open water squat predictions for halifax, kingston and

Defence Research andDevelopment Canada

Recherche et developpementpour la defense Canada

Open Water Squat Predictions for HALIFAX, KINGSTON andORCA Classes

Kevin McTaggartDRDC – Atlantic Research Centre

Defence Research and Development Canada

Scientific ReportDRDC-RDDC-2017-R075April 2017

Open Water Squat Predictions for HALIFAX,KINGSTON and ORCA Classes

Kevin McTaggartDRDC – Atlantic Research Centre

Defence Research and Development CanadaScientific ReportDRDC-RDDC-2017-R075April 2017

c⃝ Her Majesty the Queen in Right of Canada, as represented by the Minister of NationalDefence, 2017

c⃝ Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de laDéfense nationale, 2017

Abstract

This report presents predictions of squat for the HALIFAX, KINGSTON and ORCAclasses in shallow water. Squat is the physical phenomenon of a ship at speed beingattracted toward the ocean bottom, possibly resulting in grounding. A potential flowpanel method was developed for predicting hydrodynamic forces in shallow water andthe associated change in ship position. The method provides squat predictions overmost operational speeds, with the exception of transcritical flow conditions havingwater depth Froude numbers ranging from approximately 0.8 to 1.2. Presented resultsof bottom clearance as a function of ship speed can provide guidance to ship operatorsfor determining safe ship speeds in given water depths. The results are given for shipsin unconfined waters. If ships are expected to travel in confined waters, such as canals,then additional computations should be performed using the developed method, whichalready has the capability to model canal walls.

Significance for defence and security

Squat predictions are now available to operators of HALIFAX, KINGSTON andORCA class ships. These predictions will help to decrease the risk of grounding.The squat predictions were obtained using detailed modelling of the flow around eachship, and are expected to be more accurate than predictions from simplified methods.Squat predictions on a desktop workstation typically require less than five minutesfor each combination of loading condition, water depth, and ship speed; thus, themethod is practical for examining a wide range of operational conditions. This hy-drodynamic solution method will be applied to other problems of high relevance tothe Royal Canadian Navy, including prediction of ship resistance and maneuveringforces.

DRDC-RDDC-2017-R075 i

Résumé

Le présent rapport comporte les prévisions d’enfoncement en eaux peu profondesapplicables aux classes HALIFAX, KINGSTON et ORCA. L’enfoncement consiste ence phénomène physique selon lequel un navire en mouvement est attiré vers le fondde la mer, situation qui peut entraîner un naufrage. Nous avons conçu une méthodepotentielle de panneau bas en vue d’estimer les forces hydrodynamiques en eaux peuprofondes, ainsi que le changement de position connexe du navire. La méthode fournitdes prévisions d’enfoncement dans le cas de la plupart des vitesses opérationnelles, àl’exception des conditions d’eau peu profonde critiques qui présentent des nombres deFroude d’environ 0.8 à 1.2. Le rapport comporte des résultats en matière de hauteur defonds en fonction de la vitesse du navire qui peuvent servir de guide aux exploitantsde navires en ce qui a trait à déterminer les vitesses sûres dans des profondeursd’eau données. Les résultats visent les navires en eaux non restreintes ; si les naviresdoivent traverser des eaux restreintes, comme des canaux, il faut exécuter des calculssupplémentaires à l’aide de la méthode conçue, qui a déjà la capacité de modéliserdes parois de canal.

Importance pour la défense et la sécurité

Les exploitants des navires des classes HALIFAX, KINGSTON et ORCA ont mainte-nant à leur disposition des prévisions d’enfoncement pour aider à réduire les risquesde naufrage. Ces prévisions d’enfoncement ont été obtenues en effectuant une mo-délisation détaillée de l’écoulement autour de chaque navire, et elles devraient êtreplus précises que les prévisions obtenues à l’aide de méthodes plus simples. Il est pos-sible d’obtenir des prévisions d’enfoncement en moins de cing minutes à l’aide d’unordinateur de bureau, quelle que soit la combinaison des conditions de charge, de laprofondeur de l’eau et de la vitesse du navire. La méthode permet donc d’évaluerun large éventail de conditions opérationnelles. Cette méthode fondée sur les forceshydrodynamiques sera utilisée pour tenter de régler certains problèmes d’importancepour la Marine royale canadienne, notamment pour prévoir la résistance des navireset les forces de manœuvre.

