V--Models for Estimating Dimensional and Capacity Characteristics of
Oceangoing vessels for Use in Port Planning
Ti©PINISCHE UNIIVERSITST Laboratorium veer I Scheepshydromechanica Archlef Mekelvieg 2, 2628 CD Delft Vida 016-766673 - Rut 016- /81633
by
A N. Perakis*
invited paper
submitted for presentation
at the
International Association of Maritime Economists
London Conference
,Sept. 22-23, 1997
Ann Arbor, Michigan
March 1997
*Department of Naval Architecture and Marine Engineering,
University of Michigan, Ann Arbor, Michigan 41809, U.S.A.
I. Introduction
In the last few decades, ports and associated deep-draft navigation facilities worldwide
have faced more and more challenges resulting from the rapid growth in both ship size and
sea-borne trade volume. Since World War II, ship sizes have increased substantially, benefiting form the significant economiesof scale as well as from the more advantageous speed-resistance characteristics (and therefore reduced fuel consumption) of large ships. Crude tankers have reached a maximum size of 5651)00 dwt (deadweight tons) and a corresponding draft of up to 28 m (90 ft), althoughnobody builds any tankers greater than 320,000 dwt today. Bulkers for ore and coal of up to 3651)00 dwt were built in the '80s
with drafts exceeding 20 m (65 ft). Moreover, new design ideas have been developed, such
as unitized transport by containerships, whose size has also been constantly growing,
currently to a maximum of f,800 TEU (20-ft equivalent units), and is expected to reach 8,000 TEU in the near future.
Currently, most U.S. ports can only handle ships with a maximum draft of 12 - 15 m,
sometimes with the help of natural tide, and traffic congestion frequently occurs (run, et
al 1989). Other navigation constraints, such as the maximum drafts currently allowed by the Panama and Suez Canals (12.2 m (40 ft) and 16.2 m (53ft) respectively), also play a
major role. Moreover, the revolution of containerized transport has made conventional
ports unfit for use, since specific cargo handling facilities and large storage space (up to 12 hectares) are required (Brunn, et al 1989). Significant efforts that include new construction
and rehabilitation have been made in upgrading ports nationwide. However, vigorous
interport competition and/or poorly planned projects could lead to: (1) unnecessary capacity
expansion of existing ports/terminals, or (2) construction of new ports/terminals with
2
scarce sources (Brunn, et al 1989). Solving these problems rationally and economically is
therefore crucial for the economic and environmental development of a nation.
This paper discusses three issues relevant to port planning and related projects such as
dredging of ports ar.d associated water channels. The first issue focuses on the
determination of a ship's fully-loaded cargo capacity primarily from its deadweight (DWT),
for each of the four major oceangoing commercial vessel types (tankers, bulkers, general cargo ships and containerships). This approach provides a simple but reasonably reliable
method in estimating the maximum amount of cargoes allowed to be loaded/unloaded in a
port or terminal over a certain period (e.g., a year), inasmuch as the number of ships
calling at it over that period and the deadweights of these ships are known. It is critical for port planning and management; i.e., whether a new berth should be built at a port, and how much the cargo handling capacity of that berth is, can be evaluated based on the estimate of
the maximum amount of cargoes loaded/unloaded in that port. For that purpose, three different regression models are established according to vessel type, based on extensive data provided by the Navigation Division, Institute for Water Resources (IWR), U.S.
Army Corps of Engineers.
The second issue deals with the estimation of the increase in the cargo deadweight of a Ship, if the maximum allowable draft in a given port increases by a certain incremental amount, measured by the tons per inch immersion (TPI) of that ship. TPI measures the increase in displacement when a ship's draft increases by one inch, starting at a specific
draft and waterline, usually the light load or full load draft.
In order to evaluate an unknown WI for a ship, regression models have been developed. IWR currently uses a 10-base logarithmic model, which seems to be less appropriate in
clearly imply not a simple logarithmic but rather a .2t3 power" model. This "2/3 power"
model is therefore established, and extensive regression analyses are carried out to compare
this model with the logarithmic model for all the four oceangoing vessel types. The results
show that this new model is consistently more accurate than the logarithmic model.
