STEVENS INSTITUTE of TECHNOLOGY
THIRD SUMMER SEMINAR 13 through 20 June 1960
Research Objectives
Instrumentation for Wave
Research
Hydrofoil Craft
Full-Scale Trials
Model Tests
Semi-Submerged Ships
Theoretical Developments
P1960-1
SHIP BEHAVIOR
L a of Na4a11,16,va...1,4
American Embaasy,
London
AT SEA
ARCHIEF
44'
Onderafdelin
t.--961ibouwkunde
nische FlogeschooCEMI DOCUMEN:ATIE 1:/03
DATUM:THIRD SUMMER SEMINAR
SHIP BEHAVIOR AT SEA
.
v.
c eeps ouwkunde
Technische Hogeschool
Delft
THIRD SUMMER SEMINAR
SHIP BEHAVIOR AT SEA
LECTURES ON NEW DEVELOPMENTS AND BASIC PRINCIPLES--NIGHLIGHTED AND ABSTRACTED
13
THROUGH 17 JUNE .1960
SPONSORED BY:
OFFICE OF NAVAL RESEARCH
AND
DAVIDSON LABORATORY
DAVIDSON LABORATORY
Stevens Institute
of
Technology
Hoboken, New Jersey
GUEST LECTURERS:
William E. Cummins, D.Sc. J.G. Goodrich, B.S. James J. Henry, B.S. Paul Kaplan, D.Sc. B. V. Korvim-Kroukovsky, Sc.M. Ernst Frankel, M.S. James L. Mills, Jr., B.S. T. Francis Ogilvie, Ph.D.STAFF:
John Dalzell, M.S. Winnifred Jacobs, M.A. Edward V. Lewis, M.S.Wilbur Marks, M.S. Edward Numata, M.S.
Paul Van Mater, Jr., M.S.E.
Head of Seaworthiness and Fluid Dynamics Division, David Taylor Model Basin. National Physical Laboratory, Ship Hydro-dynamics Division, Feltham, England. President,J. J. Henry Co. Inc., N. Y. C.
Chief Hydrodynamicist, Technical Research Group, Syosset, N. Y.
Research Professor (Retired), Stevens Institute of Technology; Consultant in Hydrodynamics.
Associate Professor, Dept. of Naval Archi-tecture and Marine Engineering, Massa-chusetts Institute of Technology.
Supervising Naval Architect, Preliminary Design Branch, Bureau of Ships.
Head Ship Wave Analysis Section, David Taylor Model Basin.
Research Engineer. Research Engineer.
Head, Transportation Research Group. Head, Ship Hydrodynamics Division. Head, Ship Research Division. Research Engineer.
ACKNOWLEDGMENT
It would be difficult to name all the people responsible for the success of the seminar. Nevertheless, a clear debt of thanks is owed to the Office of Naval Research for sponsoring, with us, this meet-ing. The guest lecturers and staff lecturers are owed a debt of thanks for the time and effort spent in preparation of their informative talks. Thanks are also due to the many Davidson Laboratory staff members, whose contributions in the matter of detailed arrangements made the seminar an
uncomplicated relaxing experience for the attendees. The administration of the Stevens Institute of Technology graciously supported the meeting by donating the use of essential facilities. Lastly, a word of thanks
to Professor Edward V. Lewis who organized the seminar, coordinated the various activities, chaired most of the sessions, and was generally an able and energetic shepherd.
Wilbur Marks 1/9/61
PREFACE
As the name implies, the Davidson Laboratory biennial summer seminars are a course of study on those aspects of ship behavior at sea in which recent advances have been made and that are of current interest to researchers in the field. In further keeping with the course of study idea, where possible, subjects that are being treated simultaneously at different establishments (hydrofoils, near-surface craft, etc.) have been included. This results not only in the dissemination of knowledge but in the opportunity, for the student,to critically appraise different
techniques and facilities applied to the same general problem. To pro-vide the attendees with the tools to appreciate the selected lectures, films and equipment demonstrations as well as basic lectures on the theory of ship behavior were added to the program.
The seminar was held during a period of five days of which the morning sessions were devoted to the lectures for which the meeting was
assembled. These lectures were semi-formal, two to a morning, and each lasted about one hour with ample time for discussion at the end. These transactions are the digested essence of the lectures; it is hoped that the lecturers will forgive the editorial license taken to reduce the content in the interest of brevity. For the reader, it is hoped that these summaries will arouse sufficient interest to induce a further search of the literature suggested by the references given at the end of most of the papers.
The institution of the panel discussion is a new innovation in our summer seminars. We believe that a course of study is enhanced by
a lively debate of a current topic.
The afternoon sessions were divided into two parts. The first part was a formal lecture series that reviewed the theoretical structure
of ship motions in waves. Professor B. V. Korvin-Kroukovsky gave the first two lectures on "Ship Motion Theory for Regular Waves" and
Professor E. V. Lewis gave the last two lectures on "Ship Motion Theory
for Irregular Waves." In addition, J. Dalzell and W. Jacobs lectured on "Routine Ship Motion and Bending Moment Calculations."
The second part of each afternoon session was devoted to films
and demonstrations to complement the morning lectures. Among the films
were three on hydrofoils--two of model tests at the Davidson Laboratory and David Taylor Model Basin and one on the full-scale Gibbs and Cox
craft SEALEGS. A Bureau ofShips (U.S. Navy) film on conducting full-scale trials and a Davidson Laboratory film on model tests to increase sea speed by varying hull proportions emphasized seakeeping studies on
surface ships. Davidson Laboratory presented a film on oblique-sea
tests to describe recent results and to point up some problems associated with steering models in oblique waves; films of a destroyer with large bulbs at the bow and stern and of a semi-submerged craft were shown to point up the interest in the unusual hull forms that are used to attain
high speeds.
The afternoon demonstrations were; Passive anti-rolling tanks,
Head sea model tests,
Six degrees of freedom motion-apparatus,
Analog computer for solving differential equations.
The attendees were invited to a banquet on the second evening. The absence of a formal program permitted a free exchange of ideas,
which afterwards characterized the brief breaks in the daily lecture
program.
--A WORD OF WELCOME
Vice Admiral Howard E. Orem--Director
of
ResearchThis meeting had as its objective a survey of the subject of ship behavior at sea, with special emphasis on the dissemination of new developments--new developments here at Stevens, new developments in cer-tain areas where you people work, and wherever they may have occurred. And, as many of you know, those developments have been brought about largely because of the support of the Office of Naval Research, Bureau of Ships, and David Taylor Model Basin, and I believe it correct to say that had it not been for the support and cooperation of those agencies
we would not be here today. For that support and cooperation, we here
at Stevens are especially grateful.
At this time, I would like to take advantage of the opportunity
to give you some information about this University. For instance,
Burchard Auditorium, the building in which the Seminar took place, was
completed in 1958. It is the largest educational science-engineering building built in the greater New York area in the last two decades. I
hope that those who were here took advantage of the opportunity to go through itsvarious laboratories. Across the street from the Burchard Building are the chemical engineering and chemistry laboratories. Cur-rently in progress on the campus of Stevens is a six and a half million
dollar building program.