ii DRDC-RDDC-2017-R075

Table of contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Significance for defence and security . . . . . . . . . . . . . . . . . . . . . . . i

Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Importance pour la défense et la sécurité . . . . . . . . . . . . . . . . . . . . . ii

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Overview of Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Squat Predictions for HALIFAX Class . . . . . . . . . . . . . . . . . . . . 5

4 Squat Predictions for KINGSTON Class . . . . . . . . . . . . . . . . . . . 11

5 Squat Predictions for ORCA Class . . . . . . . . . . . . . . . . . . . . . . 17

6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Annex A: Methodology for Squat Evaluation . . . . . . . . . . . . . . . . . . 27

A.1 Boundary Conditions for Flow Solution . . . . . . . . . . . . 27

A.2 Modelling of Transom Flow . . . . . . . . . . . . . . . . . . . 28

A.3 Integration of Forces on Ship Hull . . . . . . . . . . . . . . . 29

A.4 Iterative Process for Solution of Sinkage and Trim . . . . . . 29

A.5 Panelling of Hull and Free Surface . . . . . . . . . . . . . . . 29

DRDC-RDDC-2017-R075 iii

List of figures

Figure 1: Profile of Ship and Baseline. . . . . . . . . . . . . . . . . . . . . . 4

Figure 2: Profile of Ship in Calm Water. . . . . . . . . . . . . . . . . . . . . 4

Figure 3: Profile of Ship with Squat. . . . . . . . . . . . . . . . . . . . . . . 4

Figure 4: HALIFAX Class Deep Departure at 10 knots, Water Depth of 8.0 m. 6

Figure 5: HALIFAX Sinkage, Trim and Bottom Clearance inWater Depth of 8.0 m. . . . . . . . . . . . . . . . . . . . . . . . . 7




Figure 9: KINGSTON Class Deep Departure at 9 knots, Water Depth 5.0 m. 12

Figure 10: KINGSTON Class Sinkage, Trim and Bottom Clearance,Water Depth 4.5 m. . . . . . . . . . . . . . . . . . . . . . . . . . . 13




Figure 14: ORCA Class at 9 knots, Water Depth 5.0 m. . . . . . . . . . . . . 18

Figure 15: ORCA Class Sinkage, Trim and Bottom Clearance inWater Depth of 4.0 m. . . . . . . . . . . . . . . . . . . . . . . . . 19


iv DRDC-RDDC-2017-R075



DRDC-RDDC-2017-R075 v

List of tables

Table 1: HALIFAX Class Loading Conditions. . . . . . . . . . . . . . . . . 5

Table 2: KINGSTON Class Loading Conditions. . . . . . . . . . . . . . . . 11

Table 3: ORCA Class Loading Conditions. . . . . . . . . . . . . . . . . . . 17

vi DRDC-RDDC-2017-R075

1 Introduction

When a ship is travelling at speed in shallow water, hydrodynamic pressures act-ing on the ship hull typically cause the ship to be sucked toward the bottom. Thisphenomenon is referred to as squat, and is sufficiently great to influence safe opera-tion of vessels. Squat will be influenced by many factors, including ship speed, waterdepth, and channel walls that might be present. To assist with safe operations ofthe Royal Canadian Navy, this report presents squat predictions for the HALIFAX,KINGSTON and ORCA classes.

It should be noted that ship squat is highly dependent on the water depth Froudenumber, defined as:

Fh =U√g h

(1)

where U is ship forward speed, g is gravitational acceleration, and h is water depth.When the water depth Froude number is below 1.0, the flow is referred to as be-ing subcritical. Conversely, supercritical flow occurs when the water depth Froudenumber is greater than 1.0. For supercritical flow, surface waves can only propagatedownstream, causing the flow around the ship and the resulting squat behaviour todiffer significantly from subcritical flow. This report also refers to transcritical flow,with water depth Froude numbers ranging from approximately 0.8 to 1.2.

