Squat Effects: A Practical Guide to Its Nature, Measurement and Prediction
Donald M. MacPherson VP Technical Director HydroComp, Inc.
ABSTRACT “Squat” is the term commonly used for the sinkage and trim a ship exhibits when traveling in shallow or confined waters. Sinkage and trim from squat can be considerable, and calculations for these effects are mandated by both the USCG and IMO, and are a part of the IMS code. In the wake of highly-publicized maritime accidents – for which squat was a contributing factor – the time for naval architects and professional mariners alike to fully appreciate this essential hydrodynamic effect is long overdue. This paper will describe squat in both physical and hydrodynamic terms, introduce techniques for the prediction of squat, and offer a review of contemporary techniques to measure squat on ships in real-time.
INTRODUCTION Most maritime professionals can honestly say that they know about “squat” – the sinkage and trim that a vessel experiences when operating in shallow water or in a channel. There is growing evidence, however, that most do not fully appreciate the serious potential magnitude of squat effects. For example, forensic analyses of recent, highly publicized maritime accidents have revealed that squat was a contributing factor. It also comes as a surprise to many that both the U.S. Coast Guard (USCG) and the International Maritime Organization (IMO) require a prediction of squat effect, and that squat effect calculations are a recommended part of the ISM Code, STCW training and the ICS Bridge Procedures Guide. This deficiency in understanding of a critical design topic is quite surprising given the extensive research and publications on squat. However, it seems that the design community has deemed squat be relatively unimportant. (Even Principles of Naval Architecture has but one page devoted to squat.) It is the hope of this author that naval architects will begin to treat the subject more seriously. MARAD
Deputy Administrator John Graykowski said it best in his welcome to the 1995 SNAME Workshop on Ship Squat: “Ship squat and the ability to accurately predict its magnitude is an important area that strongly affects maritime transportation efficiency, safety and pollution prevention. U.S. ports, in particular, have limited water depths with respect to the laden drafts of modern ships. Every extra inch of permissible ship draft offers a significant increase in transport productivity. Safety of operations and environmental damage are also of great concern in the United States. Practical tools that can accurately predict a ship’s proximity to the channel bottom are sorely needed along with an enlightened and shared understanding of the principles and state-of-the-art by those piloting and controlling ships in U.S. waterways.”
Copyright © 2002 HydroComp, Inc. All rights reserved. Presented to the SNAME New England Section, January 2002.
Accidents Perhaps the most popular anecdotal illustration of the contribution of squat to a maritime accident is the grounding of the Queen Elizabeth 2 off the coast of Massachusetts in 1992. The 950’ QE2 was running at 24.5 knots in 39 feet of water at a draft of 32 feet. The accident inquiry concluded that neither master nor pilot predicted at the time that the squat effect would indeed be enough to ground the vessel. Fortunately, the damage was only structural and financial (on the order of $3 million in repairs and $50 million in estimated lost revenue) – it was not tragic. Tragic, however, does describe two European ferry disasters where the evidence points to squat effects as a contributing factor. In 1987, the ferry Herald of Free Enterprise sank with some 200 lives lost. High speed in shallow water combined to produce a sinkage and trim so that water was able to flood the car deck through the open bow door. The ship lost its transverse stability and capsized. Similar to the Herald, it is believed that squat played a part in the loss of the ferry Estonia in the Baltic. The attempt to run at high speed in the relatively shallow Baltic Sea gave the ship a draft and attitude that helped push water through the bow door. Regulations The following sections include pertinent text from various U.S. and international regulations relating to squat effects and their contribution to the prediction of underkeel clearance. 33 CFR 157.455 – Rules for the Protection of the Marine Environment Relating to Tank Vessels Carrying Oil in Bulk (NAVC 2-97, CH-1) Paragraph 5.H “Minimum Under-Keel Clearance” states that “tankship owners or operators must provide tankship masters with written under-keel clearance guidance”, and that the “master is responsible for estimating the minimum under-keel clearance along the transit route of the vessel”. Specific mention to squat effects is made, whereby “The effect of squat should be included as a factor to consider with calculating the ship’s deepest navigational draft. Although prescriptive methods for calculating under-keel clearance are not provided in the final rule, consideration of squat and how it may affect the vessel’s maneuverability during a transit is required by 33 CFR 164.11 for all vessels.”
