Some Aspects of Submarine Design
Part 2. Shape of a Submarine 2026
Prof. P. N. Joubert 1
1University of Melbourne
Defence Science and Technology Organisation
DSTO–TR–1920
ABSTRACT
A shape for a next generation submarine has been drawn based on a survey
of available knowledge. The reasons for each detailed portion of the shape are
explained. The aim of the design is to produce a submarine with minimum
practical resistance and with minimum water flow noise especially over the
forward passive sonar while still carrying out all its normal functions.
It is assumed the role of the submarine would be little different from the
current vessel but may be powered differently and carry different equipment.
The diameter of the hull has been increased while the length has been
decreased compared to the present vessel. It is estimated the comparative
resistance will be reduced by ten percent. The larger diameter will allow an
extra deck over a portion of the length of the vessel giving greater flexibility to
internal arrangements. All openings in the first five metres of the shape have
been moved elsewhere including the torpedo tubes and interceptor array, to
give the smoothest possible flow over the forward passive sensors.
The nose shape is derived from a NACA forebody with a 14.2 percent
thickness-length ratio and shows a favourable value of the minimum pressure
over its length. The question of achieving natural laminar flow over this short
length is discussed and found to be possible but is unproven.
APPROVED FOR PUBLIC RELEASE
DSTO–TR–1920
Published by
Defence Science and Technology Organisation
506 Lorimer St,
Fishermans Bend, Victoria 3207, Australia
Telephone: (03) 9626 7000
Facsimile: (03) 9626 7999
c© Commonwealth of Australia 2006
AR No. 013-761
December, 2006
APPROVED FOR PUBLIC RELEASE
ii
UNCLASSIFIED DSTO–TR–1920
Some Aspects of Submarine Design Part 2. Shape of a
Submarine 2026
EXECUTIVE SUMMARY
In about the year 2026, the present class of Australian submarines, the Collins class,
will be approaching obsolescence. The machinery, the structure, communications, sensors,
weaponry will need updating and replacing and the hull structure will have reached the
end of its design life. This represents an opportunity to improve certain aspects of the
design which is only possible with a new vessel.
One of the most important aspects of submarine operation is to move as silently as
possible and to be able to detect others with passive sonar. Consequently this exercise in
developing the shape of a new design has three aims, 1) to move as silently as possible with
the lowest practical resistance, thus giving a greater top speed and less fuel consumption
at transit speeds, 2) to give the best possible flow over the forward passive sonar and 3)
a more flexible interior volume with more deck space. All this should be possible without
in any way compromising all the other functions and operations.
A shape is shown with the best practical ratio of length-to-diameter which gives the
minimum resistance. The diameter has been increased while the length has been decreased
compared to Collins. The increase in diameter allows an extra deck over portion of the
length of the vessel but should not increase the draft to a limit which would interfere
with navigation in ports or when docking. It will add to the minimum depth for dived
operations where a mission justifies risking the submarine. It will also add to the minimum
operational depth of water which enables a submarine to duck under a ship. In order to
maintain the same diving depth as Collins, the frames need to stronger. This should be
accomplished by deeper webs.
A mathematically derived nose shape has been drawn which maintains perfect symme-
try over the first five meters from the nose. This shape should give the planned pressure
distribution and properly constructed to the finest tolerances, will probably give laminar
flow in this region. The passive sonar would then have superior capabilities. The problems
with maintaining laminar flow are discussed and it does appear feasible. In the event the
boundary layer is tripped to turbulence the result will still represent a vast improvement
over the present nose shape and flow over the sonar.
The construction of the pressure hull follows standard practice, with successive trun-
cated cones forming part of the forebody and all the afterbody. A length of parallel
mid-body joins the nose and tail. The casing is not formed until aft of station 5000 (5
metres) and the distortion from circular is gradual thus preserving the symmetry of the
nose ahead. The casing is blended into the circular hull smoothly without longitudinal
valleys. The torpedo tubes have been moved aft from a horizontal line across the nose to
two vertical lines on either side with the most forward part of the shutter at station 5000.
The turtle back has been shaped in an attempt to minimise lateral pressure variation.
