Comparative Naval Architecture Analysis of Diesel Submarines

by

Kai Oscar Torkelson

M.S., Mechanical Engineering Virginia Tech, 1998

B.S., Mechanical Engineering Virginia Military Institute, 1991

Submitted to the Department of Ocean Engineering in Partial Fulfillment of the Requirements

for the Degrees of

Master of Science in Naval Architecture and Marine Engineering

and

Master of Science in Ocean Systems Management

at the
Massachusetts Institute of Technology
June 2005

( 2005, Kai 0. Torkelson

All rights reserved

The author hereby grants to MIT and the United States Government permission to reproduce
and to distribute publicly paper and electronpppies of this thesis document in whole or in part.

Signature of Author ....... .......................................

Department of Naval Architecture and Marine Engineering
May 6, 2005

Certified by ................. ..........................................................

David S. Herbein
Professor of Naval Architecture and Marine Engineering
n - Thesis Supervisor

Certified by ... ..... ...............................................

Henry S. Marcus
Professor of Ocean Engineering
Thesis Supervisor

Accepted by .......... ............................................

Michael S. Triantafyllou
Chairman, Department Committee for Graduate Students
MASSACHUSETTS INSTInrTE.1 Professor of Ocean Engineering
OF TECHNOLOGY

SEP1 12005

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 Comparative Naval Architecture Analysis of Diesel Submarines

by

Kai 0. Torkelson

Submitted to the Department of Ocean Engineering in Partial

Fulfillment of the Requirements for the Degrees of Master of
Science in Naval Architecture and Marine Engineering and
Master of Science in Ocean Systems Management

Abstract
Many comparative naval architecture analyses of surface ships have been performed, but few
published comparative analyses of submarines exist. Of the several design concept papers,
reports and studies that have been written on submarines, no exclusively diesel submarine
comparative naval architecture analyses have been published. One possible reason for few
submarine studies may be the lack of complete and accurate information regarding the naval
architecture of foreign diesel submarines. However, with some fundamental submarine design
principles, drawings of inboard profiles and plan views, and key assumptions to develop
empirical equations, a process can be developed by which to estimate the submarine naval
architectural characteristics. A comparative naval architecture analysis creates an opportunity
to identify new technologies, review the architectural characteristics best suited for submarine
missions and to possibly build more effective submarines. An accurate observation is that
submarines designed for different missions possess different capabilities. But are these unique
capabilities due to differences in submarine naval architecture? Can mission, cost, or other
factors affect the architecture? This study examines and compares the naval architecture of
selected diesel submarines from data found in open literature. The goal is to determine weight
group estimates and analyze whether these estimates provide a relevant comparison of diesel
submarine naval architecture.

Thesis Supervisor: Professor David S. Herbein

Title: Professor of Naval Construction and Engineering

Thesis Supervisor: Professor Henry S. Marcus

Title: Professor of Ocean Engineering

2
 Acknowledgements

"I can answer for but three things: a firm belief in the justice of our cause, close attention in
the prosecution of it, and the strictest integrity." - George Washington

"Better to dare Mighty Things and fail, than to live in a gray twilight where there is neither
victory nor defeat." - Theodore Roosevelt

"Be an opener of doors for such as come after thee." - Ralph Waldo Emerson

The work of a thesis brings together the efforts of so many people besides the author.
I am therefore thankful to the many individuals from several organizations that provided
invaluable background, technical assistance, and contributed time and support to this
endeavor. I would like to acknowledge the contributions and advice from these people with
sincere appreciation.
On the technical and writing side of the thesis, I recognize those that have had a direct
contribution to the work. Rear Admiral Paul E. Sullivan, NAVSEA Deputy Commander for
Integrated Warfare Systems (SEA-05), served as the thesis sponsor and provided the initial
topic for the study, as well as making his staff available for data and reviews. My advisors,
CAPT David S. Herbein and Professor Hank Marcus, were of great assistance in regular
meetings to discuss the scope, direction and expected outcomes of the study. I also gratefully
acknowledge the assistance of Electric Boat Corporation of General Dynamics in supplying
photographs and drawings of many of the submarines studied. The willingly offered help of
Mr. Carl Fast was especially appreciated.
On the support side, I recognize those that provided me with encouragement, prayers
and growth. My family and friends are too numerous to list here, so I will mention a few
representative of the rest. I give the most thanks to my mom, who's had the added
responsibility of filling in for my dad's support since his death, but she has always been there
to give this support. The many friends I have come to know through St Paul Lutheran
Church, the Lutheran Episcopal Ministry at MIT, the brothers of SSJE, the monastery in
Harvard Square, Big Brothers of Mass Bay, the cabin 'up north', and the opportunities in the
area and elsewhere they provided, were all supportive in my time away from the books. To
the many athletes who helped add competition to workouts including running, swimming,
cycling and hiking, I thank you for pushing me to relieve stress through my favorite sports.
Last but not least of all, I want to pay tribute to the American taxpayers for ultimately
providing the funding, and to the US Navy, the Submarine and the Engineering Duty Officer
communities, where I was able to achieve the breadth of experience necessary to perform a
study of this kind. I also owe a debt of gratitude to MIT for providing the very favorable
environment most conducive to this endeavor. I hope that this study will contribute to the
Navy's pursuit of advanced submarine designs and assessment of foreign submarine
capabilities.

I dedicate this work to my parents: Leif 0. Torkelson, M.D. and Betty K. Torkelson

3
 Table of Contents

Abstract .................................................................................................................................................. 2
A cknow ledgem ents .............................................................................................................................. 3
T able of C ontents.................................................................................................................................4
List of Figures ....................................................................................................................................... 6
List of T ables.........................................................................................................................................7
1 Introduction ....................................................................................................................................... 8
1.1 Purpose of the Study.......................................................................................................... 10
1.2 Problem .................................................................................................................................... 11
1.3 B ackground ............................................................................................................................. 12
1.4 G eneral A pproach/M ethodology .................................................................................... 12
1.5 C riteria for Success................................................................................................................. 12

2 Subm arine D esign Process ....................................................................................................... 13

2.1 D esign H istory ........................................................................................................................ 13

2.2 Subm arine D esign .................................................................................................................. 13
2.3 D esign W eight to Space Relationship ............................................................................. 14
2.4 W eight E stimates and W eight G roups........................................................................... 18
2.5 D esign Summ ary..................................................................................................................... 18
3 D evelopm ent of Procedure ..................................................................................................... 20

3.1 Approach ................................................................................................................................. 20

3.2 Procedure D escription........................................................................................................ 20
3.2.1 Subm arines Selected for Analysis ............................................................................. 21
3.2.2 M ath M odel Developm ent ....................................................................................... 28
3.2.2.1 Major Compartment and Space Calculations................................................. 31
3.2.2.2 Area and Volume Calculation Error Checks.................................................... 34
3.2.3 W eight G roup Calculations....................................................................................... 35
3.3 O verall Analysis Process................................................................................................... 42
3.4 V alidation of M odel O utputs............................................................................................ 43
4 C omparative N aval A rchitecture .............................................................................................. 45

4.1 D ata Presentation ............................................................................................................ 45

4.2 Analysis of R esults.................................................................................................................. 49
4.2.1 H istorical T rends ....................................................................................................... 49
4.2.2 M ission E ffects................................................................................................................ 50
4.2.3 Construction E ffects ................................................................................................... 51
4.2.4 C ost E ffects ..................................................................................................................... 53
4.3 D iscussion of R esults.......................................................................................................... 54

5 C onclusions..................................................................................................................................... 55

5.1 Sum mary of Work .................................................................................................................. 55

4
 5.2 Future W ork and Recom mendations ............................................................................... 56
5.2.1 Survey Size ........................................................................................................................ 56
5.2.2 M ath M odel ...................................................................................................................... 56
5.2.3 R eserve Buoyancy....................................................................................................... 57
5.2.4 A dvanced T echnology ................................................................................................ 57
5.3 Closing.......................................................................................................................................58
References............................................................................................................................................59
Appendices .......................................................................................................................................... 60
Appendix A : D esign Spiral.......................................................................................................... 61
A ppendix B : SS D esign Flow chart .............................................................................................. 63
A ppendix C : M ath M odel..................................................................................................................65
Appendix D: Submarine Profile and Plan Drawings ............................................................... 79
A ppendix E: Submarine Shape Factors ...................................................................................... 90

5
 List of Figures

Figure 1: Group 1 Weight vs. Operating Depth......................................................................... 38

Figure 2: Weight Summary as Percentage of A-1........................................................................ 46
Figure 3: Weight Group Percentages of NSC Compared to Published SSK (5) .................... 48
Figure 4: Group 6 Trend Shown as Space per Man.................................................................... 50

6
 List of Tables

Table 1: Specific G ravity Typical Values....................................................................................... 16

Table 2: Weight/Space Relationship of Typical Diesel Submarines........................................17
Table 3: Submarine Weight Breakdown and Estimating........................................................... 36
Table 4: Group 4 Weight (from measured volume) as Percentage of NSC .............. 40
Table 5: Group 5 & 6 Weight Summary as Percentage of NSC ................................................... 41
Table 6: Published Dimensions of Selected Submarines.......................................................... 42
Table 7: Model Results Measure of Accuracy............................................................................. 44
Table 8: Math Model Submarine Characteristics Output........................................................... 45
Table 9: Weight Groups as Percentage of A-1............................................................................. 46
Table 10: W eight G roups/A-1 Variation..................................................................................... 47
Table 11: Weight Groups/A-1 Variation Without AGSS 569 ................................................ 47

7
1 Introduction

Several design concept papers, books and studies have been written on submarines but no

exclusively diesel submarine comparative naval architecture analyses have been published. A

comparative naval architecture analysis creates an opportunity to identify new technologies,

review the architectural characteristics best suited for submarine missions and to possibly

build more effective submarines. This study focuses on diesel submarine naval architecture

from the end of the nineteenth century to present day. Over that time period, several

significant technologies have vastly improved the capability of submarines. From the first

combination of gasoline engines and energy-storing batteries in the USS Holland, to the

development of the true diesel submarines of the first half of the twentieth century, to the

advent of nuclear propulsion and its adaptation to the submarine in the 1950s, and recently to

Air Independent Propulsion (AIP) systems, submarines have advanced to highly complex,

systems-intense machines.

The urgency of submarine development, as with other military systems, was driven by

the World Wars and Cold War, demanding improvements in acoustics, weaponry, safety,

automation and submerged endurance. In the years leading up to and during World War II,

over 1000 undersea boats and diesel submarines were built by Germany alone (1). During

periods of WWII, Germany was producing over 35 diesel submarines per month. In fact, the

total number of world submarines constructed during WVWII, not including Japan, was well

over 2500 (2). Although the focus was on rapid development and construction during WWI

and WWII, submarine designs improved, especially in weapons and communications systems.

With the advent of the Cold War and the need for longer submerged endurance, the focus

shifted to nuclear submarines, causing an explosion in submarine production over the next 30

8
years. From 1955 to 1989 the Soviet Union and United States alone built over 350 nuclear

submarines (3). From a high Cold War world count of 400 nuclear submarines in 1989, there

are only approximately 160 today, as nuclear submarine production has experienced a

significant slowdown worldwide (3). Building of nuclear submarines is limited to the United

States, Russia, England, France, India and China. In the US, the production rate of nuclear

submarines is only projected to be one per year over the next ten years.

While the nuclear submarine production rate has decreased recently, diesel submarine

production rate today is growing. There are about 400 diesel submarines in the world today.

Builders of diesel submarines include Sweden, Germany, Spain, Netherlands, France, Italy,

Russia, China, Japan, and Australia. The world diesel submarine production rate is predicted

to reach eight per year between 2004 and 2023 (4), which would increase the world diesel

submarine count above 500 in the next twenty years. Additionally these predicted diesels

possess advanced technology as evidenced by the spread of diesel electric with AIP systems.

With such systems, diesel submarines may be suitable for more than coastal defense type

missions and operate in more blue-water type scenarios.

Diesel submarine architecture seems quite similar at first glance from country to

country and mission to mission. The basic submarine shape includes ellipsoidal or parabolic

end caps, is either a hull of revolution or contains a parallel midbody in the center, and has

various appendages attached along the body. Generally, diesel submarine designs tend to be

of the single hull version, with a singular pressure hull over most of the midbody length and

outer hulls at the ends used to create the ballast tanks and provide a hydrodynamic fairing for

any other gear attached to the outside of the pressure hull. But, are there differences in the

naval architecture of diesel submarines? Can distinct differences be noted, even when

comparing two similar ships? Capability differences exist, such as propulsion, acoustic

9
performance, and weapons systems. Do these capability differences affect the naval

architect's approach to submarine design? What new construction techniques have been used

worldwide? What shipyards have been most effective/efficient in submarine design and

construction? How have submarine construction methods changed due to new shipyard

methods or technology?

