 0.268 0.064 31.101 (1) 0.000 Deck Imm.
33.57p 0.33a 2.984 0.300 0.087 29.674 (1) −0.333  
38.57p 0.24a 2.738 0.310 0.114 27.943 (1) −0.683  
43.57p 0.11a 2.309 0.297 0.141 26.002 (1) −1.028  
48.57p 0.01a 1.948 0.264 0.165 23.863 (1) −1.366  
53.57p 0.07f 1.579 0.220 0.186 21.545 (1) −1.696  
58.57p 0.13f 1.208 0.169 0.203 19.066 (1) −2.016  
63.57p 0.17f 0.837 0.115 0.216 16.441 (1) −2.332  
68.57p 0.16f 0.483 0.066 0.224 13.688 (1) −2.642  
73.57p 0.11f 0.162 0.057 0.229 10.813 (1) −2.957  
78.57p 0.05f −0.154 0.040 0.233 7.860 (1) −3.248  
83.57p 0.00a −0.510 −0.038 0.234 4.879 (1) −3.479 RaZero
81.14p 0.02f −0.331 0.012 0.234 6.324 (1) −3.377  
83.57p 0.00a −0.510 −0.038 0.234 4.879 (1) −3.479  
88.57p 0.06a −0.879 −0.149 0.226 1.883 (1) −3.663  
91.71p 0.11a −1.107 −0.222 0.216 −0.001 (1) −3.760  CrtPt
93.57p 0.14a −1.241 −0.266 0.208 −1.116 (1) −3.812  
98.57p 0.25a −1.594 −0.383 0.179 −4.096 (1) −3.925  
103.57p 0.37a −1.935 −0.499 0.141 −7.035 (1) −4.001   
Critical point
Name L,T,V (m) Height (m)
(1)   Top of Fore Mast 28.200f, 0.000, 39.000 35.242

Appendix D - Righting Arms vs. Heel (image 3)

Limit Report
Limit Min/Max Actual Margin Pass
(1) Absolute Angle at Crit. >0.00 deg 91.71 91.71 Yes
(2) Absolute Angle at Deck Immersion >0.00 deg 28.88 28.88 Yes

Appendix E – Occurrence sail plan

Appendix E - Occurrence Sail Plan

Appendix F – Wind speed calculations

Righting Arm (RA) Curves: Wind Heeling Arm (WHA) Curves:
From AutoHydro Output for Occurrence
Loading Condition
where,
Based on the relationship:
 WHA(θ) = WHA(0) × cos1.3 θ
For Critical Point Immersion:
Displ (t) = 441.97 From RA Curve: θ CrtPt 10 deg Curve of Critical Angle
RA @CrtPt 0.08 m x y
10 0
θ RA Model Notes θ WHA HMMT 10 0.5
(deg) (m)     (deg) (m) (t.m)
3.57 0 FM Equil 0 0.082 36.1
8.57 0.063 FM 8.57 0.080 35.5
13.57 0.122 FM 13.57 0.079 34.8
18.57 0.175 FM 18.57 0.076 33.6
23.57 0.222 FM video angle 23.57 0.073 32.2
28.57 0.265 FM 28.57 0.069 30.5
28.88 0.268 FM Deck Imm. 33.57 0.064 28.5
33.57 0.3 FM 38.57 0.059 26.2
38.57 0.31 FM MaxRA 43.57 0.054 23.7
43.57 0.297 FM Deck rail midship 48.57 0.048 21.1
48.57 0.264 FM 53.57 0.041 18.3
53.57 0.22 FM 58.57 0.035 15.5
56.49 0.194 FM Galley Door 63.35 0.029 12.7
58.57 0.177 FM Mess Door 68.57 0.022 9.7
63.35 0.134 AHO Deck edge@whlhse 73.57 0.016 7.0
68.57 0.114 AHO Radio Room 78.57 0.010 4.4
73.57 0.158 AHO 83.57 0.005 2.1
78.57 0.188 AHO 88.57 0.001 0.3
83.57 0.141 AHO 90 0.000 0.0
88.57 0.07 AHO
91.71 −0.222 HO Mast Heads

