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NPS-OR-96-007 



NAVAL POSTGRADUATE SCHOOL 
Monterey, California 




Predicting Ship Fuel Consumption: Update 

by 

David A. Schrady 
Gordon K. Smyth 
Robert B. Vassian 

July 1996 



Approved for public release; distribution is unlimited. 

Prepared for: Naval Postgraduate School 
Monterey, CA 93943 



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Predicting Ship Fuel Consumption: Update 


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David A. Schrady, Gordon K. Smyth, and Robert B. Vassian 


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Naval Postgraduate School 
Monterey, CA 93943 


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13. ABSTRACT (Maximum 200 words) 

This report is concerned with the prediction of ship propulsion fuel consumption as a 
function of ship speed for U.S. Navy combatant and auxiliary ships. Prediction is based on 
fitting an analytic function to published ship class speed-fuel use data using nonlinear 
regression. The form of the analytic function fitted is motivated by the literature on ship 
powering and resistance. The report discusses data sources and data issues, and the impact of 
ship propulsion plant configuration on fuel use. The regression coefficients of the exponential 
function fitted, tabular numerical comparison of predicted and actual fuel use data, the 
standard error of the estimate, and plots of actual and fitted data are given for 22 classes of 
Navy ships. 


14. SUBJECT TERMS 

Operational Navy Logistics; Ship Fuel Use Prediction 


1 5. NUMBER OF PAGES 
70 


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Standard Form 298 (Rev. 2-89) 

Prescribed by ANSI Std. 239-18 



Table of Contents 



1. INTRODUCTION page 1 

2. SHIP FUEL CONSUMPTION DATA 2 

2.1 Data Sources 2 

2.2 Data Issues 2 

3. METHODOLOGY 4 

3.1 Conventional Wisdom 4 

3.2 Theory of Ship Powering and Resistance 5 

3.3 Theoretical Model of Ship Fuel Consumption verses Speed 9 

4. DATA FITTING AND RESULTS 10 

4.1 Data Source Utilized 10 

4.2 Zero Points 10 

4.3 Plant Configuration 1 1 

4.4 The Regression Software 12 

4.5 The Results 12 

5. CONCLUSION 13 



REFERENCES 15 

APPENDIX: Ship Class Fuel Use Prediction Results 17 

Initial Distribution List 6 3 



PREDICTING SHIP FUEL CONSUMPTION 

1. INTRODUCTION 

This report is concerned with predicting the fuel consumption (DFM/F-76) of U.S. Navy 
ships. Fuel consumption will be stated in gallons per hour as a function of speed for each class of 
ship. A data analysis approach is taken with reference made to the hydrodynamics of ship resistance 
and powering requirements as it motivates the analytical form of the function which is fitted to the 
data. Given that sea trials are conducted and that data is taken on fuel consumption for a given 
speed and class of ship, and that these observations are made for a number of different speeds, one 
can attempt to fit the speed-fuel use data with an analytic function using nonlinear regression. This 
is what is meant by a data analysis approach. 

The reason this analysis was undertaken relates to operational logistics and the need to 
estimate ship and battle group/battle force endurance, fueling-at-sea (FAS) requirements, and tanker 
shuttle ship requirements to sustain the combat logistics force (CLF) station ship. One of the authors 
is involved in the development of a computer-based battle group tactical logistics support system 
concerned with planning, tracking, and predicting fuel and ordnance consumption and replenish- 
ment. The system requires analytical functions from which to compute predicted ship fuel 
consumption. 

This report is an update of an earlier (1990) report on the same subject, Ref (1). This report 
omits much of the analysis detailed in the earlier report, omits results on ship classes decommis- 
sioned by the Navy, and includes results for ship classes brought into service since 1990. Also the 



form of the analytic fuel use prediction function fitted by regression has been changed from a power 
function to an exponential form resulting in smaller standard error of the prediction. 

2. SHIP FUEL CONSUMPTION DATA 

2.1 Data Sources 

Data on ship fuel consumption as a function of speed for all major USN ship classes are 
published. Sources include the old NWIP 11 -20(D), Ref (2), NWP 11-1 (Combatants), Ref (3), 
NWP 11-2 (Auxiliaries), Ref (4), and the new NWP 65 series. Additionally, data on the DD-963 
class ships was obtained from the Surface Warfare Officer School, Newport Ref (5), and data on 
amphibious warfare ships was obtained from COMNAVSURFPAC and PHTORONs 7 and 9, Ref 
(6), Ref (7), and Ref (8). Data on newly commissioned ship classes has been provided by the 
NAVSEA Propulsion Branch. 

2.2 Data Issues 

Issues regarding such data include 1) the amount of speed-fuel use data available, 2) the 
range of ship speeds in the data, and 3) the consistency of the data when there are multiple sources 
of data for the same ship class. 

With respect to the amount of data available, NWP 11-1 generally has 7 to 9 speed-fuel use 
pairs for each class of combatant ship. NWP 11-2 generally gives 3 to 6 speed-fuel use pairs for 
each class of auxiliary ship. In fitting any sort of analytical function the more data the better, and 
the NWP series has only minimal amounts of data; actually insufficient amounts of data for the 
auxiliary ship classes. The NWP 65 series is for combatant ship classes only and is inconsistent in 
its treatment of ship fuel consumption. For some ship classes speed-fuel use data is provided, for 



one ship class a series of fuel consumption curves is provided (curves depend on plant/shaft 
configurations), and for some ship classes the NWP 65 document does not address fuel consumption 
at all. The older NWIP 1 1-20 provided more data, generally 15-20 speed-fuel use pairs, for the ships 
included in this publication. Of course important, newer classes are not included in NWIP 11-20. 
Because the method of fitting a continuous function to the data is regression, the amount of data 
essentially remains a methodological problem affecting the robustness of the fuel consumption 
estimation equations derived. 

The second data issue is the ship speed ranges for which data exists. Generally NWP 11-1 
data exists for combatant speeds above 12 knots, sometimes well above 12 knots, and NWP 11-2 
data exists for auxiliary speeds above 10 knots. The lowest speeds for which NWIP data exists 
ranges from 6 to 12 knots. The speed range of the data is important in terms of the behavior of the 
regression equation at low ship speeds. 

The third data issue is the consistency of ship fuel consumption data from different sources. 
Obviously data validity is a serious issue but one that cannot be resolved here. In actuality there are 
precious few sources of ship fuel consumption data and, in addition to limitations on the amount of 
data and the speed range covered by the data, none of the data available includes information about 
how the propulsion plant and shafts were being operated or the condition of the ship's hull. Where 
different sets of data were obtained with the ship's plant in different configurations or with a fouled 
rather than clean hull, or in different sea states or temperatures, one should expect different fuel 
consumption data. 



3. METHODOLOGY 
3.1 Conventional Wisdom 

In fitting an analytic function to ship speed-fuel use data, it is helpful to know a priori what 
sort of function it is supposed to be. The conventional wisdom is that ship fuel use is a cubic 
function of ship speed. In connection with their own studies, the Center for Naval Analyses has used 
cubic polynomial regression to fit speed-fuel use data. This produces relatively high coefficients 
of determination, r-squared values; generally 0.97 or higher. Residuals, the differences between the 
actual fuel use at a given speed and the fuel use predicted by the cubic regression equation evaluated 
at that speed, were generally acceptable with maximum errors being on the order of 10% within the 
range of ship speeds contained in the data. However there is the problem of controlling the cubic 
equation at low ship speeds. In the CNA report, Ref (9), ship speed-fuel use data is fitted with the 
cubic polynomial equation, 

F = c o + c x V + c 2 V 2 + c 3 V 3 (1) 

where F is fuel use in gallons per hour and V is ship speed in knots. When cubic polynomial 
regression is used and data exists only for higher ship speeds, the equation can curve upward at low 
speeds (e.g., predicting that the ship will use more fuel at 5 knots than at 1 5 knots) or the curve can 
go negative (e.g., the coefficient c is negative, at slow speeds the ship is making fuel!). Some 
reports get around this by noting that the fuel consumption prediction equations should only be used 
with ship speeds above, say , 14 knots. In reality however, speeds below 14 knots are important and 
one must be able to predict fuel use for speeds below 14 knots. 