This study attempts to answer the questions posed above. The information

researched and gathered was all collected from open literature and therefore is not technical

source data from countries or manufacturers. Due to this open literature approach, much of

the work was done by estimating volumes from drawings, pictures, similar submarine data

bases, and from previous work in references (5), (6) and (10). One distinct difference from

previous submarine comparative studies, as will be seen in chapter 3, is that standard

Expanded Ship Work Breakdown Structure (ESWBS) weight groups are determined for each

submarine included in the study and will be used throughout this report. These weight groups

are defined as follows:

Group 100 Hull Structure

Group 200 Propulsion Machinery
Group 300 Electric Plant
Group 400 Command and Surveillance
Group 500 Auxiliaries
Group 600 Outfit and Furnishings
Group 700 Weapons Systems

Furthermore, a method is proposed to calculate these weight groups for any submarine, based

on drawings, historical design databases and equations included in the appendices.

1.1 Purpose of the Study

The purpose of this study is twofold. First, it attempts to determine if diesel submarine

architecture varies from country to country. Do factors such as mission, cost, or tradition

10
affect submarine naval architecture? An in depth comparison is performed of six diesel

submarine designs from four different countries to measure and compare any differences that

may exist in their naval architecture. The outcome of these comparisons will also provide

some tools to current and future submarine designers, possibly to better assess the attributes

of a particular design.

Secondly, and perhaps more importantly for the author, a significant benefit in taking

on such a study is to gain a better understanding of submarine design and construction. In

order to determine if the submarine naval architecture differs from class to class and/or

country to country, one must be familiar with the submarine design process and terminology.

This understanding of submarine design will also provide possible advantages or spawn novel

concepts by future designers.

1.2 Problem

Submarine design is a complex engineering systems process. To start with a blank sheet of

paper and produce volumes and weights required for submarine design is a monumental task.

Similarly, to determine the basic weight groups that make up a completed submarine is no

easy task. Design in general begins with definition of requirements and progresses to

performance characteristics, to concept studies, to feasibility studies, and finally to achieving

the final level of detail for structure, arrangement, hydrodynamics, systems and hydrostatics

(5). The goal of the designer is to accurately estimate weight groups, so that a satisfactory

weight/buoyancy balance is attained. This study shares the goal of estimating submarine

weight groups but differs from initial design by starting with the finished product and working

"backwards" to accurately estimate the naval architectural characteristics that the submarine

designer used to create the initial design.

11
1.3 Background

Previous work was completed in this particular area by John K. Stenard, ComparativeNaval

Architecture ofModern Foreign Submarines, in May 1988 (10). That study included a comparative

design review of conventional and nuclear-powered fast attack submarines. Stenard's

significant contribution was the initial parameterization of diesel submarine data and the

development of equations to determine volume estimates for various submarines. As

mentioned this study differs from the previous work by actually calculating the standard

weight groups of diesel submarines, based both on hand-measured values from published

drawings and relationships developed with the assistance of several references as described in

subsequent chapters.

1.4 General Approach/Methodology

An open literature search was accomplished to find sufficient characteristics on a selected

number of submarines to provide a useful comparison. Submarine weight groups were

determined using measured volumes, developed equations, reference equations from previous

work, known submarine databases, and estimates to "reverse engineer" the design

characteristics of the submarine being studied. The weight group and naval architectural

results of the selected submarines were then compared and analyzed.

1.5 Criteria for Success

Two areas to measure success: 1) Is the reverse engineering method valid? Does it produce

accurate results?

2) Does the data produced allow for a relevant comparison of naval architecture of the various

platforms?

12
2 Submarine Design Process

2.1 Design History

Before proceeding to the analysis of comparative naval architecture, this chapter is devoted to

explaining the submarine concept design process. H.A. Jackson, R. Burcher and L. Rydill,

E.S. Arentzen and P. Mandel have written very comprehensive and technical descriptions

about submarine design history and methods. Rather than attempt to cover submarine design

to an equivalent level of detail, this chapter focuses on some key aspects of the design process,

that, once understood, will assist in the reverse engineering methodology of the study found in

subsequent chapters.

History is rich with attempts to design and build successful submarines; several such

designs were David Bushnell's Turtle in 1775, Robert Fulton's Nautilus in 1800 and John

Holland's Holland VI in 1899. The Holland V, built and tested in 1899 by the US Navy,

foreshadowed several significant design features like low length/diameter ratio, axisymmetric

circular form, single screw propeller and a small superstructure. These features have proven

effective in achieving near optimum configuration of a submarine (5). In all of these early

trials, the designers returned to the drawing boards many times to modify and improve their

designs, a practice still present today in the iterative methods to develop a reasonable design

that meets the design requirements.

2.2 Submarine Design

The most accurate one word description of submarine design is "iterative". Starting with a

definition of requirements, the designer creates a concept "cartoon" (a broad-brush

description of a possible design), proposes a set of estimates, works through many calculations

13
by computer or by hand in feasibility studies, and derives an answer which often does not

match the initial concept cartoon (6). The designer must then go back with new, more-

accurate assumptions, and rework the calculations. The new answer should be close but may

require further iterations. The process described can be summarized by the design spiral,

often used in US Navy ship designs, shown in Appendix A.

Due to the complexities of submarine design, a database of volume and weight

characteristics of previous designs is often used to obtain initial estimates. These estimates are

applied to the designer's initial submarine "cartoon". Using math models to parameterize the

design, feasibility studies are then performed to check the results against the owner's

requirements and mission areas. Next the process is iterated until the design balances, i.e.

where the buoyancy created by volume supports the weight of the submarine, and meets the

owner's requirements. Finally the selected feasibility study is developed to sufficient detail for

production drawings to be produced (5). Along with the design spiral, a flow chart shown in

Appendix B is used to visually illustrate a conventional diesel (SS) submarine design process.

2.3 Design Weight to Space Relationship

H.A. Jackson stated in a submarine design paper, "The volume of the hull of the submarine is

fixed by the weight of the submarine. If more volume is mandatory, it can only be provided

by making the submarine larger, but this will increase the amount of lead to be carried and

reduce the speed if the same power is provided. If the power is increased in order to meet the

speed requirements, the submarine will grow even larger. The skill and experience of the

designer is put to a crucial test in making a satisfactory design." (6) This statement is

representative of the interrelated character of submarine design where changes to one

14
parameter cause others to be adjusted and attempting to hold fixed any group of parameters is

most difficult.

But there are fixed external limits to the size of the submarine. For instance,

submarines have practical limits regarding diameter. Even when on the surface, as much as 90

percent of the submarine hull could be below the water surface. When considering a

submarine diameter of 30 feet, the maximum draft could be 27 feet, significantly more than

most surface ships. Although this draft would not present a problem in the open ocean, the

submarine draft may be too deep for many ports and harbors, as well as impact coastal

operations. Therefore the designer is limited to some practical limit of diameter, depending

on the port of operation and the desired submarine missions. This maximum hull diameter in

turn limits internal volume of the submarine.

Because of the limits on maximum diameter, the resulting limited hull volume of a

submarine, and the required strength of the hull to withstand submergence pressures at deep

depths, a significant amount of the designer's time and effort is devoted to the weight and

space relationship. Unlike surface ship designs, in which the total enclosed volume is greater

than the displacement, submarine designs start as "volume limited". This terminology of

volume limited is common in ship design and simply means that the designer must creatively

assess how to fit all of the structural and payload requirements into the volume of the hull.

Design books may also use the term "space driven". For now, consider the hull volume as the

limiting feature of design but as will be pointed out later, this limitation may change over the

course of the design process.

Hull volume determines several significant properties of a vessel. The volume of the

hull submerged compared to the total hull volume determines a vessel's reserve buoyancy

(RB), which is the amount of excess buoyancy available in the event of an emergency or

15
casualty which allows the sea to enter a portion of the submerged volume. A surface vessel

has an RB due to the freeboard of the main hull and any superstructure which is watertight.

The total volume of the vessel is larger than the volume underwater, i.e., the volume of water

displaced. A submarine that is completely submerged does not have a freeboard and therefore

does not have excess RB. The ratio of displaced volume to total volume can be used to

develop some characteristic properties of ships shown in the following ratio (5):

Ratio of the volume of displacement to the total volume = 1 (1)

1+ RB

Because the buoyancy of volume displaced must equal the weight of the vessel by Archimedes'

law,

1
= Specific gravity of the vessel relative to sea water, (2)
1+ RB

which provides a measure of the overall density of the vessel. Table 1 shows typical values of

specific gravity for surface ships and submarines.

Table 1: Specific Gravity Typical Values

Specific Gravity, Percentage of total

Ship 1 volume above
1+ RB waterline
Frigate 0.3 70
Aircraft Carrier 0.2 80
Bulk Carriers/Tankers 0.8 20
Surfaced Submarine 0.9 10
Submerged Submarine 1.0 0

From Table 1, the submerged submarine is therefore the densest of all marine vehicles.

Another useful comparison is the weight to space relationship for typical diesel submarines,

shown in Table 2 developed from reference (5).

16
 Table 2: Weight/Space Relationship of Typical Diesel Submarines

Component Weight Space Density Relative to

Percentage Percentage Seawater (unity)
Payload 9 28 < 1
Structure 43 *>> 1
Main and Auxiliary 35 56 < 1
Machinery
Accommodation and 4 11 < 1
Outfit
Stores 1 5 < 1
Permanent Ballast 8 > 1
* Structure and ballast take up relatively very little space

Table 2 may be used as a guide to densities by considering for each item the ratio of its weight

percentage to its space percentage as shown in the far right column. If this result is unity, the

item would be as dense as seawater, while the lower the ratio, the less dense the item (5). As

can be seen in Table 2, the high overall submarine density is not due to payload or cargo but

rather due to structure and the fact that in most cases the submarine needs to have a heavy

pressure hull structure to enable it to achieve owner-specified depth requirements.

As a result of the high density of submarine structures, the design may evolve into one

limited by weight rather than volume. The reason for transition from volume to weight

limited is because once the volume is set, according to the space required to enclose all of the

requirements, this volume must be able to support the weight of the submarine. In other

words, Archimedes' principle of buoyancy matching weight must be met. If excess weight is

present, buoyancy must be increased by expanding the volume, which in turn, causes weight

to increase. As can be imagined, this process of increasing weight and expanding volume may

soon exceed the size restrictions of the design. Unlike a surface ship, where a higher than

estimated weight only results in a deeper draft, the lack of RB in a submarine requires the

designer to increase size, as mentioned above, or reduce the amount of permanent ballast,

which could result in a reduction of hydrostatic stability (5). In addition, the potential volume

17
expansion has the effect of creating an upheaval in internal compartment arrangements and an

impact on many other aspects of design including structure, maneuvering and control, and

propulsion. Thus the criticality in submarine design of achieving accurate weight assessment

cannot be overstated.

2.4 Weight Estimates and Weight Groups

As seen in the section above, weight assessment is a tedious but critical portion of submarine

design. Without the use of weight data tables from previous designs, the work involved in

weight assessment would increase significantly. The goal of the weight estimating process is

developing design values for the weight groups of the submarine.

Parametric relations have been developed from previous submarine designs and are

very useful in developing the initial weight group values. These initial values can be adjusted

for the new requirements in refining the weight groups to a specific design. Once the revised

weight estimate is complete and the ship balances, i.e., the buoyancy supports the weight and

the ship balances longitudinally and transversely, the rest of the design process (per Appendix

B flowchart) can proceed.

2.5 Design Summaiy

This chapter has given a brief introduction to submarine design and will be referred to in

subsequent chapters as the dissection of submarine designs is carried out. The overall

submarine concept design is a complex systems engineering process which utilizes many

design tools to solve. Recall the starting point involved weight tables from previous designs,

parametric relations to calculate new values, and a concept "cartoon". There are many

requirements that may affect the volume and arrangement of the designer's concept

submarine. Some of these requirements are speed, crew size, endurance (both submerged and

18
surfaced), number of torpedo tubes, number of weapon stowage positions, cost constraints,

diving depth, special features such as lockout trunks or special warfare interfaces, and acoustic

performance or quieting. Additionally, the owner may place special emphasis on one specific

design factor, such as the acoustic performance over the other requirements.

The product of the concept design should provide initial weights, initial volumes,

initial hull shape, and a balanced ship. The concept design will then be analyzed under

feasibility studies, model testing and finally be refined to give sufficient detail for production

drawings (5).

19
3 Development of Procedure

3.1 Approach

The MathCAD computerized submarine synthesis tool entitled "MIT Math Model" was used

initially to gain understanding of the submarine design process (11). This math model was

developed at MIT, based on the submarine design process described in chapter 2 and draws

heavily on notes from CAPT Harry Jackson's MIT Professional Summer Course "Submanne

Design Trends" (9). The use of computerized mathematical software with adequate

mathematical solving capability allows the designer to proceed quickly and efficiently through

the complex design process.