Appendix F - Occurence Loading Condition and Sail Plan

Sail Areas and Centres (Source: Stability Book and Sail Plan Drawing)
No. Name of Sail Area
(m3)
Centre
Above BL
(m)
Moment
(m3)
If in Use
enter:
x
Area
(m2)
Centre
Above B
(m)
Moment
(m3)
1 Flying Jib 41.00 29.15 1195.15   0.00 0.00 0.00
2 Outer Jib 78.00 17.80 1388.40   0.00 0.00 0.00
3 Inner Jib 57.00 15.65 892.05 x 57.00 15.65 892.05
4 Fore Topmast Staysail 48.00 13.80 662.40 x 48.00 13.80 662.40
5 Fore Upper Topgallant 34.00 35.20 1196.80   0.00 0.00 0.00
6 Fore Lower Topgallant 50.00 30.80 1540.00   0.00 0.00 0.00
7 Fore Upper topsail 58.00 25.85 1499.30 x 58.00 25.85 1499.30
8 Fore Lower Topsail 70.00 20.60 1442.00 x 70.00 20.60 1442.00
9 Fore Sail 104.00 14.00 1456.00   0.00 0.00 0.00
10 Main Topgallant staysail 41.00 30.45 1248.45   0.00 0.00 0.00
11 Main topmast staysail 55.00 23.65 1300.75   0.00 0.00 0.00
12 Main Staysail 60.00 14.40 864.00 x 60.00 14.40 864.00
13 Main Gaff Topsail 55.00 28.90 1589.50   0.00 0.00 0.00
14 Main Sail 112.00 17.30 1937.60 x 112.00 17.30 1937.60
15 Mizzen Gaff Topsail 48.00 28.15 1351.20   0.00 0.00 0.00
16 Mizzen 123.00 17.20 2115.60   0.00 0.00 0.00
 
  Main Sail Reefed 24.00 11.65 279.60 0.00 0.00 0.00
  Mizzen Reefed 55.00 14.50 797.50 x 55.00 14.50 797.50
 
  Total: 1034.00 20.97 21679.20  
 
  In Use:         460.00 17.60 8094.85
            44.49  ° of Total Area
Under Water Lateral Plane: Area (m^2): 125.47
(calculated for the occurrence loading condition) Centre abv BL (m): 2.04
Item: Area, A Centre Lever, h Coeff, C Product
    Abv BL     A.h.C
  (m^2) (m) (m)   (m^3)
           
Masts, Booms, Rigging, Rails, Vents, Hatch Coamings, etc.:
(constant – derived from stability book)
82.31 14.85 12.81 1.00 1054.56
 
Sails: 460.00 17.60 15.56 1.00 7157.37
(calculated above and using range of value for Csails)       2.00 14314.74
           
Hull and Deckhouses: 190.47 6.16 4.12 1.00 784.74
(calculated for the occurrence loading condition)          
 
Total Moments of Area: Cs = 1.0 8996.66
  Cs = 2.0 16154.03
Wind Heeling Arm:
(for upright condition as calculated above)
WHA (m): 0.082         
Ship Displacement:
(calculated for the occurrence loading condition)
Displ (kg): 441970             
Density of air: ρ (kg/m^3): 1.20             
          
Wind Pressure: P (N/m^2): 39.33 Cs = 1.0           
  21.90 Cs = 2.0           
          
Wind Speed: v (m/s): 8.10 Cs = 1.0           
  v(knots): 15.74             
          
  v (m/s): 6.04 Cs = 2.0           
  v(knots): 11.74             
Righting Arm (RA) Curves: Wind Heeling Arm (WHA) Curves:
From AutoHydro Output for Occurrence
Loading Condition
where,
Based on the relationship:
 WHA(θ) = WHA(0) × cos1.3 θ
For Critical Point Immersion:
Displ (t) = 441.97 From RA Curve: θ CrtPt 23.57 deg Curve of Critical Angle
RA @CrtPt 0.222 m x y
23.57 0
θ RA Model Notes θ WHA HMMT 23.57 0.5
(deg) (m)     (deg) (m) (t.m)
3.57 0 FM Equil 0 0.249 109.9
8.57 0.063 FM 8.57 0.245 108.3
13.57 0.122 FM 13.57 0.240 105.9
18.57 0.175 FM 18.57 0.232 102.5
23.57 0.222 FM video angle 23.57 0.222 98.1
28.57 0.265 FM 28.57 0.210 92.8
28.88 0.268 FM Deck Imm. 33.57 0.196 86.7
33.57 0.3 FM 38.57 0.181 79.8
38.57 0.31 FM MaxRA 43.57 0.164 72.3
43.57 0.297 FM Deck rail midship 48.57 0.145 64.2
48.57 0.264 FM 53.57 0.126 55.8
53.57 0.22 FM 58.57 0.107 47.1
56.49 0.194 FM Galley Door 63.35 0.088 38.7
58.57 0.177 FM Mess Door 68.57 0.067 29.7
63.35 0.134 AHO Deck edge@whlhse 73.57 0.048 21.8
68.57 0.114 AHO Radio Room 78.57 0.030 13.4
73.57 0.158 AHO 83.57 0.014 6.4
78.57 0.188 AHO 88.57 0.002 0.9
83.57 0.141 AHO 90 0.000 0.0
88.57 0.07 AHO
91.71 −0.222 HO Mast Heads