33 CFR 164.11 – Navigation under way: General This code states that “The owner, master, or person in charge of each vessel underway shall ensure that:” ... “(p) The person directing the movement of the vessel sets the vessel’s speed with consideration for:” ... “(3) The tendency of the vessel underway to squat and suffer impairment of maneuverability when there is small underkeel clearance.” IMO Resolution A.601(15) – Provision and Display of Maneuvering Information on Board Ships This resolution pertains to the display of a poster of maneuvering information for the use by pilots. Squat effects are required to be considered for the preparation of this information. USCG Notice To Mariners 1/02 part 59 – Vessel Squat in Shallow Water This notice was written with the intent that it “describes the phenomenon of ‘squat’ and is intended to help mariners recognize circumstances where it could significantly affect the navigational draft of their vessels”. This NTM is a fairly welldeveloped “snapshot” for the mariner who may be unfamiliar with the potential severity and seriousness of squat effects. The NTM goes on to point to both the USCG CFR and the IMO Resolution as regulations that must be maintained. ISM Code Clause 7 This part of the ISM Code is for the “Development of plans for shipboard operation”. One of the requirements of this clause is the preparation of plans for the safe operation of the ship, including preparation for sea, navigational safety and passage with a pilot on board – all of which would include assessment of squat effects. [maritimeChain.com, 2002]. Ports and Agency Mandates In light of these national and international requirements, many agencies and ports are publishing their own sets of instructions and requirements. Just a few examples are: • • • Port of Hong Kong (Marine Dept Notice 139) U.S. Army (AR 56-9 part 1-4. Marine policies) Canadian National Maneuvering Guidelines
Economic Benefits The mandates for the calculation of squat do not end with regulations. There is solid evidence as to the enhanced economic benefit of reliable prediction of squat. An interesting project in Australia concluded that cargo loading could safely be increased if better modeling of squat were available for individual ships [O’Brien, 2000]. This project promoted the use of realtime measurement as a way to achieve this (albeit an expensive way). However, the conclusions were clear – better quantitative analysis of squat could lead to millions of dollars per year of increased cargo throughput at each port. THE HYDRODYNAMICS OF SQUAT Squat is often described as having something to do with the “Bernoulli effect” or “venturi effect”. While this is not incorrect, it is incomplete. To fully develop an understanding of squat, let’s “think like the water”. As a water particle passes a body, it must move some distance out of the way, follow along the length of the body and then return to its original position. If the body is a submarine, we can easily visualize the path of the particle as flow lines along the body. These outward/inward paths are longer than a straight line in the axial direction of motion. Therefore, for the particle to return to its original position (as it must for an incompressible fluid), it must move faster than the nominal velocity. Now enters Bernoulli, with his theorem that states there will be a pressure drop around the body due to the increase in velocity. If the body is a surface ship, however, then a particle near the surface acts somewhat differently than described above. It is not only forced to the side, but it may find the “path of least resistance” to be vertical – producing surface waves at the bow and stern. The vertical asymmetry due to the fluid boundary surface (between air and water) also creates a vertical pressure difference relative to the ship. (In other words, the reduced pressure only happens on the bottom of the ship – there is no matching drop in pressure above the ship.) This distribution of lower pressures creates a region sometimes called a “moving dish”, where the water surface around a ship is actually depressed by some measurable amount. We don’t notice the depression in ships at sea because (a) the magnitude of the depression is small, and (b) there is a corresponding lowering of the ship to maintain buoyant equilibrium. Since there is no change in draft relative to the depressed water surface, we simply don’t notice it.
When Water is Constrained Simple relationships of flow, velocity and crosssectional area state that for a constant flow, velocity must increase if cross-sectional area is reduced (the venturi effect). Shallow water, and more significantly, constrained water (as in a channel of finite width), cause the flow line velocity to be greater than that in deep water (see Figure 1 below).
Figure 1 – Illustration of squat effects With this local increase in flow line velocity, comes a greater corresponding Bernoulli pressure drop and a deeper “moving dish” depression. As clearance to the bottom (and channel sides) decreases, the velocity gets even greater creating even more pressure drop below the hull. In shallow water, the width of the “dish” can extend a full ship’s length to the side of the ship [Sturzel, 1966] as illustrated in the figure below for a towed ship model. The figure also indicates that local velocity (and subsequently pressure drop) is greatest near the bow.