For the study of existing submarines, the MIT math model was modified,

incorporating several of the parametric equations from reference (9), to determine standard

weight groups starting from open literature submarine drawings. As stated in section 1.2, the

method used in this comparative naval architecture analysis of existing submarines starts at the

opposite end of the design spiral from that of traditional submarine design. In other words,

traditional submarine design begins with design requirements and ends with a finished

submarine; this study starts with the finished submarine, measures the major areas and

volumes, estimates the standard weight groups and draws conclusions from those naval

architectural characteristics.

3.2 Procedure Description

The evaluation procedure consists of working backwards through submarine concept design

and reverse engineering diesel submarine weight groups and naval architecture from the open

literature, available drawings, and photographs. The author's goal was to develop a procedure

20
to determine submarine characteristics that allow reasonable estimates to be made of

submarine weight groups from the open literature information. Two approaches were utilized

in order to draw accuracy comparisons from the set of results: 1) Dimensions were obtained

from inboard profile and plan drawings that were then used to calculate volumes based on

geometric equations; and, 2) Parametric equations were developed from historical designs and

other references which were then used to calculate volumes and weight groups.

3.2.1 Submarines Selected for Analysis

This study compares diesel to diesel submarines, all of axisymmetric shape and single pressure

hull design. A brief description is given below for each submarine studied, with a full

description including pictures and drawings in Appendix D.

21
SS 580 USS Barbel

Surface Displacement: 2146 Ltons

Submerged Displacement: 2639 Ltons

Length: 67 m

Diameter: 8.8 m

Complement: 77 (8 officers)

Electrical Generator Capacity: 1700 KW

Propulsion Motor Power: 4800 SHP

Maximum Surfaced Speed: 14 Kts

Maximum Submerged Speed: 18 Kts

Diving Depth: 213 m

Overall Endurance Range: 14,000 Nm

Deployment Endurance: 90 Days

Torpedo Tubes: 6

Torpedo Capacity: 18

Builder: Portsmouth Naval Shipyard

Year: 1959

Other: Decommissioned 1989

22
AGSS 569 USS Albacore

Surface Displacement: 1692 Ltons

Submerged Displacement: 1908 Ltons

Length: 63 m

Diameter: 8.4 m

Complement: 52 (5 officers)

Electrical Generator Capacity: 1634 KW

Propulsion Motor Power: 7500 SHP

Maximum Surfaced Speed: 25 Kts

Maximum Submerged Speed: 33 Kts

Diving Depth: 183 m

Overall Endurance Range: 10,000 Nm

Deployment Endurance: 50 Days

Torpedo Tubes: 0

Torpedo Capacity: 0

Builder: Portsmouth Naval Shipyard

Year: 1953

Other: Experimental submarine; Decommissioned 1972

23
Type 209/1200

Surface Displacement: 1100 Ltons

Submerged Displacement: 1285 Ltons

Length: 56 m

Diameter 6.2 m

Complement: 33 (6 officers)

Electrical Generator Capacity: 2800 KW

Propulsion Motor Power: 4600 SHP

Maximum Surfaced Speed: 11 Kts

Maximum Submerged Speed: 22 Kts

Diving Depth: 250 m

Overall Endurance Range: 7,500 Nm

Deployment Endurance: 50 Days

Torpedo Tubes: 8

Torpedo Capacity: 14

Builder: Howaldtswerke-Deutsche Werft GmbH (HDW)

Year: 1993

Number of ships: 9 (one built at HDW, remaining in South Korea)

Other: Possible AIP Backfit

24
Collins 471

Surface Displacement: 3050 Ltons

Submerged Displacement: 3350 Ltons

Length: 78 m

Diameter: 7.8 m

Complement: 42 (6 officers)

Electrical Generator Capacity: 4420 KW

Propulsion Motor Power: 7344 SHP

Maximum Surfaced Speed: 10 Kts

Maximum Submerged Speed: 20 Kts

Diving Depth: 300 m

Overall Endurance Range: 11,500 Nm

Deployment Endurance: 70 Days

Torpedo Tubes: 6

Torpedo Capacity: 22

Builder: Australian Submarine Corp, Adelaide

Year: 1996

Number of ships: 6

Other: Kockums' Design

25
Type 212A

Surface Displacement: 1450 Ltons

Submerged Displacement: 1830 Ltons

Length: 56 m

Diameter: 7m

Complement: 27 (8 officers)

Electrical Generator Capacity: 3120 KW

Propulsion Motor Power: 3875 SHP

Maximum Surfaced Speed: 12 Kts

Maximum Submerged Speed: 20 Kts

Diving Depth: 350 m

Overall Endurance Range: 8,000 Nm

Deployment Endurance: 60 Days

Torpedo Tubes: 6

Torpedo Capacity: 12

Builder: Howaldtswerke-Deutsche Werft GmbH (HDW)

Year: 2004

Number of ships: 4

Other: Siemens PEM 306 KW Fuel Cell

26
IZAR S80/ P650

Surface Displacement: 1744 Ltons

Submerged Displacement: 1922 Ltons

Length: 67 m

Diameter: 6.6 m

Complement: 40 (8 officers)

Electrical Generator Capacity 2805 KW

Propulsion Motor Power: 4694 SHP

Maximum Surfaced Speed: 12 Kts

Maximum Submerged Speed: 20 Kts

Diving Depth: 350 m

Overall Endurance Range: 7,500 Nm

Deployment Endurance: 70 Days

Torpedo Tubes: 6

Torpedo Capacity: 18

Builder: IZAR, Cartegena Spain

Year: 2007

Number of ships: 4 (plus 4 as an option)

Other: MESMA AIP 600kW Fuel Cell

27
3.2.2 Math Model Development

Characteristics

Several data files were created in Excel to provide the necessary submarine characteristics to

MathCAD. An open literature search was performed to gather sufficient data on selected

submarines to input into the Excel files. Submarine characteristics such as normal surfaced

condition (NSC), submerged displacement (Aub), length overall (LOA) and diameter (D) were

read into MathCAD using an Excel read file function of MathCAD. Then each

characteristic was assigned a descriptive variable name within the math model, such as NSC(i)

where the 'i' identifies the specific submarine. These variables were then used in a simple

iteration loop within MathCAD to calculate the results described below for each submarine.

The MathCAD model file is included in Appendix C.

Volume Calculations

Inherent relationships exist between the volume and the weight of an ocean vessel.

Archimedes showed that in order for a body to be neutrally buoyant, the weight of the volume

of water displaced must equal the weight of the body. A goal of the submarine designer is to

design the submarine to be neutrally buoyant when submerged. Therefore, by measuring

volumes of a submarine, the weight of the vessel and that of the individual weight groups can

be calculated. The procedure of volume measurements and subsequent weight estimation is

the basis from which the final weight groups are derived. But first, the volumes of each major

weight division are needed.

As stated, the study was limited to information available in open literature drawings,

published submarine characteristics, and photographs. This limitation ensured the report

would remain unclassified and provided some useful parametric equations which may be used

28
in future diesel submarine analyses. The goal of the literature search was to obtain detailed

inboard profile and internal deck plan view drawings. However, locating detailed scaled

drawings in the open literature was not always possible, so a range of published drawings was

used (as shown in Appendix D). Information sources ranged from historical records

maintained in the MIT Naval Construction and Engineering library to internet websites to

foreign shipbuilding company presentations on submarine designs. Scales of drawings were

not available. Basic characteristics such as LOA and D are available in a variety of resources,

and from these published dimensions along with the drawing measurements, a scale was

determined from which to calculate the full size dimensions.

Areas of the major submarine spaces were then calculated and entered into MathCAD,

where deck height, a hull curvature factor and passageway factor were applied to calculate the

space volume. The hull curvature and passageway factors were obtained from parametric

diesel electric submarine data of reference (11). All diesel submarines included for analysis

contained only two compartments: 1) Engineroom (ER); and, 2) Operations (OPS). The

overall method for calculating volume is summarized in the following steps:

* Measure the deck area for the following spaces

" Command, Control, Communications, and Intelligence Functions

* Propulsion Machinery and Battery Spaces

* Motor Generators and Electrical Switchboards

" Auxiliary Machinery Spaces

* Berthing and Messing Spaces

* Storerooms

* Offices, Lockers, Laundry and Activity Spaces

29
 " Armament/Weapons Spaces

" Tanks

" Multiply deck area by deck height

" Apply factors for hull curvature and passageway from reference (9)

The following calculation provides an example of the basic procedure for a major

space.

A wep (0) = 77.331_m2

HDwep (0) = 3.934m

fCurve 1.12

fPway 1.08

Vwep(i)= IDwep(i)'Pway'fCurve-Awep(i)

Vwep(O) = 367.973_m3

Some compartments and spaces were not clearly shown in open-literature drawings.

For example, variable ballast tank measurements were not included in the drawings used.

Where accurate measurements, or even estimated measurements, could not be obtained,

parametric equations relying on historical databases and those developed by Jackson in

reference (9) were used. Several of the parametric equations base the volume calculation on

percentages of total pressure hull (PH) volume, which required an accurate estimate of the

pressure hull volume (Vs). This volume was calculated using offsets of a body of revolution,

as presented in Submarine Concept Design (7). These calculations are shown in the

MathCAD model printout of Appendix C. The method used to determine each major

compartment area and volume is described in the next section.

30
3.2.2.1 Major Compartment and Space Calculations

Engineroom

Propulsion machinery, motor generators, aft battery (except BarbelandAlbacore), and

electrical switchboard areas were summed to obtain total ER area, which was then used as in

the example above to calculate ER volume. Although most diesel submarines have both

forward and aft batteries, the location of these batteries may not be divided between the

forward (OPS) and aft (ER) compartments. In older diesel submarines such as Barbeland

Albacore, both forward and aft batteries are contained in the OPS compartment. More recent

foreign diesel submarines locate the aft battery in the ER and the forward battery in the OPS

compartment. Therefore the ER volume equations differ for older US and foreign modern

diesel submarines.

OPS Compartment

OPS Compartment area was calculated by adding the deck areas for Command and

Control, Auxiliaries, Berthing and Messing, Storerooms, Forward Battery (and aft battery for

BarbelandAlbacore), Weapons and Other Spaces (offices, lounges, etc.). This area was

converted to a volume as in the example above and designated as OPS volume measured

(VOP,). Then from the VpH calculation, equations (3) and (4) from reference (9) were used to

find auxiliary tank and variable load volumes, which were then added to the V., above to

yield the total V,,, as in equation (5).

Vaux(i) = 0.041VpH(i) + .529an3- NT(i)

NT(i) = Complement

VVB(i) = 0.064VpH(i) (4)

V0ps(i) = Vopsm(i) + Vaux(i) + VVB ) (5)

31
Outboard Volume and Sonar Array

All items outboard of the pressure hull but within the outer shell, such as air flasks,

access trunks and fuel tank structure that displace water are considered outboard volume

(Vob). Due to the difficulty of measuring such items, generally absent from open literature

drawings, their volume is estimated as a percentage of pressure hull volume, based on

reference (9). Where major items such as bow sonar arrays are shown and have measurable

dimensions, their volume is calculated. For all submarines studied, the bow sonar array was

cylindrical, so calculating sonar array volume (V) was accomplished using the equation for a

cylinder.

Sonar Dome Water

The water in the space around the sonar array would typically be given in new designs

and may be easily estimated for sonar ipheres based on historical data. To estimate the

gyindricalsonar array space water volume, measurements were taken of the submarines studied

and a factor of multiplication was determined for the array space volume. The general

conclusion was that sonar space water for a cylindrical array was significantly less than for a

spherical array and in fact some sonar spaces may actually be free flood areas. To be

consistent, the submarines in the study were assumed to contain a certain volume of dome

water (Vd) surrounding the sonar array which was not counted as free flood.

Everbuoyant Volume

The everbuoyant volume (Veb) is comprised of the pressure hull, the outboard items

and sonar systems. Summing the volumes and multiplying by sea water density provides the

everbuoyant displacement (Aeb).

Veb = VPH + Vob + Vsa + Vd (6)

32
Aebr = Veb-P SW (7)

In a balanced ship, Aeb is equal to NSC. These two values are compared as a check of model

validation and can be viewed in Appendix C.

Main Ballast Tank (MBT) Volume

The difference in Asub and NSC is equal to the MBT displacement. Multiplying by the

factor 35 ft /lton yields the MBT volume. Another method used in submarine design to

estimate MBT volume is to multiply the NSC by the reserve buoyancy (RB), which is specified

in the owner's requirements. Because the RB was not available in the open literature, MBT

volume was calculated from the given NSC and Aub.

Submerged Volume

Submerged displacement (A,,Sb) is a given characteristic in open literature sources.

Assuming the source to be accurate allows a validity check of the calculations and

measurements used to this point by using the fact that A,,b is equal to the sum of Aeb and MBT

displacement.