A major job of the U.S. Army Corps of Engineers is port, river, and canal upgrades
(widening, deepening). A key variable associated with these large-scale projects is the draft
of the ships using (or expected to use) these facilities. Draft, traditionally denoted as T, is
defined as the depth of a ship below its full load waterline. Two different regression
models are developed and compared to estimate T as a function of only the deadweight (DW1).
Finally, the conclusions from our research are presented. Details of the regression models
developed are included in the Appendix.
II. Data
The data used in our research were provided by INVR, of which some are initially issued by
Lloyd's Maritime Information Services, Ltd. (MIS) and others by Fairplay. These data are contained in diskettes in spreadsheet form, which can be used in an IBM compatible
personal computer. Although the contents of the data files from these two different sources
(LMIS and Fairplay) are somewhat different, the same major technical characteristics of ships are contained in both: i.e., vessel type, deadweight (DINT), tons per inch immersion (TPI), length (L), beam (B), draft (T), shaft horsepower (SHP), speed (V), bale capacity
(Vbc), number of TEU (WEL). Other helpful entries include: date of building/delivery (of a vessel), type of engine, crew number, etc. Almost all ships were built after the early 1970s
and are currently in operation. Most of the data are given in metric units, while the rest in 3
British units, or a mix of the two, due to tradition or convenience generally accepted by
naval architects. For instance, TPI is far more widely used than TPcm (tons per cm
immersion).
Sample size is important in ensuring accurate and unbiased regression results. Except maybe for TPI, our data are adequate in that respect. Table 1 gives the numbers of ships
(sample sizes) used in various parts of our research.
insert Table 1)
Although TPI is a very useful quantity, it is not readily available for all ships. TPI data are usually estimated by ship captains based on experience, rather than directly calculated and provided by the shipbuilders, as are I.., B, T and DWT. Furthermore, one can expect, due to the above reason, that the accuracy of some TPIs could be questionable. In our case, of 439 vessels in the LMIS data file, TPI (full load ) is given for only 271 vessels, or 61.7%
of the total; in addition, we have also observed that, for each vessel type, there are a few ships whose TPIs are significantly higher or lower than those of the same type of ships
with similar technical characteristics. Considering that the sample sizes for TN estimates are not large enough (especially for general cargo ships and containerships) and that these outlier data can significantly affect the regression results, a limited adjustment to that part of the data has been made, discarding these few ships with outlier TPLs.
Finally, we would like to point out that a ship (with non-box-shaped underwater hull) may
have several TN values, depending on the corresponding draft. Usually there are two
specific such values considered important light load TPI and full load TN. The data issued by LM1S are full load TPIs, including those of tankers, bulkers, general cargo ships and
containerships. Those from Fairplay are light load TPIs for tankers and bulkers. However,
there are no such data available for general cargo ships and containerships.
III. Methodology and Models
Our goal is to estimate the variables of interest (e.g., cargocapacity, tons per inch
immersion and draft) as a function of the deadweight (DWT), which is one of the most readily available technical characteristics of ships. This approach is simple, but could be
reasonably reliable, as long as the regression models which are developed later are
appropriate and these data used for regression analyses have adequate sizes.
In our research, single variable regression technique is applied, following an IWR request that DWT be selected as the single regression input variable, as it is readily available for almost any ship. Fortunately, our analysis shows that DWI' strongly correlates with each
of the regression output variables,(cargo capacity, tons per inch immersion and draft).
The derivations of the models are accomplished by either theoretically exploring the inherent relation between the input and output variables, or practically undertaking
graphical analysis (i.e., scatter diagram of T against DWT).These will be discussed in
greater detail in the following.
