ARCHIEF
15 SEP. 97?(V
boheek van
Onderadei!1
T4ÇÍhe
Hogescho&i tje4-.
HYDRODYNAMICS AND SIMULATION IN THE CANADIAN HYDROFOIL PROGRAM
BY
R. T. Schrnitke and E. A. Jones
DEFENCE RESEARCH ESTABLIS}-INT ATLANTIC DARTMOUTH, N. S.
CANADA
For presentation at the
9TH SYMPOSIUM ON NAVAL HYDRODYNAMICS PARIS August 1972
Á3
Lab. y.Scheepsbouwkunde
Technische Hog'schooI
DeiftI
Hydrodynamic aspects of the Canadian hydrofoil program are discussed, with particular reference to F-IIICS BRAS D'OR. Associated
simulation studies are described and key results of BRAS D'OR seakeeping trials are presented.
HYDRODYNPNICS AND SIMULATION IN THE CANADIAN HYDROFOIL PROGRAM
INTRODUCTION
For more than a decade the Canadian hydrofoil program has been synonymous with the design, construction and trials of }-U1CS BRAS
D'OR1
(Fig. 1). The recent suspension of trials and subsequent mothballing
of
the ship make this an appropriate time for a comprehensive review of design experience in the light of trials observations. This paper is particularly concerned with the hydrodynamics of the hydrofoil system
and associated simulation studies.
Factors governing foil system configuration and hydrodynamnic design are described, with some details of development experience at the model scale and a thorough discussion of full scale trials observations. The mathematical models used in simulation studies are then presented, and predictions of steady state and. dynamic performance are compared with trials data. The paper concludes with ari analysis of BRAS D'OR
seakeeping trials.
FOIL SYSTEM HYDRODYNAraCS System Configuration
Since its inception the Canadian hydrofoil program has been based on passively stable surface-piercing hydrofoil systems, thereby
complement-ing U. S. effort on automatically controlled fully-submerged systems. The principal relative merits of each type are listed
below2.
lly-submerged systems offer:
a smoother ride in rroderate to heavy seas, higher lift-drag ratio,
lower foil system weight,
greater foilborne manoeuvrability, retraction capability.
Surface-piercing systems offer: inherent stability,
a wider range of foilborne speeds, better sea-keeping at huilborne speeds,
higher potential for remaining foilborne in extreme seas, greater tolerance to off-design loads, such as those imposed by towed sonar.
Successful contouring of large waves requires that the bow foil respond rapidly to changes in immersion depth; for satisfactory following
sea operation, the bow foil must also be reasonably insensitive to wave orbital velocities. Together these requirements dictate that the bow
foil combine high rate of chage of lift with draft, -, with low rate of change of lift with angle, .
The after foil, on the other hand, must have high to provide adequate damping of seaway-induced motions. Furthermore, - must be lower than at the bow foil in order that downward heave displacements cause upward trim. Since foil efftciency generally increases with
a canard configuration is the logical result, with the bow foil carrying as little weight as dynamically feasible.
A secondary but significant advantage of the canard configuration is that it lends itself to a hull with very fine bow lines. This is necessary for reduced pounding due to wave impact when foilborne and is
-3-particularly important for the Canadian rle with its emphasis on good huilborne performance and seakeeping.
The Sub-Cavitating Main Foil
In addition to providing adequate heave damping through high the main foil unit must provide roll stiffness without undue heave stiffness. The BRAS D'CR unit (Fig. 2) accomplishes this by use of
anhedral and dihedral surface-piercing elements at either end of a fully-submerged main foil unit. The latter serves as the primary lifting
element and, combined with the dihedrals, provides the required character-istics with high efficiency. The upper anhedral panels are highly cambered
and twisted to develop high lift at take-off. The anhedral tips are incidence-controlled to augment roll stability at low foilborne speeds
and improve turning performance.
The theoretical tools required for hydrodynamic design of a sub-uivitating foil system have been obtained by adding free surface corrections to methods borrowed from subsonic aerodynamics. The prevention of cavita-tion is the chief hydrodynamic constraint in seccavita-tion design, and cavitacavita-tion-
cavitation-free operation above 4C knots necessitates a departure from conventional low speed aerofoils to delayed-cavitation sections such as illustrated in Fig. 3. The design of the particular sections used in BRAS D'OR is
described in They are highly efficient and provide an approximately uniform pressure distribution when operating over a wide range of angle-of-attack in close proximity to the free surface. The practical upper limits of the delayed-cavitation regime are approximately 60 knots in calm water and 50 knots in rough seas - the design speeds for BRAS D'CR.