Figure 2 – Local velocities of a ship in a channel [Sturzel, 1966]
Sinkage and Trim It is now time to “think like the ship” and consider the buoyant force and moment relationships. Vertical equilibrium of buoyancy determines the overall sinkage of the vessel moving in shallow or confined water. The equilibrium of trimming moment gives us the ship’s trim. As local velocity increases in shallow water, so does the Bernoulli pressure drop. This pressure drop causes a lowering of the water surface (as described above), as well as causing the ship to sink even lower in the water relative to the new surface. In other words, total sinkage is cause by two components – (a) the small lowering of the water surface (the “moving dish”) and (b) the much larger sinkage of the hull into the water. The relatively higher velocities near the bow (as shown in Figure 2) result in greater pressure drop near the bow. This results in the oft-quoted tendency for a “bow-down” trim in shallow water and for maximum squat to be at the bow. This may be true for towed models, but for a proper analysis, additional dynamic effects need to be considered. Propeller Effects Any model of squat effects would be incomplete without an analysis of the propeller’s contribution. Ahead of any propeller is a region of low pressure derived from blade lift – that is how propellers function, after all. (The close proximity of the propeller to the hull actually pulls back on the hull. This is what makes up the thrust deduction.) When the clearance to the ocean bottom is small, the propeller can produce large suction forces against the bottom. Since this suction is located at the stern, it will tend to pull the stern down. Add to this the propeller’s acceleration of the water at the stern, and the effect is to increase the overall sinkage, but reduce the “bow-down” trimming moment relative to the towed model (see Figure 3 below).
produce the highest trim by the stern. For example, selfpropelled model tests of a Nimitz class aircraft carrier showed the stern sinkage to be some 15% greater than that at the bow [Silver, 1996], and full-scale testing in Australia of the cruise liner Crystal Symphony showed squat 30 cm (12”) greater at the stern [Deeker, 1999]. Bottom Material A non-solid sandy or muddy bottom can affect both sinkage and trim. The shifting bottom shape will alter the local velocity profiles and the higher density can offer an increase in buoyancy. When bottom clearance is small, a bottom of fluidized silt or mud can be beneficial as the weightier material provides a cushion between the ship and the solid bottom. However, if the clearance is large the higher density actually helps develop lower Bernoulli pressures, leading to slightly larger sinkage and trim [Vantorre, 1996a]. Ships Passing While it is outside the scope of this paper, it should be mentioned that there are notable effects on squat and maneuvering characteristics when ships pass in a channel. This, of course, is due to the additional blockage in the channel caused by the presence of another ship. (For those interested in this subject, numerous technical papers can be found.) THE METHODOLOGY OF SQUAT It should be clear that squat will be a function of a ship’s speed and shape, as well as the clearance to the water bottom (water depth) and sides (channel width). The development of a universal methodology to represent these effects, however, has not been as clear. Speed The first thing to point out is that there are three speed regimes pertaining to squat. These regimes are given the names subcritical, critical and supercritical. One can use sinkage (the vertical position of CG) as a physical indicator of transition between these regimes. The critical speed is defined as the point of greatest sinkage (which is also the point of greatest added drag due to squat). Speeds below this point are subcritical, with a lowering of the CG. Above this point, speeds are called supercritical and the CG actually rises in response to dynamic bottom pressure. (A planing hull getting on plane is a good illustration of the observed motion.) The non-dimensional speed parameter used to define these regimes is the depth-based Froude number:
Figure 3 – Propeller effects The amount of trim depends on the waterplane inertia (the “moment-to-change-trim”). Full ships, such as tankers and bulkers, will have a tendency to trim less, where a finer hull (such as a containership) will have greater sensitivity to the trimming moment. Ships of high speed and fine waterplane area will often
where, v = ship speed g = gravitational constant h = waterway depth
the author’s personal interest in the method. Omission of a particular method below is not meant to indicate that it is to be considered unsuitable or ineffective. Tuck Variants Following the formula given in the section above, a universal coefficient for CS of 1.4 was initially presented [Tuck, 1970]. Empirical testing, however, indicated that this under-predicted sinkage. A variety of different figures for the coefficients have been given over the years, but they typically range from 1.7 to 2.4. Naval architects are not the only engineers affected by squat – port designers and planners are also quite interested. PIANC (Permanent International Association of Navigation Congresses) has adopted a coefficient of 2.4 for its prediction of maximum sinkage [PIANC, 1980]. This figure was based on analysis of a variety of model tests [Huuska, 1976]. An extension to the coefficient was developed to allow for the effect of channel blockage. This model was also adopted for use by the U.S. Army Corps of Engineers [Kriebel, 2000]. Millward developed equations for the coefficients based on the results of seven model tests [Millward, 1992]. The models are of a broad range of ship types and parameters (e.g., CB from 0.44 to 0.83). However, as the results were from towed models, they do not include any propeller effects. Also, the method does not account for blockage. None of the methods above consider the effect of the propeller, which is very important to properly evaluate sinkage and trim. Although the importance of propeller effects (which was clearly demonstrated over 25 years ago [Hooft, 1974]) seem to have been largely ignored until recently, the results from Tuck variant methods can still be applied successfully in the right circumstances. For example, full-form ships will be less affected by the trimming moment, so these methods would give reasonable results for maximum sinkage. In many cases, because propeller effects will reduce bow trim, these methods tend to over-predict. Simple Predictions In addition to the PIANC method noted above, the U.S. Army Corps of Engineers also recommended a simple method for the prediction of squat [Kriebel, 2000]. This method was for maximum sinkage only [Norrbin, 1986]. USCG Notice To Mariners 1(59)02 provided a very simple algorithm for a “conservative rule-ofthumb for estimating squat”. The equation is a function of CB and ship speed. The only use of water depth is in the determination of the upper recommended speed range. Obviously, this algorithm should not be used for anything other than a conservative estimate.