DRDC-RDDC-2017-R075 1

2 Overview of Methodology

Squat for HALIFAX, KINGSTON and ORCA classes was evaluated using a physics-based method that evaluates the flow around the ship, the pressures on the shiphull, and the resulting sinkage and trim. Annex A gives a detailed description of theapproach. Figures 1 to 3 show profile views of relevant ship dimensions, including incalm water and with squat. The following equations give the clearance between thebottom of the ship and water bottom:

c(xfore) = h− Tmid − s(U) + [tstern + τ(U)]xfore − xmid

L+ zbl(xfore) (2)

c(xaft) = h− Tmid − s(U) + [tstern + τ(U)]xaft − xmid

L+ zbl(xaft) (3)

where c is the clearance from the bottom, h is the water depth, Tmid is the shipdraft at midships, s(U) is the sinkage at midships due to ship speed, tstern is theship hydrostatic trim by stern, τ(U) is the trim by stern due to ship speed, x is thelongitudinal position relative to the ship centre of gravity, and zbl is the elevationrelative to the ship baseline of the lowest object near the bow or stern, such as asonar dome in the fore portion of the ship or a propeller in the aft portion. The foreand aft longitudinal locations xfore and xaft refer to local locations most likely toexperience grounding.

The following equation was used for evaluating the minimum clearance between thelowest point on the ship and the ocean bottom:

cmin = min (c(xfore), c(xaft)) − Tmid ϵc (4)

The term ϵc accounts for possible overprediction of clearance by the numerical method.Analysis of numerical predictions with the present method and available model testdata for two different ships were used to produce the following envelope for the clear-ance overprediction:

ϵc =

0.1 Fh for Fh < 0.7

0.1 + 3.0 (Fh − 0.7) for 0.7 ≤ Fh < 0.8

0.4 for 0.8 ≤ Fh < 0.9

0.4 − 1.5 (Fh − 0.9) for 0.9 ≤ Fh < 1.1

0.1 for Fh ≥ 1.1

(5)

The model test data for a Series 60 hull with block coefficient of 0.60 [1] includesubcritical, transcritical, and supercritical flow conditions. The model test data fora very large crude carrier [2] with block coefficient of 0.81 are limited to subcriticalflow conditions. Of the two ships with available experimental data, the Series 60 hull

2 DRDC-RDDC-2017-R075

is more representative of the navy ships in this study, which have block coefficientsranging from 0.44 to 0.54. Equation (5) indicates that the maximum clearance error is0.4 Tmid, and occurs for depth Froude numbers between 0.8 and 0.9 (in the transcriti-cal flow region). In the portion of the transcritical flow region where sinkage and trimpredictions are unavailable, Equation (5) accounts for errors caused by interpolationusing results from predictions at subcritical and supercritical conditions. It shouldbe emphasized that Equation (5) is an initial attempt to estimate clearance overpre-diction error. Significant uncertainty exists in squat prediction errors, especially fortranscritical flow cases.


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zbl

Baseline

Figure 1: Profile of Ship and Baseline.

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Waterline↑|

Tmid

|↓ tstern

Figure 2: Profile of Ship in Calm Water.

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...................................................................................................................................................................................... Waterline

↑|Tmid + s(U)

|↓↑|

tstern + τ(U)

|↓

Figure 3: Profile of Ship with Squat.


3 Squat Predictions for HALIFAX Class

Squat predictions were made for the HALIFAX class in deep departure and opera-tional light loading conditions from August 2006 as given in Table 1. When evaluatingclearance at the fore and and aft regions, the sonar dome extending 2.332 m belowthe baseline and the propeller extending 2.055 m below the baseline were considered.

Figure 4 shows the computed wave elevations and ship orientation for a sample squatcomputation. Figures 5 to 8 give squat predictions for water depths of 8.0 m, 9.0 m,10.0 m, and 11.0 m. The presented sinkage and trim values are from the numericalpredictions, while the bottom clearance values are based on Equation (4) and includean allowance for clearance overprediction error. For example, Figure 5 indicates thatthe ship in the deep departure condition will experience grounding at a ship speed of7.8 knots. For water depths of 10.0 m and 11.0 m, the numerical method is unable toprovide sinkage and trim predictions in the transcritical flow region, which includesspeeds in the vicinity of 20 knots; thus, there are gaps in predicted values for sinkageand trim in Figures 7 and 8. Bottom clearance predictions in the transcritical flowregion are based on interpolation of sinkage and trim values from the nearest availablespeeds in the subcritical and supercritcal flow regions. This approach for evaluatingbottom clearance was selected based on consultation with naval operators. Whenconsidering all squat predictions of the HALIFAX class, it is evident that a shipspeed of 15 knots should only be exceeded for water depths of 11.0 m and greater.