Asub = Ab + MBT (8)

Free Flood (ff)

As the name implies, free flood volume encompasses all those areas that are open to

the ingress and egress of water within the outer shell of a submarine. Areas such as the sail,

superstructure, "mud tank" (area surrounding the shaft exit from the hull), appendages, and

torpedo tube shutter doors, among a few others, make up the free flood volume. A value of

four to seven percent of the envelope volume for single hull submarines is given to calculate

free flood volume in reference (9). Seven percent was used for this study because it produced

the minimum error when cross checks were done.

33
Envelope Displacement

The entire volume enclosed by the outer shell of the submarine is called the envelope.

Therefore, envelope displacement is the sum of submerged and free flood displacement.

Using the estimate from above that free flood is seven percent of An, the following

relationships can be expressed:

Aenv Af
.ASb+ (9)

Aff= 0.0 7 * A.v (10)

Therefore, Anv = Ab + 0.07 * Anv (11)

and Aenv = Asub/0.93 (12)

Envelope displacement is the final displacement value not including the sail and

appendages such as rudder and control planes. Estimating volumes of such appendages is

tedious and their contribution to the overall displacement is generally quite small. During

initial design, these values may or may not be included, as long as the convention is consistent

throughout the hull design (9). Therefore, appendage volumes were not included in this

study. After obtaining required volumes and displacements, the next step is calculating the

submarine weight groups.

3.2.2.2 Area and Volume Calculation Error Checks

For comparison purposes, parametric equations from reference (9) were used to calculate

certain areas, as would be done in initial design. These areas were then compared to the

measured areas for a check of parametric equations. For individual spaces, the majority of

parametric area and volume equation results did not match the measured areas and volumes

with any consistent level of error.

34
 However the difference between whole-boat volumes of parametric results and the

calculated volumes based on measured whole-boat dimensions were all within twenty percent.

This difference in the individual volumes but not the overall sum indicates a possible

difference in designations of certain spaces, inconsistencies in area measurements from

inaccurate drawings or a combination of these. Rather than attempt to revise the detailed

measurements or modify the parametric equations, the results were left as calculated,

accepting a threshold error of twenty percent with a goal of ten percent comparison errors.

Section V of the math model in Appendix C contains a summary of calculation error checks.

3.2.3 Weight Group Calculations

Weight Definitions

Standard weight groups were presented in section 1. The standard weight groups summed

together account for a weight condition called A-1:

Group 100 Hull Structure

Group 200 Propulsion Machinery
Group 300 Electric Plant
Group 400 Command and Surveillance
Group 500 Auxiliaries
Group 600 Outfit and Furnishings
Group 700 Weapons Systems
Total Condition A-1

Table 3 provides a summary of the weight breakdown of submarines and what each group is

dependent upon.

35
 Table 3: Submarine Weight Breakdown and Estimating

Group Number Name Function of

1 Hull Structure NSC

2 Propulsion Machinery SHP & Battery Volume
3 Electric Plant KW
4 Command and Surveillance NSC
5 Auxiliaries NSC
6 Outfit and Furnishings NSC
7 Weapons Systems V,
A-1 Z (1-7) Weight Groups
Lead Ballast A-1
A Z (A-1 + Lead)
VL Variable Load NSC
NSC Z (A + VL)
MBT Main Ballast Tanks
Asub Z (MBT + NSC)
FF Free Flood
Aenv Y (A,, + FF)

Adding the lead ballast to condition A-1 results in condition A (also known as the standard

displacement of the Washington Treaty) (6). To condition A is added the variable load (VL),

which is the combination of all the weights that can change from day to day plus the variable

ballast required for the submarine to remain in equilibrium, and this sum of condition A and

VL is the NSC.

In order to submerge, weight must be added to the submarine, which is done by filling

large MBTs external to the pressure hull with water from sea. The result of NSC and MBT

weight as shown in section 3.2.2 above is the submerged displacement (Aub). Then adding the

FF to Asb yields the A., as shown in Table 3.

36
Weight Estimation

As stated, the overall goal of this study is to compare the naval architecture of selected

submarines. The weight groups can be considered the basic building blocks of submarine

architecture. Therefore developing accurate estimates of weight groups is the primary goal of

the math model. Of course the most accurate method would be to add the known individual

weights of all material and equipment (i.e., frames, steel plates, cabinets, etc.) that made up

each group. However, even in initial concept design, the material and equipment weights

must be estimated and such weights are definitely not listed in the open literature of diesel

submarines. A much more detailed time consuming search could be performed, gathering

information from vendors, shipping companies and experts in the submarine design field, but

the lack of complete and accurate weight information in open literature sources would still

require making some estimates. Model validation with acceptable error levels is explained in

section 3.4.

This study includes a hybrid method of estimating weights. The first step is taking

measurements of areas and computing volumes of the major compartment groups. Then

these volumes are used in parametric equations developed from a combination of references

(6) and (9) along with historical databases. The actual weight group breakdown was known

for at least one submarine included in the study, the USS Barbel. Using the known values for

Barbel, the parametric relationships were checked for validity and in some cases parametric

equations from reference (6) for nuclear submarines were adjusted for use with diesel

submarines.

37
Parametric Weight Estimates

Group 1 Hull Structure

Reference (6) contains a parametric relationship based on NSC and hull material.

Whereas many of the reference (6) relationships are based on nuclear submarine databases,

group 1 (GR 1) weight is less dependent on type of propulsion system and more dependent

on diving depth, NSC and hull material. Using Figure 1 from reference (6), a factor of GR 1

to NSC weight is determined and equation (13) is used to estimate GR 1 weight.

WI est = W IfracNSC (13)

25 - - ---- -
-

20

Q Good Design Range

S15
Q.
4)

10

0 ------------
-

0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50

%ofNSC

Figure 1: Group 1 Weight vs. Operating Depth

38
 Group 2 Propulsion Machinery and Group 3 Electric Plant

As shown in Table 3, Weight Groups 2 and 3 are functions of SHP and KW,

respectively. In a diesel submarine, both weight groups 2 and 3 are also functions of battery

volume. However, to avoid double counting the battery volume, it was only included in the

GR 2 parametric relationship. Although both Barbeland Albacore designs are over 50 years

old, the study assumes that power densities have not changed significantly because diesel

engines and lead acid batteries are still in use. If future submarines use new types of engines

or new batteries, a different parametric equation would have to be developed.

To determine GR 2 alone, a parametric equation was developed from the known

propulsion weights of Barbeland Albacore. Battery volumes were measured from drawings and

equation (14) was developed:

Iton Iton
West = 1.759
W~et3 hp -SHP
.VBat + 0.005-
m (14)

VBat = BatteryVolume

To determine GR 3, equation (15), a factor was again determined from Barbel known

weight groups and electric plant generating capacity in KW.

W3est K3-KWi (15)

K3= 0.0126-
kW

KWi = KWinstalled

Group 4 Command and Surveillance

The estimation of GR 4 weight is complicated; technology of the equipment that

makes up the group is rapidly changing and the magnitude of the group strongly depends on

the submarine's mission (9). Mission components that make up the group weight include

39
 .........
. ...........

navigation, sonar, fire control and radar systems. To initially calculate this weight group, the

volume of command and control (including all navigation, sonar, fire control and radar areas)

was converted to displacement in Ltons and then compared to NSC. Results are shown

below in Table 4.

Table 4: Group 4 Weight (from measured volume) as Percentage of NSC

SS 580 AGSS 569 209 471 212A P 650

GR 4 as Wcc/NSC 6.3% 8.2% 6.2% 6.8% 8.7% 9.2%
GR 4 Weight (Ltons) 134.7 138.8 67.8 207.0 125.9 161.0

The percentages of GR 4 to NSC and the GR 4 weights in Table 4 are higher than

expected. The GR 4 weight from Table 4 is greater than 30 percent higher than the published

GR 4 weight for Barbel of 48.8 Ltons. This error may be due to inaccurate drawings or

counting all of the arrangeable volume in addition to that taken up by equipment. In order to

obtain GR 4 weights more consistent with expected GR 4 weights, the general formula for

GR 4 weight estimate from reference (9) of 4.2 percent of NSC, equation (16) was used for all

submarines studied.

W4est = NSC-0.042 (16)

Group 5 Auxiliaries and Group 6 Oudit and Furnishings

Similar to GR 4, the weights of groups 5 and 6 are proportional to the total weight of

the submarine (9). As noted with the initial attempt to calculate GR 4 weight from volume

measurements, GR 5 and 6 weights calculated from volume measurements were unexpectedly

high. Therefore another method had to be used. In new submarine designs, a database of

historical percentages for GR 5 and 6 is used to obtain the approximate percentage of NSC.

Because a database of recent diesel submarines was not available, a database of US diesel

submarines was used. Table 5 contains GR 5 and 6 weights as a percentage of NSC for four

40
US diesel submarines. The average percentages are used in equations (17) and (18) as an initial

estimate of GR 5 and 6 weights for the submarines studied.

W5est = W5frac-NSC (17)

W6est = W6frac NSC (18)

Table 5: Group 5 & 6 Weight Summary as Percentage of NSC

Submarine
Group A B C D AVG
5 5.66% 8.72% 9.12% 7.20% 7.67%
6 3.52% 2.99% 3.21% 4.13% 3.46%

Group 7 Weapons Systems

Weapons systems weight depends on the volume of the weapons spaces, the number

of torpedo tubes and handling systems. The following parametric equation (19) was modified

from reference (10):

W7est = 0.002ton -Vwep + TT-6

ft3 (19)

TT = Torpedo-tubes

Lead and Variable Load (VL)

Lead is used as permanent ballast in diesel submarines. For a diesel of axisymmetric

form and single hull configuration, eight percent of standard displacement (condition A) is

generally allocated to permanent ballast (5). Therefore lead ballast will make up 8.7 percent of

condition A-I as shown below.

A-1 + Pb = A (20)

Pb = 0.08*A

A = 12.5*Pb (21)

41
Substituting (21) into (20) yields: Pb = 0.087*A-1

VL includes fluid and gas stowage (auxiliary loads), storerooms, personnel, weapons

and variable ballast (9). It can be calculated as a percentage of NSC. To determine the

fraction for this study, the percentages of NSC were calculated for auxiliary loads and variable

ballast volumes. Storerooms, personnel and weapons were included in these percentages and

not identified individually. For all submarines studied, average percentages of NSC for

auxiliary loads and variable ballast were five and six percent, respectively. Therefore, adding

these averages yielded eleven percent of NSC for VL estimates.

WVL frac= 0.11

WVL(i) = WVLfradNSCi) (22)

Finally, knowing the weight group, lead and VL estimates allows the NSC and Aub to

be calculated and compared to published values of NSC and A,. The analysis process is

described in the next sections.

3.3 OverallAnalysis Process

From the six selected submarines presented in section 3.2.1, the published dimensions are

shown again in Table 6 below.

Table 6: Published Dimensions of Selected Submarines

Albacore Type 209 Collins' IZAR

ClassBarbel
AGSS 569 ] / 1200 471 Type 212A S80/P650
Displacement Surf 2145.7 1692 1100 3050 1450 1744
Ltons Subm 2639.2 1908 1285 3350 1830 1922
LOA m 66.8 62.6 56 77.8 56 67
Diameter m NNM 8.8 8.4 6.2 7.8 J 7 6.6

42
Manual measurements were taken from the open literature drawings. Then using these

dimensions along with published properties such as surfaced and submerged displacement, the

calculations in section 3.2 above were completed. The MathCAD model results were output

to tables where the results could be easily compared. The calculated characteristics and

comparisons will be discussed in chapter 4.

3.4 Validation ofModel Outputs

Two methods were used to validate the results of the method used to derive naval architecture

characteristics in this study. First, if the actual weight group values are known for a particular

submarine, the calculated weight groups can be compared directly to the known values. The

actual weight groups are known for the Barbelandthe Albacore, so their model weight group

estimates and published weight group values are compared directly to obtain a measure of

accuracy.

For cases where the actual weight groups are not known, a measure of accuracy can

still be performed by comparing the model results of NSC and A,,b with the published values

of NSC and Asub. Additionally, model results of A-1 and envelope displacement can be

compared with derived values of A-1 and envelope displacement. The envelope displacement

accuracy check is shown below. Equation (23) relies only on LOA, D, and a shape factor K1,

which is described following the equation.

x.D3 Iton. LOA- I

env 140 ft3 D (23)

i f = Entrancefactor Cyf = forwardprismaticcoefficient

'1 a = Run-factor Cpa = after-prismatic-coefficient

43
 .1 - alllluu
n1111M11n11111mn111111M1111mu
millilio
unlilll"""
"""""""" """"
"""

KI= 6 - 2.4Cp - 3.6-Cpa (24)

KI = shapecoefficient

Cpf and C, are calculated from the hull offsets, determined by the published LOA, D and

measured length forward and aft. Therefore the only unknowns in equation (23) are the shape

factors of the ends, r9 and 'q,, the entrance and the run, respectively. A fairly accurate

estimate may be made of rj and rl from Figure 18 in Appendix E (9). The envelope

displacement from equation (23) is then compared to that calculated in section 3.2 from area

measurements.