Since all our data are given in large, IBM-compatible Lotus 1-2-3 worksheets, the
regression analyses are also performed on IBM PCs, using Lotus 1-2-3. The regression outputs are given in a fixed format produced by Lotus 1-2-3, including the coefficient of
the input variable (e.g., DWT, log DWT, etc.), the value of R2, and other statistical entities
(see Tables 2-4). The goodness of fit of our various models is evaluated primarily using
Cargo Capacity
In naval architecture, oceangoing commercial vessels may be classified into four different
categories, according to their function: "deadweight ships", "volume ships", "linear dimension ships" and "tonnage ships"' (Watson and GilfiLIan 1976). Based on this
concept, three different models for estimating fully-loaded cargo capacity are built for the four major vessel types in question. Details regarding the development of these models are given below.
Tankers and bulkers: These belong to the category of "deadweight ships" (Watson and GilfilIan 1976). They frequently move under a long-term contract for transportation of a single, uniform, bulk commodity such as ore or petroleum between two ports only. The
cargoes carried have high density, with stowage factor ranging from 0.417 to 1.530 m3/ton (15 to 55 cu ft/ton). "Deadweight ships" are usually built to their maximum sizes limited by
the depth (and sometimes width) of the actual route between the origin and destination
(Watson and Gilfillan 1976).
It can be shown (Parsons 1988) that
DWTc DWT - (Wro + Wpr W10), ( 1 )
Where DWrc = cargo weight of a "deadweight ship" when fully loaded(tons),
Wfo = weight of fuel oil stored (tons),
Wfw = weight of fresh water stored (tons),
Wpr = weight of provisions stored (tons), and Wio = weight of lube oil stored (tons).
1. The last one refers to tugboats. ferryboats, etc.. which will not be discussed hereafter.
The weight of fuel oil stored (typically sufficient for at least a round trip voyage) is the
major part of non-cargo deadweight It may be expressed as (Parsons 1988)
Wf0=- Cm Rf S SHP/V, (2-a)
where Rf = fuel consumption rate (tons/bhp hr),
S = route distance perround trip (nautical miles),
SHP = ship's shaft horsepower (bhp),
V = ship's service speed (knots), and
Cm = margin coefficient, typically assumed between 1.10 and 1.15 (Parsons 1988), to account for uncertaintiesduring a voyage, as well as fuel consumption
at port.
In order to estimate Wro primarily from only the DWT, as requiredby IWR, extensive Statistical analyses have been undertaken by us to explore the relation between DWT
andthe
variables on the right side of Equation (2-a), such as SHP and V. These statistical
analyses show that SHP/V sufficiently correlates with DWT for both tankers and bulkers
(see Table 2a). Therefore Equation (2-a) may be modified as
Wfo = Cm Rf S f(DWI), (2-b)
where f(DWT) = SHP/V, a function of the DWT which is determined through regression, as shown below.
Rf and S can be considered as parameters, largely independent of DWT. Based on the observation of the scatter diagrams of SHP/V against DWI' for 157 tankers and 816 bulkers, two different mathematical models are established to capture the relationship
between SHP/V and DWT: a "112 power" model' anda 10-base logarithmic model. The
former takes the form as
SFIP/V = a (DWT) + b, (3-a)
while the latter as
log(SHP/V) = a log(DWT) + b, or
SHWV 10b (DWT)a, (3-b)
where a and b are values to be determined through regression.
As to other non-cargo weights, we use a "miscellaneous deadweight" accounting for fresh water and provisions (Wfw and Wpr) of 400 tons per round trip, recommended by the U.S. Maritime Administration. This "miscellaneous deadweight" is not considered to be greatly
dependent on ship size, since it representscrew, effects and consumable supplies which vary little with ship size (Kiss 1980). Alternatively, the sum of these two weight terms (Wfw + Wpf) can be directly calculated fora specific ship, assuming the values of two more variables, the crew number (Na) and the amount of time (days) per round trip voyage
(Tip), are known. If this is the case, (Parsons 1988) recommends:
Wfw Wrg = 0.18N Tip (tons)
The lube oil weight (W10) is considerably smaller than the other weight terms mentioned above. It is consumed at a very low rate (ranging from 0.0010 to 0.0025 lb/hp hr for large
8
1. Exponential models with other fraction powers like 113, 1/4, etc were also tested, but the 112power
vessels) and can be re-used (Parsons 1988). Therefore, it may be neglected without
causing much error in estimating cargo deadweight. For example, a tanker of between 200,000 and 300,000 dwt, with a Diesel engine of about 35,000 bhp takes only 15 - 40
tons of lube oil per round trip voyage(Parsons 1988).