Table 1: HALIFAX Class Loading Conditions.

Deep departure Operational light

Draft at midships, Tmid 5.138 m 4.871 m

Trim by stern, tstern −0.266 m 0.608 m

Displacement, ▽ 4961 tonnes 4516 tonnes

Height of CG, KG 6.535 m 6.902 m


Figure 4: HALIFAX Class Deep Departure at 10 knots, Water Depth of 8.0 m.


7 8 9 10 11 120.0

0.1

0.2

0.3

0.4

Ship speed U (knots)

Sin

kage

s(U)

(m)

7 8 9 10 11 12−0.3

−0.2

−0.1

0.0


Trim

τ(U

)(m

)

7 8 9 10 11 120.0

0.1

0.2

0.3

0.4

0.5

0.0


Bot

tom

clea

ranc

ec m

in(m

) Deep departureOperational light

Figure 5: HALIFAX Sinkage, Trim and Bottom Clearance inWater Depth of 8.0 m.


8 10 12 140.0

0.1

0.2

0.3

0.4

0.5

0.0


Sin

kage

s(U)

(m)

8 10 12 14−0.5

−0.4

−0.3

−0.2

−0.1

0.00.0


Trim

τ(U

)(m

)

8 10 12 140.0

1.0

2.0

0.0


Bot

tom

clea

ranc

ec m

in(m




0 10 20 30−0.5

0.0

0.5

1.0

1.5

0.0


Sin

kage

s(U)

(m)

0 10 20 30−1.0

0.0

1.0

2.0

3.0

4.0

5.0

0.0


Trim

τ(U

)(m

)

0 10 20 300.0

1.0

2.0

3.0


Bot

tom

clea

ranc

ec m

in(m




0 10 20 30−0.5

0.0

0.5

1.0

1.5

0.0


Sin

kage

s(U)

(m)

0 10 20 30−1.0

0.0

1.0

2.0

3.0

4.0

5.0

0.0


Trim

τ(U

)(m

)

0 10 20 300.0

1.0

2.0

3.0

4.0


Bot

tom

clea

ranc

ec m

in(m




4 Squat Predictions for KINGSTON Class

Squat predictions were made for the KINGSTON class in deep departure and opera-tional light loading conditions as given in Table 2. The fore perpendicular (FP) andaft perpendicular (AP) are located at frames 0 and 98 respectively. When evaluat-ing clearance at the bow and stern, the bottom of the ship was taken as being atthe baseline (zbl = 0.0) because neither the hull nor appendages extend below thebaseline.

Figure 9 shows the computed wave elevations and ship orientation for a sample squatcomputation. Figures 10 to 13 give squat predictions for water depths of 4.5 m,5.0 m, 6.0 m, and 7.0 m. For the smallest water depth of 4.5 m, grounding in the deepdeparture condition is predicted at a ship speed of 9.8 knots. Flow conditions aresubcritical for all KINGSTON class squat predictions, which determined the limitingship speeds of 12 knots and 13 knots for water depths of 6.0 m and 7.0 m respectively.

Table 2: KINGSTON Class Loading Conditions.


Draft at FP 3.067 m 2.767 m

Draft at AP 3.283 m 3.105 m

Displacement, ▽ 991.32 tonnes 886.80 tonnes



Figure 9: KINGSTON Class Deep Departure at 9 knots, Water Depth 5.0 m.


6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5


Sin

kage

s(U)

(m)

6 7 8 9 10−0.20

−0.15

−0.10

−0.05

0.00


Trim

τ(U

)(m

)

6 7 8 9 100.0

0.5

1.0

1.5


Bot

tom

clea

ranc

ec m

in(m

)

Deep departureOperational light

Figure 10: KINGSTON Class Sinkage, Trim and Bottom Clearance,Water Depth 4.5 m.