The cross checking of model output as a measure of accuracy is shown in Table 7.

The goal was to obtain differences within ten percent, with a threshold of fifteen percent.

Refined measurements could be made to further reduce the error but the accuracies attained

are considered sufficient for the comparative study to follow.

Table 7: Model Results Measure of Accuracy

SUBMARINES
Parameter SS 580 AGSS 59__ 209 _471 212A P 650
1664 1403 896 2351 1198 1316
1757 1385 901 2497 1187 1428
Error -6% 1% 0% -6% 1% -8%
Surfaced Dispi. Published 2146 1692 1100 3050 1450 1744
1961 1686 1084 3145 1457 1570
Error 9% 0% 1% -3% 0% 10%
-Subm ered, Disl Pubished 12639 1908 1285 3350 1830 1922
2461 1868 1394 3409 1731 1916
Error 7% 2% -9% -2% 5% 0%

2838 2052 1382 3602 1968 2067

2778 2248 1375 3154 1699 1861

Error 2% -10% 0% 12% 14% 10%

44
 .. ..... .....
.........

4 Comparative Naval Architecture

Data results are first compared on the basis of individual weight groups. Then the effects of

differences in naval architecture are analyzed for factors of mission and cost in section 4.3.

4.1 Data Presentation

From the calculations of chapter 3, the math model output is presented in Table 8.

Table 8: Math Model Submarine Characteristics Output

Weight Breakdown SUBMARINES

(Ltons unless
noted) SS 580 AGSS 569 209 471 212A P 650
GR 1 826.1 651.4 423.5 1174.3 558.3 671.4
GR2 426.0 471.5 212.5 600.7 328.1 279.2
GR3 21.4 20.6 35.3 55.7 39.3 35.3
GR 4 90.1 71.1 46.2 128.1 60.9 73.2
GR 5 164.6 129.8 84.4 244.0 111.2 133.8
GR 6 74.2 58.5 38.1 91.5 50.2 60.3
GR 7 62.0 0.0 56.3 56.8 50.4 63.0
A-1 1664.4 1402.9 896.2 2351.1 1198.3 1316.4
Parametric A-1 1756.8 1385.4 900.6 2497.2 1187.2 1427.9
Var Load 236.0 186.1 121.0 335.5 159.5 191.8
RB (%) 25% 13% 15% 10% 28% 10%
Surfaced Displ 1960.8 1685.7 1084.1 3145.4 1456.6 1569.7
MBT Displ 499.9 182.5 310.2 264.0 274.7 346.7
MBT Vol (M) 489.1 214.1 183.4 297.3 376.6 176.4
Vol PH (M) 1742.4 1457.4 1059.7 2477.5 1179.5 1518.1
3
Veb (M ) 1962.1 1646.9 1205.5 3098.9 1348.0 1732.6
Submerged Displ 2460.7 1868.2 1394.3 3409.4 1731.3 1916.4
Free Flood 185.2 140.6 104.9 256.6 130.3 144.2
Env Displ 2645.9 2008.8 1499.2 3666.0 1861.6 2060.7
Env Dispi
(parametric eqn) 2777.9 2247.7 1375.2 3153.8 1698.6 1860.9

The output in Table 8 is difficult to compare without normalizing or relating each individual

weight as a percentage of an overall weight. Therefore a closer examination is made of the

45
weight groups as a percentage of A-1. Table 9 and Figure 2 show the results for the

submarines studied.

Table 9: Weight Groups as Percentage of A-1

SUBMARINES
Weight SS 580 AGSS 569 209 471 212A P 650
Breakdown
GR 1 49.6% 46.4% 47.3% 49.9% 46.6% 51.0%
GR 2 25.6% 33.6% 23.7% 25.6% 27.4% 21.2%
GR 3 1.3% 1.5% 3.9% 2.4% 3.3% 2.7%
GR 4 5.4% 5.1% 5.2% 5.4% 5.1% 5.6%
GR 5 9.9% 9.3% 9.4% 10.4% 9.3% 10.2%
GR 6 4.5% 4.2% 4.2% 3.9% 4.2% 4.6%
GR 7 3.7% 0.0% 6.3% 2.4% 4.2% 4.8%
A-1 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

100% GR 7
GR 6

GR 4
75% .3
-

GR
C
50%
C-
C
0
iR 1
25%
-

0% 4-
SS 580 AGSS 569 209 471 212A P 650
Submarines

Figure 2: Weight Summary as Percentage of A-1

46
The mean and standard deviation of the weight group percentages is shown in Table 10.

Table 10: Weight Groups/A-1 Variation

Weight Breakdown Mean St Dev

GR 1 48.5% 2.0%
GR 2 26.2% 4.2%
GR 3 2.5% 1.0%
GR 4 5.3% 0.2%
GR 5 9.7% 0.5%
GR 6 4.3% 0.2%
GR 7 3.6% 2.2%

GR 2, and 7 have standard deviations greater than two percent. All group percentage

variations over the submarines studied are dependent on the accuracy of the model-output A-

1. Recall from Table 7 in section 3.4 that errors in A-1 varied from one to six percent.

However, there is an added explanation for GR 2 and 7 standard deviations of 4.2 and 2.2

percent, respectively. AGSS 569 had a relatively large percentage (33.6 percent) devoted to

GR 2 because it was an experimental ship built for speed. Additionally, AGSS 569 was built

without armament and therefore has a GR 7 percentage of zero. Table 11 shows the mean

and standard deviation without the AGSS 569 outlier values.

Table 11: Weight Groups/A-1 Variation Without AGSS 569

Weight Breakdown Mean St Dev

GR 1 48.9% 1.9%
GR 2 24.7% 2.3%
GR 3 2.7% 1.0%
GR 4 5.3% 0.2%
GR 5 9.8% 0.5%
GR 6 4.3% 0.3%
GR7 4.3% 1.4%

Another observation of the small deviations in weight group percentages is that all the weight

groups are calculated from the same model, using the same parametric relationships.

47
However, the parametric relationships were developed with the aid of measured areas

converted to volumes of compartments and therefore do not degrade the accuracy of the

results. As further proof of this point, compare the weight group percentages of NSC with

published design norms for diesel submarine design from reference (5), shown below in

Figure 3. The published values are shown in the center of the figure.

100%

GR 7
GR 6
75% GR 5
-

GR 4
GR 3

GR 2
50%

25%- GRI

0%-
SS 580 AGSS 569 209 Published 471 212A P 650
SSK
Submarines

Figure 3: Weight Group Percentages of NSC Compared to Published SSK (5)

48
4.2 Analysis ofResults

4.2.1 Historical Trends

As the submarines spanned a large number of years, an historical perspective can be examined

in weight group 3, electrical systems. SS 580 and AGSS 569 both have GR 3 percentages

below 1.5% while later submarines reach nearly 4%. This growth in GR 3 can be attributed to

the increased number of electrical components onboard, requiring a greater generator kW

capacity. Possible explanations in this growth include: 1) equipment functions once

performed with hydraulics or air systems are now performed with electrical-driven motors or

actuators; 2) computer-based system increase in fire control, radar, radio, navigation and

sonar.

Going beyond the standard weight group comparison, GR 6 weight (outfit and

furnishing) can be analyzed from the perspective of space per man. GR 6 percentages have a

mean of 4.3 percent and standard deviation of 0.2 percent over the selected submarines. The

interesting aspect of GR 6 constancy is that the overall number of crewmembers has

decreased on diesel submarines. Using the equivalent volume from the GR 6 weight output

and the complement, space per man (m3) was calculated and plotted for the corresponding

year of commissioning in Figure 4.

49
 ............. .....
. ....... .........
.. --- --------

FP650

S 569

s s58(

1950 1970 1990 2010

Year

Figure 4: Group 6 Trend Shown as Space per Man

There are at least two possible explanations for this result: 1) the living accommodations per

man have steadily increased from 1950 to present day; 2) furnishings such as lounge and

recreation areas have increased on board, so the space is not only allocated to people but to

furniture as well. Additional data would be necessary to determine the actual use of the

increased volume per man.

4.2.2 Mission Effects

Mission effects on naval architecture are evident in the GR 2 and GR 7 results of AGSS 569

explained in section 4.1 above. The AGSS 569 was designed as an experimental platform,

50
with a hull of revolution or "teardrop" shape, smaller appendages and no weapons systems, all

of which clearly affect the respective weight groups.

Additionally, an apparent distinction in individual comparisons is seen in GR 7 results

of the remaining submarines. The Type 209 weight percentage of 6.3 percent, greater than

any other submarine, is due to the increased number of torpedo tubes in the 209. A possible

consequence is a reduction of RB of 15 percent in the Type 209, compared to its most similar

hull class, the Type 212A which has a RB of 28 percent. The hull dimensions of the two hulls

are similar but more volume was taken up by mission-related functions in the Type 209,

leaving less volume for MBTs and therefore smaller RB.

This relatively large RB for Type 212A is unexpected. Most US submarines have RB

values between ten and twelve percent, so a value twice that stands out. Possible reasons and

future recommendations will be discussed in chapter 5.

4.2.3 Construction Effects

The leading submarine manufacturer is Thyssen Nordseewerke (HDW/TNSW), the newly-

formed combination of long-time manufacturers Howaldtswerke-Deutsche Werft GmbH

(HDW) of Kiel and Emden, Germany and Kockums of Karlskrona, Sweden. France operates

Direction Construction National (DCN) and competes with TNSW for competing submarine

contracts. Spain has recently started building submarines at Cartegena under the manufacturer

IZAR, in collaboration with DCN. Other European countries building diesel submarines

include Greece, Turkey and Italy, all under license of HDW/TNSW. In Asia, Japan continues

to steadily produce diesel submarines and China is improving its submarine-building programs

(14). But the submarines typically built by Japan and China are for their sole use.

51
 The information found on submarine construction methods indicated a history of

modular construction techniques, similar to the recent nuclear submarine USS Virginia

construction. A look at history shows this construction method to have been extensively used

by Germany in WWII, where the U-boat construction was parceled out to many assembly

groups, each completing parts and subassemblies, termed modules. These modules were

brought together in decreasing numbers of subassemblies and finally into one shipyard for

final assembly (5). Prior to computer aided drafting (CAD) submarine designs would

sometimes be tested for fit up using full scale mock ups. More recent diesel designs have used

fifth-scale models rather than full mock ups, and CAD programs have significantly assisted

arrangements (5).

What are nations looking for in submarine capabilities? With the exception of nations

building nuclear submarines, nations seeking to obtain submarines are looking for inexpensive

but effective diesel submarines possessing advanced design without the need for extended

range (14). Specifications for bids include:

. Turbo exhaust gas blowers for diesels

. High level of automation/computerization for minimum crew size

. Either a fuel cell AIP component or a closed cycle, external combustion AIP engine

such as the Kockums Stirling.

* Hull construction of high carbon yield steel with non-magnetic, low field signature.

. Variable-speed motors and high efficiency alternators.

Diesel submarines should be suited for detection of hostile submarine intrusion into home

waters, bottom mapping of shore regions, detection of mines, detection of electronic

52
emissions and ability to carry unmanned submerged vehicles. Overall nations are looking for

minimum cost and stealth as priorities for their diesel submarine acquisitions (14).

4.2.4 Cost Effects

Cost information is difficult to find in open literature. Countries that sell diesel submarines do

not list published prices of their submarines for the general public. The only accurate data

obtained was that of the Type 212A selling for just over $500 M in 2004 (14).

An important distinction must be made between price and cost. The price of a

submarine is the amount a shipbuilder is willing to offer to build the vessel to specification.

Price depends on the number of boats planned to be built, how quickly they are required, the

level of competition, the resources, expertise of the shipbuilder, and the facilities. Thus the

price of a submarine can vary drastically, even with the same design requirements (5).

The cost, however, is the total of the individual costs of the contents. Cost is an

inherent property of a submarine usually determined early in the design stages. Cost

estimating has traditionally been based on weight group breakdown, and a cost per ton was

normally determined to find the overall cost of the submarine. But more recently, submarine

designers and builders have moved toward functional costing or relating cost directly to the

functional performance parameters of the design (5). However, the accuracy of functional

costing is difficult to predict because it is almost impossible to obtain a single valued function

to cost relationship.

With one major leading European manufacturer, TNSW/HDW, competition for

prices may be difficult. Other builders are starting interesting programs, one of which was

covered in this study, Spain's P 650 built by IZAR. From the analysis, P 650 appears to be a

very capable platform and may compete well with the German designs of HDW. But the first

53
P 650 will not be commissioned until 2007, so competition with HDW will have to be

compared at that time. Therefore, cost effects on naval architecture are largely qualitative due

to the limited amount of data available. One conclusion that doesn't require quantitative data

is that it is not feasible to put performance above all cost considerations and in most designs,

the designer must carefully account for the mix between performance, cost and resources (5).