General Cargo Ships: The general cargo ship is a typical "volume ship", whether it carries bulk or unitized cargoes (their stowage factoris low, at least 1.54 m3/ton). It is the type of ship for which internal or underdeck volume other than deadweight is the predominant requirement for determining the cargo capacity as well as other important characteristics
(Watson and GiMan 1976). As a result,bale capacity is chosen as the measure of cargo
capacity for this ship type. By definition, bale capacity (m3) is the volume below deck
beams and inbound of cargo battens which is available for stowing the typical commodities carried by general cargo ships, usually in the form of bales, barrels, bags, crates and boxes (Hamlin 1988).
In our data base, there are 3,493 general cargoships for which the values of bale capacity are presented. The scatterdiagram of bale capacity vs. DWT shows that bale capacity has a
strong positive linear correlation to DWT. Thus, the model may be simply written as
= a (DWT) + b, (4)
where Vix denotes bale capacity (m3).
Containers hips These are "linear dimension ships" for which one or more of the principal
dimensions are primarily chosen on considerations such as the size and number of
Traditionally, the number of TEU (20-ft equivalent units) is the most widely used measure of cargo capacity for conminerships.
Our data file contains 684 containerships for which their number of TEUis known. Based
on the observation of the scatter diagram of NTEu vs. DWT, it is evident that NTEU
increases exponentially with DWT. The model is therefore set up as
NTEu= a (DWT)b, (5)
where NTEu is the number of TEU (including both in the cargo holds and on the deck).
Tons Per Inch Immersion
Two different models have been developed for estimating TN. One is the 10-base
logarithmic model, which assumes that log(TPI) and log(DWT)are linearly related:
log(TPI) = a log(DWT) + b, or
TPI = 10b (DWT)a (6)
This model was developed and is currently used by IWR. It works quite well in thecase of
tankers, but is less appropriate for bulkers, general cargo ships and containerships. A
proper consideration of the geometry and the physics of the problem, given below,
produces a much more consistent and accurate "213 power" model (Perakis 1991).
By definition, and using British units:
TN LBCw/35/12, and
DWT LBTC13/35,
11
Where L is the length (ft), B is the beam (ft),
T is the draft (ft),
Cw is the waterplane coefficient, and
Cb is the block coefficient (both Cw and C.b are dimensionless values).
Since
TN
LB, DWT LBT, and (LB) {(LB1)213) [L2], it follows that TPI (13V/1)213Therefore, the model may be expressed as
TPI = a (DWT)213 b (7)
Draft:
To model the relation between T and DWT, the scatter diagram of T vs. DWT is plotted for
each of the four vessel types. They all show that T increases, more or less, logarithmically
with DWT. Then
T ;---7 a log(DWT) + b (8)
Alternatively, similar to the development of the 112/3 power" model for estimating TPI, a
"1/3 power" model can be obtained:
where T is measured in meters in both (8) and (9).
IV. Results
The regression results based on the models derived in section III are presented in Tables 2-4. The details of the corresponding regression models are presented in the Appendix. It
should be noted that whenever these models are applied, the input variables andparameters
should have the units indicated in this paper.
Table 2a gives the regression outputs of SHP/V vs. DWT for tankers and bulkers, based
on the "1f2 power" model (3-a) and the logarithmic model (3-b), respectively. It turns out
that the "1/2 power" model is better than the logarithmic one, since it yields much higher values of R2, which evidently indicates the validity of the model. In the case of bulkers, however, we have observed that newly built, very large bulk carriers (VLBCs) consume much less fuel oil than estimated using either of the models, especially when DWT>
200,000 dwt; in other words, the corresponding models for estimating thecargo capacity
of bulkers could significantly underestimate the cargo deadweights of modern VLBCs.