6 7 8 9 10 110.0

0.2

0.4

0.6


Sin

kage

s(U)

(m)

6 7 8 9 10 11−0.3

−0.2

−0.1

0.0


Trim

τ(U

)(m

)

6 7 8 9 10 110.0

0.5

1.0

1.5

2.0


Bot

tom

clea

ranc

ec m

in(m

)




6 8 10 120.0

0.1

0.2

0.3

0.4

0.5


Sin

kage

s(U)

(m)

6 8 10 12−0.4

−0.3

−0.2

−0.1

0.00.0


Trim

τ(U

)(m

)

6 8 10 120.0

1.0

2.0

3.0


Bot

tom

clea

ranc

ec m

in(m

)




6 8 10 12 140.0

0.2

0.4

0.6


Sin

kage

s(U)

(m)

6 8 10 12 14−0.4

−0.3

−0.2

−0.1

0.00.0


Trim

τ(U

)(m

)

6 8 10 12 140.0

1.0

2.0

3.0

4.0


Bot

tom

clea

ranc

ec m

in(m

)




5 Squat Predictions for ORCA Class

Squat predictions were made for the ORCA class in deep departure and operationallight loading conditions as given in Table 3. The fore draft mark is at Frame 27,28.35 m forward of Frame 0. The aft draft mark is at Frame 1, 0.643 m forward ofFrame 0. When evaluating clearance at the bow, the bottom of the ship was taken asbeing at the baseline (zbl = 0.0 m). For clearance at the stern, the bottom of the shipwas taken as being at zbl = −0.57 m, representing the lower limit of the propeller.

Figure 14 shows the computed wave elevations and ship orientation for a samplesquat computation. Figures 15 to 18 give squat predictions for water depths of 4.0 m,5.0 m, 6.0 m, and 7.0 m. For the smallest water depth of 4.0 m, grounding in thedeep departure condition is predicted at a ship speed of 9.8 knots. For water depthsof 5.0 m and higher, sinkage and trim have been predicted in both subcritical andsupercritcal flow regions, with no grounding predicted. Transcritical flow at thesewater depths occurs at ship speeds in the vicinity of 15 knots.

Table 3: ORCA Class Loading Conditions.


Draft at fore draft mark 1.729 m 2.153 m

Draft at aft draft mark 1.824 m 2.033 m

Displacement, ▽ 209.87 tonnes 204.12 tonnes



Figure 14: ORCA Class at 9 knots, Water Depth 5.0 m.


6 7 8 9 100.0

0.1

0.2

0.3

0.4


Sin

kage

s(U)

(m)

6 7 8 9 10−0.2

0.0

0.2

0.4

0.6

0.0


Trim

τ(U

)(m

)

6 7 8 9 100.0

0.5

1.0

1.5


Bot

tom

clea

ranc

ec m

in(m

)


Figure 15: ORCA Class Sinkage, Trim and Bottom Clearance inWater Depth of 4.0 m.


5 10 15 20−0.2

0.0

0.2

0.4

0.0


Sin

kage

s(U)

(m)

5 10 15 20−1.0

0.0

1.0

2.0

3.0

0.0


Trim

τ(U

)(m

)

5 10 15 200.0

1.0

2.0

3.0


Bot

tom

clea

ranc

ec m

in(m

)




5 10 15 20−0.2

0.0

0.2

0.4

0.0


Sin

kage

s(U)

(m)

5 10 15 20−1.0

0.0

1.0

2.0

3.0

0.0


Trim

τ(U

)(m

)

5 10 15 200.0

1.0

2.0

3.0

4.0


Bot

tom

clea

ranc

ec m

in(m

)




5 10 15 20−0.2

0.0

0.2

0.4

0.0


Sin

kage

s(U)

(m)


5 10 15 20−1.0

0.0

1.0

2.0

3.0

0.0


Trim

τ(U

)(m

)

5 10 15 200.0

1.0

2.0

3.0

4.0

5.0


Bot

tom

clea

ranc

ehmin

(m)



6 Discussion

The squat predictions are intended to assist operational decision making for HALI-FAX, KINGSTON and ORCA class vessels. The predictions must be combined withoperator judgement, which must consider factors such as acceptable bottom clear-ance and the quality of information regarding water depth. Fortunately, the squatpredictions give well defined trends, which will assist with operator judgement. Forexample, bottom clearance will decrease markedly with ship speed in the upper regionof subcritical ship speeds (e.g., ORCA class approaching 10 knots in water depth of4.0 m, Figure 15).