Only recently an lddition to the Davidson Laboratory was com-pleted, the first major expansion of those facilities in many years. As
some of you may know, on our campus there are three full-time research
laboratories. The Davidson Laboratory with which I presume most of you are acquainted, Dr. Breslin is the Director, the Laboratory of Psycholo-gical Studies,and the Powder Metallurgy Laboratory. The latter two are the first such laboratories to be established on any college compus in
the United States. Additionally, research is carried on in the various academic departments, which research encompasses a wide area of interests.
It is the policy of the administration at Stevens to encourage
research for many reasons. In this connection it seems appropriate to refer to a statement by Dr. Butler, the long-time president of Columbia University, in which he stated that the principal mission of that
University was the development of new knowledge through research. The
principal mission at Stevens Institute of Technology is the education of potential engineers and scientists; research contributes materially to
the accomplishment of that mission and S.I.T. has a long tradition in research, design, and development. For instance, about 300 yards from the Burchard Building, the first steam-powered train in the western hemisphere was operated. Colonel John Stevens built the first steam
engine on the American continent. He built the first sea-going steam-ship, the first steam-powered ferry, he was the first to use the propel-ler for ship propulsion. He designed the first iron-clad warship, the
present T-shaped railroad rail, the cowcatcher, elevated train, the ferry
slip, and the double-ended ferry. Those are but some of the accomplish-ments that have taken place in this area.
At present, upwards of 125 research programs are being pursued
by our scientists and our engineers. The potential contribution to science and engineering, and possibly to our way of life, of those pro-grams of course cannot now be measured. It is entirely probable that
this seminar will also be a contribution to science and engineering, and
I think it especially appropriate that it had been held on Stevens'
campus. Gentlemen, you will always be welcome guests at Stevens.
H.E.O.
--ON THE DAVIDSON LABORATORY
Dr. John P. Breslin--Director
This is a rather auspicious time. We are now marking the
twenty-fifth anniversary of the founding of the Laboratory that owes its
existance to the inspiration and imagination of the late Kenneth S. M. Davidson. He founded the Experimental Towing Tank (Davidson Laboratory) on the 4th of June 1935. Since that time, this Laboratory has changed
its complexion a great deal, but nontheless still maintains the
funda-mental concepts on which it was founded; that is, it consists of a col-lection of enthusiastic scientists--people who have a desire to make
advances in the discipline connected with seatransportation and applied mechanics in general.
The Laboratory is divided into three main groups, the
Trans-portationResearch Group, the Applied Mechanics Group, and the Facilitiesand Services Group. Within the Transportation Research Group, Headed by Proféssor Lewis, there are four divisions; Ship Hydrodynamics, under Mr. Wilbur
Marks, is devoted to the study of flow phenomena attending ship motions; Ship Research, under Mr. Edward Numata, is concerned with the stresses
induced in ship hulls working in a seaway; Ship and Yacht Development, under Mr. Randolph Ashton who has just completed his twentieth year of
meticulous work in the area of yacht experimentation for which this Laboratory originally gained its reputation; and Vehicle Research, under Mr. Joseph Finelli, is concerned with the development of a land train
for the U.S. Army and a new type of diesel engine that is capable of very high power for its weight.
In the Applied Mechanics Group, headed by Mr. Daniel Savitsky,
the Fluid Dynamics Division, under Dr. Stavros Tsakonas, is involved with
various problems of theoretical hydrodynamics, among them the
determina-tion of forces and moments on submarines in waves and the performance of
supercavitating hydrofoils moving under waves; the Fluid Physics Division, headed by Dr. Stephen Lukasik, is a new development concerned with
hydrodynamics and the real fluid behavior of shallow-water waves; the High Speed Craft Division, headed by Mr. Peter Ward Brown, is interested
in the development of hydrofoil craft and supercavitating hydrofoils,
and, the last Division of this group, but by no means the least
import-ant, is Underwater Weapons, headed by Mr. Albert Strumpf. This Division is doing exceptionally fine work on all sorts of vehicles that generally operate below the surface of the water. Mr. Strumpf is currently
inter-ested in the radical improvement of submarine stability and control. The third Group, Facilities and Services, headed by Mr. Anthony Suarez,
provides important technical services such as the manufacture of
intri-cate apparatus, photography, mathematical analysis, and the reduction of
data.
I believe that you can see from this brief recounting that the Laboratory has diverse interests that cover many fields. While you were
here, I hope you had the opportunity to speak with these researchers and
to discuss your problems with them.
J.P.B.
TABLE OF CONTENTS
Objectives of Research on Ship Behavior at Sea
--A Panel Discussion
Ocean-Wave Measurements Wilbur Marks
Hydrofoil Craft in Waves
T.Trancis Ogilvie
Full-Scale Motion Studies
J. S. Goodrich
Model Motions and Bending Moments Edward Numata
Directional Stability and Control of Craft in Rough Seas
B. V. Korvin-Kroukovsky
Research at M.I.T. on Semi-Submerged Ships
E. G. Frankel
Research at S.I.T. on Semi-Submerged Ships E. V. Lewis and Paul Van Mater
8, Hydrodynamic Coefficients
Paul Kaplan
9. Analysis of Model Tests in Irregular Waves
John Dalzell xi ILLIL 13 23 39 47 53 65 83 93 97
LIST OF ILLUSTRATIONS
Figure Page
1.1. Underwater Wave-Measurement Devices 15
1.2. Surface Wave-Measurement Devices 18
1.3. Aerial Wave-Measurement Devices 20
2.1. Two Large-Dihedral Foils, 45-Degree Rise From Horizontal 26 2.2. Geometry of Area-Stabilized Foil 26 2.3. Head-Seas Heave-Amplification Factor 30
2.4, Head-Seas Heave Phase Lead 30
2.5, Head-Seas Pitch Amplification 32
2.6, Head-Seas Pitch Phase Lead 32
2.7. Following-Seas Heave Amplification Factor 33
2.8. Following-Seas Heave Phase Lead 33
2.9, Following-Seas Pitch Amplification Factor 34
2.10. Following-Seas Pitch Phase Lead 34
5.1. Definition of Imparted Lateral Velocity 54 5.2, Coordinate System With Respect to Moving Ships 58
6.1, 2-Foot Sail Model 67
6.2 Triple Sail Model 67
6.3, Calm Water Resistance Test Curves (F vs CT) 72 6.4, Heave Amplitude in Astern Waves as Dimensionless Motion
Parameters
(ZoA)
for Model With 2-Foot Sail 736.5, Heave Amplitude in Astern Waves as Dimensionless Motion
Parameters
(zoA)
for Model With Three Sails 74 5.6. Total Pitch Amplitude for Model With 2-Foot Sail 75Figure Page 6.7, Total Pitch Amplitude for Model With Three Sails 76 6.8. Trimming Moments, Initial Trim Half Inch 78
6.9. Surge Effects on Model With 2-Foot Sail 79
6.10. Surge Effects on Model With Three Sails 80 7.1. Body Plan of Proposed Semi-Submerged Ship for High-Speed
Supercritical Operation (From Reference 3) 85 7.2. Pitching Motions in Regular 2.0L Waves 86
7.3. Heaving Motions in Regular 2.0L Waves 87
7.4. Predicted EHP in Smooth Water 88
7.5. High-Speed Semi-Submarine 89
7,6. Body Plan for Large-Bulb Ship 90
7.7. Large-Bulb Model Configurations Tested for Smooth Water
OBJECTIVES OF RESEARCH ON SHIP lEHAVIOB AT SEA
--A PANEL DiSCUSSION WiTH1 Professor E. V. LewisChairman Dr. W. E. Cummins
Mr. J. J. Henry
Professor B. V. Korvin-KroukovskyMr, J. L. Mills, Jr.