Model testing is essential to confirm design changes and to establish measured values
for speed-power relationships. It is estimated for equal volumes the total resistance would
be reduced by ten percent compared to a shape like Collins.
UNCLASSIFIED iii
DSTO–TR–1920
Author
Prof. Peter Joubert
Contractor for Maritime Platforms Division
P.N Joubert, a World War II fighter pilot, after demobilisation
from the RAAF, studied aeronautical engineering at Sydney
University. He then joined CSIRO, where he designed a ra-
dio controlled meteorological glider. Subsequently he was ap-
pointed as a lecturer in mechanical engineering at Melbourne
University specialising in fluid mechanics. In 1954 he attended
the MIT where he built and tested high-speed catamarans in
the towing tank. At Melbourne University he built a new wind
tunnel and much research was initiated and conducted there.
He has authored over 120 scientific papers, most of them in
fluid mechanics, boundary layers, roughness, and vortices and
recently with a PhD student, the flow about a submarine body
in a turn. Over the years he has received many research grants
including one from the US Navy. His work with his students
and colleagues is recognised internationally such as by the Gen-
eral Motors Research Laboratories and other international ship
research bodies. He has been studying flow patterns on sub-
mersibles since 1998 and has helped with certain modifications
to Collins. In 1972 he was granted a personal chair and since
retirement has been invited to continue as a Professorial Fel-
low. He was awarded a medal in the Order of Australia in 1996
for contributions to road and yacht safety. He was awarded
the AGM Michell medal in 2001 by the College of Mechanical
Engineers and is a Fellow of the Australian Academy of Tech-
nological Science and Engineering. In 2005 he was awarded an
honorary Doctorate of Engineering by the University of Mel-
bourne for his distinguished eminence. As a yacht designer he
has had over 100 yachts built to his designs, including a high-
speed catamaran for the world sailing speed record and ocean
racing yachts. Some of these have won against world-class com-
petition, the Sydney-to-Hobart race in 1983 and second places
in 1968, 2002 and 2003. As a sailor he has raced his own de-
signs in 27 Sydney-to-Hobart races and survived the storm of
1998. In 1993 he was awarded the Commodore’s medal of the
Cruising Yacht Club of Australia for outstanding seamanship
after his crew had rescued eight survivors from a sunken yacht
at night in a strong gale.
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DSTO–TR–1920
Contents
Glossary ix
1 Introduction 1
2 Criteria for Optimum Shape of a Submarine 2
2.1 Cross-Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Length-to-Diameter Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.4 Prismatic Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.5 Limitations on Draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.6 Diving Depth (Critical Pressure) . . . . . . . . . . . . . . . . . . . . . . . 5
2.7 Number of Decks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Length of 2026 7
4 Flow Over the Nose 7
4.1 Torpedo Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2 Intercept Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.3 Natural Laminar Boundary Layers at High Reynolds Number . . . . . . . 9
4.4 Possibilities for Natural Laminar Flow . . . . . . . . . . . . . . . . . . . . 11
4.5 Prediction of Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.6 Nose Shape for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.7 Construction Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.8 Factors Against Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . 16
4.9 Boundary Layer Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.10 Symmetrical:Asymmetrical Nose shape . . . . . . . . . . . . . . . . . . . . 17
5 Aft Body Shape 17
6 Design of the Sail 18
7 Control Surfaces 19
7.1 Stability and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8 Profile of 2026 19
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DSTO–TR–1920
9 Discussion 21
References 23
Appendices
A Circularity 25
Figures
1 Drag components for constant volume form. . . . . . . . . . . . . . . . . . . . 3
2 Total resistance components for bare hull showing effect of change in prismatic
coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Number of decks with hull diameter. Also useful deck area. . . . . . . . . . . 6
4 Number of decks with hull diameter. . . . . . . . . . . . . . . . . . . . . . . . 6
5 Externally positioned intercept array. . . . . . . . . . . . . . . . . . . . . . . . 10
6 Profiles of high speed Dolphin body and proposed X-35. . . . . . . . . . . . . 11
7 Instability points on two-dimensional elliptic cylinders and Re. . . . . . . . . 13
8 Pressure distribution on forebodies with contours according to NACA section. 15