4.3 Discussion ofResults

Reviewing again the results of Table 11 above, the lack of significant difference in standard

deviation is not surprising when considering that the basics of ship design have remained the

same. The basic law of Archimedes still applies, regardless of advances in technology, mission

differences, cost factors or construction techniques. This result may have been shown for

submarines of the same country before but never explicitly shown for submarines of different

countries. Comparative studies of surface ships have found similar conclusions. For example,

Kehoe and Graham note that although the process of design for US and foreign surface ships

varied, the average values of characteristics did not vary significantly (13).

Submarine design is typically volume-limited, with a pressure hull structure as the

limiting factor. Although technology and construction techniques have changed over the

years of submarine design, the conclusion is that the changes have not been significant enough

to alter the traditional submarine design process. Another possible reason for the similarity in

results is what was mentioned in chapter 1, that initial design starts with previous submarine

databases. Estimates are made early in the design from those databases that carry throughout

the final product, resulting in similar weight divisions. This result will be discussed in further

detail in chapter 5.

54
5 Conclusions

5.1 Summary of Work

In conclusion, this study has presented a method to obtain volumes and weight groups of

diesel submarines given dimensions normally found in open literature. Furthermore the

weight group percentages were found to not vary significantly from one design to the next.

The similarity in weight groups may be attributed to using historical databases and borrowing

from previous designs to develop the initial estimates for a new design. As Jackson notes,

"Weight and volume estimating depends on the accumulation of data from a great many

sources in a systematic manner... It is the crux of the concept design phase as weights and unit

volumes must be intelligent guesses while everything else is subject to rigorous mathematical

analysis" (7). These intelligent guesses come from databases of previous designs and therefore

are similar in proportion.

Mission factors do have an effect on weight groups, if the mission factor is of a "large

scale". Those factors found to be large enough in this study were the presence or absence of

one type of mission, such as the lack of armament or the emphasis on speed in the mission.

Cost does seem to have an implied effect of leveling the field of possible designs due

to constraints on size, cost and arrangements of submarine designs, but no quantitative data

was found for this conclusion. The fact that countries seek the least expensive, most capable

submarines gives qualitative reasoning to this statement.

No new or unusual solutions or concepts to make ships smaller, less expensive, or

more effective have been revealed by this analysis of diesel submarines. Diesel submarine hull

characteristics have grown beyond the ideal of Hollandand therefore have become less

hydrodynamically efficient than the hull of revolution design. It is difficult to reduce size

55
constraints once they have grown and been incorporated into new ships. Designers must

resist the tendency of volume growth trend but the reversal of such a trend is contrary to the

perception that a more effective platform must meet more capability based requirements.

5.2 Future Work and Recommendations

In performing this study, the following areas were identified that would expand the scope of

the comparative naval architecture analysis.

5.2.1 Survey Size

Six submarines were selected and two of those were mainly included for the development of

parametric equations. The two older US submarines provided a historical perspective but

additional modem submarines would give a more comprehensive comparison of modem

technologies. As diesel submarine numbers increase, more data may be available and

therefore should ease the task of gathering that data. Additionally, more submarine data will

enable refinement of the parametric equations used in the math model.

5.2.2 Math Model

The math model can be improved to output additional characteristics and therefore add to the

comparisons available. Volumes and weight groups were the only naval architectural

characteristics calculated. If more complete and accurate drawings are obtained, additional

weights could be calculated of frames, plates and bulkheads for instance, which could yield

more accurate estimates of structural weight. Additionally, more accurate measurements of

internal areas could be obtained to calculate more accurate volumes and to develop more

precise parametric equations for cases where drawings were not available.

56
5.2.3 Reserve Buoyancy

An interesting result is the relatively large RB of Type 212A. The RB was calculated in the

math model by dividing the MBT volume by the everbuoyant volume.

RB = MBT Vol / Veb

From Table 8 the math model output for RB was 28 percent. If RB is calculated from

published values, the result is 26 percent as shown below.

Know that in a balanced ship, Veb= NSC

And Vb, - Asub- NSC

Published values:

NSC 2 = 1450 Lton

Asub212= 1830 Lton

Therefore RB, 1 , = Vb, / NSC = (1830 - 1450) / 1450

RBz = 26
%

This result is over twice that of design-lane values of 10 to 12.5 percent, even when

considering smaller submarine hulls will have larger RB values. The possible causes were not

researched further in this report but rather left to future work.

5.2.4 Advanced Technology

This study's focus was on the comparison of submarine weight groups but more detailed

comparisons may be made of advanced technology in propulsion systems (AIP), acoustics,

new battery technology and weapon systems. Research of propulsion and weapons

capabilities would provide a more thorough comparative analysis of the submarines studied.

57
5.3 Closing

This study covered in detail the submarine design procedure, foreign diesel submarine designs,

and methods of comparative naval architecture. A math model was developed to estimate

volumes and weight groups from open literature diesel submarine drawings. The overall

conclusion is that submarine design has not changed significantly, with regard to the major

components of naval architecture, the weight groups. Submarine designers must continuously

make engineering estimates and rely on previous designs for volume and weight predictions,

then adjust these to meet operational or owner requirements.

58
 1u
".""""' . """"""""...
. . ........
11111m

References

1. Lienau, Peter. "The Working Environment for German Submarine Design During WWII."
December 2 1999 <http: / /wwvw.navweaps.com/index tech/tech-050.htm>

2. The Simon and Schuster encyclopedia of World War II / edited by Thomas Parrish; chief
consultant editor, S.L.A. Marshall. - New York: Simon and Schuster, 1978.
<http:/ /xw.angelfire.com/ct/wv2europe/stts.html>

3. "Nuclear Powered Ships." World NTuclearAssociation.October 2004.

<http:/ /www.world.nuclear.org /info /inf34.htm>

4. "Bulletin 22." Subai ne Research Center, AMI International. November 2003.

<http: / /www.submarineresearch.com/bulletins.html>

5. Burcher, Roy, and Louis Rydill. Concepts in Submatine Design. Cambridge: Cambridge UP,
1994.

6. Jackson, Harry A., P.E., CAPT USN (Ret). "Fundamentals of Submarine Concept Design."
SNAME Transactions, Vol. 100, pp 419-448, October 1992.

7. Jackson, Harry A., P.E., CAPT USN (Ret). "Submarine Concept Design." ASNE, October
5 1988.

8. Arentzen E.S., Capt, USN, and Philip Mandel. "Naval Architectural Aspects of Submarine
Design." SNAME, November 17-18, 1960.

9. Jackson, Harry A., P.E., CAPT USN (Ret). MIT Professional Summer Course "Submarine
Design Trends", 1992.

10. Stenard, John K., LT, USN. ComparatieNaialArchitecture of Modern Foreign Submarines.
Massachusetts Institute of Technology. May 1988.

11. Cann, Glenn, et al., eds. Introduction to Submarine Design. 1995 LAP Submarine Design
Course notes. Dept of Ocean Engineering, Massachusetts Institute of Technology, 13
December 1994.

12. Jane's Information Group Limited. Jane'sFghtingShips 2002-2003, One HundredFfth edition.
Commodore Stephen Saunders RN, editor. Coulsdon Surrey, UK, 2002.

13. Kehoe, James W., Jr, CAPT USN, and Clark Graham, CDR USN, Kenneth Brower, and
Herbert A. Meier. "Comparative Naval Architecture Analysis of NATO and Soviet Frigates."
Naval Engineers Journal, October 1980.

14. "Bulletin 25." Submarine Research Center, AMI International.January 2004.

<http:/ /www.submarineresearch.com bulletins.html>

59
Appendices

60
Appendix A: Design Spiral

61
 Submarine Design Spiral

Requirements

Profile
Dynamics

Volume Requ ired

Cost

Volume Avail ble

U-

Structure

Weight Re quired Speed /Power

Stanc balance
Polygon Arrangement

Professional Summer Program at

Massachusetts Institute of Technology, 2004

62
Appendix B: SS Design Flowchart

63
 |
I|||IIII|
|||IjI

SS DESIGN GUIDE FLOWCHART

Design Equilibrium
Requirements Polygon

Goals, Thresholds, Modify Tanks)

Constraints
j NO)<sat?>

YES

Volume
Required Powering

Ever buoyant Volume Structures

MBT, Freefloods, "Cartoon"

Initial Sizing
_ - Layout Maneuvering
- Deck Ht

Volume
Avail Req'd Cost

Iterate
Re-Arrange Weight
Estimate

NO All
Req'ts
Gross Char Met?

YES

NO W=B? Feasible
Boat

YES
Fuel
Calculation

NO Long YES
Bal?

64
Appendix C: Math Model

65
 Diesel Submarine Comparative Naval Architecture Analysis Math Model
Developed from the MIT Math Model
Kai 0. Torkelson, LCDR, USN, 6 May 2005
i. CONSTANTS

pW- 1020 k -urve

1.12 Iton := 1016.Ocg NM := 1852m knt := INM kW:= 1.34102p
3 1-hr
m

fCurve = factor forhull curvature fcurve obtained from 1994 SS design section of Introduction to Submarine Design

Input excel file containing dimensions of submarines 0 through i:

The input excel file, Mathcad input.xls, draws from a variety of input excel files which provide all necessary submarine data that is
used throughout this model to calculate the the desired output characteristics. Each input is read from the input matrix individually
and assigned a range variable, such as NSC(i) or LOA(i), for the i-number of submarines included as candidates.

i:=0. 5
I. CHARACTERISTICS
Surfaced Displacement NSC(i) :1 0, i Iton Normal Surfaced Condition = Surfaced Displacement

Submerged Displacement Asub' 'I, i Iton

Length Overall LOA(i) :=12, i m

Diameter D(i):= 13, i

m

Complement Ncrew-officeri) :14,i

Ncrew other (i) := 15, i

NT(i):= (Ncrewofficer(i) + Ncrew-other('))

Speed max surfaced Vsurfaced () :=16, i-knt

Speed max submerged Vsubmerged (i) := 17 .knt

Number of Torpedo Tubes: TT(i) := 18

Patrol endurance, days E(i) := 19i

66
Diving Depth (m):
DD(i) =10,i m

Passageway Factor:
f~way 1.08 1.08 as used in 1994 Intro to Sub Design for SS (diesel subs)

Deck Height Measured: HDeck(i) := 11, i m

SHP Installed: SHP(i) := I12, ihp

Electric Plant Power Installed: KWi(i):= I13 ,kW

67
 II. VOLUME CALCULATIONS
This section calculates compartment and space volumes within the submarine, based on input data from plan and inboard profile
drawings. The Variables indicate the type of volume and the subscript indicates the location.

A. Engineroom Volume:

Using submarine profile drawings/pictures, measure the area for the Engine Room (ER):

ER Area: AERi):= 114, im2

Aft Battery Area: AAB(i):= 29, ni2 HBatt() :=I 31,im

ER Volume: fCurve'fPway(AER(i- HDeck()) VAB(i) := AAB(i)-HBatt(i)

VERO)

B. OPS Compartment Volume

OPS Compartment will be calculated by a deck area analysis for Auxiliaries. Berthing & Messing, Storerooms, and
Other Spaces. For comparison purposes. parametric equations have been used to calculate certain areas, as would be done in initial
design. These areas can then be compared to the measured area for a check of parametric equations. The subscript m indicates
measured areas for various spaces.

1. Command & Control: 115, i mn2 vcc(i) := fpway' t Curve HDeck(i)Acc(i)

A ccd :=

2
2. Berth & Mess: Abm(i) :=22.4 ft NT(i)

Measured Berth & Mess: Abmm ) 116 , im2

3. Storerooms: Asr(i) := 8.3.ft 2-Ri)

Measured Storerooms: Asnn0) 1 m7.