(insert Table 2a)
The reduction in fuel oil consumption by VLBCs and VLCCs started in the late 70s, when
marine engine builders reacted to the jump of fuel price resulting from the second "oil
crisis". They tried to lower fuel costs by perfecting the combination of low speed Diesel engines and very large diameter propellers revolving at ultra low speed. Furthermore, extensive waste heat recovery and hull forms designed to achieve favorable propulsive performance also have contributed to the reduction. As a result, the VLBCs (DWT > 200,000 dwt) should he grouped and analyzed separately. Nevertheless, since we lack
adequate numbers of VLBCs (only 8 VLBCs are available in the database given to us), it is hard to develop accurate statistical models.
In Table 2b, the regression results for estimating cargo capacity for general cargo ships and containerships axe presented. Even though both models are rather simple, they do capture
the correlation between the measures of cargo capacity (e.g., Vbc, NTEU) and Dwr, with
remarkably high values of R2. Users should note that there could be an additional term Vcn in model (A-3) in the Appendix, whenever necessary, to take into account the total volume
of containers carried on deck of general cargo ships, since some ships operating today are actually multi-purpose carriers and load containers on the deck and/or in the cargo holds (containers in the cargo holds, if any, are not considered here because their volumes have
already been counted in the cargo holds). Vcn can be calculated by multiplying the number of TEU on the deck by the volume of a single TEU (=36.2 m3).
(insert Table 2b)
From Tables 3a and 3b, the "213 power" model for estimating TPI consistently produces
higher values of R2 than the logarithmic model for bulkers, general cargo ships and
containerships. For tankers, however, the values of R2 are just slightly higher in favor of
the logarithmic model (0.6% on the full load condition and 0.84% on the light load
condition). The highest gain with respect to the value of R2 occurs for bulkers in the case of light load TPI, where the value ofR2 yielded by the "213 power" model is significantly higher than that by the logarithmic model (0.968233 versus 0.857800). It is therefore fair
to conclude that for bulkers, general cargo ships and containerships, the "2/3 power" model
is more accurate than the logarithmic model, while for tankers, it is equally as good. However, the "213 power" model should be further tested for general cargo ships and containerships, since (1) the sample sizes regarding full load TPI are small and (2) it has
not been tested under the light load condition due to unavailability of the light load TPI data.
(insert Tables 3a and 3b)
Containerships exhibit considerable scatter in the distribution of TPI against DWT. This
mainly results from the fact that containerships with similar deadweight may have
considerably different hull forms (for example, Panamax and Post-Panamax designs). One possible approach could be to divide containerships into subcategories, pinpoint some other technical characteristics (e.g., length and width) as input variables and apply multivariable regression technique, provided sufficient data are available. Our evidence shows that this is neither necessary nor advisable for all other (non-containership) vessel types.
The regression results from estimating T for the four major vessel types are given in Table
4. The "1/3 power" model is as a whole better than the logarithmic model, although the latter seems slightly better for containerships, from the standpoint of the value of R2 (0.912690 against 0.897880). It should be noted that, despite of the strong correlation between T and DWT, as shown in Table 4, the assumption that T can be predicted as a function of only the DWT is neither realistic nor theoretically proper. In practice, T is commonly restricted primarily by the depth of water in ports, water channels, docks, etc. The models for estimating T given in the Appendix (from A-11 to A-14), may tend to overestimate T for ships with large DWT. Therefore, caution has to be exercised when applying them to large DWT ships by considering the physical limitation (the depth of
water) imposed by canals, waterways and ports where the shipsoperate.
(insert Table 4)
Conclusions
In the case of bulkers of greater than 200,000 dwt, the model for estimating cargo capacity (model A-2 in the Appendix) is less reliable and therefore not recommended, as it tends to overestimate the tonnage of fuel oil (Wfo) and correspondingly underestimate the cargo
deadweight (DWTc). One approach for accurately estimating the fuel oil weight is to
directly use Equation (2-a) given in section Ill, in which SHP and V are required as inputs other than DWT.
Our "213 power" model for TPI estimates is generally more accurate than the logarithmic model. In particular, for large bulkers, the logarithmic model tends to overestimate cm the
case of light load condition) or underestimate Cm the case of full load condition) TPI.