9 Profiles of 2026 and Collins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
viii
DSTO–TR–1920
Glossary
AIP Air Independent Propulsion
CSIRO Commonwealth Scientific and Industrial Research Organisation
MPD Maritime Platforms Division
NACA National Advisory Council of Aeronautics (forerunner to NASA)
NASA National Aeronautical and Space Administration
RAAF Royal Australian Air Force
SSPA Swedish Maritime Research Laboratory
µ Fluid viscosity
ρ Fluid density
A Surface area
D Body diameter
Ff Friction force
L Body length
U∞ Freestream fluid velocity
Re Reynolds number, a ratio of fluid inertial and viscous forces, = ρU∞Lµ
Rex Local value of Reynolds number, usually measured at transition point
Cp Pressure Coefficient = Pressure1
2
ρU2∞
Cf Skin-friction Coefficient =
Ff
1
2
ρU2∞A
CP Prismatic Coefficient =
Displaced Volume
Midship Area×Waterline Length
t Sail thickness
c Sail chord (length)
ix
DSTO–TR–1920
1 Introduction
Considering a replacement design for the Collins Class Submarine which might be
required about the year 2026, at this time of writing, the operational tasks required of
this submarine would not appear to be greatly different to what was listed in the report
of December 2003, [1]. If the tasks are altered then of course the design will need to be
altered.
What is discussed here is preliminary; it is intended that it may form a basis for what
eventually is decided.
It is highly likely the range requirements would be at least as large as Collins (10,000
nautical miles) and probably extended given the expanded area of interest flagged in the
Minister’s Defence update 15 December 2005.
It would be highly desirable if the transit speed could be increased to minimise time
lost in transit.
The type of power unit must be left to later developments. AIP may have possibilities.
Nuclear power would allow a fast transit but is not yet acceptable in Australia.
Diving depth is a most important variable and some designs have gone to much trouble
and expense in order to achieve the deepest possible operating depth. Whether this feature
needs to be altered I cannot say, but it will be assumed that there is no change required.
In which case the pressure hull can be ended with flat bulkheads as with Collins Class. A
deeper diving depth would require domed end closures which present greater difficulties to
construct (Daniel [3]). The whole submarine then becomes more expensive. The greater
depth would require a stronger hull and as a result the hull weight would be increased
leaving less available for fuel, machinery and other items. This in turn means a slower
vessel. One makes a design choice and suffers the consequences.
Weaponry is being altered on a continuous basis. Launch systems which allow the use
of stand-off land attack missiles, surface to air missiles and anti-ship missiles will probably
need to be considered and included.
The ability to carry and launch unmanned underwater vehicles will be part of the wish
list as will likely be the operational support of special operations forces.
Detection and communications are being improved constantly. Covert forward intel-
ligence gathering and surveillance is an important activity and it is equally important
to be able to communicate this information. The ability to communicate real time data
with voice transfer would surely be an aim. Sloan [2] discusses some of these factors from
the designers vewpoint. At some stage decisions are made, the design is commenced and
thereafter the process becomes difficult to alter in any major way.
The aim of this design study is to produce a shape with the following features,
1. Minimum resistance within all other design constraints, thus increasing cruising
range, top speed and reducing fuel consumption.
2. Minimum flow noise especially over the forward sonar and other sensors.
3. A flexible interior giving most deck space for a given volume.
1
DSTO–TR–1920
2 Criteria for Optimum Shape of a Submarine
Gertler, in 1950 [10], reported the results of resistance experiments on a systematic
series of twenty four mathematically related streamlined bodies of revolution, showing how
the resistance of these bodies at deep submergence varies with changes in five selected
geometrical parameters. These geometrical parameters were the fineness ratio, prismatic
coefficient, nose radius, tail radius and the position of the maximum section. Before this
work was undertaken there was no systematic data on the resistance of streamlined forms
deeply submerged in a fluid.
The series forms were compared on an equal volume basis including the estimated
added resistance due to control surfaces necessary for prescribed directional stability char-
acteristics. These comparisons indicated that there is a large variation in submerged
resistance among these forms and that there is a definite minimum resistance on each
parameter variation except for the nose radius.