Critical speed typically occurs at FNH of 0.9 to 1.0. For most commercial ships, the speed range of interest is for FNH below 0.7, which is fully subcritical. Sinkage and Trim No review of the methodology of squat effects would be complete with an introduction to the work by Tuck [Tuck, 1966]. Although analytical systems to define the effects of squat have been used since the 1800s, Tuck put forth the relationships that have been the underpinning to many of the prediction methods in use today. Slender body theory was used to develop the following formula:
∇ FNH s = CS 2 L 1 − FNH 2 ∇ FNH θ = Cθ 3 L 1 − FNH 2
where, s = sinkage θ = trim (angular) CS, Cθ = sinkage and trim coefficients ∇ = displaced volume L = length FNH = depth-based Froude number Blockage It is important to note that the Tuck sinkage and trim formula are for the shallow water case – no account for a restricted channel is included. Certainly, when evaluating operation in a channel, some kind of correction needs to be applied for the effect of limited waterway width as well as depth. The ratio of cross-sectional area of the ship to the channel is the non-dimensional parameter that is used to define the channel blockage (the reduction in area). As blockage can be as large as 0.25, this has a significant effect on sinkage and trim. THE PREDICTION OF SQUAT The author has identified no fewer than two dozen different prediction algorithms for the sinkage due to squat. (There are far fewer algorithms for the trim.) Only a handful will be described here, based on the following subjective criteria – (a) existing popularity of their use, (b) their mandate by maritime agencies, or (c)
Empirical Methods The Canadian Coast Guard has adopted a prediction formula based on empirical studies of fullform ships for its National Manoeuvering Guidelines [Eryuzlu, 1994]. This method was based on selfpropelled model tests of some 1000 data points for five models. The models represent a fairly small scope (e.g., bulkers and tankers), in that they all have bulbs, a CB greater than 0.80 and a narrow range of L/B and B/T. The equation is purely empirical in nature and it provides only the sinkage at the bow, but it does include propeller effect and correction for blockage. The U.S. Army Corps of Engineers has supported development of a widely-applicable method for the prediction of squat to be used for maneuvering simulations [Ankudinov, 1996] [Ankudinov, 2000]. The method has different formula for deep and shallow conditions, with individual parameters for speed, bulb, propeller, waterway width, and even transom-stern. It provides for both sinkage and trim, and it includes the effect of both propeller and channel blockage. Validation If one were to plot the results of the many available prediction methods against each other, you would find a significant scatter. For example, a look at the various squat predictions for a tanker (see Figure 4) does little to instill confidence [Vantorre, 1996b].