4. Other Spaces (offices, etc) Aos(i) := 1O-ft2 + .7.ft2NT(i))

Measured Other Spaces

(offices. etc) Aosm(i) 118. i

5. Forward Battery: AFB(1 30i2

VFBGi := AFB(') -HBatt('

6. Weapons Handling: Axvep(i) 19.im HDwep(i) : 1 Vwep(i) := HDwep() fPway' CurveAwep(i)
2 0 ,im

68
7. Parametric-Calculated Ops Volume: (Barbel and Albacore aft batteries are included in ops compartment)
Apopsi) fPway-flurve-(Acc(i) + Abm(i) + Asr(i) + Aos(i) + Awep(i) + AFB(i))

Apops(i) : (Apops(i) + fPway-fCurve-AAB(i)) if < 3

<i
Apops(i) if 3

0 '() fPway'fCurve-[HDeck(i)-(Acc(i) + Abm(i) + Asr(i) + Aos(i) + Awep(i)) + HBatt(i)AFB(i)]

VPops(

(VPops0 () + fPway'fCurve-HBatt(i)-AAB(i)) if i<3

VPOPS(i):=
i
Vpops(i) if 3

8. Measured Ops Volume:(Barbel and Albacore aft batteries are included in ops compartment)
Aopsm(i) := fPway'fCurve-(Acc(i) + Abmm(i) + Asm(i) + Aosm(i) + Awep(i))

Aopsm(i):= (Aopsm(i) + fPway'fCurve-AAB(i)) if i < 3

i
Aopsm(i) if 3 <

Vopsm(i):= fPway' urve-[HDeck(i)-(Acc(i) + AbmrMi) + A srm(i) + Aosm(i) + Awep(i)) + HBatt(i)-AFB(i)]

Vopsm(i) := (Vopsm(i) + fpway'fCurve-HBatt(i).AAB(i)) if i < 3

I Vopsm(i) if 3 < i

C. Auxiliary andPressure Hull Volume:

I. Using the pressure hull measured values of L, D, and length of parallel mid-body and forward & aft shape factors.

hull shape
Entrance: ' fph(i) :=34, Note: These factors are for the pressure hull only, not the overall

Run: aph () 35, i Lfph(i) :=I37 , im

Lph 36,im Laph(i):=138,im

check:
Lpmbph(i) := Lph(i) - Lfph(i) - Laph(i)
Lfph(i) Laph(i) Lpmbph(i)
one(i) := +
Dph(i):=I jm
+

P 46,i Lph(i) Lph(i) Lph(i)

2. Entrance & Parallel Mid-Body:

fphh)
1
ph(xl) := L Y
fLfph(i) - x)
Lfph i) ) j
Dph()
2

69
 1 1,
, 1 d01

3. Run:

aph,' I xI - (Lfph(i) + Lpmbph(i))

-Laph(1 1
1
_
Dph(i)
2

4. Total Pressure Hull: offtph(xli') Yflph(xl,') if X1 < 1 fph(')

Dphfi)
2 if fph(') xl fph(') + Lpmbph(I)
1
yaph(xli') if xI > 1ph() + Lpmbph(I)
5. Pressure Hull Volume

PHLph i
VPH(i) Jf ) O-tph (xi) dx VPH
O-ft

VPHO
Aph(')
)

3
350.02831685-
lton

From PH volume, calculate auxiliary and variable ballast volumes:

Vaux equation from Harry Jackson's notes. This includes auxiliary machinery, tanks,
Vaux(VPH,i) :=0.041VpH(i) + .529n -NT(i)
etc.
VV4VPH, i) 0.06 4 VpH(i) VVB equation from Harry Jackson's notes. Volume of variable ballast tanks.

Vaux(i):= VauxVPH,)

VVfi):= VV4VPH,)

D. Total Ops Compartment:

Vops ):=Vopsm(i) + Vaux(i) + VVE

Aphm(i) := Vphm(i)PSW
0 (i) + VER(i)
Vphm(i) := Vops

VPH(i) - Vphm(i)
ErrVphf i)
VPH(i)
If Errph 0, then calculated volume is smaller than that derived from drawing measurements.
<
If ErIph > 0, then that derived from drawing measurements is larger than calculated volume.
IF ERROR > +/- 10% ADJUST YOUR HULL CHARACTERISTICS - LOOK CLOSELY AT MEASURED VOLUMES.

E. Outboard Volume:

Vob(i) := .12-VPH(i) 0.12 obtained from Intro to Sub Design (SS) 1994

70
 . . ..... ..
... ........... ..... ...........
..

F. Sonar Arrays *Assumes a cylindrical bow sonar array*

Measure radius and height of bow sonar array: rsa(i) im hsa(i) 133 im Vsa(i) := l-rsa(i) -hsa(i)

G. Sonar Dome Water:

Vdfi) := Vsa(i)-5

H. Everbuoyant Volume: The everbouyant volume is used later to compare with NSC weight.

Veb(i) VPH(i) + Vob(i) + Vsa(i) + Vd(i)

Aebr(i) eb(')P SW

I. Main Ballast Tank Volume: Determinant of reserve buoyancy

Vbt(i) Aub(i) - NSC(i)){ 35.j!L

)

Vbt(i)
RB~i) :=
Veb(i)

J. Submerged Volune:
Vs(i) := Veb(i) + Vbt(i)
As(i) := Vs(i).P SW

K. Envelope Volunte Envelope volume

eqn from IIJ notes
Enter submerged free flood fraction of envelope displacement. check: K (i) := 142, i in Submarine
p(i) := I.,
Concept Design
Vs( i)
Si n-.D(i)
140
Iton
ft 3
LOA(i)
D( i)
K
Venv(i) envcxl

)
S ( P(i)

Aenv(i) := Venv(i)'P SW

IL. Free Flood Volume:

Vgti):= p(i)-env(i)

Afti):= Vtji)-p SW

71
III. ENVELOPE VOLUME BY PARAMETRIC EONS
A. Hull Characteristics:

Using the volume requirements calculated in Section 11 and measured values of (Figures 2-1, 3-1/2/3, 5-2/3) - L, D, and length of
parallel mid-body and forward & aft shape factors.

Measured values and calculations:

Entrance: J t i) := '40, i
Run: L(i) := LOA(i)
rla(') 141,i
14 (i)
LOA(i) Lt1i):= 2.4- D(i) fwd endfrac(i)
Calculate L/D: LO(i):=

-
D(i)
D(i)
LOD= function L = function
Lafi)
L~a(i) := 3.6.D(i) aft_endfrac (i) := --
D(i)

Lpmb(i):= (LOri) - 6)-D(i)

check:
Lf(i) La(i) Lpmb(i)
oneh(): +

+
LOA(i) LOA(i) LOA(i)
B. Volume Calculations for total ship:

1. Entrance & Parallel Mid-Body:

.rlf(i)

D(i)
yfl(x1,i)
li{i)
)

2. Run: La = function

xF i.i + ILpmb(i) Di
va(xF,i):= I- D(i)
2
2La(i)

3. Total Ship: otft(xl, i) := vfl(xl, i) if xl < Lf(i)

D(i)
if Lt{i) xl Lt) + Lpmb(1)

ya(xl,i) if xl > I{i) + Lpnib(0)

4. Total Ship Volume

Vtt(i) {tL(i)
Compare to envelope volume from above:
Vtot~i) :=olft(xl, i)2't dxl Vtot = function
O-ft Vtot(i) - Venv(i)
Erenv (i)=
Vto t(i)

If Er;,, <0, then calculated volume is smaller than that derived from drawing measurements.
If Err,, > 0. then that derived from drawing measurements is larger than calculated volume.
IF ERROR> +/- 10% ADJUST YOUR HULL CHARACTERISTICS - LOOK CLOSELY AT MEASURED VOLUMES.

72
5. Total Prismatic Coefficient
Vtot(i)
CD(i) := 2 C = function
D1i))

6. Forward Prismatic and Wetted Surface Area Coefficients:

-2.4- D(i)
,f2.t
O-ft
2
i offt(x, i) .n dxl
T2.4-D(i)
0-ft
2.offt(xl, i) -n dx1

Cpf i) := Cwsf(i) := Cwsf = finction

C f = function
D(i) 7c- D(i)-- 2.4
1C 2.4
4

7. After Prismatic and Wetted Surface Area Coefficients:

f L(i) 2
Ofit(x1, i) -n dx1 f L(i)
( L(i)-3.6-D(i))
2-offt(xl, i)-n dx1

Cwsa(" .): Cwsa = function

p (L(i)-3.6.D(i))
Cpa(l) := I
n - -3.6
4

8. Wetted Surface Area, Envelope Displacement & misc. Coefficients:

K2(i) := 6 - 2.4Cwsf(i) - 3
KI(i) := 6 - 24Cpf(i) - 3 .6-Cpa(i) .-&Cwsa(i) WS(i) i-i)2.(LOD~i) - K2(i))]
:=Lx

Ki = function K2 = function L(i)

WStot(i) : 2.7-offt(xl,i) dxl
WS = function WStot = function 0-ft
Hull wetted surface coefficient calculation
Eqn (12-24) from Gilmer and Johnson Cs(i) := 1.03C(i) from Gilmer and Johnson

n-D(i) LOA(i)
DIon
Aenvd()
)

:= - A - Kl(i)
end 140 ft3 D(i)

9. Envelope Volume Balance.

Note: The outboard volumes external to the main envelope of the submarine are not included in the hull sizing.

Aenvd(i) - Aenvc(i)
Aenvc = function Aenvd = function Errdenv(i) := Aenvd 0)

Check of calculatcd displacemit andithat derived from KI ostiiatc - 1:

If Err <0, then calculated displacement is smaller than that derived from K1 estimate.
If Err> 0. then that derived from Ki estimate is larger than calculated displacement.
IF ERROR +/- 100%ADJUST YOUR HULL CHARACTERISTICS - LOOK CLOSELY AT KI ESTIMATE IN envc.

73
IV. INTERNAL LAYOUT
Based on yonr data and inboard profile drawings , input the longitudinal location of the following bulkheads measured from fore to aft.
The general methodology is to work from fore and aft towards amidships. Starting forward and working aft....

A. Dome:
Sonar Dome Bulkhead location: Domeaft(i) := 11im

B. Fwd MBT aft Bulkhead:

FWD MBT aft Bulkhead (FWD OPS) location: FMBTaft() :=22, i m

NOW, starting aft and working forward, still using the prufi I dra \in L as the basis input the following locations...

C. Forward bulkhead of the mud tank:

Mud Tank Bulkhead location: MUDfwd() := 123, m

L(i) - MUDfwd(i)

D. Forward Bulkhead of AMBT (ER aft Bulkhead):

AFT ER (AMBT fwd) Bulkhead location: ERaft(i) := 1, 4 .m

RER(i) := offt(ERaft(i) i

Aft MBT length: MLDfwd(i) - ERaf(i) PHaft(i) := ERaft(i) + RER(i) PHad = function

E. Forward Bulkhead of ER:

FWD ER Bulkhead location: E'fwd() :=25,im

ER Stack length actual: ERlength(i) := ERaft(i) + RER(i) - ERfwd(i) ERlength = function

F. Fwd OPS Bulkhead

FWD MBT aft Bulkhead (FWD OPS) location: OPSfwd) := 16, m
OPS fwd bulkhead location:
ROPSc(i) := offt(OPSfwd0))

Rp(i) := of(OPSfwd(i), I)

PHfwd(i) := OPSfwd(i) - RepS(i)

1
PI fwd = function

OPS Stack length actual: OPSlength(i) := ERfwd(i) - OPSfwdi) + ROpS(i) OPSlength = function

74
 V. Summary of Error Checks
A. Overall measured PH vs. calculated PH volume

VPH(i) Vphmdi)
-
Errvph(i)- - Errvph)
VPH') 3.22

%
-19.88
16.224
18.717
If Errph < 0, then calculated volume is smaller than that derived from drawing measurements.
If Errph > 0, then that derived from drawing measurements is larger than calculated volume. 13.066
IF ERROR > +/- 10% ADJUST YOUR HULL CHARACTERISTICS - LOOK CLOSELY AT MEASURED VOLUMES.

B. Overall total ship measured vs. total ship calculated volume

tot(i) - Venv(i)
Elnenvi) Vtot( i) Erenv) ~
4.265

%
10.172
-9.575
-16.833
If Errny <0, then calculated volume is smaller than that derived from drawing measurements. -10.156
If Errenv > 0, then that derived from drawing measurements is larger than calculated volume. -11.297
IF ERROR > +/- 10% ADJUST YOUR HULL CHARACTERISTICS - LOOK CLOSELY AT MEASURED VOLUMES.
C. Overall parametric-derived envelope vs. measured envelope displacement

Aenvd(i) - Aenvc(i)
Aenvd(i) ErrAenvy0)
0.394%
-3.12
-0.014
0.142
If Err, < 0, then calculated displacement is smaller than that derived from KI estimate.
If Err, > 0, then that derived from KI estimate is larger than calculated displacement.
IF ERROR ->+/- 10% ADJUST YOUR HULL CHARACTERISTICS - LOOK CLOSELY AT KI ESTIMATE IN envc.