Our attempts to control the low speed behavior of the cubic polynomial included using in- 
port fuel allowances as the amount of fuel used at zero speed and spline fit routines to generate 



missing low speed data, as described in Ref (1). None of these attempts to control the low speed 
behavior of the cubic polynomial was satisfactory. Because of this and because it is simply more 
satisfying to try to determine the theoretical relationship which should exist between ship speed and 
fuel consumption, some effort was made to study the subject of ship powering and resistance. 
3.2 Theory of Ship Powering and Resistance 

Figure 1 is intended to illustrate the relationship between fuel input and ship speed. Fuel is 
consumed by a prime mover (fossil fuel steam turbine, gas turbine, or diesel) and the output is brake 
horsepower (BHP). This power generally acts through gearing to a shaft or shafts and ultimately 
to propellers, the output being effective horsepower (EHP). The EHP acts to move the hull through 
the water at some speed completing the chain from fuel input to ship speed achieved. The EHP must 
equal the total resistance generated by the ship moving through the water. For displacement hulls, 
total resistance has two principal components: friction resistance and wave-making resistance. At 
slow speeds friction resistance dominates, but at higher speeds wave-making resistance dominates 
and increases rapidly as hull speed is approached. EHP is the horsepower required to equal the 
ship's total resistance at a given speed. 

In 1876, William Froude in England gave the formula for EHP as, Ref (10): 

EHP = -L p — V 3 (2) 

2 550 

where 

C T = coefficient of total resistance, 

p = fluid density in slugs per cubic foot, 

S = wetted area of the hull in square feet, and 

550 = one horsepower in foot-pounds per second. 









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Figure 1. Ship Propulsion System 



Thus we know that the EHP required is theoretically a cubic function of ship speed. 

An alternate explanation of this relationship is that hull resistance is proportional to speed 
squared, and that resistance times velocity is by definition power. Either way it follows that EHP 
depends on the cube of ship speed. Further it is assumed in current practice, Ref (1 1), that EHP is 
a constant fraction of BHP. The ultimate relationship between fuel input and ship speed is then 
cubic in ship speed, but further depends on the relationship between fuel input and BHP produced 
by the prime mover. Thus more must be said about the relationship between fuel consumption and 
output power for the types of prime movers used in U.S. Navy ships; diesel, steam turbine, and gas 
turbine. 

One would ideally like to know the theoretical relationship between fuel input and 
horsepower output. After extensive discussion with mechanical and naval engineers and a review 
of applicable literature, it was determined that no single theoretical model (something like Froude's 
result) of fuel consumption as a function of power output exists. The relationship is always specific 
to 1) the type of prime mover (steam turbine, gas turbine, or diesel), 2) the particular prime mover 
in question (manufacturer, size, specific characteristics), and 3) how the prime mover is actually 
operated in its application. 

Even though there is no single theoretical model for fuel consumption as a function of power 
output, some indication of this relationship can be gained from examining the characteristics of some 
specific prime movers. The approach to describing fuel consumption as a function of horsepower 
was to use specific fuel consumption (SFC) vs. horsepower curves for each type of prime mover. 
SFC is given in, or can be converted to, units of gallons per horsepower-hour. Multiplying SFC by 
horsepower yields the desired fuel consumption measure, gallons per hour. A typical SFC versus 



horsepower curve shows a function in which SFC is quite large for low output (horsepower) and 
falls rapidly with increasing output reaching something of a lower bound, and possibly rising 
modestly as maximum output is approached. When converted to gallons per hour versus horsepower 
the relationship is typically a function which is a monotone increasing convex curve for steam 
turbine and diesel prime movers. A gas turbine, however, is different in that it is most efficient at 
maximum output. The gallons per hour versus horsepower relationship for a gas turbine is concave. 
In general, in no case are such curves linear. 

It is assumed that the concave or convex fuel gallons per hour verses horsepower function 
may be described by the equation 

F=b,+b/' BHP (3) 

where F is fuel use in gallons per hour and BHP is brake horsepower. Equation (3) is only an 
intermediate form which will affect the form of the analytic function actually fitted to the speed-fuel 
use data. In the earlier report, Ref (1), Equation (3) had the form 

F = b + *, [BHPf . 
While the form of Equation (3) is arbitrary so long as the form can produce monotone increasing 
convex or concave functions over the appropriate ranges, use of the exponential form for Equation 
(3), when combined with Froude's result, Equation (2), produces superior prediction functions. 
3.3 Theoretical Model of Ship Fuel Consumption verses Speed 

In Section 3.2 it was shown that theory dictates that the power required to move a 
displacement hull through the water at velocity V was proportional to V 3 . It was also indicated that 
Effective Horsepower is a constant fraction less than on of Brake Horsepower. Also in that section, 
it was stated that there is no single theoretical relationship for the conversion of fuel to horsepower 



8 



in a prime mover. The relationship depends on all the prime mover specifics and how it is actually 
operated in a given application. 

Referring again to Figure 1 and Equation (2), we know that 

C c 

EHP = — p — V 3 = cV 3 . 
2 550 

If we assume 

EHP = a-BHP 



where 0<a< 1, then 



Then if, as in Equation (3), 



it follows that 



or finally 



where 



BHP - ™L = C 1L - dV> 



a a 



r-, , , b 2 BHP 

F= b Q + b x e 7 



17 L L M ** 1 



F= p n + p,e 2 



Po + Pi e2 (4) 



p x = b l , and 
/> 2 = M- 



In application the coefficients p , p, , and p 2 will be determined by regression performed on 
ship class speed-fuel use data. Equation (4) will be referred to as an exponential model of fuel use 
as a function of ship speed. 

4. DATA FITTING AND RESULTS 

4.1 Data Source 

The source of the data used in developing the fuel use prediction for each ship class is 
indicated on the data page for the ship class in the Appendix. Generally the source with the largest 
number of speed-fuel use data pairs is used. For the newer classes of ships, however, ship trials data 
obtained from the NAVSEA Propulsion Branch is used and is the only known source. 

4.2 Zero Points 

The problem with the low speed behavior of the cubic polynomial prediction function has 
already been discussed. An early attempt to control low speed behavior lead us to try to determine 
how much fuel a ship (ship class actually) burned at zero speed. Such data is not available and we 
took as a surrogate the published In-Port Steaming Allowances obtained from CINCLANTFLT. 
These were referred to as "zero points". Though the power functions controlled low speed behavior 
very much better than the cubic polynomial functions, there was a minor problem in that the 
predicted low speed fuel use values were excessive for the CV-63, DD-963, and CG-47/52 classes. 
Zero points were not used in producing the power function results in Ref (1) because they did not 
improve low speed behavior significantly and did tend to produce predictions in the speed range for 
which data was available which were not as good as the regressions run without zero points. 



10 



Still the excessive low speed fuel use of the three ship classes noted above, lead to 
reevaluating the use of zero points and a decision to use them this time; this time was the first time 
for the four ship classes introduced since 1990 (LHD-1, DDG-51, AOE-6, and PC-1). In the process 
of doing this one of the authors, Gordon Smyth, came along and said that he had been using Ref (1) 
in teaching the Data Analysis course in the Operations Research and Operational Logistics curricula 
at NPS and that he found that an exponential functional form produced better fits than did the power 
functions. Thus the form of the relationship between fuel input and horsepower output was changed 
and resulted in the exponential expression shown in Equation (4) for the relationship between fuel 
use and ship speed. As before the final decision is that the best results obtain from not using the In- 
Port Steaming Allowances as a proxy for fuel use at zero speed. 
4.3 Plant Configuration 

All ship classes whether steam, diesel or gas turbine are powered by pairs or multiple pairs 
of engines. Plant configuration refers to the number of engines which are 'on line' and working to 
propel the ship through the water. A ship with, say, four LM 2500 gas turbine engines may be 
operated with a single engine, two engines, or four engines on line. In general a ship must use more 
power, and more engines to make greater speed, but the speed ranges of each mode of plant 
configuration overlap. For a ship with four LM 2500 gas turbines and three plant configurations 
(single engine, two engine, and four engine), there are really three different speed-fuel use curves. 
While this phenomenon is real and exists for all ship classes regardless of their type of prime mover, 
the regressions produced here correspond to a single speed-fuel use relationship which "smoothes" 
the transitions between plant configurations. 