This has led many to consider prediction of sinkage and trim to be unreliable. A few quotes from the 1995 SNAME Workshop on Ship Squat sum it up: “I’m not sure if we have a good feeling that we are in the right ballpark with some of these calculations.” “The formulas have a lot of variability in them.” “To me it became more confusing.” So why is this the case? The answer has to do with (a) the scope of the data set used to make up the method, (b) the completeness of the method, and (c) exactly what is being predicted. The scope of the method may be the most important consideration. The extent of the important parameters (such as Froude number, depth/draft ratio, blockage ratio) will dictate if the method is suitable for the vessel under consideration. In other words, using a method developed only for high-block ships on a fast container ship would be risky. You must also consider if the method includes all of the important pieces of the hydrodynamic puzzle. Many of the methods are for shallow water only – they do not account for blockage in a channel. Similarly, not all of the methods include propeller effects. Fine-form ships would certainly need to use methods that include propeller effects. The results of the methods are not all of the same form. Some methods provide answers for both sinkage and trim, some only for maximum sinkage, others offer only an estimate for a conservative maximum. Our office has undertaken to evaluate the reliability of these prediction methods. The methods of interest have been compiled and compared against test results. This work is on-going, and Appendix A contains examples of some of a few of these validation studies. When the methods noted herein are used appropriately (meaning with consideration of the scope, completeness and calculation), the results are quite good, leaning toward a bit of conservative over-prediction. THE MEASUREMENT OF SQUAT There are numerous outstanding technical papers on the subject of the real-time measurement of full-ship squat [Hewlett, 1996] [Huff, 1996]. It is not the intent of this paper to reiterate this large body of work, but simply to introduce the reader to some of the techniques being employed to measure squat in the field. Early measurements were performed through the analysis of photographs. This requires a clear channel and good lighting, which makes its use limited. Most of the current techniques for measuring squat are based on GPS. Unfortunately, standard GPS is much too imprecise to be of much good. Differential
Figure 4 – Scatter of various squat predictions [Vantorre, 1996b]
GPS offers greater accuracy, where the vertical precision of high-end DGPS systems over short periods of time is on the order of 10 cm (4”). DGPS applies an error correction based on a transmission from a network of land-based beacons with known positions. The USCG provides and maintains the U.S. network of DGPS beacons. This level of precision can be used effectively with post-processing to reduce scatter in measured squat data. For example, full-scale testing of the liner Crystal Symphony indicated that mean squat was about 90 cm (35”) [Deeker, 1999]. A 10 cm error is about 11% of the squat and 1% of the 7.6 m (25 ft) draft. This study placed two GPS receivers on the ship and one on shore to provide for additional correction of the data. Using a similar strategy, a newer derivative of DGPS measurement – called real-time kinematic (RTK) measurement – has been developed which uses shoreside data in real-time. Think of this as a DGPS system with your own personal land-base transmitter. By placing an accurately positioned transmitter on shore in the area of your test, precision can be increased to about 1 cm (0.5”). This reduces errors to about 1% of the squat measurement for large ships. CONCLUSION As stated in the opening paragraph, it is the hope of this author that naval architects will begin to treat the subject of squat effects more seriously. It all begins, of course, with an understanding of the basic principles. Reliable prediction methods are available, but like all prediction methods, they must be used appropriately. As real-time measurement of squat becomes commonplace, we will have additional data for the validation of existing methods and development of new methods. I would encourage all ship operators to utilize the existing GPS systems that they have on-board to begin to record vertical measurement when running in shallow water or a channel. While this may not have immediate use in real-time, the data may have value to engineers studying squat effects. ACKNOWLEDGEMENTS The author would like to thank Jay Brown and Toshi Yuta, engineering students from UNH employed by HydroComp, for their assistance in the preparation and analysis of the validation studies, as well as development of code for the squat prediction software. REFERENCES Ankudinov, V.A., Daggett, L.L., Hewlett, J.C., and Huval, C, "Squat Predictions for Maneuvering
Applications", Proceedings Copenhagen, 1996.
Ankudinov, V.A., Daggett, L.L., Hewlett, J.C., and Jakobsen, B.K., "Prototype Measurement of Ship Sinkage in Confined Water", Proceedings MARSIM 2000, Orlando, 2000. Deeker, W., “Measuring Squat With GPS”, CRCSS Space Industry News, Issue 82, March 1999, [www.crcss.csiro.au/spin/spin82/spin8206.htm] Eryuzlu, N.E., Cao Y.L., and D'Agnolo, F., "Underkeel Requirements for Large Vessels in Shallow Waterways", Proceedings 28th International Navigation Congress, PIANC, Seville, 1994. Hooft, J., "The Behavior of a Ship in Head Waves At Restricted Water Depths", International Shipbuilding Progress, 1974. Huuska, O., “On the Evaluation of Underkeel Clearances in Finnish Waterways”, Helsinki University of Technology, Ship Hydrodynamics Laboratory, Otaniemi, Report No. 9, 1976. Kriebel, D.L., Alsina, M.V., Godfrey, M.L., Waters, J.K., and Mayer, R.H., “Deep-Draft Navigation Channel Design: A Comparison of U.S. and International Practice”, Institute for Water Resources, U.S. Army Corps of Engineers, 2000. MacPherson, D.M., "Ten Commandments of Reliable Speed Prediction", Small Craft Symposium, Univ. of Michigan, 1996. maritimeChain.com, ISM Clause 7 - Development of plans for shipboard operations, Jan 2002, [www.maritimechain.com/ism/code/code.asp?clause=7] Millward, A., "A Comparison of the Theoretical and Empirical Prediction of Squat in Shallow Water", International Shipbuilding Progress, 1992. Norrbin, N., “Fairway Design with Respect to Ship Dynamics and Operational Requirements”, SSPA Report 102, 1986. O’Brien, T., “Experience in Using Underkeel Clearance Prediction Systems at Australian Ports: Selected Case Studies and Recent Developments”, IHMA Conference, Dubai, April 2000. PIANC, ICORELS (International Commission for the Reception of Large Ships) Report of Working Group IV, PIANC Bulletin, No. 35, 1980.