Appendix F - Occurence Loading Condition and Sail Plan (image 2)

Sail Areas and Centres (Source: Stability Book and Sail Plan Drawing)
 
No. Name of Sail Area
(m^2)
Centre
Abv BL
(m)
Moment
(m^3)
If in Use
enter:
x
Area
(m^2)
Centre
Abv B
(m)
Moment
(m^3)
1 Flying Jib 41.00 29.15 1195.15 0.00 0.00 0.00
2 Outer Jib 78.00 17.80 1388.40 0.00 0.00 0.00
3 Inner Jib 57.00 15.65 892.05 x 57.00 15.65 892.05
4 Fore Topmast Staysail 48.00 13.80 662.40 x 48.00 13.80 662.40
5 Fore Upper Topgallant 34.00 35.20 1196.80 0.00 0.00 0.00
6 Fore Lower Topgallant 50.00 30.80 1540.00 0.00 0.00 0.00
7 Fore Upper topsail 58.00 25.85 1499.30 x 58.00 25.85 1499.30
8 Fore Lower Topsail 70.00 20.60 1442.00 x 70.00 20.60 1442.00
9 Fore Sail 104.00 14.00 1456.00 0.00 0.00 0.00
10 Main Topgallant staysail 41.00 30.45 1248.45 0.00 0.00 0.00
11 Main topmast staysail 55.00 23.65 1300.75 0.00 0.00 0.00
12 Main Staysail 60.00 14.40 864.00 x 60.00 14.40 864.00
13 Main Gaff Topsail 55.00 28.90 1589.50 0.00 0.00 0.00
14 Main Sail 112.00 17.30 1937.60 x 112.00 17.30 1937.60
15 Mizzen Gaff Topsail 48.00 28.15 1351.20 0.00 0.00 0.00
16 Mizzen 123.00 17.20 2115.60 0.00 0.00 0.00
 
  Main Sail Reefed 24.00 11.65 279.60 0.00 0.00 0.00
  Mizzen Reefed 55.00 14.50 797.50 x 55.00 14.50 797.50
 
  Total: 1034.00 20.97 21679.20  
 
  In Use:         460.00 17.60 8094.85
            44.49  ° of Total Area
Under Water Lateral Plane: Area (m^2): 125.47
(calculated for the occurrence loading condition) Centre abv BL (m): 2.04
Item: Area, A Centre Lever, h Coeff, C Product
    Abv BL     A.h.C
  (m^2) (m) (m)   (m^3)
           
Masts, Booms, Rigging, Rails, Vents, Hatch Coamings, etc.:
(constant – derived from stability book)
82.31 14.85 12.81 1.00 1054.56
 
Sails: 460.00 17.60 15.56 1.00 7157.37
(calculated above and using range of value for Csails)       2.00 14314.74
           
Hull and Deckhouses: 190.47 6.16 4.12 1.00 784.74
(calculated for the occurrence loading condition)          
 
Total Moments of Area: Cs = 1.0 8996.66
  Cs = 2.0 16154.03
Wind Heeling Arm:
(for upright condition as calculated above)
WHA (m): 0.249         
Ship Displacement:
(calculated for the occurrence loading condition)
Displ (kg): 441970             
Density of air: ρ (kg/m^3): 1.20             
          