Full scale trials showed that in general the BRAS D'OR main foil unit has successfully met its design requirements for high efficiency,
low and high . The only significant hydrodynamic problems
encount-ered were associated with emergence of the anhedral-dihedral foil intersections at about 45 knots, which resulted in lateral jerkiness even in calm water. There were two specific problems. The first was caused by intermittent ventilation of the dihedral foils and anhedral tips and was countered by installing additional anti-ventilation fences. The second was fundamental to the main foil geometry and was more difficult to solve. It was due to increased roll and heave stiffness below the
intersections, when both the arthedral tips and the dihedral foils become surface-piercing. It was alleviated by reducing the mean angle-of-attack of the anhedral tips by 2°. This increased main foil immersion and
delayed the emergence of the arihedral-dihedral intersections to approxima-tely 50 knots. The net result was a significant increase in riding comfort in small to moderate waves at speeds up to 50 knots.
Main foil cavitation was never observed during calm water trials, even at 62 knots, indicating that section design met all expectations in this very important respect. No problems arose from hydrodynamic inter-ference between individual foil elements. However, both full scale trials and model tests at the National Physical Laboratory showed that
bow foil wake reduces main foil lift by approximately 10%. The Super-ventilated Bow Foil
Operating conditions for the bow foil are demanding. At foilborrie
-5
of both immersion and angle-of-attack. The hydrofoil system is wholly area-stabilized longitudinally and the lightly-loaded depth-sensitive bow foil is the primary source of control, so that smooth lift vs. immersion and lift vs. angle-of-attack characteristics are essential. Sub-cavitating hydrofoil sections are prone to ventilation in rough water and the result-ing sharp losses in lift at the primary longitudinal control element cause an unacceptable diving
tendency4.
Superventilated sections arethere-fore used for the bow foil, despite their lower efficiency. In this case, occasional suppression of ventilation gives sharp lift increases, but unlike the converse situation with subcavitating sections this is an
inherently safe effect.
The BRAS D'CR bow foil is of diamond configuration (Fig. 4) with a sub-cavitating centre strut and super-ventilated dihedral and anhedral elemants. Tulin Two-Term lower surfaces5 were chosen for the super-ventilated sections (Fig. 5) because these appeared to offer the best
compromise between hydrodynamic efficiency and structural strength. Design incidence is nominally 5° above zero lift (as established by model tests), and rake angle of the unit is adjustable in flight to permit operation at optimum incidence for the prevailing sea condition.
Little information was available on the practical operation of surface-piercing super-ventilated hydrofoils, so that extensive experi-mental development was necessary. Model size had to be as large as practical to minimize scale effects; consequently, the bulk of the work was done at quarter scale, taxing the limits of available towing tank facilities. The same bow foil was also used as part of a complete quarter
scale manned model of the system. A great strength of the development program lay in the ability to test the same model both in the controlled environment of towing tanks and as a functional unit in realistic seaways.
A major concern of the experimental program was upper surface
design, with the objective of inhibiting and controlling intermittent flow reattachment. The leading edge was made as fine as practicable and, to enforce reattachment to occur in stages and hence reduce the severity of accompanying lift increases, two additional break points were incorporated in the upper surface, at 66% and 87% chord. A major problem of the
initial manned model trials was that the anhedral foils served as fences to inhibit the spread of ventilation down the dihedrals, leading to cyclic pitching at speeds close to intersection emergence. This was overcome by adding another large upper surface spoiler to the anhedral sections in the neighbourhood of the intersection.
The most comprehensive set of quarter scale towing tank data was obtained at the National Physical Laboratory (NPL) under Froude-scaled conditions, providing good definition of bow foil characteristics (Figs. 6 and 7). Data points have been coded to show the spanwise extent of leading edge ventilation down the dihedral foils from the upper surface. (For all test conditions of interest, the cavities behind the midback spoilers remained consistently ventilated.) Spanwise extent of leading edge ventilation is indicated by the degree of openness of the points, e.g.:
lO4
fully open O5 50% open
-7-Fig. 9 shows that the lift-curve slope decreases gradually with increasing rake angle as ventilation spreads down the leading edge of the dihedrals.
The most interesting quarter scale tank tests took place at the Lockheed Underwater Missile Facility (LUNF), where both cavitation and Froude numbers were scaled. Cavitation scaling was found to have no significant effect on flow state, lift or drag. An equally significant
finding was that lift values obtained at NFL were much higher than at LUNF (Fig. 8). These differences were later shown to be due in large part to deterioration of the foil surfaces and leading edges during the time interval between the two series of tests.