However, both models, which assume TPI is a function of only one variable (DWT),
appear to be less appropriate to estimate TPI for containerships than for other three vessel
types. Moreover, the "2/3 power" model should be tested for bothgeneral cargo ships and
containerships based on larger sample sizes Offiill load TPI data, as well as light load TPI
data.
A "113 power" model and a logarithmic model are established to estimate T from DWT. Regression analyses show that T and DWT are strongly correlated for each of the four ship types, and therefore T can be estimated as a function of only the DWT. The "1/3 power" model is shown to be better than the logarithmic one for tankers, bulkers and general cargo ships, while it is as good as the logarithmic model for containerships.
Finally, users of our models should strictly adhere to the conditions indicated in this paper,
such as the units of variables and parameters, and the ranges of DWT, specified in
parentheses below each sample size in Table 1, for which these models are valid.
Acknowledgments
This work was sponsored by the U.S. Army Corps of Engineers of Institute for Water Resources (Dr. Lloyd G. Antle) under the auspices of the U.S. Army Research Office
Scientific Services Program administered by Battelle, Inc. (Delivery Order 0306, Contract
No. DAAL03-91-C-0034). The work was performed between September, 1992 and
August, 1993 at the University of Michigan. Mr. Richard L. Schultz and his successor,
Mr. Phil Thorpe of the Navigation Division of IWR, have given us both extensive materials and advice. Mr. Jun Li, a graduate research assistant, has helped with the implementation of the regression analyses and the preparation of the tables of this paper. The Department of Naval Architecture and Marine Engineering of the University of Michigan has awarded
Mr. Li initially a Benton Fellowship and subsequently a Frank & Evans Panlow
References
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Fleet Forecasts for the United States to 2020, Final Report (1990). IWR Report 91-R-2,
DRI/McGraw-Hill, Temple, Barker & Sloane, Inc., and Lloyd's Maritime Information Services, Ltd.
Hamlin N. A. (1988) Ship Geometry. In V. Lewis (Ed.), Principles of Naval Architecture,
Vol. I, pp. 51-61. The Society of Naval Architects and Marine Engineers, Jersey City,
NJ.
Kiss R. K. (1980) Mission Analysis and Basic Design. In Robert Taggart (Ed.), Ship Design and Construction, p. 23. The Society of Naval Architects and Marine
Engineers, New York, NY..
Merchant Fleet Forecast of Vessels in U.S. - Foreign Trade (1978). Final Report for U.S. Department of Commerce Maritime Administration. Temple, Barker & Sloane, Inc. Parsons M. G. (1988) NA 470 Ship Design 11. Lecture Notes for Course NA 470, pp.
81-91. Department of Naval Architecture and Marine Engineering, University of Michigan,
Ann Arbor, MI.
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Appendix:
Regression Models
Cargo Capacity:
Tankers: DWTc = DWT - 148.24 Cm RS [(DWT/1000)112 - 4.25] - 400 (A4) (8,000 tons 5.. DWT 460,000 tons) Bulkers: DWTc = DWT - 113.88 Cm Rf S [(DWT/1000)112 + 0.97] - 400 (A-2) (8,000 tons 5 DWT 5 365,000 tons) General Cargo Ships:Vbc = 1.2685 DWT + 285.10 (A-3)
(900 tons 5 DWT 5 37,000 tons)
Containerships:
NTEu = 0.03379 (DWT)1.05206 (A4)
(1,000 tons 5 DWT 5 61,000 tons)
Full Load TPI:
Tankers: TN =0.1454483 (DINT)0.64466, or (A-5a) TPI =0.105543 (DWT)2/3 + 12.58 (A-5b) (18,000 tons 5 DWT 5 480,000 tons) Bulkers: TPI = 0.098681 (DV/1)2/3 + 16.10 (A-6) (8,000 tons 5 DWT 5 230,000 tons) General Cargo Ships:
TPI = 0.119696 (DINT)2/3 - 3.51 (Al)-(12,000 tons 5 DWT 5 42,000 tons)
Containerships:
TPI = 0.125263 (DWT)213 + 15.10 (A-8) (9,000 tons 5 DWT 60,000 tons)
Light Load TPI:
Tankers
TPI = 0.146741 (DWT)0.632737, or (A-9a)
TPI = 0.092135 (DINT)213 + 13.44 (A-9b) (8,000 tons 5 DINT 5 550,000 tons)
Bulkers:
TPI =0.096757 (DWT)213 +3.95 (A-10)
(8,000 tons 5 DWT 5 270,000 tons)
Draft: Tankers: T = 0.315347 (DW1)113 + 0.22 (10,000 tons 5 DWT 5460,000 tons) Bulkers: T = 0.285771 (DWT)113 + 1.56 (9,000 tons 5 DWT 5 230,000 tons)
General Cargo Ships:
T = 0.370388 (DWT)1/3 - 0.17 (A-13)
(9,000 tons 5 DWT 5 44,000 tons)
Containerships:
T = 0.3198 (DWT)In + 0.68, or (A-14a)
T 5.96531 log(DWT) - 16.03 (A-14b)
(14,000 tons 5 DWI' 5 61,000 tons)
*: deadweight range in sample.