Wind Pressure: P (N/m^2): 119.82 Cs = 1.0           
  66.73 Cs = 2.0           
          
Wind Speed: v (m/s): 14.13 Cs = 1.0           
  v(knots): 27.47             
          
  v (m/s): 10.55 Cs = 2.0           
  v(knots): 20.50             
Righting Arm (RA) Curves: Wind Heeling Arm (WHA) Curves:
From AutoHydro Output for Occurrence
Loading Condition
where,
Based on the relationship:
 WHA(θ) = WHA(0) × cos1.3 θ
For Critical Point Immersion:
Displ (t) = 441.97 From RA Curve: θ CrtPt 38.57 deg Curve of Critical Angle
RA @CrtPt 0.31 m x y
38.57 0
θ RA Model Notes θ WHA HMMT 38.57 0.5
(deg) (m)     (deg) (m) (t.m)
3.57 0 FM Equil 0 0.427 188.7
8.57 0.063 FM 8.57 0.421 185.9
13.57 0.122 FM 13.57 0.411 181.8
18.57 0.175 FM 18.57 0.398 176.0
23.57 0.222 FM video angle 23.57 0.381 168.5
28.57 0.265 FM 28.57 0.361 159.4
28.88 0.268 FM Deck Imm. 33.57 0.337 148.8
33.57 0.3 FM 38.57 0.310 137.0
38.57 0.31 FM MaxRA 43.57 0.281 124.1
43.57 0.297 FM Deck rail midship 48.57 0.250 110.3
48.57 0.264 FM 53.57 0.217 99.8
53.57 0.22 FM 58.57 0.183 80.9
56.49 0.194 FM Galley Door 63.35 0.151 66.5
58.57 0.177 FM Mess Door 68.57 0.115 51.0
63.35 0.134 AHO Deck edge@whlhse 73.57 0.083 36.5
68.57 0.114 AHO Radio Room 78.57 0.052 23.0
73.57 0.158 AHO 83.57 0.025 11.0
78.57 0.188 AHO 88.57 0.004 1.6
83.57 0.141 AHO 90 0.000 0.0
88.57 0.07 AHO
91.71 −0.222 HO Mast Heads

Appendix F - Occurence Loading Condition and Sail Plan (image 3)

Sail Areas and Centres (Source: Stability Book and Sail Plan Drawing)
 
No. Name of Sail Area
(m^2)
Centre
Abv BL
(m)
Moment
(m^3)
If in Use
enter:
x
Area
(m^2)
Centre
Abv B
(m)
Moment
(m^3)
1 Flying Jib 41.00 29.15 1195.15 0.00 0.00 0.00
2 Outer Jib 78.00 17.80 1388.40 0.00 0.00 0.00
3 Inner Jib 57.00 15.65 892.05 x 57.00 15.65 892.05
4 Fore Topmast Staysail 48.00 13.80 662.40 x 48.00 13.80 662.40
5 Fore Upper Topgallant 34.00 35.20 1196.80 0.00 0.00 0.00
6 Fore Lower Topgallant 50.00 30.80 1540.00 0.00 0.00 0.00
7 Fore Upper topsail 58.00 25.85 1499.30 x 58.00 25.85 1499.30
8 Fore Lower Topsail 70.00 20.60 1442.00 x 70.00 20.60 1442.00
9 Fore Sail 104.00 14.00 1456.00 0.00 0.00 0.00
10 Main Topgallant staysail 41.00 30.45 1248.45 0.00 0.00 0.00
11 Main topmast staysail 55.00 23.65 1300.75 0.00 0.00 0.00
12 Main Staysail 60.00 14.40 864.00 x 60.00 14.40 864.00
13 Main Gaff Topsail 55.00 28.90 1589.50 0.00 0.00 0.00
14 Main Sail 112.00 17.30 1937.60 x 112.00 17.30 1937.60
15 Mizzen Gaff Topsail 48.00 28.15 1351.20 0.00 0.00 0.00
16 Mizzen 123.00 17.20 2115.60 0.00 0.00 0.00
 
  Main Sail Reefed 24.00 11.65 279.60 0.00 0.00 0.00
  Mizzen Reefed 55.00 14.50 797.50 x 55.00 14.50 797.50
 
  Total: 1034.00 20.97 21679.20  
 
  In Use:         460.00 17.60 8094.85
            44.49  ° of Total Area
Under Water Lateral Plane: Area (m^2): 125.47
(calculated for the occurrence loading condition) Centre abv BL (m): 2.04
Item: Area, A Centre Lever, h Coeff, C Product
    Abv BL     A.h.C
  (m^2) (m) (m)   (m^3)
           