11 



Still one could fit separate fuel prediction functions depending on plant configuration. One 
study, Ref (9), suggested using three different fuel use prediction functions depending on ship speed. 
This would require more detailed information and more computational complexity for each ship 
class. However, given the total number of variables involved (sea state, hull condition, plant 
configuration, and many others for which specific information will not exist off-ship), these 
complications seem unwarranted. 

4.4 The Regression Software 

The statistical package used to perform the regressions for each ship class was S-PLUS 
published by Statistical Sciences, Inc., Ref (12). This PC-based software computes the values of 
the three parameters of Equation (4) using the minimization of the standard error of the estimate as 
its fit criterion. 

4.5 The Results 

The results, values of the fitted regression parameters, tabulation of the numerical actual and 
predicted fuel use in gallons per hour as a function of speed, and plots of the actual data and the 
prediction function for 21 USN ship classes is presented in the Appendix. 

6. CONCLUSION 

As stated in the Introduction, the authors' use of ship fuel use prediction functions is in 
connection with a battle group logistics support system. The support system allows the planning for, 
tracking of) and prediction of future fuel and ordnance consumption and replenishment requirements. 
It can be argued that if one can predict the daily fuel use of a given ship to within 1-2% of capacity, 
such prediction capability is adequate and useful for the purposes intended. With fuel reserve levels 



12 



of 50% or more, fueling-at-sea (FAS) will be required every 3-7 days for most surface combatants 
depending on ship class and speed. Prediction errors of 1-2% of capacity per day are small enough 
that FAS requirements planning would indicate the correct day (but not the correct hour) on which 
FAS was required by a given ship. Of course the exact hour is of little real interest. Further, if the 
tactical situation allows daily ship reporting, daily updates of predicted values to actual values can 
be made eliminating the compounding of prediction errors. 

Review of the difficulties involved in ever making truly accurate predictions of the fuel use 
of a given ship on a given day is instructive. First there are problems with the data on which any 
prediction function is based: few sources of data, relatively little data available from any source, 
little or no low speed data, and inconsistency between different data sources. None of the data 
sources provide information on the plant condition, hull condition, temperature, sea state, etc., all 
of which effect fuel consumption. Difficulties in using any fuel use prediction function at sea in real 
operations include knowing sea state, ship speed (something that varies often throughout a given day 
depending upon the assigned activities of a given ship), and operational specifics which may dictate 
that the ship has more horsepower on line than is required for its speed at a given time; e.g., the ship 
is in plane guard role, the ship is in an underway replenishment evolution, the ship is navigating 
restricted waters, the ship is in a high threat situation, etc. These factors will not be known with any 
certainty by a planner or afloat logistics coordinator. 

For all these reasons the question is not whether one can predict ship propulsion fuel usage 
accurately, but rather whether on can predict ship fuel use to a useful approximation. It was argued 
above that predicting ship fuel use to within 1-2% of capacity per day was adequate. Thus while 
there are a plethora of reasons why the fuel use prediction functions in this report will not produce 



13 



"spot on" accurate estimates of the fuel use of a given ship on a given day, it is asserted that they do 
in fact produce operationally adequate and useful estimates. 



14 



REFERENCES 



1. D.A. Schrady, D.B. Wadsworth, R.G. Laverty, and W.S. Bednarski, Predicting Ship Fuel 
Consumption, Naval Postgraduate School Technical Report NPS-OR-91-03, October 1990 

2. Naval Warfare Information Publication 1 1 -20(D), Volume II, Missions and Characteristics 
of U.S. Navy Ships and Aircraft (U), Confidential, May 1974 

3. Naval Warfare Publication 11 -1(B), Characteristics and Capabilities of U.S. Navy 
Combatant Ships (U), Confidential, January 1983 

4. Naval Warfare Publication 1 1-2(B), Characteristics and Capabilities of U.S. Navy Auxiliary 
Ships (U), Confidential, January 1983 

5 . Surface Warfare Officers School, DD-963 Class Speed/RPM/Pitch Tables and Fuel Curve 
Tabular Data, undated (circa 1989) 

6. Interview between COMNAVSURFPAC Operations Officer and LT Bednarski, 23 February 
1990 

7. Telephone conversation between LCDR Cate, COMPHIBRON 7, and LT Bednarski, 28 June 
1990 

8. Interview between RMC Provost, COMPHIBRON 9, and LT Bednarski, 23 February, 1990 

9. Jodi Tryon, CubeS: A Model for Calculating Fuel Consumption for Gas-Turbine Ships, 
Center for Naval Analyses Research Memorandum CRM 86-213, October 1986 

10. T.C. Gillmer and B. Johnson, Introduction to Naval Architecture, Chapter 11 "Ship 
Resistance and Powering", Naval Institute Press, 1982 

1 1 . P.F. Pucci, Supplemental Notes for Marine Gas Turbines, class notes, Naval Postgraduate 
School, January 1990 

12. Statistical Sciences, Inc., S-PLUSfor Windows, Reference Manual, 1993 



15 



16 



APPENDIX 



This Appendix presents the fuel use prediction functions for 22 U.S. Navy ship classes and 
is organized as follows: 

Ship Class 

CV-63/67 

CG-47/52 

DDG-51 

DD-963/DDG-993 

FFG-7 

PC-1 

LCC-19 

LHD-1 

LHA-1 

LPH-2 

LPD-4/AGF-11 

AGF-3 

LSD-41 

LSD-36 

AD-37 

AOE-6 

AOE-1 

AOR-1 

TAE-26 

TAFS-1 

AO-177(J) 

TAO-187 



17 



Class: CV-63/67 
Source: NWIP 11-20 (D) 

Speed KGal.Hr Predicted 






.0 


NA 


1928 


.3 


1 


.0 


NA 


1928 


.6 


2 


.0 


NA 


1931 


.1 


3 


.0 


NA 


1937 


.9 


4 


.2 


1653 


1954 


.6 


5 


.0 


NA 


1972 


.7 


6. 


.4 


1905 


2021 


.7 


7. 


.0 


NA 


2050 


.7 


8 


.7 


2194 


2164 


.6 


9. 


.0 


NA 


2190 


.1 


10, 


.0 


NA 


2289 


.1 


11 


.1 


2482 


2424 


.7 


12, 


.0 


NA 


2559 


.3 


13, 


.4 


2887 


2816, 


.8 


14, 


.0 


NA 


2947, 


.3 


15, 


.6 


3392 


3363, 


.0 


16, 


.0 


NA 


3483, 


.9 


17. 


.7 


4143 


4086, 


.1 


18, 


.0 


NA 


4208, 


.7 


19. 


.9 


5081 


5118, 


.6 


20. 


,0 


NA 


5173, 


.5 


21. 


,0 


NA 


5766, 


.9 


22. 


.1 


6510 


6522, 


.0 


23. 


,0 


NA 


7231, 


.2 


24. 


,2 


8503 


8325, 


.9 


25. 


,0 


NA 


9164. 


.8 


26. 


,3 


11014 


10747. 


,9 


27. 


,0 


NA 


11730. 


,8 


28. 


,3 


14146 


13845, 


.6 


29. 


,0 


NA 


15165. 


.4 


30. 


,3 


17842 


18022. 


.4 


31. 


,9 


21941 


22438. 


,4 


32. 


,0 


NA 


22753. 