Table 1
Numbers of Ships with Data Available for Regression Analysis
Ship Type Cargo Capacity Full Load TN Light Load TPI Draft
Tankers 157 (3.003-460.000 totu) , 146 (18.000-480.000 loos) 464 (8.003-550.000 tons) 156 (10.000460.000 mos) Bulkers 816 45 452 91
(8.000.345.030 tons) (8.000-230,030 tads) (11.00)-270.030 um) (9.030.230.000 sons)
,
Gen. Cargo 3,493 25 NA 3,586
Ships (900-37.000 tom) (12.000-42.000 tom) (9.000-44.0X1 was)
Constain' erships 648 40 NA 670
Table 2a
Regression Outputs for Tankers and Bulkers: SHP/V vs. DINT
Tankers Bulkers
"1/2 Power" Model "1/2 Power" Model
Constant -142.9290 Constant 134.3197
Std Err of Y Est 247.4379 Std Err of Y Est 147.8716
R Squared 0.878661 R Squared 0.705587
No of Observations 157 No of Observations 816
Degrees of Freedom 155 Degrees of Freedom 814
X Coefficient(s) 4.687673 X Coefficient(s) 3.492654
Std Err of Coef. 0.139921 Std Err of Coef. 0.079076
Logarithmic Model Logarithmic Model
Constant 0.363069 Constant 0.892097
Std Err of Y Est 0.083061 Std Err of Y Est 0.065140
R Squared 6.865473 R Squared 0.682921
No of Observations 151 No of Observations 816
Degrees of Freedom 155 Degrees of Freedom 814
X Coefficient(s) 0.550429 X Coefficient(s) 0.439621
Table 2b
Regression Outputs for General Cargo Ships and Containerships: Cargo Capacity vs. DWT
General Cargo Ships Containerships
Constant 285.1028 Constant -1.47130
Std Err of Y Est 1303.496 Std Err of Y Est 0.09348
R Squared 0.968372 R Squared 0.94227
No. of Observations 3493 No. of Observations 684
Degrees of Freedom 3491 Degrees of Freedom 682
X Coefficient(s) 1.26850 X Coefficient(s) 1.05206
Table 3a
Regression Outputs for the Four Vessel Types:
Full Load WI vs. DINT
Vessel Type "2/3 Power" Model Logarithmic Model
Constant 12.58141 Constant -0.842710
SW Err of Y Est 22.48914 Std Err of Y Est 0.036963
R Squared 0.974785 R Squared 0.970699
Tankers No of Observations 143 No of Observations 143
Degrees of Freedom 141 Degrees of Freedom 141
X Coefficient(s) 0.105543 X Coefficient(s) 0.644660
SW Err of Cod. 0.001430 SW Err of Coef. 0.008495
Constant 16.08946 Constant -0.494920
SW Err of Y Est 9.495248 SW Err of Y Est 0.033647
R Squared 0.985367 R Squared 0.974846
Bulkers No of Observations 44 No of Observations 44
Degrees of Freedom 42 Degrees of Freedom 42
X Coefficient(s) 0.098681 X Coefficient(s) 0.569358 SW Err of Coef. 0.001856 SW Err of Coef. 0.014112
Constant -3.509220 Constant -1.045710
SW Ert of Y Est 8.479723 SW Err of Y Est 0.046746
Gen. Cargo R Squared 0.804736 R Squared 0.754023
Ships No. of Observations 21 No. of Observations 21
Degrees of Freedom 19 Degrees of Freedom 19