Masts, Booms, Rigging, Rails, Vents, Hatch Coamings, etc.:
(constant – derived from stability book)
82.31 14.85 12.81 1.00 1054.56
 
Sails: 460.00 17.60 15.56 1.00 7157.37
(calculated above and using range of value for Csails)       2.00 14314.74
           
Hull and Deckhouses: 190.47 6.16 4.12 1.00 784.74
(calculated for the occurrence loading condition)          
 
Total Moments of Area: Cs = 1.0 8996.66
  Cs = 2.0 16154.03
Wind Heeling Arm:
(for upright condition as calculated above)
WHA (m): 0.427         
Ship Displacement:
(calculated for the occurrence loading condition)
Displ (kg): 441970             
Density of air: ρ (kg/m^3): 1.20             
          
Wind Pressure: P (N/m^2): 205.72 Cs = 1.0           
  114.57 Cs = 2.0           
          
Wind Speed: v (m/s): 18.52 Cs = 1.0           
  v(knots): 35.99             
          
  v (m/s): 13.82 Cs = 2.0           
  v(knots): 26.86             

 

Appendix G – Wind speed calculations with added water ballast

Righting Arm (RA) Curves: Wind Heeling Arm (WHA) Curves:
From AutoHydro Output for Occurrence
Loading Condition
where,
Based on the relationship:
 WHA(θ) = WHA(0) × cos1.3 θ
For Critical Point Immersion:
Displ (t) = 462.19 From RA Curve: θ CrtPt 45.0 deg Curve of Critical Angle
RA @CrtPt 0.33 m x y
45.0 0
θ RA Notes θ WHA HMMT 45.0 0.5
(deg) (m)     (deg) (m) (t.m)
3.33 0 Equil 0 0.518 188.7
8.33 0.065 8.57 0.510 185.9
13.33 0.127 13.57 0.499 181.8
18.33 0.188 18.57 0.483 176.0
23.33 0.241   23.57 0.462 168.5
28.29 0.29 Deck Imm. 28.57 0.437 159.4
28.33 0.291   33.57 0.408 148.8
33.33 0.331 38.57 0.376 137.0
38.33 0.346   43.57 0.341 124.1
39.16 0.347 MaxRA 48.57 0.303 110.3
43.33 0.338 53.57 0.263 99.8
48.33 0.31 58.57 0.222 80.9
53.33 0.27   63.35 0.183 66.5
54.35 0.261 CrtPt (Theoretical) 68.57 0.140 51.0
58.33 0.228   73.57 0.100 36.5
63.33 0.202   78.57 0.063 23.0
68.33 0.216 83.57 0.030 11.0
73.33 0.311 88.57 0.004 1.6
78.33 0.395 90 0.000 0.0
80.85 0.406
83.33 0.395  
88.33 0.361  
93.33 0.311  
98.33 0.253  
103.33 0.188  
108.33 0.12  
113.33 0.053  
117.64 0 RA Zero

Appendix G - Wind Speed Calculations with Added Water Ballast

Sail Areas and Centres (Source: Stability Book and Sail Plan Drawing)
 
No. Name of Sail Area
(m^2)
Centre
Abv BL
(m)
Moment
(m^3)
If in Use
enter:
x
Area
(m^2)
Centre
Abv B
(m)
Moment
(m^3)
1 Flying Jib 41.00 29.15 1195.15 0.00 0.00 0.00
2 Outer Jib 78.00 17.80 1388.40 0.00 0.00 0.00
3 Inner Jib 57.00 15.65 892.05 x 57.00 15.65 892.05
4 Fore Topmast Staysail 48.00 13.80 662.40 x 48.00 13.80 662.40
5 Fore Upper Topgallant 34.00 35.20 1196.80 0.00 0.00 0.00
6 Fore Lower Topgallant 50.00 30.80 1540.00 0.00 0.00 0.00
7 Fore Upper topsail 58.00 25.85 1499.30 x 58.00 25.85 1499.30
8 Fore Lower Topsail 70.00 20.60 1442.00 x 70.00 20.60 1442.00
9 Fore Sail 104.00 14.00 1456.00 0.00 0.00 0.00
10 Main Topgallant staysail 41.00 30.45 1248.45 0.00 0.00 0.00
11 Main topmast staysail 55.00 23.65 1300.75 0.00 0.00 0.00
12 Main Staysail 60.00 14.40 864.00 x 60.00 14.40 864.00
13 Main Gaff Topsail 55.00 28.90 1589.50 0.00 0.00 0.00
14 Main Sail 112.00 17.30 1937.60 x 112.00 17.30 1937.60
15 Mizzen Gaff Topsail 48.00 28.15 1351.20 0.00 0.00 0.00
16 Mizzen 123.00 17.20 2115.60 0.00 0.00 0.00
 