Silver, A. and Kopp, P., “Recent Squat Model Test Work on Aircraft Carriers ad Submarines in Shallow Channels”, 1995 SNAME Workshop on Ship Squat in Restricted Waters, Washington, 1996. Sturtzel, W., Graf, W., and Muller, E., “Untersuchung der Verformung der Wasseroberflache durch die Verdrangungsstromung”, 83 Mitteilung der VBD, Forschungsbereichte des Landess Nordrhein-Westfalen Nr. 1725, 1966. Tuck, E.O., “Shallow-water Flows Past Slender Bodies”, Journal of Fluid Mechanics, No. 26, 1966.
Tuck, E.O. and Taylor, P.J., “Shallow Water Problems in Ship Hydrodynamics”, 8th Symposium on Naval Hydrodynamics, ONR, Washington, 1970. Vantorre, M., “Influence of Fluid Mud Layers on Squat Effects”, 1995 SNAME Workshop on Ship Squat in Restricted Waters, Washington, 1996a. Vantorre, M., “A Review of Practical Methods for Prediction of Squat”, 1995 SNAME Workshop on Ship Squat in Restricted Waters, Washington, 1996b.
APPENDIX A – Example validation plots These are two examples of the validation studies for squat prediction. The plots show the error of the predicted value for the point of maximum sinkage. The error is displayed as a percentage of the actual underkeel clearance. We look for positive values, as negative values means actual clearance is less than predicted. Example 1 – MARAD Std Series, Model E, tanker/bulker, towed model test, maximum sinkage at bow This is a model test in very shallow water with high blockage for a full ship. Note how most methods underpredict the results by a sizeable amount (up to 10%-15% of the available clearance), including the conservative USCG Notice to Mariners method. Waterway Water depth Channel width Vessel Length Beam Draft Displacement Bulb Number props Cx Parameters L/H H/T Cb As/Ac L/B B/T
ft ft ft ft ft LT
68.14 1065 851.6 170.33 56.78 200000 no 0 0.994 12.50 1.20 0.849 0.132 5.00 3.00
A nkudi nov 1996
A nkudi nov 1996 D eep PI NC A 1980 M il d lwar 1992
5 Error/Clearnce %
0 0 -5 0.05 0.1 0.15 0.2 0.25 0.3 0.35
N or bi r n 1986 N or bi r n 1996 CCGNM S 1999 A nkudi nov 2000
USC G N TM 2001
Example 2 – CCGNMS, 110000 DWT tanker/bulker, self-propelled model test, maximum sinkage at bow This test is for a full-from ship in shallow water, with almost no blockage. Note how the methods predict sinkage to within 8% of the available clearance, and have very good precision or slightly overpredict (with exception of the method that is exclusively for deep water). Waterway Water depth Channel width Vessel Length Beam Draft Displacement Bulb Number props Cx Parameters L/H H/T Cb As/Ac L/B B/T
ft ft ft ft ft LT
73.7 5900 907.2 135.8 48.5 132780 yes 1 0.99 12.31 1.52 0.798 0.015 6.68 2.80
10 8 6 4 2 0 0 -2 -4 -6 -8 Fnh 0.1 0.2 0.3 0.4 0.5
A nkudi nov 1996 A nkudi nov 1996 D eep PI NC A 1980
M il d lwar 1992 N or bi r n 1986 N or bi r n 1996 CCGNM S 1999 A nkudi nov 2000 USC G N TM 2001