X Coefficient(s) 0.119696 X Coefficient(s) 0.690760 SW Err of Coef. 0.013410 Std Err of CoeL 0.090512
Constant 15.09527 Constant -0.540770
Std Err of Y Est 16.11863 Std Err of Y Est 0.065444
R Squared 0.805356 R Squared 0.754381
Containerships No. of Observations 39 No. of Observations
39
Degrees of Freedom 37 Degrees of Freedom 37
X Coefficient(s) 0.125263 X Coefficient(s) 0.596926 SW Err of CoeL 0.010124 SW Err of Coef. 0.055996
Table 3b
Regression Outputs for General Cargo Ships and Containerships: Light Load TN vs. DINT
General Cargo Ships
,
Containerships
"2/3 Power" Model "2/3 Power" Model
Constant 13.44076 Constant 3.945307
Std EIT of Y Est 22.44234 Std Err of Y Est 11.34299
R Squared 0.968076 R Squared 0.968233
No. of Observations 4.64 No. of Observations 452 Degrees of Freedom 462 Degrees of Freedom 450 X Coefficient(s) 0.092135 X Coefficient(s) 0.096757
Std Err of Cod. 0.000778 Std Err of Coef. 0.000826
Logarithmic Model Logarithmic Model
Constant -0.833450 Constant -1.004300
Std Err of Y Est 0.046161 Std Err of Y Est 0.078907
R Squared 0.974853 R Squared 0.857800
No. of Observations 464 No. of Observations 452
Degrees of Freedom 462 Degrees of Freedom 450 X Coefficient(s) 0.632737 X Coefficient(s) 0.096757
Table 4
Regression Outputs for the Four Vessel Types:
T vs. DINT
Vessel Type "1/3 Power" Model Logarithmic Model
Constant 0.221376 Constant -36.66590
Std Err of Y Est 0.971134 Std Err of Y Est 1.289941
R Squared 0.949048 R Squared 0.910104
Tankers No. of Observations 156 No. of Observations 156 Degrees of Freedom 154 Degrees of Freedom 154 X Coefficient(s) 0.315347 X Coefficient(s) 11.03060 Std Err of Coef. 0.005888 Std Err of Coef. 0.279106
Constant 1.563011 Constant 0.221376
Std Err of Y Est 0.835741 Std Err of Y Est 0.867836
R Squared 0.879379 R Squared 0.869937
Bulkers No. of Observations 91 No. of Observations 91
Degrees of Freedom 89 Degrees of Freedom 89
X Coefficient(s) 0.285771 X Coefficient(s) 7.790066
Std Err of Cod. 0.011219 Std Err of Coef. 0.319285
,
Constant -0.167260 Constant -12.96690
Std Err of Y Est 0.605857 Std Err of Y Est 0.619023 Gen. Cargo R Squared 0.893440 R Squared 0.869937
Ships No. of Observations 3568 No. of Observations 3568
Degrees of Freedom 3566 Degrees of Freedom 3566
X Coefficient(s) 0.370388 X Coefficient(s) 7.790066
Std Err of Coef. 0.000212 Std Err of Coef. 0.013410
Constant 0.681990 Constant -16.02500
Std Err of Y Est 0.726420 Std Err of Y Est 0.671720
R Squared 0.897880 R Squared 0.912690
Containerships No. of Observations 670 No. of Observations 670 Degrees of Freedom 668 Degrees of Freedom 668
X Coefficient(s) 0.319800 X Coefficient(s) 5.965310 Std Err of Coef. 0.004170 Std Err of Coef.