Panel members wereasked to adopt a pro or con attitude and to present a
brief argument on the
fol-lowing proposition: The
basic problems of ship behavior at sea have been solved and the only
research that remains is in the nature of mopping-up operations--that
is, available tools should be refined and applied to specific design problems. After these presentations by the panelists, the chairman per-mitted each a brief period to present additional thoughts or rebuttal to the arguments of the other panelists. After the second round of
state-ments, the floor was thrown open to general questions trom the audience.
Each panelist was then asked to make concluding remarks. The concluding remarks made by the chairman summarized the results of the discussion.
In order that the proposition be adequately treated, it was
necessary that every viewpoint in the field of naval architecture be
represented. To this end, the panel was selected with great care with the result that the proposition was treated in a broad yet comprehensive manner.
To further orient the panel, Professor Lewis elaborated on
recent advances in our know'edge of seakeeping and the improvement of ship behavior. The problem of rolling, once considered quite
formidable, has
succumbed to research and development in the form of active and passive roll stabilization systems that can virtually achieve any desired degree
of roll reduction. The effect of lateral motions on steering and control in rough water was cited as another example. Although, automatic steer-ing systems are not perfect, there is little complaint from users so that future work in this area will be in the nature of minor refinements.
behavior, have been given much attention and noteworthy progress has been
made. Heave and pitch calculations based on the strip theory and
tak-ing coupltak-ing into account are well established as evaluators of
perform-ance of different hull forms in regular waves. The linear superposition theory and probabilistic notions and statistical methods permit treatment
of ship motions in irregular waves. Advances in wave-generation tech-niques in the model tank have elevated the laboratory to a first class
analog of actual conditions at sea.
Professor Lewis concluded that ships could be designed to operate in the subcritical region (of violent motions) or in the
super-critical region to reduce motions. In addition, damping devices also
could be installed. He also suggested that because the basic design information is now known, no minor changes in the physical or geometrical setup of a ship will improve matters greatly and that large changes in form will produce large changes in certain behavior characteristics, but
a comparatively high price must be paid elsewhere to achieve this.
The panel was again asked whether all the basic knowledge on ship behavior at sea is known and can it further be said that all that is left is a mopping-up operation that would use available theoretical
and experimental tools or do some really fundamental and important problems that need attention still exist. The panel also was asked to
define the important problems that still exist, if any, and to suggest
the best pbssible use of research money and effort to solve these
problems.
MORE BASIC RESEARCH REQUIRED
Dr. Cummins suggested that the technical advances, described by the chairman, show what really needs to be done rather than define the job as completed and that these rapid advances have left many
import-ant gaps in research. For example, it has been found th.j117,_a_s_tha_shi4 length increases, heave and pitch decrease. However, the minimum ship
length re uired for acceptable erformance for each class of ship is not
known. This requires a precision in design that is not yet available.
Supercritical ship design is at first appealing, but ships, at one -time
or another, also must travel at low speeds. Much research needs to be
done before the construction of supercritical ships can be seriously
recommended. With regard to small changes in hull form that yield small changes in performance, it can be said that this aspect of research must
also be given serious consideration. It is the job of research to
pro-vide a basis for compromise in design of form against structure and
per-formance against cost.
With regard to what needs to be done in research, Dr. Cummins suggested that a start could be made with the coupled linear-theory that predicts the response of conventional ships to regular waves. He cited the limited knowledge on the frequency-dependent coefficients in the
equations of motions and the necessity for concentrated effort in this
area. In addition, he further stated that the strip theory, especially in damping calculations, must be verified before it can be considered a
basic tool. The principle of linear superposition next came under fire, because it has been verified for only head and following, long-crested, irregular seas. The validity of the use of this tool to analyze ship behavior in short-crested, irregular seas and all relative headings is
still debatable. Dr. Cummins was enthusiastic about the development of
the model tank as an analog for actual sea conditions, but not without
qualification. He stressed the absolute necessity for model versus full-scale correlations in both sea state and ship behavior. This implies the solution of a number of subsidiary problems, each major.
OPERATIONAL PROBLEMS
Mr. Mills by-passed the well-traveled areas in research such as: safety, comfort, and reduced hull loadings, to dwell almost
exclus-ively on some of the Navy's operational problems. Aircraft carrier landings are of particular interest because it is the motion of the ramp (after-end of flight deck) and the sink rate of the aircraft that
of the ramp can be reduced, then ramp clearance of the aircraft is
likewise reduced and a shorter trip to the arresting gear results.
Mr. Mills further mentioned a case where an aircraft carrier had to suspend operations in the same seaway that a shorter vessel continued to
operate. It was found that coupling of certain motions caused higher
amplitudes of motion in the ramp of the longer carrier. This deserves further study.
Another item of importance mentioned by Mr. Mills was the
effect of ship motions on the reliable detection range of sonar equipment. The hydrodynamic flow noise generated by the ship, discomfort and
inef-ficiency of the sonar operator, and non-coincidence of transmitting and receiving beams all stem in part from ship motions. Mr. Mills called for research to determine methods to reduce ship motion and suggested that drastic reductions could only be realized by unconventional hull
forms. He emphasized the need to concentrate on pitch and heave, because
these motions are primarily responsible for shipping of water and planing.
Specifically, he asked for methods that, during the design stage, could be used to predict (a) heave and pitch, for all sea conditions, and basic
hull forms, (b) when shipping of water and planing will occur, and guid-ance in hull design to minimize occurrence and intensity of such pheno-mena, and (e) hull proportions, shape, and weight distributions necessary
to reduce motions.
COMMERCIAL REQUIREMENTS
Mr. Henry stated that interest, from the commercial viewpoint,
in seakeeping stems from the performance of high-speed cargo ships. In particular, hull form and especially the bow line is of prime concern. Mr. Henry favored ships that show good rough-water behavior and poor
calm-water behavior to those that showthe opposite trends. On the matter of longer ships, he believed that the cost was not as important a factor as the inability of present harbor facilities to accept such vessels. Roll stabilization on commercial ships is a relatively expensive
proPosi-tion ($600,000 in a $12,000,000 ship) and not feasible at this time.
Mr. Henry concluded that desirable commercial vessels would operate at
high speeds in rough water. To realize this, an optimum hull design must be found that will reduce motions so that maximum average speed in
rough water can be attained.
BASIC RESEARCH COMPLETE?