,9 


33. 


,2 


26662 


26973, 


.4 


34. 


,2 


31672 


31201, 


,4 


35. 


,0 


NA 


35151, 


.4 


Formula : 


KGal.Hr 


- cbind 



exp(b * (Speed/100) "3) ) 

Parameters : 

Value Std. Error t value 

b 32.6666 1.41696 23.05400 

-8937.6000 894.86500 -9.98766 

10865.9000 822.30100 13.21400 

Residual standard error: 264.591 on 13 degrees of freedom 






U 1 I ^f(lo z t t$9tt 



CV-63/67 



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10 



20 



30 



Speed (Knots) 



19 



Class: CG-47/52 
Source: NAVSEA Trials 



Speed 


KGal.Hr 


Predicted 





NA 


786.4 


1 


NA 


786.4 


2 


NA 


787.0 


3 


NA 


788.6 


4 


NA 


791.7 


5 


NA 


796.8 


6 


NA 


804.4 


7 


NA 


815.0 


8 


NA 


829.3 


9 


NA 


847.7 


10 


NA 


871.0 


11 


NA 


899.7 


12 


NA 


934.6 


13 


NA 


976.5 


14 


NA 


1026.3 


15 


NA 


1085.1 


16 


1076 


1154.0 


17 


1172 


1234.3 


18 


1287 


1327.6 


19 


1414 


1435.8 


20 


1700 


1561.0 


21 


1827 


1705.7 


22 


1966 


1873.0 


23 


2116 


2066.5 


24 


2272 


2290.5 


25 


2427 


2550.2 


26 


2605 


2852.1 


27 


3364 


3204.0 


28 


3687 


3615.2 


29 


4065 


4097.7 


30 


4622 


4666.0 


31 


5372 


5338.2 


32 


NA 


6137.0 


33 


NA 


7091.3 


34 


NA 


8237.4 


35 


NA 


9621.9 



Formula: KGal.Hr ~ cbind(l, exp(b 



: Speed/100) "3) ) 



Parameters : 

Value Std. Error t value 
b 37.4831 6.4865 5.77862 



-1429.0400 
2215.3900 



727.9950 -1.96298 
646.2490 3.42807 



Residual standard error: 113.925 on 13 degrees of freedom 



20 



CG-47/52 



CO 
O 



o 
o 
o 

CO 



o 
o 
o 

CD 



O 
O 

o 



o 
o 
o 




10 



20 



30 



Speed (Knots) 



21 



Class : 


DDG-51 








Source: 


NAVSEA 


Trials 




Speed : 


KGal.Hr 


Predicted 







NA 




615.2 




1 


NA 




615.3 




2 


NA 




615.8 




3 


NA 




617.1 




4 


NA 




619.8 




5 


NA 




624.1 




6 


NA 




630.7 




7 


NA 




639.8 




8 


NA 




652.1 




9 


613 




668.1 




10 


658 




688.2 




11 


700 




713.3 




12 


741 




743.8 




13 


784 




780.8 




14 


832 




825.0 




15 


886 




877.6 




16 


950 




939.8 




17 


1025 




1013.2 




18 


1115 




1099.5 




19 


1222 




1200.9 




20 


1348 




1320.1 




21 


1496 




1460.2 




22 


1669 




1625.3 




23 


1920 




1820.1 




24 


2070 




2050.7 




25 


2280 




2324.9 




26 


2460 




2652.0 




27 


2780 




3044.3 




28 


3730 




3517.3 




29 


4220 




4091.0 




30 


4800 




4791.2 




31 


5600 




5651.6 




32 


NA 




6716.8 




33 


NA 




8045.6 




34 


NA 




9716.9 




35 


NA 


: 


11837.3 




Formula 


: KGal.Hr 


- cbindd, 


exp (b 


Parameters : 








Value Std. 


Error t 


value 


b 51 


.5925 


3 


.76872 13 


.68960 


-764 


.4330 220 


.15400 -3 


.47226 


1379 


.6200 191 


.05800 7 


.22095 



(Speed/100) A 3) ) 



Residual standard error: 98.2004 on 20 degrees of freedom 



22 



DDG-51 



03 
CD 




Speed (Knots) 



23 



Class: DD-963/DDG-993 
Source: NWP 11-1 (B) 

Speed KGal.Hr Predicted 






NA 


1285 


.0 


1 


NA 


1285 


.1 


2 


NA 


1285 


.7 


3 


NA 


1287 


.3 


4 


NA 


1290 


.4 


5 


NA 


1295 


.5 


6 


NA 


1303, 


.2 


7 


NA 


1313. 


.9 


8 


NA 


1328. 


.3 


9 


NA 


1346. 


.8 


10 


NA 


1370, 


,0 


11 


NA 


1398, 


.7 


12 


NA 


1433, 


.4 


13 


NA 


1474, 


.9 


14 


NA 


1523, 


.9 


15 


NA 


1581, 


.4 


16 


1600 


1648, 


.3 


17 


NA 


1725, 


.7 


18 


1800 


1814, 


.8 


19 


NA 


1917, 


.0 


20 


2100 


2034, 


.0 


21 


NA 


2167, 


.6 


22 


2350 


2319, 


.9 


23 


NA 


2493, 


.3 


24 


2700 


2690, 


.9 


25 


NA 


2915, 


,8 


26 


3150 


3172. 


.3 


27 


NA 


3464, 


.8 


28 


3750 


3799, 


,1 


29 


NA 


4181, 


.8 


30 


4650 


4620, 


,8 


31 


NA 


5125, 


.6 


32 


NA 


5707, 


.9 


33 


NA 


6381, 


.4 


34 


NA 


7163, 


.3 


35 


NA 


8074, 


.2 



Formula: KGal.Hr ~ cbind(l, exp(b * (Speed/100) "3 ) ) 

Parameters : 

Value Std. Error t value 

b 27.0667 5.42175 4.99225 

-1812.9200 951.22300 -1.90588 

3097.9700 898.85400 3.44658 

Residual standard error: 48.2 814 on 5 degrees of freedom 



24 



DD-963/DDG-993 



O 
O 

o 



CO 

o 



o 
o 
o 

CO 



o 
o 
o 

CO 




Speed (Knots) 



25 



Class : 


FFG-7 




Source: 


NWP 11- 


KB) 


Speed 


KGal.Hr 


Predicted 





NA 


405.4 


1 


NA 


405.5 


2 


NA 


405.8 


3 


NA 


406.7 


4 


NA 


408.6 


5 


NA 


411.6 


6 


NA 


416.1 


7 


NA 


422.5 


8 


NA 


431.0 


9 


NA 


442.1 


10 


NA 


456.1 


11 


NA 


473.4 


12 


472 


494.6 


13 


NA 


520.2 


14 


553 


550.9 


15 


NA 


587.4 


16 


649 


630.6 


17 


NA 


681.6 


18 


764 


741.5 


19 


NA 


811.9 


20 


914 


894.7 


21 


NA 


992.1 


22 


1087 


1106.9 


23 


NA 


1242.4 


24 


1313 


1402.9 


25 


NA 


1593.8 


26 


1917 


1821.7 


27 


NA 


2095.2 


28 


2400 


2425.1 


29 


NA 


2825.5 


30 


NA 


3314.6 


31 


NA 


3916.1 


32 


NA 


4661.4 


33 


NA 


5592.0 


34 


NA 


6763.5 


35 


NA 


8251.4 



Formula: KGal.Hr ~ cbindd, exp(b * (Speed/100) ^3 ) ) 

Parameters : 

Value Std. Error t value 

b 51.8843 11.1081 4.67084 

-545.7160 382.7230 -1.42588 

951.1170 344.6340 2.75979 

Residual standard error: 57.6276 on 6 degrees of freedom 



26 



FFG-7 



CO 

O 



o 
o 
o 

CO 



o 
o 
in 
c\j 



o 
o 
o 

CM 



o 
o 



o 
o 
o 



o 
o 
in 




Speed (Knots) 