75
VI. WEIGHT ESTIMATION
A. Initial A-1 Weight Estimation:

Input the Group 1 fraction of NSC (Fig 1): W lfrac:= .385 W Iest(i) := W Ifrac-NSC(i)

Calculate the Group 2 weight from parametric equation:

Total battery volume: VBat(i) := VFB(i) + VABi)

Iton Iton
W2est(i) := 1.759 *VBat(i) + 0.005 -SHP(i)
3 hp
m

Iton
Input the Group 3 K3 (developed from SS580): K3:= 0.0126- W3est(i) := K3-KWi(i)
kW

Input the Group 4 percentage of NSC: W4frac 43,i W4est(i) := NSC(i)-W4frac)

W5frac0) 144,i 5es t (i) = W5frac(i).NSC(i)

Input the Group 5 fraction of NSC:

W6frac(i) 145,i W 6 est(i) := W6frac(i). NSC(i)

Input the Group 6 fraction of NSC:

Calculate Group 7 Weight (Use moditied Stenard W7est(i) 0.003ton -Vwep(i) + 61ton-TT(i)
parametric equation): ft3

Sum the weight estimates to get A-1:

A l(i) := W lest(i) + W2est(i) + W 3 est(i) + W4est(i) W5est(i) + W 6 est(i) + W 7 est0)

+

WPBfrac:= .087 WPB(i) := WPBfrac-A 1(i)

Input the lead fraction of A-I:

Input the Variable Load %o of NSC: WVLfrac:= . I I WVL(i) := WVLfrad NSC(i)

A-I fraction of NSC: Alfrac= - WVLfrac Alfrac = 0.819 Alc(i) := NSC(i)-Alfrac

1+ WPBfrac
W5est2(i) := A lc(i)-W5frac()
Write in terms of Surfaced Displacement to solve for NSC displacement in terms
of weight: W 6 est 2 (i):=Alc(i)-W6fracJ)

Vd(i)
(1 + WPBfrac. W lest(') + W2est(i) + W 3 est(i) + + W7est()
35-- -i)

Asurfest 0 W 4 frac(i) 11
(1 - WVLfra) - (1 + WPBfrac)' + W5frac(i) + W6frac(i) Al frac
( AIfrac ) _

76
VII. OUTPUT
VER(O) VER(l) VER( 2 ) VER( 3) VER( 4) VER(5) N

2 3 Vopsm( 4 ) Vopsm(5)
Vopsm(O) Vopsm(l) Vopsm( ) Vopsm( )
Vaux(O) Vaux( 1) Vaux(
2 Vaux( 3 Vaux(
4 Vaux(5)

)
)
VVB(2) VVB(3) VVB(4) VB(5)
VVB(O) VVB(1)
VPH( 1) VpH(2) VpH(3 VpH(4 VpH(5)
VPH(0)

)
)
Vs(O) Vs(l) Vs(2) Vs(3) Vs(4) Vs(5)
4 Venv(5)
Venv(O) Venv(l) Venv(2) Venv(3) Venv(

)
Vg(0) Vff(l) Vf( 2 Vff( 3 Vff( 4 Vff(5)

)
)
)
Volumes:= 3
Vob(O) Vob(1) Vob( 2 Vob( Vob( 4 Vob(5)

)
)

)
2 3
Vsa(O) Vsa(I) Vsa( Vsa( Vsa( 4 Vsa(5)

)
)

)
3 4
Veb(O) Veb( 1) Veb( 2 Veb( Veb( Veb(5)

)
)
)

3 4
Vbt(0) Vbt( 1) Vbt( 2 Vbt( Vbt( Vbt(5)

)
)
)

Vtot(2) Vtot(5)
Vtot(0) Vtot( 1) tot(3) Vtot(4)

VFB(
2
VFB(
3 VFB( 4 VFB(5)
VFB(O) VFB(l)
)
)
)

VAB(3) VAB(4) VAB(5)

VAB(0) VAB() VAB(2)
VeC(O) VeC(1) VeC(2) Vcc(3) Vcc(4) Ve (5

A sr( 0) A sr( 1) A s(2) A sr( 3 ) A sr( 4 ) )

A sr( 5)

A os(5) '
A os(0) A os(1) A 0 s(2) A os(3) A os(4)
Areas A opsm(0) A opsm(1) A opsm( 2) A opsm( 3)
A opsm( 4) A opsm(5)

WS tot( 0) WS tot( 1 ) WS tot( 2) WS tot( 3) WS tot( 4) WS tot( 5

)

L f(0) L f(l) L f(2) L t( 3 ) L f(4) L f(5)

'

L a(0) L a(') L a( 2 ) L a( 3 ) L a( 4) L a(5)

Lengths := L pmb(0 ) L pmb(1) L pmb( 2) L pmb( 3) L pmb( 4) L pmb( 5

)

ERlength(0) ERlength(1) ERlength( 2) ERlength( 3 ) ERlength(4) ERlength(5)

3
OPS length(0) OPS length( 1) OPSlength(2) OPS length( ) OPS length(4) OPS length (5))

77
 WIest(0) Wlest(l) WIest( 2 ) WIest( 3 ) WIest(4) Wlest(5)

W2est(o) W2est(l) W2est( 2) W2est( 3 ) W2est( 4) W2est(5)

W3est(O) W3est(1) W3est( 2) W3est( 3 ) W3est(4) W3est(5)

W4est(O) W4est(l) W4est( 2) W4est(3) W4est( 4 ) W4est(S)

W5est(O) W5est(l) W5est(2) W5est(3) W5est( 4 ) W5est(S)

W6est(O) W6est(l) W6est( 2 ) W6est( 3) W6est( 4 ) W6est(5)

W7est(0) W7est(1) W7est(2) W7est(3) W7est(4) W7est(5)
Weights Alc(O) Ali(i) Alc(2) Alc(3) Alc(4) Alc(5)

surfest (0) Asurfest (1) Asurfest(2) Asurfest(3) Asurfest(4) Asurfest(5)

As(0) As(l) As(2) As(3) As(4) As(5)

Aff(O) Aff(l) Aff( 2) Aff( 3 ) Aff(4) A f(5)

Aenv(0) Aenv(l) Aenv(2) Aenv(3) Aenv( 4) Aenv(5)

Aenvd(0) Aenvd(1) Aenvd( 2) Aenvd( 3) Aenvd( 4 ) Aenvd(5)

WVL(0) WVL(l) WVL(2) WVL(3) WVL(4) W VL(5)

LOD(O) LOD(1) LOD(2) LOD(3) LOD(4) LOD(5))

HullForm:= C (0) Cp(1) Cp(2) Cp(3) Cp(4) C (5)

Cs (O) Cs(1) Cs(2) Cs(3) Cs(4) Cs(5)

(Erlph(O) Errvph(1) Ervph( 2) Efvph( 3) Erkph( 4) Errvph(5)

Error-checks := Erenv(O) Elrenv(1) Elrenv( 2 ) Erlenv( 3 ) Erenv( 4 ) Elrenv(5)

EITAenv(O) ErrAenv(l) ErrAenv( 2 ) ErrAenv( 3 ) ErTAenv( 4 ) ErrAenv(5))

END

78
Appendix D: Submarine Profile and Plan Drawings

79
SS 580 USS Barbel

Surface Displacement: 2146 Ltons

Submerged Displacement: 2639 Ltons
Length: 67 m
Diameter: 8.8 m
Complement: 77 (8 officers)

Electrical Generator Capacity: 1700 KW

Propulsion Motor Power: 4800 SHP

Maximum Surfaced Speed: 14 Kts

Maximum Submerged Speed: 18 Kts
Diving Depth: 213 m

Overall Endurance Range: 14,000 Nm

Deployment Endurance: 90 Days
Torpedo Tubes: 6
Torpedo Capacity: 18
Builder: Portsmouth Naval Shipyard
Year: 1959
Other: Decommissioned 1989

* Plan and Profile dimensions obtained from Submarine SS 580 Booklet of General Plans,
BUSHIPS NO. SS 580-845-1702763, Naval Shipyard Portsmouth, NH

80
AGSS 569 USS Albacore

Surface Displacement: 1692 Ltons

Submerged Displacement: 1908 Ltons
Length: 63 m
Diameter: 8.4 m
Complement: 52 (5 officers)

Electrical Generator Capacity: 1634 KW

Propulsion Motor Power: 7500 SHP

Maximum Surfaced Speed: 25 Kts

Maximum Submerged Speed: 33 Kts
Diving Depth: 183 m

Overall Endurance Range: 10,000 Nm

Deployment Endurance: 50 Days
Torpedo Tubes: 0
Torpedo Capacity: 0
Builder: Portsmouth Naval Shipyard
Year: 1953
Other: Experimental submarine; Decommissioned 1972
Low L/D ratio of 7.5:1
Counter-rotating propellers
"X" Shaped Stem
Batteries: Lead-Acid produced 7500 SHP
Silver-Zinc produced 15,000 SHP

* Scaled plan view dimensions obtained from SS 580

81
 USS ALB3ACOREJ(,-IGSS 569)

"W. WSW
0"Wpas 41116SIEW11 NOW
.!z DOW MAIN DECK
-7 y
U10" -"WW

LPO-Aftt WAY MOT CAPSTAN

j
Z L
Ska"AL
CAOSTAN 04ASCM047
am camir 41"CATAIlLf. QAAT
L144T P-L ATE I
&

AFTSAR INRDFIscoo

1'~~~~~~0c ~1 p~g
TVL
I FWDE r~ TUT

______p 100 MIT-4&.4 PROFILE3*36 P0PflUI

66 IS- O po 5 60 65 So- 41 40 41 Vf N a ~is 1 sc -Im

&A.-

Profile Viewv
Type 209/1200

Surface Displacement: 1100 Ltons

Submerged Displacement: 1285 Ltons
Length: 56 m
Diameter: 6.2 m
Complement: 33 (6 officers)

Electrical Generator Capacity: 2800 KW

Propulsion Motor Power: 4600 SHP

Maximum Surfaced Speed: 11 Kts

Maximum Submerged Speed: 22 Kts
Diving Depth: 250 m

Overall Endurance Range: 7,500 Nm

Deployment Endurance: 50 Days
Torpedo Tubes: 8
Torpedo Capacity: 14
Builder: Howaldtswerke-Deutsche Werft GmbH (HDW)
Year: 1993
Number of ships: 9 (one built at HDW, remaining in South Korea)
Other: Possible AIP Backfit

faJ I

83
 Type 209/1200

L- --__----

1.

Profile and Plan Views

Collins 471

Surface Displacement: 3050 Ltons

Submerged Displacement: 3350 Ltons
Length: 78 m
Diameter: 7.8 m
Complement: 42 (6 officers)

Electrical Generator Capacity: 4420 KW

Propulsion Motor Power: 7344 SHP

Maximum Surfaced Speed: 10 Kts

Maximum Submerged Speed: 20 Kts
Diving Depth: 300 m

Overall Endurance Range: 11,500 Nm

Deployment Endurance: 60 Days
Torpedo Tubes: 6
Torpedo Capacity: 22
Builder: Australian Submarine Corp, Adelaide
Year: 1996
Number of ships: 6
Other: Kockums' Design

85
 I

'COLLINS' Class Submarine I2 FA x4rL

pt4^

Cross-Sectiona evaton - Taken from Ceotre-line Looking to Port

F- --L- T
-- -1 .-- C

-
Plan View - 1st Level

~ 9- - ~ ~ i~ U

[Ilam
- LiJE-2 CJSD)s 'Eu
B
Plan View - 2d Level

~uC~
21 II --

)
~ ~~~]--
0=

EC

Profile and Plan Views

Type 212A

Surface Displacement: 1450 Ltons

Submerged Displacement: 1830 Ltons
Length: 56 m
Diameter: 7m
Complement: 27 (8 officers)

Electrical Generator Capacity: 3120 KW

Propulsion Motor Power: 3875 SHP

Maximum Surfaced Speed: 12 Kts

Maximum Submerged Speed: 20 Kts
Diving Depth: 350 m

Overall Endurance Range: 8,000 Nm

Deployment Endurance: 60 Days
Torpedo Tubes: 6
Torpedo Capacity: 12
Builder: Howaldtswerke-Deutsche Werft GmbH (HDW)
Year: 2004
Number of ships: 4
Other: Siemens PEM (Proton Exchange Membrane)
306 KW Fuel Cell

* Scaled plan view dimensions obtained from Type 209/1200

87
IZAR S80/ P650

Surface Displacement: 1744 Ltons

Submerged Displacement: 1922 Ltons
Length: 67 m (AIP Add-on Section, 9 m)
Diameter: 6.6 m
Complement: 40 (8 officers)

Electrical Generator Capacity: 2805 KW

Propulsion Motor Power. 4694 SHP

Maximum Surfaced Speed: 12 Kts

Maximum Submerged Speed: 20 Kts
Diving Depth: 350 m

Overall Endurance Range: 7,500 Nm

Deployment Endurance: 50 Days
Torpedo Tubes: 6
Torpedo Capacity: 18
Builder: IZAR, Cartegena Spain
Year: 2007
Number of ships: 4 (plus 4 as an option)
Other MESMA (Module Energie Sans-Marin Autonome)
AIP 600kW Fuel Cell
Indiscretion Rate: 17% @ 8 knots; 6.5% @ 4 knots SOA
Diving Endurance: 400 nm @ 4 knots (1,500 nm with AIP)
Masts: Hoisting mechanism for 7 masts; only penetrating
mast is the attack periscope
Batteries: Two Groups of 200 Battery Cells

88
 P 650

00

Profile and Plan Views

Appendix E: Submarine Shape Factors

90
 Figure 18 from Reference (9)

A'f= 1.84
A = 1.84

if = 2.00
= 2.00

C m = 2.50
S= 2.50

D ilf = 3.00
Tb = 3.00 I -D
11111

00
= 4.
E
T = 2.75 D

11111 D
If = 2.50
F
= 2.75

Figure 18 contains profiles of submarines developed from equations in reference (9).

Hull A is near the optimum in the series 58 model basin tests (9).

91