Professor Korvin-Kroukovsky agreed that the basic solution to
the pitching and heaving problem is available and that all that is needed is mopping-up. He defined the mopping-up operation as the solution of auxiliary problems, which would probably extend through the collective lifetimes of the seminar participants. He further stated that application of basic knowledge to heave and pitch could be extended to unconventional
ship forms through reliance on a rational approach (based on fundamental laws of hydrodynamics) rather than on empirical data. However, Professor
Korvin-Kroukovsky believed that the case of lateral ship motions, in connection
with rolling and steering, was quite another matter. Athough he agreed
with Professor Lewis that roll stabilization design was far advanced, he
could not see universal adoption in cargo ships. Perhaps passive tanks
will be more widely used some years from now, but until that time it will be necessary to study the fundamental problem of rolling and
steer-ing, which has lagged behind the study of pitching.
Professor Korvin-Kroukovsky mentioned that little has been
con-tributed to the basic usable knowledge on rolling since Fraude (1860). In fact, present studies in oblique seas (particularly quartering seas)
completely disregard the hydrodynamics of water flow about the ship. He
continued his opening remarks with a discussion of the importance of
coupling and its function in defining the phase relationships that govern most everything concerning ship motions. Coupling has been studied for
pitch and heave but, to date, nothing has been done about rolling and
steering (yawing) especially on a rational basis as a part of one coupled set of motions. For cargo ships this is the most important
problem, and
basic as well, and is definitely not part of the mopping-up operation. Professor Korvin-Kroukovsky disputed the statement that automatic steering
was satisfactory because there were no complaints. He stated that the
apprenticeship system fostered a be-satisfied attitude, regardless of
how poor a particular tool might be. He bolstered his argument by citing cases where the automatic steering was discontinued in favor of manual steering in sea states as low as that corresponding to a Beaufort 4 wind
force.
RESEARCH OH LATERAL MOTIONS
Dr. Cummins agreed with Professor Korvin-Kroukovsky that the greatest unknowns are in the field of lateral motions, where very little
has been done. In particular, little experimentation, has been conducted that was concerned with rolling,at forward speeds. Coupling of roll and
sway was also considered important. Dr. Cummins mentioned that, in the case of rolling, the superposition principle probably left something to
be desired. He did not agree that all the problems in longitudinal
motions have been solved. He further stressed the deficiencies in the evaluation of hydrodynamic coefficients, especially for unconventional
hulls. In the case of slamming, Dr. Cummins called for an adequate theory to predict slamming pressures around any hull to supplement our present knowledge, which only permits us to estimate orders of magnitude. He supported Mr. Henry's contention about the importance of bow lines and cited the trials of a pair of Liberty Ships in which the
bow-length-ened version showed 1 to 2 knots better average speed than the unchanged
ship, in North Atlantic winter service.
LOCAL MINIMIZATION OF MOTION
Mr. Mills suggested that it might well be preferable for sonar to follow a given path at a fixed depth than to seek a path of no
motion. Mr. Mills analyzed the effect of increased length of naval ves-sels in contrast to Mr. Henry's analysis for merchant ships. Because naval vessels carry payloads on the ship (armament) rather than in it
(cargo), lengthening the ship requires adequate draft to avoid slamming, etc. However, increased draft, raises the center-of-gravity of the
pay-load, and to maintain desired stability, the beam must be increased.
Consequently, lengthening the ship results in an increase in all
dimen-sions. Mr. Mills concluded his remarks by commenting on the chairman's
suggestion that model tests be used to provide design information.
Mr. Mills accepted the validity of this premise in principle, though he
stated that, in fact, the time demand for a new design was such, that thorough model testing could not be permitted. Perhaps, suggested
Mr. Mills, a change in design methods is in order to permit complete
evaluation of the proposed hull form.
ANTI-ROLLING TANKS AND STEERING
Mr. Henry responded to the chairman's suggestion that available
tanks on merchant ships, presently used for fuel, water, cargo, etc, might easily be converted to usefull passive anti-rolling tank systems.
Hethought that a tank that could be made to do double duty was certainly
worth looking into. Modification costs did not seem to be prohibitive.
The bow lines were again mentioned and here Mr. Henry spoke up for
aban-donment of lines design based on calm-water conditions. He favored specific designs related to the prevalent sea conditions that would be encountered in the expected travel lanes of each ship. On steering,
Mr. Henry agreed that there was little complaint from the commercial
people. However, this, in some measure, was caused by their acceptance
of compromises in the form of larger rudder areas and larger angles in
contrast to rapid steering. Of course, on occasion, automatic steering is abandoned in heavy seas and the ship is steered by hand, though this
does not imply that the ship could maintain a better overall speed one
way or the other.
GAPS IN BASIC KNOWLEDGE
--A MATTER OF SEMANTICS
Professor Korvin-Kroukovsky stated that quite a bit of the discussion was a matter of semantics rather than differences of opinion.
Research still must be conducted in many areas and the problems that do
exist will probably not be solved in our lifetime.
The pattern of research in pitching and heaving is well
estab-lished and no unexpected surprises will occur in that basic pattern,
though in directional steering and rolling a basic pattern of researth
has not been established.
Although considerable technical advances have occurred in the past few years in the prediction of ship motion by calculation, at the moment, this knowledge is limited to a few specialists who still carry
it out with considerable effort. The knowledge is not widespread among
naval architects.
Professor Korvin-Kroukovsky further stated that only a small part of the presentformaltechnicaleducationis important;more important
is the training of people to understand the basic physical processes and to encourage the use of this knowledge as it should be applied to specific
problems.
In addition, much more data on damping and more ability to
handle non-linear considerations are required. The problems associated
with aircraft carriers can be handled,to a large extent, by existing
theories. The problems of whether slamming will occur and how much the ramp will move are primarily governed by the heave-pitch phase relation-ship. However, at the moment, there is not enough understanding of the
meaning of the coefficients of the cross-coupling terms.
All of these problems,however, are part of the mopping-up required. This does not mean that it is not a major problem; though it
does mean that the directions are already indicated. Whether the problem of directional stability and control is important or not is debatable. Mr. Henry indicated that it is not important. At present, steering characteristics have high priority in the U.S. and in England. A lot of
money has been spent to determine steering characteristics. This simply indicates that this problem requires constant study of an empirical
At present, models cannot be used to determine directional
and rolling characteristics and coupling of rolling and yawing. A simple
technique is not available to determine how the high damping of the roll-ing motion can effect the coupled motion of ships in oblique seas, and
direct tests of ship behavior in quartering seas in a square tank are not very meaningful.
However, if a small fraction of the money spent to solve basic oblique-sea operational problems experimentally was diverted to
theoreti-cal research on problems associated with steering and lateral motion,
huge savings in ship construction and research would result.
The audience was
invited to
participate in a general question-answer period. Mr. Marvin Haar of the Martin Co. asked whether the lines forunconven-tional hull forms are developed from theoretical
con-siderations or from empirical evidence.
Mr. Mills stated that the particular form considered was derived from
considerations other than seakeeping characteristics. The unconventional changes were to achieve another end and the
effects on seakeeping characteristics were only of secondary importance.