These test results formed the basis for the choice of the shape of the USS Albacore [25],
whose construction was authorised in 1951. This experimental vessel was the forerunner
of all successful US Navy submarines such as Barbel and Skipjack.
2.1 Cross-Section
To withstand the high pressures on the hull at depth, the most efficient structural
shape with the lowest stresses is one of circular cross-section.
Departures from absolute circularity have to be minimised as discussed by Capt. H.
E. Saunders [4], otherwise early failures can result (see Appendix A). The circle has the
lowest wetted surface for a given contained volume so this is an advantage for underwater
resistance.
For surface travel the circle contributes no hull form stability which is a disadvantage
especially when a vessel rises to the surface with water in the voids of the sail and casing
thus momentarily increasing the height of the centre of mass and decreasing the stability
margin.
2.2 Length-to-Diameter Ratio
The ratio of length-to-diameter bears a strong effect on the total resistance. The
two main portions of the underwater resistance of the bare hull are due to pressure drag
(sometimes called form drag) and skin friction.
The pressure drag is created by the streamlines on the rear of the body being displaced
from the geometric surface by the thickening boundary layer. Consequently the rise in
pressure near the tail of the body as the streamlines widen, is not as great as would occur
without a boundary layer. This imbalance between nose and tail produces a nett pressure
force on the submarine creating a drag force.
Skin friction drag acts tangentially at the surface and is proportional to the wetted
surface. The more wetted surface the greater the skin friction. Therefore if the displaced
2
DSTO–TR–1920
Drag
Total
SkinFriction
PressureDrag
Length:DiameterRatio
6 10
Figure 1: Drag components for constant volume form.
volume of the submarine is contained in a long thin shape, then the skin friction is greater
than for a shorter, beamier shape of the same volume which has less wetted surface.
The variation in the two components of resistance, pressure drag and skin friction,
looks like the plot in Figure 1.
The combined resistance shows a minimum at about L/D of 6 to 7; the curve has no
defined minimum being almost horizontal in this range.
It is proposed that a new shape be considered of shorter length and greater diameter
which will reduce the total drag coefficient closer to the ideal.
2.3 Surface Roughness
The main factor, apart from surface area, which affects the skin friction resistance is
the roughness of the surface. It is important that designers limit the effects of surface
openings, raised edges, recessed joins (shutters), lateral arrays and other features which
cause added resistance.
2.4 Prismatic Coefficient
The prismatic coefficient defines the amount of volume in the ends of the submarine. It
is formed as the ratio of the displaced volume with that contained in a prism formed by the
3
DSTO–TR–1920
mid-ship cross-sectional area and the length. The variation of the submerged resistance
with this parameter can be significant (see Figure 10 in Gertler [10]). R. J. Daniel in
his paper on submarine design [3] suggests an optimum value of about 0.6 (also shown in
Gertler).
Collins has a prismatic coefficient greater than 0.8, while the new shape for 2026
calculates as 0.76.
The variation of the resistance with change in prismatic is shown by Arentzen and
Mandel [6] in their Figure 6. Figure 2 shows this variation.
The combined effect of the reduction in L/D and CP should give a reduction in total
resistance coefficient of over eight percent.
Figure 2: Total resistance components for bare hull showing effect of
change in prismatic coefficient (Arentzen and Mandel [6]).
4
DSTO–TR–1920
2.5 Limitations on Draft
It should be possible to increase the floating draft of a submarine to greater than
that of Collins, which is nominally 7.0 metres, and still be able to navigate the important
harbours where it docks and berths.
The weight of any new vessel needs to be established early in the design. Hence
the floating draft can be established from the displaced volume required to support this
weight added to all the other loadings. Arentzen and Mandel [6] suggest that 36 feet
(10.98 metres) is the upper practical limit for the diameter of a military submarine which
would have a draft of 30 feet (9.14 metres).
Of more importance is the operational requirement of a dived intrusion in shallow
water where the submarine may be at risk. The bottom clearance plus the hull diameter
with the casing height plus the fin and periscope heights are now increased by the larger
hull diameter.
A similar i