The squat predictions for the HALIFAX, KINGSTON and ORCA classes exhibittrends similar to those observed elsewhere, including experimental data for a shipin shallow water travelling at both subcritical and supercritical ship speeds [3]. Forsubcritical speeds, ship sinkage increases with ship speed. In cases of very low clear-ance between the ship bottom and water bottom, the sinkage can increase rapidlywith speed as the suction effects become more pronounced. Trim in the subcriticalflow region is often quite dependent on ship geometry, which influences the variationof hydrodynamic forces along the length of the ship. For supercritical speeds, shipsinkage will often be less than at subcritical speeds, and the ship will exhibit trim bythe stern.

The presented predictions are for ships in open water. The developed method can alsopredict squat for ships in confined waters, such as canals. Predictions for confinedwaters must include modelling of canal walls or other side barriers.

7 Conclusion

Squat predictions have been presented for the HALIFAX, KINGSTON and ORCAclasses for relevant ranges of water depths and ship speeds. The predictions were madeusing a potential flow panel method, which was selected based on requirements foraccuracy and acceptable computational time. The predictions are intended to provideguidance to operators when selecting safe ship speeds in shallow water.


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References

[1] Takeshi, H., Hino, T., Hinatsu, M., Tsukada, Y., and Fujisawa, J. (1987), ITTCCooperative Experiments on a Series 60 model at Ship Research Institute –Flow Measurements and Resistance Tests, (Technical Report) Ship ResearchInstitute, Japan.

[2] Lataire, E., Vantorre, M., and Delefortrie, G. (2012), A Prediction Method forSquat in Restricted and Unrestricted Rectangular Fairways, OceanEngineering, 55, 71–80.

[3] Jiang, T. (1998), Investigation of Waves Generated by Ships in Shallow Water,In Twenty-Second Symposium on Naval Hydrodynamics, Washington.

[4] Ferreiro, L. (1992), The Effects of Confined Water Operations on ShipPerformance: A Guide for the Perplexed, Naval Engineers Journal, 104(6).

[5] Millward, A. (1990), A Preliminary Design Method for the Prediction of Squatin Shallow Water, Marine Technology, 27(1), 10–19.

[6] Yao, J. and Zou, Z. (2010), Calculation of Ship Squat in Restricted Waterwaysby using a 3D Panel Method, In Ninth International Conference onHydrodynamics, Shanghai, China.

[7] Bertram, V. (2012), Practical Ship Hydrodynamics, 2nd ed, Oxford:Butterworth-Heinemann.

[8] McTaggart, K. (2015), Ship Radiation and Diffraction Forces at ModerateForward Speed, In World Maritime Technology Conference, Providence, RhodeIsland.

[9] Irvine, M., Longo, J., and Stern, F. (2013), Forward Speed Calm Water RollDecay for Surface Combatant 5415: Global and Local Flow Measurements,Journal of Ship Research, 57(4), 202–219.

[10] Tarafder, M. S. and Khalil, G. M. (2006), Calculation of Ship Sinkage and Trimin Deep Water using a Potential Based Panel Method, International Journal ofApplied Mechanics and Engineering, 11(2), 401–414.

[11] Dawson, C. (1977), A Practical Computer Method for Solving Ship-waveProblems, In Second International Conference on Numerical ShipHydrodynamics, Berkeley, California.

[12] Jensen, G., Söding, H., and Mi, Z.-X. (1986), Rankine Source Methods forNumerical Solutions of the Steady Wave Resistance Problem, In SixteenthSymposium on Naval Hydrodynamics, pp. 575–581, Berkely, California.