Mr. S. Caldwell of the Electric Boat Co, in the nature of a general
com-ment, echoed Mr. Mills' lament on insufficient model
tests before a design becomes a reality. Apparently,
the philosophy is that there is plenty of time to correct errors later
on. Dynamic stability on course was another point mentioned by Mr. Caldwell. If a ship is dynamically unstable and this is known to be
caused by an inadequate hydraulic system, it is very difficult and expensive, from the administrative standpoint alone, to discard the system. The importance of studying aircraft carrier vertical motions
and the need for reducing them were reinforced by Mr. Caldwell who recounted some personal exp riences on the USS VALLEY FORGE, where the vertical accelerations were so large that he could get from one deck to another with almost no effort (with proper phasing).
Commander F. J. Bryant of the U.S. Coast and Geodetic Survey also
com-mented on the importance of directional stability
and the value of its consideration early in the design stage. Directional instability leads to operational difficulties
even in moderate sea states, though arLadequate rudder and an
insuffi-ciently powerful steering engine still permit a directionally stable ship,
to be held on a straight and steady course even in severe sea conditions. On the subject of the forward lines, Commander Bryant favored the
be gained in fuel consumption and propulsion efficiency in calm water,
the gain is wiped out when ships slam, thus losing speed and risking
serious damage forward. Also mentioned was the phenomenon of slamming without bow emergence. Commander Bryant defined this occurrence as a high-frequency, vibratory hull-motion caused by rapid pressure variations
forward as incident wave and ship produce synchronism without bow
emerg-ence. A heavy sea is not requisite to the occurrence of this unpleasant
event.
Dr. Cummins stated that slamming without bow emergence has been observed; that is, the entire ship is set into vibration in its first
mode without any evidence of impact, and that another form
of the same phenomenon could be caused by excessive flare. This is
com-mon with aircraft carriers; when the flared sections strike the water surface, the result is equivalent to a slam associated with bow emergence.
It has been observed on many records of full-scale trials that in the
absence of evidence of impact, there is significant first mode
vibra-tion generated.
Professor Lewis added that it has been said that this type of vibration
is prevalent among shallow-draft, flexible-hull ships such as the old type of aircraft carrier. This type of
flexible hull has a long natural frequency of vibration that may attract the (sometimes appreciable) energy, in the wave spectrum at this frequency, without affecting pitch very much.
Mr. T. L. Soo-Hoo of the Office of Chief of Naval Operations stated that research on ship behavior at sea was rather far from
being a closed issue and was in fact just beginning. That is, at present, it is necessary to identify the problems. In fact,
with the present coming of age of electronic devices, it is now possible to conduct sophisticated experiments in the model tank and at sea. This
is not to say that less objective data collection techniques, such as
ships° logs, do not produce much valuable information. However, it seems that many problems will yield to solution if just some suitable records can be obtained. Instrumentation is just one aspect of dealing with data. Mr. Soo-Hoo lamented the waste of scientific personnel required to nurse the instrumentation along. He also took issue with the collec-tion of reels of data that are only partially and laboriously analyzed and finally presented after a few years. He cited a recent example of
such a happening where, in addition, the organizers of the program and
those who collected the data were gone from the scene and the analysis had to be done by others. Mr. Soo-Hoo's final comment concerned the funding of research. He stated, emphatically, that there was all too
little money spread over the great variety of problems that need atten-tion. He looked for a unification of funding with sensible data
collec-tion and streamlined analysis so that some solucollec-tions to pressing problems Can be gotten efficiently.
Professor Lewis made a plea for not letting elaborate instrumentation obscure basically simple problems--for example, to
determine the value of acceleration that generates the upper limit of
passenger comfort, the amount of water over the bow that forces speed
reduction,and the specific events that force course changes. Model tests can be used only to determine what will happen under certain given con-ditions, What is needed is a guide from the operators on limiting
criteria that govern subjective decisions to change speed and course. Then, model tests may become more meaningful. Professor Lewis solicited comments on these views.
Professor Korvin-Kroukovsky stated that full-scale trials lose their
worth when there is no measure of the
environment in which the experiment was con-' ducted--that is, the sea state must be accurately measured and described.
Dr. Cummins mentioned that accurate sea-state measurement devices--for example, the Splashnik recorder--are only a recent
develop-ment. In addition, there have been remarkable advances in data reduction. At present, data can be processed almost as fast as it is collected.
Commander Peter Du Cane, managing director of Vosper, Ltd., was surprised
at Mr. Henry's cost estimate for anti-rolling fin installation on cargo ships. His own firmes installation on a four million dollar yacht came to $25,000 or about 0.6
percent of the total cost in contrast to Mr. Henry's figure of 7 percent.
Of course, the British fins were not retractable, but this does not seem to be too important. There are however problems connected with
fins; one arose when a fin, designed for maximum
damping at a forward speed of 14 knots, gave best results at 7 knots. Because the lift on the fin is proportional to the square of the speed, it is difficult to see how this happened.
CONCLUDING REMARKS
Dr. Cummins made a strong case for the use of the model
tank to solve many of the problems that are notpresently amenable to analytical treatment, and stated that no theory is adequate until it has
been checked out in the model tank. Although Dr. Cummins personal interest is in elegant mathematical theory rather than semi-empirical studies, he sees no value to unverified theory. Tanks like those at
Wageningen, Davidson Laboratory, and the David Taylor Model Basin are
essential in this regard. As for the new DTMB seakeeping facility,
Dr. Cummins defended its size and cost with the pronouncement that it
may not be large enough. Because it is designed to accommodate 20 to 30 foot models, it is relatively smaller than the Wageningen tank which
accommodates 12-20 foot models. To remedy the difficulty, DTMB plans to
test with 12 to 15 foot models.
Mr. Henry agreedwithCommanderBryant and Professor Korvin-Kroukovsky that directional stability was a key to better ship
perform-ance and better schedule keeping.
Professor Korvin-Kroukovsky emphasized the need to stop sepa-rating theory from the other parts of research--that is, few theories can be accepted without experimental verification; few seakeeping
experi-ments can be correctly evaluated without theory.
IN SUMMATION
Professor Lewis, as panel chairman, summarized the discussion by stating that it was clear there was still much to be done on the pro-blem of ship behavior; in fact, basic studies were needed to refine and
improve present theory. This basic work should include, among other items: accurate determination of the coefficients in the equations of motion, three dimensional effects, fundamental studies of rolling, and
the coupling of lateral motions. The chairman was particularly pleased
that specific problems such as minimizing local motions on carriers,
improving steering on commr-cial ships, and hull forM-slamming
relation-ship were brought to the fore. He stressed the importance of bringing
the problems to the researcher so he might better serve the needs of the designer and operator.
1.
OCEAN-WAVE MEASUREMENTS
Wilbur Marks
INTRODUCTION
Ocean waves enter into the ship behavior picture in a causal capacity; therefore, a description of the sea surface is essential to the interpretation of almost all prototype investigations of ship per-formance. Depending on the nature of the particular problem, the seaway
can be adequately defined by (1) some convenient statistics like average height and period, (2) the energy spectrum of the waves, (3) the time
history of the waves passing a fixed (or moving) point, and (4) by
various other means. Regardless of the sea-state definition used, it is usually worthwhile to first obtain an electro-mechanical measurement of
the waves (wave record).