27 



Class: 


PC-1 




Source : 


Ship tests 




Speed 


KGal.Hr Predicted 





NA 


11.0 


1 


25 


11.0 


2 


25 


11.2 


3 


25 


11.8 


4 


25 


12.8 


5 


25 


14.5 


6 


25 


17.0 


7 


25 


20.5 


8 


25 


25.2 


9 


25 


31.2 


10 


33 


38.6 


11 


47 


47.5 


12 


48 


58.2 


13 


54 


70.7 


14 


61 


85.0 


15 


83 


101.4 


16 


107 


119.7 


17 


132 


140.1 


18 


159 


162.6 


19 


186 


187.2 


20 


216 


213.7 


21 


246 


242.2 


22 


277 


272.6 


23 


310 


304.7 


24 


344 


338.4 


25 


378 


373.5 


26 


414 


409.9 


27 


450 


447.2 


28 


487 


485.4 


29 


525 


524.1 


30 


564 


563.1 


31 


603 


602.1 


32 


642 


640.9 


33 


683 


679.3 


34 


710 


716.9 


35 


750 


753.6 


Formula 


: KGal.Hr ~ 


cbind 



(Speed/100) ~3) ) 



Parameters : 

Value Std. Error t value 

b -24.3044 1.30277 -18.6560 

1158.2800 41.26510 28.0692 

-1147.2600 40.20400 -28.5360 

Residual standard error: 9.24413 on 32 degrees of freedom 



28 



PC-1 



o 
o 

CO 



CO 

o 



o 
o 



o 
o 

CM 



o - 




Speed (Knots) 



29 



Class: 


LCC-19 




Source: 


NWP 11- 


KB) 


Speed 


KGal . Hr 


Predicted 





NA 


791.6 


1 


NA 


791.7 


2 


NA 


792.2 


3 


NA 


793.7 


4 


NA 


796.7 


5 


NA 


801.6 


6 


NA 


808.9 


7 


NA 


819.2 


8 


NA 


833.3 


9 


NA 


851.6 


10 


873.6 


875.3 


11 


NA 


905.1 


12 


945.0 


942.4 


13 


NA 


988.6 


14 


1045.8 


1045.8 


15 


NA 


1116.2 


16 


1201.2 


1203.1 


17 


NA 


1310.5 


18 


1444.8 


1443.8 


19 


NA 


1610.0 


20 


1818.6 


1818.8 


21 


NA 


2083.1 


22 


NA 


2420.7 


23 


NA 


2856.5 


24 


NA 


3425.4 


25 


NA 


4177.4 


26 


NA 


5184.4 


27 


NA 


6552.6 


28 


NA 


8439.7 


29 


NA 


11084.6 


30 


NA 


14854.7 


31 


NA 


20325.2 


32 


NA 


28411.5 


33 


NA 


40598.4 


34 


NA 


59340.1 


35 


NA 


88773.2 


Formula 


i : KGal . Hr - cbind 



(Speed/100) A 3) 



Parameters : 

Value Std. 
b 112.9410 2 

92.0583 29.36670 



Error t value 

80061 40.32750 

3.13479 



699.5530 



27.14310 25.77270 



Residual standard error: 2.18812 on 3 degrees of freedom 



30 



LCC-19 



O 

o 
o 



CO 

CD 



o 
o 
m 



o 
o 
o 




Speed (Knots) 



31 



Class: LHD-1 

Source: NAVSEA Propulsion Branch 

Speed KGal.Hr Predicted 






NA 


1338. 


.6 


1 


NA 


1338. 


.8 


2 


NA 


1339, 


,9 


3 


NA 


1342. 


.9 


4 


NA 


1348, 


.8 


5 


NA 


1358. 


.6 


6 


NA 


1373, 


.3 


7 


NA 


1394, 


.0 


8 


NA 


1421, 


.9 


9 


NA 


1458, 


.3 


10 


NA 


1504, 


.5 


11 


NA 


1562, 


.3 


12 


1489 


1633, 


.7 


13 


NA 


1720. 


.9 


14 


1845 


1826, 


.8 


15 


NA 


1954, 


.6 


16 


2080 


2108, 


,7 


17 


NA 


2294, 


.1 


18 


2700 


2517, 


.2 


19 


NA 


2786, 


.4 


20 


3280 


3111, 


.9 


21 


NA 


3507, 


.0 


22 


3893 


3989, 


.2 


23 


NA 


4580 


.8 


24 


5000 


5311, 


.6 


25 


6433 


6221, 


.0 


26 


NA 


7362, 


.0 


27 


NA 


8806. 


.4 


28 


NA 


10652. 


.4 


29 


NA 


13036, 


.3 


30 


NA 


16148 


.4 


31 


NA 


20258 


.5 


32 


NA 


25753 


.4 


33 


NA 


33193 


.9 


34 


NA 


43404 


.8 


35 


NA 


57614 


.9 


lUla: 


KGal . Hr 


~ cbii 


id 



exp(b * (Speed/100) "3) ) 

Parameters : 

Value Std. Error t value 
b 78.209 27.5816 2.835550 

-700.811 1458.8500 -0.480386 

2039.410 1276.9900 1.597040 

Residual standard error: 216.814 on 5 degrees of freedom 



32 



LHD-1 



O 
O 
O 
ID 



O 
O 
O 
O 



Us 



o 
o 
o 
to 




Speed (Knots) 



33 



Class: LHA-1 

Source: COMPHIBRON 9 

Speed KGal.Hr Predicted 






NA 


952 


5 


1 


NA 


952 


7 


2 


NA 


954 


5 


3 


NA 


959 


4 


4 


NA 


968 


9 


5 


961.8 


984 


6 


6 


NA 


1008 


2 


7 


NA 


1041 


2 


8 


NA 


1085 


3 


9 


NA 


1142 


4 


10 


NA 


1214 


4 


11 


NA 


1303 


4 


12 


1398.6 


1411 


7 


13 


1570.8 


1541 


8 


14 


1751.4 


1696 


6 


15 


1936.2 


1879 


3 


16 


2100.0 


2093 


8 


17 


2242.8 


2344 


3 


18 


2499.0 


2635 


8 


19 


2977.8 


2974 


4 


20 


3498.6 


3366 


8 


21 


3897.6 


3821 


6 


22 


4300.8 


4348 


5 


23 


4888.8 


4959 


5 


24 


5703.6 


5669 


1 


25 


NA 


6494 


5 


26 


NA 


7457 


2 


27 


NA 


8583 


.3 


28 


NA 


9905 


.0 


29 


NA 


11462 


.3 


30 


NA 


13304 


9 


31 


NA 


15495 


5 


32 


NA 


18112 


9 


33 


NA 


21257 


2 


34 


NA 


25056 


4 


35 


NA 


29675 


2 


Formula 


: KGal.Hr 


- cbii 


id 



exp(b * (Speed/100) "3) ) 

Parameters : 

Value Std. Error t value 

b 39.3264 8.20849 4.79093 

-5577.6800 1811.58000 -3.07890 

6530.1500 1768.23000 3.69305 

Residual standard error: 78.8921 on 11 degrees of freedom 



34 



LHA-1 



O 
O 

o 
o 



CO 

o 



o 
o 
o 

CO 



o 
o 
o 

CM 




Speed (Knots) 



35 



Class : 


LPH-2 




Source: 