Symbols and Abbreviations

AP aft perpendicular

CG centre of gravity

c clearance between ship and ocean bottom

Fh forward speed Froude number based on water depth h

FP fore perpendicular

g gravitational acceleration

h water depth

KG height of centre of gravity above baseline

L ship length between perpendiculars

s sinkage (+ down)

Tmid draft at midships

tstern hydrostatic trim (+ by stern)

U ship speed

x longitudinal coordinate relative to ship CG

xaft longitudinal coordinate of aft position likely to experience grounding

xfore longitudinal coordinate of fore position likely to experience grounding

zbl elevation relative to ship baseline

ϵc nondimensional overprediciton error for bottom clearnace

τ speed-induced trim (+ by stern)

▽ ship mass displacement


Annex A Methodology for Squat Evaluation

Ferreiro [4], Lataire, Vantorre, and Delefortrie [2], and Millward [5] give overviewsof squat and also present relatively simple methods for predicting squat. Lataire,Vantorre, and Delefortrie include experimental data for the KLVCC2 very large crudecarrier. Yao and Zou [6] used a 3D panel method assuming potential flow to evaluatesquat for a Series 60 hull with block coefficient of 0.60, and include comparisons withexperimental data.

A panel method similar to that presented by Yao and Zou [6] was developed forpredicting squat of Royal Canadian Navy vessels. Bertram [7] gives many detailsregarding the underlying theory and numerical implementation for such methods.DRDC’s ShipMo3D seakeeping software [8] was extended to include panelling of thefree surface in the vicinity of a ship moving with steady forward speed. The panelmethod uses a potential flow solution, which assumes that viscous forces are negligible.Validation with experimental data [2, 6, 9] has shown that the assumption of negligibleviscous forces is acceptable for squat prediction, which is expected because verticalforces on the hull are dominated by normal pressures. Computational fluid dynamics(CFD) methods with detailed modelling of viscous flow are available for computingsquat; however, these methods were not used for the present work due to very longcomputation times (e.g., several days of computational effort using multi-processorcomputing for each combination of ship load condition, water depth, and ship speed).

A.1 Boundary Conditions for Flow Solution

For each combination of ship loading condition, water depth, ship speed, and esti-mated squat, the flow must be solved in the vicinity of the hull. The flow solutionmust satisfy the following boundary conditions:

1. The flow entering the fluid domain must have negligible variation with longitu-dinal coordinate x.

2. The flow velocity normal to the hull surface must be zero.

3. The flow velocity normal to the water bottom must be zero.

4. The flow velocity normal to any other solid boundaries (e.g., canal walls) mustbe zero.

5. The pressure on the free surface must be zero.

6. The flow velocity normal to the free surface must be zero. This boundary con-dition must account for any elevation slope present at the free surface.


The most challenging aspect of the boundary value problem is simultaneously satisfy-ing the free surface boundary conditions of zero pressure and zero normal flow velocity.Four different approaches have been implemented for modelling the free surface:

1. The double body solution assumes that the free surface is flat. The double bodysolution models both the hull and its mirror image above the free surface, butdoes not require modelling of the free surface because the presence of the hullmirror image causes the vertical flow velocity to be zero at the free surface. Thisapproach is valid for ships travelling at low speeds, and has the advantages ofbeing very efficient and robust.

2. The uniform linearized solution linearizes the free surface boundary conditionsbased on the uniform flow velocity U , similar to the approach of Tarafder andKhalil [10]. This approach works well for vessels that are fully submerged (e.g.,submarines) or have gradual variation of beam with x at the free surface (i.e.very slender vessels).

3. The double body linearized solution linearizes the free surface boundary con-ditions based on the double body solution, similar to the approach presentedby Dawson [11]. For non-slender surface-piercing vessels, this approach givesnoticeably better results than the uniform linearized solution.

4. The nonlinear solution uses an iterative approach to fully satisfy the free surfaceboundary conditions, and is similar to the approach presented by Bertram [7]and Jensen, Söding and Mi [12]. The nonlinear solution requires a very goodinitial solution, which is provided by the double body linearized solution. Ex-perience to date indicates that the nonlinear method is quite robust in deepwater, but has greater challenges obtaining solutions in shallow water.

For the present squat predictions, the double body linearized solution was used be-cause it achieves a balance of accuracy and robustness.

A.2 Modelling of Transom Flow

The potential flow panel method does not include direct modelling of flow separationat transom sterns. To approximate the influence of transom flow separation, a transomstern can be replaced with a narrowing virtual stern that extends from the transom toa location approximately 10 percent of the ship length aft of the transom. The aftmostlocation of the virtual stern should have zero width. Validation of the present squatprediction method using virtual sterns has given very good results for a very largecrude carrier [2] and a destroyer [9].