To facilitate a comparison of the physical principles, advan-tages, and disadvantages of some of the wave-recording devices that may be applicable to the study of ship behavior at sea, wave measuring
devices may be grouped as:
Underwater Wave-Measurement Devices Surface Wave-Measurement Devices Aerial Wave-Measurement Devices
UNDERWATER WAVE-MEASUREMENT DEVICES
The underwater wave meters measure pressure variations on the ocean bottom as waves pass overhead(Figure 1.1). If the wave-length (X) is long compared with the depth (d), the amplitude of the pressure fluctuation (p) is directly proportional to the wave height (a) without correction, as follows:
a = p cosh 2nd/x
Pressure changes are detected and communicated through cables to shore recorders by transducers that use various elements--such as inductance
bridges, strain gages, thermocouples, and others.
300 FLOAT
---
PRESSURE T RANSDUVER -r PRE-SSURE INVERTEDECHO SOUNDER- AN CH OR SYS TEN
.
a.-PRE SS_U,RE
FIGURE I.Ir
UNDERWATER WAVE - MEASUREMENT DEVICES
0-REC ORDER
Pressure transducers mounted on the ocean bottom are of little use to ship behavior studies in deep water, because waves attenuate with
depth and, unless corrected, yield erroneous results. Pressure trans-ducers may, however, be placed in close proximity to the surface by
anchoring them to the bottom. This has not been tried in ship work,
because it is a difficult problem that does not merit the effort in view
of simpler methods that are available. Pressure recorders mounted in hulls of ships have been used with some success and will be discussed
with the surface recorders.
In principle, a pressure recorder suspended from the surface by a float and immersed deep in the water is promising. If the pressure
element is sufficiently deep, it is insensitive to all surface-wave
com-ponents. Pressure variations proportional to wave height are detected
by the pressure element,which rises and falls as waves pass the float. The faithful response of the pressure recorder to the motion of the float
is questionable.
The echo sounder measures oceanbottom contours by observing the travel time of a sonic beam reflected off the ocean bottom. If the
echo sounder is inverted, the sound pulses are reflected off the
air-sea interface, and thus provide a means of wave measurement. The inverted
echo sounder can be mounted on the ocean bottom, suspended from the ocean
bottom, or linked to a ship by cable. Difficulties arise because of the
wide angle af the sound beam (which looks at a wide area of surface), and
because the receiver primarily detects the first returned pulse, which usually reflects from troughs and sides of waves and thus neglects crests.
White caps muddle the echo, and this increases the measuring difficulty.
It is possible, however, to tow the instrument; launching and retrieving
SURFACE WAVE-MEASUREMENT DEVICES
Surface wave-measurement (Figure 1.2) offers a number of possibil-ities to the ship researcher. Visual observations, however unreliable,
are still the easiest to make; these are recorded periodically in the
ships° deck logs. Visual observations augmented by photographs would
certainly be more valuable. Optical systems, based on the coupled rangefinder principle, with a scale in the eyepiece, are an attempt to
mechanize visual observations. If properly developed, such a system will greatly enhance the value of log data. Replace the eye by a camera, and
quantitative data may be had.
The probe or wave pole has enjoyed some popularity among
ocean-ographers. The probe may be fixed to a firmly anchored structure or,in deep water, it may be stabilized by a drogue, or set of tanks, or other
means. If the probe is graduated, it may be photographed, but such data
are clumsy to analyze even when the pictures are good. Usually, the probe is part of an electric circuit such as the plate of a condenser or as a
resistor; as the water rises and falls on the probe, the change in the
electrical variable thus measured is proportional to wave height. The
basic mechanical difficulty with probes is the necessity to hold down their vertical motion or, at least,to keep their frequency response
out-side the frequency range of gravity waves. The major disadvantage,
how-ever, is the launching and retrieving of the usually cumbersome gear.
In addition, the height of the waves that can be measured is limited by
the length of the probe.
A surface sea-state meter that overcomes the objections of the
probe is the accelerometer wave-buoy. A vertical accelerometer mounted in a float senses the apparent vertical acceleration of the float and hence of the waves. The acceleration signal is telemetered to a ship which is physically free of the buoy. Such an instrument is easily
launched and one kind, presently in use, is sufficiently inexpensive that it may be abandoned. The signal received on the ship can be doubly
integrated to yield a wave-height record or, after spectrum analysis of
STEREO
PHOTOGRAPHY-w:-"
WAVE POLE RESISTANCE CAPACITANCE INDUCTANCE
ACCELEROMETER .:CABLE ...-TRANSMISSION ace.» ACCELEROMETER BUOY ras- PRESSURE"-CAMERA FIGURE 1 . 2 .
SURFACE WAVE-MEASUREMENT DEVICES
... -GRADUATED ... POLE . .. DROGUE.
FIXED WAVE POLE
Ple"`
."`
.7= _ er.--r,saifigo.-7-the acceleration signal, ifigo.-7-the spectrum of wave height may be obtained by
an algebraic operation. Because the raft (hence accelerometer) tilts
with the wave slope, spurious acceleration information results. It has
been shown that this is not serious for most sea states. However, it has
been found that the buoy drifts with wind and waves, the line of sight
transmission can be obscured by large waves, the limited available
electrical power restricts telemetry to about 10 miles and the
trans-mitting life of the system is about 8 hours. If the buoy is connected
to the ship by electric cables, transmitting problems disappear but the
ship is then not free to maneuver.
Another popular surface instrument is the shipborne wave
recorder. A pressure transducer mounted on one side of the hull
amid-ships measures the height of the water surface above it. An accelero-meter measures the vertical motion of the pressure transducer. The
accelerometer output is doubly integrated and added to the output of the pressure transducer to produce a record of wave height. A similar sys-tem is installed on the other side of the ship and the average output of the two is supposed to account for wave reflection and ship rolling in
oblique seas. Of course, high-frequency waves are attenuated by the
pressure transducer. In addition, the wavemaking of the ship prevents
the instrument from being reliable when the ship is underway, especially
in following seas. However, all instrumentation is aboard ship, which is very appealing, especially in heavy seas. The difficulties that arise
from the pressure transducer can be eased by replacing it with a sonic or capacitance probe at the bow. These possibilities are being studied. Of all the surface type ins'truments, the shipborne wave recorder and the accelerometer buoy show the most promise for ship motion studies.
SONIC PROSE STEREO° PNOTOORAPHY RADAR ALTIMETER
:4--
tO'dÌ
-... --__-_ . -FIGURE 1.1 AERIAL WAVE MEASUREMENT DEVICES STRIP CAMERASAERIAL WAVE-MEASUREMENT DEVICES
Aerial wave-measuring devices(Figure usually require air-craft, which makes them unsuitable for ordinary full-scale
experimenta-tion. However, when aircraft are involved in an experiment or for sea-planes in general, certain of these methods can be used to good advantage. The airborne radar altimeter mounted in a low, fast plane sends a narrow beam to the surface; the beam reflected is recorded in terms of round trip travel time and therefore defines the distance to the surface (which
is a measure of wave elevation). Such a unit on the bow of a ship might work well with an accelerometer. Aerial stereophotography was first used to measure sea states by mounting two cameras, oriented toward the
hori-zon, on the mast of a ship. On an aircraft the cameras would be oriented straight down and two aircraft flying several thousand feet apart and
several thousand feet high would be required.