COMPHIBRON 9 


Speed 


KGal.Hr Predicted 





NA 


475.6 


1 


NA 


475.7 


2 


NA 


476.5 


3 


NA 


478.8 


4 


NA 


483.2 


5 


504.0 


490.5 


6 


NA 


501.3 


7 


NA 


516.2 


8 


NA 


535.8 


9 


NA 


560.5 


10 


579.6 


590.8 


11 


621.6 


626.8 


12 


663.6 


668.7 


13 


714.0 


716.5 


14 


768.6 


769.9 


15 


831.6 


828.5 


16 


898.8 


891.8 


17 


966.0 


959.0 


18 


1029.0 


1029.4 


19 


1100.4 


1101.8 


20 


1171.8 


1175.3 


21 


NA 


1248.7 


22 


NA 


1321.0 


23 


NA 


1391.1 


24 


NA 


1458.1 


25 


NA 


1521.0 


26 


NA 


1579.3 


27 


NA 


1632.3 


28 


NA 


1679.9 


29 


NA 


1721.9 


30 


NA 


1758.3 


31 


NA 


1789.3 


32 


NA 


1815.3 


33 


NA 


1836.7 


34 


NA 


1854.0 


35 


NA 


1867.7 


Formula 


: KGal . Hr 


- cbind 



(Speed/100) *3) ) 



Parameters : 

Value Std. Error t value 

b -83.8886 9.50305 -8.82755 

1906.9000 117.77400 16.19120 

-1431.3100 113.67300 -12.59150 

Residual standard error: 7.37016 on 9 degrees of freedom 



36 



LPH-2 



CO 
O 



o 
o 

CM 



O 
O 
O 



O 
O 
CD 



O 
O 
CD 




Speed (Knots) 



37 



Class: LPD-4/AGF-11 
Source: COMPHIBRON 9 



Speed 


KGal.Hr 


Predicted 





NA 


442, 


.4 


1 


NA 


442 


.5 


2 


NA 


443 


.6 


3 


NA 


446 


.4 


4 


NA 


452 


.0 


5 


462.0 


461 


.2 


6 


NA 


475 


.0 


7 


NA 


494. 


.5 


8 


NA 


520, 


.8 


9 


NA 


555, 


.3 


10 


592.2 


599, 


.3 


11 


651.0 


654, 


.6 


12 


726.6 


723, 


.4 


13 


814.8 


808, 


.0 


14 


919.8 


911. 


.6 


15 


1041.6 


1038. 


.0 


16 


1184.4 


1192. 


.1 


17 


1369.2 


1380. 


.0 


18 


1608.6 


1609. 


.6 


19 


1902.6 


1891, 


.2 


20 


2234.4 


2238. 


.3 


21 


NA 


2668. 


.5 


22 


NA 


3205. 


.4 


23 


NA 


3881. 


,1 


24 


NA 


4739. 


.0 


25 


NA 


5839. 


.0 


26 


NA 


7264. 


.5 


27 


NA 


9133. 


.6 


28 


NA 


11614. 


.6 


29 


NA 


14951. 


.4 


30 


NA 


19502. 


.1 


31 


NA 


25799. 


.6 


32 


NA 


34649. 


.4 


33 


NA 


47287. 


,4 


34 


NA 


65640. 


.3 


35 


NA 


92761. 


.4 



Formula: KGal.Hr ~ cbind(l, exp(b * (Speed/100 ) ^3 ) ) 

Parameters : 

Value Std. Error t value 

b 95.4647 3.81939 24.9947 

-1124.4300 94.06040 -11.9543 

1566.7900 89.75880 17.4556 

Residual standard error: 7.61684 on 9 degrees of freedom 



38 



LPD-4/AGF-1 1 



CD 



o 
o 
o 

CO 



o 
o 
in 

CM 



o 
o 
o 

CM 



o 
o 



o 
o 
o 



o 
o 

IC 




10 



15 



20 



Speed (Knots) 



39 



Class : 


AGF-3 




Source : 


COMPHIBRON 9 


Speed 


KGal.Hr Predicted 





NA 


306.2 


1 


NA 


306.3 


2 


NA 


307.2 


3 


NA 


309.8 


4 


NA 


314.6 


5 


378.0 


322.7 


6 


NA 


334.8 


7 


NA 


351.8 


8 


NA 


374.6 


9 


NA 


404.2 


10 


399.0 


441.6 


11 


NA 


488.0 


12 


529.2 


544.7 


13 


596.4 


613.3 


14 


680.4 


695.4 


15 


789.6 


793.0 


16 


919.8 


908.6 


17 


1058.4 


1045.0 


18 


1230.6 


1205.5 


19 


1407.0 


1394.2 


20 


1591.8 


1616.1 


21 


NA 


1877.3 


22 


NA 


2185.1 


23 


NA 


2548.8 


24 


NA 


2979.8 


25 


NA 


3492.7 


26 


NA 


4105.5 


27 


NA 


4841.3 


28 


NA 


5729.8 


29 


NA 


6808.9 


30 


NA 


8128.2 


31 


NA 


9752.3 


32 


NA 


11766.6 


33 


NA 


14284.5 


34 


NA 


17458.1 


35 


NA 


21493.5 


Formula 


l: KGal.Hr 


~ cbind 



1, exp(b * (Speed/100) A 3)) 



Parameters : 

Value Std. Error t value 

b 52.2391 20.7173 2.52152 

-2218.8100 1246.8100 -1.77959 

2525.0000 1228.5600 2.05525 

Residual standard error: 30.2495 on 8 degrees of freedom 



40 



AGF-3 



O 
O 
O 
CM 



O 
O 
lO 



CO 

o 



o 
o 
o 



o 
o 
in 




Speed (Knots) 



41 



Class: LSD-41 

Source: COMNAVSURFPAC & COMPHIBRON 7 

Speed KGal.Hr Predicted 






NA 


238 


.7 


1 


NA 


238 


,8 


2 


NA 


239 


.5 


3 


NA 


241 


.3 


4 


NA 


244, 


.7 


5 


289.8 


250 


.4 


6 


NA 


258 


.9 


7 


NA 


270 


.8 


8 


NA 


286 


.7 


9 


NA 


307 


.0 


10 


298.2 


332 


.4 


11 


NA 


363 


.5 


12 


361.2 


400 


.8 


13 


NA 


444, 


.9 


14 


533.4 


496 


.5 


15 


NA 


556, 


.0 


16 


596.4 


624, 


.2 


17 


NA 


701, 


.7 


18 


831.6 


789, 


.0 


19 


NA 


886 


.8 


20 


978.6 


995, 


.9 


21 


NA 


1116. 


.8 


22 


NA 


1250, 


.3 


23 


NA 


1397, 


.2 


24 


NA 


1558, 


.1 


25 


NA 


1733, 


.9 


26 


NA 


1925, 


.3 


27 


NA 


2133, 


.2 


28 


NA 


2358, 


.6 


29 


NA 


2602, 


.2 


30 


NA 


2865, 


.1 


31 


NA 


3148, 


.4 


32 


NA 


3453, 


.0 


33 


NA 


3780, 


.2 


34 


NA 


4131, 


.0 


35 


NA 


4506, 


.8 



Formula: KGal.Hr ~ cbind ( 1 , exp(b * (Speed/100) A 3 ) ) 

Parameters : 

Value Std. Error t value 

b 2.86188 62.5409 0.0457601 

-32454.80000 722767.0000 -0.0449035 

32693.50000 722740.0000 0.0452355 

Residual standard error: 46.2148 on 4 degrees of freedom 



42 



LSD-41 



CO 
O 



O 

o 

CM 



O 
O 
O 



O 
O 

co 



o 
o 



O 

o 

"3- 



o 
o 

CO 




Speed (Knots) 



43 



Class: LSD-36 

Source: COMNAVSUEFPAC & COMPHIBRON 7 



Speed 


KGal.Hr Predicted 





NA 


409.0 


1 


NA 


409.1 


2 


NA 


409.9 


3 


NA 


411.9 


4 


NA 


415.8 


5 


453.6 


422.3 


6 


NA 


432.0 


7 


NA 


445.8 


8 


NA 


464.3 


9 


NA 


488.6 


10 


491.4 


519.7 


11 


NA 


558.8 


12 


588.0 


607.4 


13 


NA 


667.3 


14 


739.2 


740.8 


15 


NA 


830.7 


16 


961.8 


940.5 


17 


NA 


1074.7 


18 


1239.0 


1239.1 


19 


NA 


1441.4 


20 


1688.4 


1691.6 


21 


NA 


2003.0 


22 


NA 


2393.2 


23 


NA 


2886.6 


24 


NA 


3516.3 


25 


NA 


4328.1 


26 


NA 


5386.6 


27 


NA 


6783.6 


28 


NA 


8651.0 


29 


NA 


11181.7 


30 


NA 


14661.1 


31 


NA 


19518.3 


32 


NA 


26407.9 


33 


NA 


36344.4 


34 


NA 


50927.0 


35 


NA 


72719.0 


ormula 


: KGal.Hr 


~ cbind 



(Speed/100) "3) ) 