A.3 Integration of Forces on Ship Hull

The squat of the ship arises from hydrodynamics forces which differ from those forcesacting on the ship in a static condition. After the flow field has been solved for a givenset of conditions (loading condition, water depth, ship speed, sinkage, and trim), thehydrodynamic forces acting on the hull are evaluated by integrating normal pressuresacting on the hull panels. The present method integrates hull pressures based on theactual wetted hull surface, including the influence of sinkage, trim, and local waveelevation. For a ship with modelling of a virtual stern, the pressures on the virtualstern are not included when evaluating virtual forces on the ship hull.

A.4 Iterative Process for Solution of Sinkage and Trim

For each combination of loading condition, water depth, and ship speed, the sink-age and trim are evaluated using an iterative process. During each iteration, the shipsinkage and trim are adjusted based on integrated hull forces and hydrostatic stiffnessproperties. Convergence toward balance of forces is typically obtained within 5 iter-ations. Computations of squat on a desktop workstation typically require less than5 minutes for each combination of loading condition, water depth, and ship speed.

A.5 Panelling of Hull and Free Surface

Squat prediction values are dependent upon the panelling of the hull and free surface.Due to lateral symmetry, only the port side of each ship and the associated free surfaceneed to be modelled. Satisfactory free surface meshes have several thousand panels(port side only).

The utilization of a panel method for modelling the steady wave field around a shipintroduces some numerical challenges. The panel method cannot model the effects ofwave breaking or spray; thus, fine meshing immediately adjacent to the ship hull cancause a numerical solution to give unrealistic results. When modelling the free surfacefor the present work, it was found that the best approach is to use the smallest panelwidth (y direction, lateral) that gives a robust numerical solution. The length of freesurface panels (x direction, longitudinal) should be sufficiently small that 6 or morepanels are used for each longitudinal wavelength.


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1. ORIGINATOR (The name and address of the organization preparingthe document. Organizations for whom the document was prepared,e.g. Centre sponsoring a contractor’s report, or tasking agency, areentered in section 8.)

DRDC – Atlantic Research CentrePO Box 1012, Dartmouth NS B2Y 3Z7, Canada

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UNCLASSIFIED

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(NON-CONTROLLED GOODS)DMC AREVIEW: GCEC DECEMBER 2013

3. TITLE (The complete document title as indicated on the title page. Its classification should be indicated by the appropriateabbreviation (S, C or U) in parentheses after the title.)

Open Water Squat Predictions for HALIFAX, KINGSTON and ORCA Classes

4. AUTHORS (Last name, followed by initials – ranks, titles, etc. not to be used.)

McTaggart, K.

5. DATE OF PUBLICATION (Month and year of publication ofdocument.)

April 2017

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40

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Scientific Report

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DRDC – Atlantic Research CentrePO Box 1012, Dartmouth NS B2Y 3Z7, Canada

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DRDC-RDDC-2017-R075

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13. ABSTRACT (A brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highlydesirable that the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of thesecurity classification of the information in the paragraph (unless the document itself is unclassified) represented as (S), (C), or (U). It isnot necessary to include here abstracts in both official languages unless the text is bilingual.)

This report presents predictions of squat for the HALIFAX, KINGSTON and ORCA classes inshallow water. Squat is the physical phenomenon of a ship at speed being attracted toward theocean bottom, possibly resulting in grounding. A potential flow panel method was developed forpredicting hydrodynamic forces in shallow water and the associated change in ship position. Themethod provides squat predictions over most operational speeds, with the exception of transcrit-ical flow conditions having water depth Froude numbers ranging from approximately 0.8 to 1.2.Presented results of bottom clearance as a function of ship speed can provide guidance to shipoperators for determining safe ship speeds in given water depths. The results are given for shipsin unconfined waters. If ships are expected to travel in confined waters, such as canals, thenadditional computations should be performed using the developed method, which already hasthe capability to model canal walls.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and couldbe helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such asequipment model designation, trade name, military project code name, geographic location may also be included. If possible keywordsshould be selected from a published thesaurus. e.g. Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus identified.If it is not possible to select indexing terms which are Unclassified, the classification of each should be indicated as with the title.)

heave; pitch; sinkage; squat; trim

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open water squat predictions for halifax, kingston and

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