Nothing has been said aboW- measuring the directional properties of waves, which is important in many practical problems. Here, some of the already mentioned methods may be adapted for use. The shipborne wave
recorder will yield the mean direction of wave travel if a series of runs with varying relative headings is made. The accelerometer buoy, if out-fitted with pitch and roll gyros, can produce a measure of the directional beam width of the waves. Aerial stereophotographs have also been used to obtain directional wave spectra,but the method is costly. Theory has been developed to extract the wave directions from the outputs of arrays of
probes. It goes without saying that visual observations may also be used
for crude estimates.
Although there are many wave-measurement systems, none is per-fect and new ideas are always in demand.
2.
HYDROFOIL CRAFT IN WAVES
T. Francis OgilvieINTRODUCTION
The first attempts at building hydrofoil craft were made in
the same decade that saw the first successful aircraft. Thus, the
sub-ject of hydrofoil craft--as an engineering subsub-ject--is over half a
cen-tury old. However, intensity of interest was low; until the 1940's, generally, only a few illustrious persons kept the subject just barely
alive. Just before 1920, for example, Alexander Graham Bell fitted a hull with two aircraft engines with air screws and some ladder foils;
he pushed his craft to a claimed 70 mph. In the 1930's, there were
several German experiments with hydrofoils; these ended in aborted attempts to make war vehicles toward the end of World War II. Their
technological advances were absorbed by both the United States and the
Soviet Union after the war. The USSR apparently has been busy in this 'field; they have a few rather large passenger ferry hydrofoil craft
operating on inland waters. Now hydrofoils are being forced to the forefront and activity is burgeoning in several directions at once.
The original interest in hydrofoils was to be found in their
still water charcteristics. As the foils lift the hull clear of the water, the wake practically disappears and resistance decreases markedly. To transport high-priority cargo at high speeds, hydrofoil craft will be
more efficient than conventional displacement craft. Passengers are a typical high-priority cargo: commericial use of hydrofoil craft as
passenger ferries is promi:,ing.
At some point in the earlier experiments with hydrofoil craft, an unexpected characteristic was observed. When these craft encounter
waves, their behavior is drastically different from that of conventional craft. Often, when conventional craft heave, pitch, and roll violently, the hydrofoil craft remains comparatively stable. However, even in
fairly mild sea conditions the hydrofoil craft may not take off, or, if it does manage to take off, it will sometimes nose down and burrow deep
into the waves. It was only about ten years ago that an attempt
was made to understand and predict these phenomena quantitatively. The first attempt was made by Weinblum. The results appear in a David Taylor
Model Basin (DTMB) report of 1954 (reference 1).
In 1955, DTMB started a project to check Weinblum's results
experimentally. Some interesting results were obtained by Leehey and
Steele (reference 2), and this work has been extended recently at the University of Minnesota (reference 3) under a DTMB contract.
In 1954, Dr. Kaplan (reference 4) published a paper in which he considered a simpler problem from a much more sophisticated point of
view.
In 1956 and 1957, I had the opportunity to restudy Weinblum's problem (reference 5) and I was able to modify it in such a way that it
checked rather well with the experimental results of Leehey and Steele. The more recent work at Minnesota also checks quite well, generally, with these theoretical predictions.
There are several major gaps in the state-of-the-art and there are severe shortcomings of the conventional approach to building hydrofoil craft, as shown both by experience and by the analytical
procedures. At present, various directions are being taken in research
to rectify these difficulties.
Several configurations of hydrofoils have found favor in the
last thirty years. Figure 201 shows one of the simplest of these
--two large-dihedral airfoils, 45 degree rise from the horizontal. These
foils were used in some of the Leehey and Steele experiments (reference 2), and in all of the Minnesota experiments (reference 3). Only
the
motions of the foil-borne craft were studied in these projects;no hull
was used. The mass and moment of inertia of the hull were simulated byweights attached to the structure above the foils,
Normally, the craft rides with about half of each foil
sub-merged. If for some reason the vessel pitches downward, the submerged area of the forward foil increases and the submerged area of the after
foil decreases. This increases the lift forward and decreases the
lift aft and produces a moment that tends to right the craft. Similarly,
FIGURE 21 TWO LARGE-DIHEDRAL FOILS , 45-DEGREE RISE FROM HORIZONTAL
I f
C.G.
ba bf
d
FIGURE 2.2.
GEOMETRY OF AREA-STABILIZED FOIL
perturbation in heave and roll are resisted by the changing forces due
to changes of submerged foil areas. This system (area-stabilized) and variations of it dominated the field until early in 1950.
THEORETICAL ANALYSIS OF AREA-STABILIZED FOILS
The simplest way to analyze the forces that affect an area stabilized hydrofoil system is to assume that the lift can be given by
L (1/2 p V2) (C0 + c9 a) S
where,
V = forward speed
a = angle of attack
Co = lift coefficient for a =
C2 = lift curve slope
S = projection on a horizontal plane of the submerged area of the foil.
For a foil of this type, near a free surface, this formula can, at
present, only be justified empirically. For steady motion of a hydrofoil through otherwise calm water, this formula is valid when the variations in a and S are not too great.
Figure 2.2 shows an end view of the foil. If the angle-of-dihedral is p. and the submergence of the foil apex is d, then:
span = 2 d cot p
and if the chord is a constant (b), theng
S = projected planform area = 2 d b cot p.
These formulas apply reasonably well only for steady flight in
calm water. They can be checked under such conditions. Only by a
sig-nificant extrapolation can these formulas be extended to unsteady con-ditions. To analyze the forces generated by two area-stabilized foils,
Newton's law states that:
m = Lf + La -W
I 1; fLf aLa
where,
m = mass of craft,
I = moment of inertia about the center-of-gravity, W = weight of craft = mg.
The dots over the variables indicates time differentiation, and
the subscripts, f and a, refer to appropriate quantities for the fore
and aft foils, respectively.
The previous expression for the lift of each foil, can be
sub-stituted into these equations of motion. If there are incident waves, a and S explicitly depend on the expressions for the amplitude, phase, and
wave length. They also depend on the instantaneous position and vertical
velocity of the foils. In fact, it is readily shown that.
af * - 1/V + f * + aw Af sin (vt, + kif)]
Sf = 2b cot
EJf0 -Z-R
+acos (Tut + where,a = amplitude of the waves
m circular frequency of the waves at a fixed observation point = circular frequency of encounter
Af = a constant that approximates the
effect of decay of orbital
motions with depth
d
df for steady motion in still water.
These expressions are substituted into the formulas for'lift,
which are then substituted into the equations of motion. The results are given in reference 5.
Several points should be noted:
There are terms in the equation of the form af Sf. Because both of these quantities include z and * and their time derivatives, the
equations are nonlinear in z and *. Thus, some typical nonlinear effects are expected. For example, if the incoming waves are sinusoidal, as assumed above, the response will include a component at the frequency of incidence of the waves. Because of the nonlinearities, two other
compo-nents are expected in the response: (a) harmonics of the fundamental frequency and (b) a steady-state or d.c. response. The calculations never showed the presence of harmonics, but d.c. responses did appear.