Parameters : 

Value Std. Error t value 
b 98.678 20.8562 4.73136 

-657.897 343.2460 -1.91669 

1066.930 328.0590 3.25227 

Residual standard error: 25.6232 on 4 degrees of freedom 



44 



LSD-36 



CO 



o 
o 
o 

CM 



O 

o 
in 



o 
o 
o 



o 
o 




Speed (Knots) 



45 



Class: 


AD-37 




Source : 


NWP 11- 


2(B) 


Speed 


KGal.Hr 


Predicted 





NA 


306.8 


1 


NA 


306.9 


2 


NA 


308.0 


3 


NA 


311.0 


4 


NA 


316.8 


5 


NA 


326.4 


6 


NA 


340.7 


7 


NA 


360.7 


8 


386 


387.5 


9 


NA 


422.1 


10 


466 


465.7 


11 


NA 


519.4 


12 


584 


584.7 


13 


NA 


663.0 


14 


760 


755.8 


15 


NA 


865.0 


16 


992 


992.6 


17 


NA 


1141.0 


18 


1310 


1312.9 


19 


NA 


1511.3 


20 


1741 


1739.8 


21 


NA 


2002.7 


22 


NA 


2305.0 


23 


NA 


2652.5 


24 


NA 


3052.3 


25 


NA 


3512.6 


26 


NA 


4043.6 


27 


NA 


4657.3 


28 


NA 


5368.3 


29 


NA 


6194.5 


30 


NA 


7157.6 


31 


NA 


8284.4 


32 


NA 


9608.0 


33 


NA 


11169.4 


34 


NA 


13019.9 


35 


NA 


15223.9 



Formula: KGal.Hr ~ cbindd, exp(b * (Speed/100) ^3 ) ) 

Parameters : 

Value Std. Error t value 

b 33.4188 2.15993 15.4721 

-4368.6500 348.04700 -12.5519 

4675.4300 346.06200 13.5104 

Residual standard error: 2.76573 on 4 degrees of freedom 



46 



AD-37 



CO 



o 
o 
o 

CM 



O 
O 



O 

o 
o 



o 
o 
m 




10 



15 



20 



Speed (Knots) 



47 



Class: 


AOE-6 




Source : 


NAVSEA 


03XN 


Speed 


KGal.Hr 


Predicted 


0.0 


NA 


-115.2 


1.0 


NA 


-114.8 


2.0 


NA 


-112.6 


3.0 


NA 


-106.6 


4.0 


NA 


-95.0 


5.0 


NA 


-75.8 


6.0 


NA 


-47.2 


7.0 


NA 


-7.4 


8.0 


NA 


45.3 


9.0 


NA 


112.6 


10.0 


NA 


196.2 


11.0 


NA 


297.6 


12.0 


NA 


417.9 


13.7 


580 


669.6 


14.0 


NA 


720.5 


15.0 


NA 


904.4 


16.8 


1420 


1292.7 


17.0 


NA 


1340.4 


18.0 


NA 


1592.8 


19.2 


NA 


1925.5 


20.0 


NA 


2165.0 


21.0 


NA 


2483.4 


22.0 


NA 


2821.9 


23.0 


NA 


3178.9 


24.2 


3575 


3629.4 


25.0 


NA 


3941.5 


26.0 


4390 


4342.6 


27.2 


4695 


4836.9 


28.3 


5435 


5298.8 


29.8 


5910 


5935.0 


30.0 


NA 


6019.9 


31.0 


NA 


6443.3 


32.0 


NA 


6862.5 


33.0 


NA 


7274.9 


34.0 


NA 


7677.6 


35.0 


NA 


8068.1 


Formulc 


l: KGal.Hr ~ cbind 



(Speed/100)^3) ) 



Parameters : 

Value Std. Error t value 

b -25.7866 8.92627 -2.88885 

12117.2000 2993.10000 4.04836 

-12232.3000 2873.71000 -4.25663 

Residual standard error: 131.131 on 4 degrees of freedom 



48 



AOE-6 



O 

o 
o 
10 



CO 



o 
o 
o 

CO 



o 
o 
o 



o - 




Speed (Knots) 



49 



Class: AOE-1 

Source: NWIP 11-20 (D) 



Speed 


KGal.Hr Predicted 





NA 


267.8 


1 


NA 


268.1 


2 


NA 


270.5 


3 


NA 


277.0 


4 


NA 


289.6 


5 


NA 


310.5 


6 


NA 


341.6 


7 


NA 


385.0 


8 


NA 


443.0 


9 


NA 


517.5 


10 


NA 


610.9 


11 


NA 


725.4 


12 


NA 


863.4 


13 


NA 


1027.2 


14 


1259 


1219.5 


15 


1470 


1442.9 


16 


1712 


1700.3 


17 


1980 


1994.8 


18 


2300 


2329.5 


19 


2690 


2708.1 


20 


3100 


3134.3 


21 


3560 


3612.3 


22 


4150 


4146.7 


23 


4750 


4742.5 


24 


5440 


5405.2 


25 


6130 


6140.9 


26 


7000 


6956.4 


27 


7930 


7859.3 


28 


8780 


8858.1 


29 


NA 


9962.2 


30 


NA 


11182.4 


31 


NA 


12530.5 


32 


NA 


14020.3 


33 


NA 


15667.0 


34 


NA 


17488.1 


35 


NA 


19503.5 


Formula 


: KGal.Hr ~ cbind 



(Speed/100) ~3) ) 



Parameters : 

Value Std. Error t value 

b 12.2579 1.7891 6.85145 

-27553.4000 4703.1800 -5.85846 

27821.2000 4668.4700 5.95939 

Residual standard error: 42.9629 on 12 degrees of freedom 



50 



AOE-1 



CO 

(3 



o 
o 
o 
o 



o 
o 
o 

00 



o 
o 
o 

CO 



o 
o 
o 



o 
o 
o 

CM 



o - 




Speed (Knots) 






51 



Class: AOR-1 

Source: NWIP 11-20 (D) 



Speed 


KGal . Hr 


Predicted 





NA 


280.3 


1 


NA 


280.5 


2 


NA 


282.2 


3 


NA 


286.8 


4 


NA 


295.7 


5 


NA 


310.4 


6 


321 


332.3 


7 


358 


363.0 


8 


404 


403.9 


9 


462 


456.5 


10 


538 


522.6 


11 


619 


603.7 


12 


707 


701.5 


13 


778 


817.9 


14 


965 


954.8 


15 


1120 


1114.2 


16 


1290 


1298.4 


17 


1517 


1509.8 


18 


1760 


1751.0 


19 


2010 


2024.9 


20 


2340 


2334.6 


21 


NA 


2683.7 


22 


NA 


3076.1 


23 


NA 


3516.2 


24 


NA 


4008.9 


25 


NA 


4559.9 


26 


NA 


5175.4 


27 


NA 


5862.6 


28 


NA 


6629.7 


29 


NA 


7485.9 


30 


NA 


8442.1 


31 


NA 


9510.5 


32 


NA 


10705.2 


33 


NA 


12042.7 


34 


NA 


13542.0 


35 


NA 


15225.3 



Formula: KGal.Hr - cbindd, exp(b * (Speed/100) ^3 ) ) 

Parameters : 