  Main Sail Reefed 24.00 11.65 279.60 0.00 0.00 0.00
  Mizzen Reefed 55.00 14.50 797.50 x 55.00 14.50 797.50
 
  Total: 1034.00 20.97 21679.20  
 
  In Use:         460.00 17.60 8094.85
            44.49  ° of Total Area
Under Water Lateral Plane: Area (m^2): 125.47
(calculated for the occurrence loading condition) Centre abv BL (m): 2.04
Item: Area, A Centre Lever, h Coeff, C Product
    Abv BL     A.h.C
  (m^2) (m) (m)   (m^3)
           
Masts, Booms, Rigging, Rails, Vents, Hatch Coamings, etc.:
(constant – derived from stability book)
82.31 14.85 12.81 1.00 1054.56
 
Sails: 460.00 17.60 15.56 1.00 7157.37
(calculated above and using range of value for Csails)       2.00 14314.74
           
Hull and Deckhouses: 190.47 6.16 4.12 1.00 784.74
(calculated for the occurrence loading condition)          
 
Total Moments of Area: Cs = 1.0 8996.66
  Cs = 2.0 16154.03
Wind Heeling Arm:
(for upright condition as calculated above)
WHA (m): 0.518         
Ship Displacement:
(calculated for the occurrence loading condition)
Displ (kg): 441970             
Density of air: ρ (kg/m^3): 1.20             
          
Wind Pressure: P (N/m^2): 260.97 Cs = 1.0           
  145.34 Cs = 2.0           
          
Wind Speed: v (m/s): 20.86 Cs = 1.0           
  v(knots): 40.54             
          
  v (m/s): 15.56 Cs = 2.0           
  v(knots): 30.25             

Appendix H – Wind speed calculations with list corrected

Righting Arm (RA) Curves: Wind Heeling Arm (WHA) Curves:
From AutoHydro Output for Occurrence
Loading Condition
where,
Based on the relationship:
 WHA(θ) = WHA(0) × cos1.3 θ
For Critical Point Immersion:
Displ (t) = 441.97 From RA Curve: θ CrtPt 42.0 deg Curve of Critical Angle
RA @CrtPt 0.344 m x y
42.0 0
θ RA Model Notes List Corrected θ WHA HMMT 42.0 0.5
(deg) (m)     RA(m) (deg) (m) (t.m)
0 −0.04 FM   0              
3.57 0 FM Equil 0.04 0 0.506 223.6
8.57 0.063 FM 0.103 8.57 0.499 220.4
13.57 0.122 FM 0.162 13.57 0.488 215.6
18.57 0.175 FM 0.215 18.57 0.472 208.6
23.57 0.222 FM video angle 0.262 23.57 0.452 199.7
28.57 0.265 FM   0.305 28.57 0.427 188.9
28.88 0.268 FM Deck Imm. 0.308 33.57 0.399 176.4
33.57 0.3 FM 0.34 38.57 0.367 162.4
38.57 0.31 FM MaxRA 0.35 43.57 0.333 147.1
43.57 0.297 FM Deck rail midship 0.337 48.57 0.296 130.7
48.57 0.264 FM 0.304 53.57 0.257 113.6
53.57 0.22 FM 0.26 58.57 0.217 95.9
56.49 0.194 FM Galley Door 0.234 63.35 0.178 78.9
58.57 0.177 FM Mess Door 0.217 68.57 0.137 60.4
63.35 0.134 AHO Deck edge @whlhse 0.174 73.57 0.098 43.3
63.57 0.114 AHO Radio Room 0.154 78.57 0.062 27.3
73.57 0.158 AHO 0.198 83.57 0.029 13.0
78.57 0.188 AHO 0.228 88.57 0.004 1.8
83.57 0.141 AHO 0.181 90 0.000 0.0
88.57 0.07 AHO 0.11
91.71 −0.222 HO Mast Heads −0.182

Appendix H - Wind Speed Calculations with List Corrected