Most of the free-surface effects and unsteadiness effects
have been neglected. The fundamental formula for the lift of a foil was
based on steady-state conditions. But the motion is not steady.
There-fore, not only will wave generation be of possible importance, but the effects of,aerodynamic downwash of the foils will also be important. As the lift varies with time, the circulation around each foil varies; thus, vorticity is left behind in the wake. Particularly at high frequencies, the lift forces will be reduced drastically.
The after foil moves in the waves and wake generated by
the forward foil. The wake can probably be ignored, because the vorticity
is largely dissipated by turbulence. But the waves should not be ignored.
The nature of the waves generated by large-dihedral foils is at present unknown, except as it may be observed experimentally.
On the basis of this kind of elementarytheory, calculations were
made for one of the configurations used in the Leehey and Steele
experi-ments (Figure 2.1). The experimental points and the solutions were actually obtained at the St. Anthony Falls Hydraulic Laboratory of the University of Minnesota (reference 3) as part of a project to extend the range of earlier work.
Figure 2.3 shows the heave amplitude for the foil in head seas. The circles are experimental points and the two lines are theoretical
results. The broken line shows that the results are only slightly
changed when the unsteadiness effects are included. This means that the
vorticity in the wake has been accounted for--and apparently does not
matter much, as far as motions are concerned. One curve suffices for all wave amplitudes; therefore, the nonlinearities do notaffect the amplitude.
300
cr)250
ow200
c» u-,150
ic-c»o
10050
0.7 06 pqa 05 o 04 o o 03 E 02 0.1 o 4 8 10 12Wave Length in feet
14 16 18
FIGURE 2.3. HEAD SEAS HEAVE AMPLIFICATION FACTOR (V=10 fps)
FIGURE 2.4. HEAD SEAS HEAVE PHASE LEAD ; ( V 10fps)
Se Unsteady Linear tr.
i
.o Oo
Ouasi- steady LinearA 01 6' O
O.
\
I' que ore7
e
g 0
94110Quasi-steady Linear\
to
we
%
I 1 w for h.tr
Unsteady Linear/
i
0
o/
2 4 6 8 10 12 14 16 18The foil spacing was three feet; all tests and calculations
are for a speed of 10 fps. This corresponds to a Froude number (based
on foil spacing) of about unity. Note that the largest amplification factor is about 0.6; for incident,8-foot long waves, the amplification
is 0.3. This means simply that in 8-foot long waves of about 1-in
amplitude, the heave amplitude is 0.3 inch.
Figure 2.4 shows the phase of the heave motion with respect
to the wave phase at the center-of-gravity. In the very short waves, the
motion leads the wave peaks by about 100 degrees. For a wave length of 5 feet, the amplitude of heave went almost to zero. At wave lengths of
5 feet there is a sudden shift of phase; in longer waves, the heave-phase lead is about 270 degrees which is equivalent to a heave-phase lag of
90 degrees.
Figure 2.5 shows the pitch response. Although * is
non-dimensional, it has been multiplied by i/a to make it comparable with
the heave figure. The ordinate represents the vertical amplitude of motion of either foil on the same scale as the figure for heave motion. The greatest amplitude factor is 0.3.
Figure 2.6 shows the pitch phase lead. It is referred to the phase of the wave peak at the center-of-gravity.
Figures 2.7 through 2.10 show similar results for following
seas.
Figure 2.7 givesheave amplificationfactors. Note particularly
the difference in vertical scale. At 8-foot wavelengths, the amplification factor is greater than 3.0. In head seas, the corresponding heave
amplification factor was 0.3 -- 1/10th as much.
Figure 2.8 shows the phase leads. Again there is practically
a discontinuity in the curve. However, agreement is again reasonably good.
Figure 2.9 shows the pitch amplification factor. Note that
the vertical scale is much different than in head seas, where the maximum amplification factor was about 0.3.
0.5
°
0.4
o
o
o
L0.3
o
c.) ;)70.2
Q. E .rz 0.1o
ET_250
1 50.c
50
o
Oo
4
6 8 10 12Wave Length in
feet
14
FIGURE 2.5. HEAD - SEAS PITCH AMPLIFICATION ( V 10 fps)
16
2
4
6 8 10 12Wave Length
infeet
FIGURE 2.6. HEAD - SEAS PITCH PHASE LEAD ( V 10 fPs)
,4.-Si
/
goe
0) 6
C Unsteady ... +. 11. Quasi-steady LinearII)
I
INGO
0
i)
... Linearf.
0
fliN Quasi-steady Linear Linear0
L UnsteadyU
0
_ 14 16O 380 340 300 260 220 180 140
Wave Length in feet
FIGURE 2.8. FOLLOWING - SEAS HEAVE PHASE LEAD ( V z 10 fps )
FIGURE 2.7. FOLLOWING - SEAS HEAVE AMPLIFICATION FACTOR, ( V z 10 fps )
/
/
/
/
Quasi-steady Linear/
2/
/
A-Unstea y LinearA3
/
o
leIll
Gie ---/H-C17---=,.0
0
C Quasi-steady mearo
Linear Unsteady g 4 5 6 9Wave Length in feet
1.5 1.0 0.5 100
50
-100 -150Quasi -steady Linear
....---..---" ....---...---" "...-- .----. ---- . 01
.../
..--."0
Unsteady Linear '.' '',
C ,".) 1?) 30
0
Quasi-steady Linear0
0
0
...0
Lineara
Unsteady "'..' -4g ... .1 ... ...00
_. 4 5 6 7 8 9Wave Length in feet
FIGURE 2.9. FOLLOWING - SEAS PITCH AMPLIFICATION FACTOR
( V = 10 fps )
2 3 4 5 6 7 8
Wave Length in feet
Figure 2.10 shows the pitch-phase leads.
It is evident that agreement between theory and experiment
is quite good in all cases. But this agreement should be taken to some extent as an accident. One might say that the right answers are
obtained for the wrong reason. The basis for this statement has been
mentioned -- neglect of unsteadiness effects. A theory on the simple
quasi-steady basis predicts forces as much as 60 percent higher than
a true unsteadiness theory. The errors however combine and cancel to give approximately correct motion predictions. The small difference in motions caused by unsteadiness is clear. Although this error does not
distort the motion predictions too much, it is obviously of great
impor-tance to the structural engineer who must design the foils and struts.
An over-estimate of 60 percent in forces is far from negligible.
To date, few measurements of forces have been made on foils in
waves. The results are quite inconclusive, and to a certain extent they agree with neither the quasi-steady nor the unsteady theories. This is
still under investigation, and perhaps before the next summer session is conducted in 1962, the answers shall be available.
The forces on a two-dimensional,completely submerged hydrofoil in unsteady motion near a free surface were first worked out by Kaplan in a Stevens dissertation (reference 4). On the basis of his work, the error due to the neglect of the free surface can be estimated; the assumptions made here are fairly reasonable in most cases.
SUMMATION
The effect of the free surface has been ignored except as it supplies the termination of the foil span. Estimates of the free-surface effects depend entirely upon interpretations of two-dimensional analyses.
At best then, such estimates are based on a strip theory. This is not
entirely satisfactory.
The two-dimensional theory referred to indicates that free-surface effects are not very important if the submergence of a foil is