Value Std. Error t value 

b 16.3917 6.05011 2.70932 

-14380.5000 5760.32000 -2.49647 

14660.8000 5754.35000 2.54777 

Residual standard error: 15.4594 on 12 degrees of freedom 



52 



AOR-1 



CO 

O 



O 

o 
o 

CO 



o 
o 
in 

CM 



o 
o 
o 

C\J 



o 
o 



o 
o 
o 



o 
o 
m 




Speed (Knots) 



53 



Class: AE/TAE-26 
Source: NWIP 11-20 (D) 

Speed KGal.Hr Predicted 






NA 


193 


4 


1 


NA 


193 


6 


2 


NA 


194 


6 


3 


NA 


197 


3 


4 


NA 


202 


6 


5 


NA 


211 


3 


6 


NA 


224 


3 


7 


NA 


242 


5 


8 


NA 


266 


6 


9 


NA 


297 


5 


10 


NA 


336 





11 


NA 


382 


9 


12 


NA 


439 





13 


520 


505 





14 


600 


581 


6 


15 


660 


669 


5 


16 


750 


769 


4 


17 


860 


881 


8 


18 


990 


1007 


3 


19 


1140 


1146 


3 


20 


1325 


1299 


3 


21 


1530 


1466 


5 


22 


1600 


1648 


3 


23 


NA 


1844 


9 


24 


NA 


2056 


4 


25 


NA 


2282 


7 


26 


NA 


2523 


8 


27 


NA 


2779 


6 


28 


NA 


3049 


7 


29 


NA 


3333 


9 


30 


NA 


3631 


6 


31 


NA 


3942 


3 


32 


NA 


4265 


3 


33 


NA 


4600 





34 


NA 


4945 


3 


35 


NA 


5300 


6 



Formula: KGal.Hr ~ cbind(l, exp(b * (Speed/100) ^3 ) ) 

Parameters: 

Value Std. Error t value 

b -8.86595 26.0028 -0.340962 

16343.70000 44805.3000 0.364772 

-16150.30000 44747.7000 -0.360919 

Residual standard error: 35.6091 on 7 degrees of freedom 



54 



AE/TAE-26 



O 
O 
CO 



o 
o 

CVJ 



CO 



o 
o 

CO 



o 
o 

CO 



o 
o 



o 
o 

CM 




Speed (Knots) 



55 



Class: AFS/TAFS-1 
Source: NWIP 11-20 (D) 



Speed 


KGal . Hr 


Predicted 





NA 


255.8 


1 


NA 


255.9 


2 


NA 


256.6 


3 


NA 


258.4 


4 


NA 


261.9 


5 


NA 


267.8 


6 


NA 


276.6 


7 


NA 


289.0 


8 


289 


305.6 


9 


321 


327.1 


10 


353 


354.4 


11 


396 


388.3 


12 


433 


429.7 


13 


490 


479.9 


14 


546 


540.0 


15 


620 


611.7 


16 


700 


696.8 


17 


803 


797.4 


18 


910 


916.2 


19 


1040 


1056.3 


20 


1210 


1221.6 


21 


1429 


1416.9 


22 


1650 


1648.1 


23 


NA 


1922.5 


24 


NA 


2249.5 


25 


NA 


2640.8 


26 


NA 


3111.2 


27 


NA 


3679.9 


28 


NA 


4371.4 


29 


NA 


5217.8 


30 


NA 


6261.1 


31 


NA 


7557.0 


32 


NA 


9179.4 


33 


NA 


11228.1 


34 


NA 


13838.1 


35 


NA 


17194.6 



Formula: KGal.Hr - cbindd, exp(b * (Speed/100) "3 ) ) 

Parameters : 

Value Std. Error t value 

b 55.5118 4.56171 12.16910 

-1471.6600 191.51800 -7.68422 

1727.4600 186.86200 9.24459 

Residual standard error: 10.0922 on 12 degrees of freedom 



56 



AFS/TAFS-1 



o 
o 

CD 



O 
O 
CM 



CO 
O 



o 
o 

00 



o 
o 

CD 



O 
O 




Speed (Knots) 



57 



Class: AO-177(J) 
Source: NAVSEA Trials 



Speed 


KGal . Hr 


Predicted 


0.0 


NA 


400. 


.3 


1.0 


NA 


400 


.4 


2.0 


NA 


401 


.0 


3.0 


NA 


402 


.7 


4.0 


NA 


405 


.9 


5.0 


NA 


411 


.3 


6.0 


NA 


419 


.4 


7.3 


412 


434 


.9 


8.6 


425 


457 


.5 


9.0 


NA 


466 


.1 


10.5 


537 


506 


.7 


11.0 


NA 


523 


.5 


12.0 


NA 


563 


.0 


13.4 


663 


633, 


.6 


14.0 


NA 


670 


.3 


15.8 


837 


809, 


.4 


16.0 


NA 


828 


.0 


17.0 


NA 


932, 


.4 


18.0 


NA 


1058, 


.6 


19.3 


1212 


1263 


.8 


20.4 


1487 


1483 


.7 


21.5 


1775 


1758, 


.5 


22.0 


NA 


1905 


.8 


23.0 


NA 


2252, 


.3 


24.0 


NA 


2684, 


.2 


25.0 


NA 


3227, 


.0 


26.0 


NA 


3915, 


.4 


27 


NA 


4797, 


.0 


28 


NA 


5938, 


.0 


29 


NA 


7431, 


.5 


30 


NA 


9409, 


.5 


31 


NA 


12062, 


.7 


32 


NA 


15668 


.9 


33 


NA 


20638, 


.9 


34 


NA 


27588 


,4 


35 


NA 


37454 


.0 



Formula: KGal.Hr ~ cbindd, exp(b * (Speed/100) "3 ) ) 

Parameters : 

Value Std. Error t value 

b 83.9283 25.061 3.34896 

-642.2810 476.553 -1.34776 

1042.5700 457.702 2.27784 

Residual standard error: 37.6589 on 5 degrees of freedom 



58 



AO-177(J) 



O 
O 

m 



CO 

CD 



o 
o 
o 



o 
o 

IT) 




Speed (Knots) 



59 



Class: 


TAO-187 




Source: 


MSC Trial 


s 


Speed 


KGal.Hr Predicted 





NA 


219.7 


1 


NA 


219.9 


2 


NA 


221.4 


3 


NA 


225.3 


4 


266 


233.0 


5 


NA 


245.6 


6 


288 


264.3 


7 


NA 


290.4 


8 


314 


324.8 


9 


NA 


368.5 


10 


388 


422.6 


11 


NA 


487.8 


12 


515 


564.7 


13 


NA 


653.8 


14 


760 


755.4 


15 


NA 


869.5 


16 


1024 


996.0 


17 


NA 


1134.4 


18 


1310 


1284.2 


19 


NA 


1444.4 


20 


1594 


1614.0 


21 


NA 


1791.5 


22 


NA 


1975.5 


23 


NA 


2164.2 


24 


NA 


2356.0 


25 


NA 


2548.8 


26 


NA 


2740.7 


27 


NA 


2930.0 


28 


NA 


3114.7 


29 


NA 


3293.2 


30 


NA 


3464.0 


31 


NA 


3625.6 


32 


NA 


3777.1 


33 


NA 


3917.5 


34 


NA 


4046.3 


35 


NA 


4163.3 


Formula 


: KGal . Hr 


~ cbind(l 



exp (b 



[ Speed/100) A 3) ) 



Parameters : 

Value Std. Error t value 

b -44.9642 23.4124 -1.92053 

4834.5400 2036.3200 2.37415 

-4614.8100 2024.1100 -2.27992 

Residual standard error: 3 4.8975 on 6 degrees of freedom 



60 



TAO-187 



O 
O 
O 
CM 



O 
O 



CO 
O 



o 
o 
o 



o 
o 
in 




Speed (Knots) 



61 



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63 



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64 



19. Senior Lecturer Gordon Smyth 
Department of Mathematics 
University of Queensland 
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Department of Mechanical Engineering 
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21. Professor David Schrady 50 

Department of Operations Research 
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65 




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