It was possible to estimate full scale bow foil lift characteristics by direct observation of depth of immersion. Figure 9 shows the steady state lift coefficient (based on horizontally projected immersed area) of the bow foil unit over the foilborne speed range. The full scale lift coefficient falls within limits established by quarter scale model tests at NPL and LUNF except at low speeds. For these, leading edge ventilation extended only partially down the span of the dihedral foils at quarter
scale but was complete at full scale, giving lower lift but more stable
flow.
The inhibiting effect of the outboard intersections was clear at quarter scale. The dihedral foils ventilated from the mid-back spoilers under most conditions, but the intersections, acting as fences, prevented
the initiation of leading edge ventilation until they emerged. It almost invariably occurred on one foil at a time since the associated loss of lift caused the intersections to re-irrimnerse, inhibiting the second dihedral more
strongly. At full scale, initial establishment of leading edge ventilation on the dihedrals still appeared to be associated with emergence of the
intersections, but invariably occurred simultaneously on both dihedral foils. Effects were less clear but full scale ventilation certainly occurred more readily and more strongly than indicated even by LUME quarter scale tests at correctly scaled Froude arid cavitation numbers. This was due at least in part to the fact that full scale trials were seldom held under really calm conditions, the practical limit for "calm" water being set at waves 3 feet in height. Occasionally, during take-off in exceptionally smooth seas, leading edge ventilation was delayed until ship speed approached 40 knots; during this interim period, pitch angles of up to 9° were observed. This situation was easily overcome by increasing speed or bow foil incidence until leading edge ventilation occurred.
Bow foil rake angle optimization trials showed that a strong and persistent ventilated cavity was achieved in calm water at the design rake angle setting (0°). In rough water optimum rake angle varied with heading to the sea; suitable flow and ship motion characteristics were generally achieved in head, beam and following State 5 seas at rake angles of -1°, 0° and l° respectively.
In short, steep seas, flow re-attachment sometimes occurred on the bow foil dihedrals during deep immersion at the face of larger waves. The resulting discontinuous increase in lift gave added impetus to bow up pitch motion. As depth of immersion decreased at the rear wave slope, ventilated flow was re-established, accompanied by a sudden decrease in
lift. Oscillograph records of vertical acceleration during these periods
-9-normal acceleration levels as the ship encountered waves of more typical size and normal ventilated flow was re-established. Because these vertical acceleration spikes were an important source of motional discomfort, an objective of future development must be to improve ventilation stability
at extreme depths of immersion.
Foilborne sea time has not been sufficient to enable firm and quantitative conclusions to be drawn regarding the suitability of bow foil
- and - for rough water operation. However, the ship never experienced
difficulty in following seas, while pitch response to head and bow seas was high. It seems probable that a reduction in - of about 20% would result
in lower vertical accelerations without compromising stability.
A high drag penalty is paid for using super-ventilated sections. The philosophy adopted during BRAS D'OR design was that this condition could be tolerated since the bow foil is primarily a control element carry-ing only 10% of total ship weight. However, trials and model test data indicate that approximately 30% of total foilborne drag is due to the bow
foil. In addition, the high bow foil drag makes fuel consumption, and hence range and endurance, extremely sensitive to longitudinal C.G. location.
BRAS D'OR sea trials have therefore specified three objectives for future super-ventilated bow foil development: reduction of drag,
optiiniza-tion of - and - for rough sea operation, and improvement in ventilated flow stability. These are important considerations, but are secondary to the demonstrated success of the super-ventilated bow foil unit in stabiliz-ing, controlling and steering the ship over a wide range of speed and sea conditions.
3. SIMULATION
Hydrofoil simulation in Canada began with the extensive and comprehensive studies carried out by the DeHavilland Aircraft of Canada Ltd. in support of BRAS D'OR
design6.
These studies weresubsequently supplemented at the Defence Research Establishment
(7,8) . . .
Atlantic , with the objective of achieving simple methods
applicable to all surface-piercing hydrofoil systems. It is largely upon the latter work that this section of the paper is based. Four
topics are treated: the general equations of motion for surf ace-piercing hydrofoil vessels, prediction of steady state performance, analysis of calm water stability and analog simulation of random seas. Because of the close similarity to aircraft practice, descriptive material is kept to a minimum.
Equations of Motion for Surface-Piercing Hydrofoil Ships
The equations of motion listed below are written with respect to the axis system illustrated in Fig. 10. The origin is at the C.G. and in the reference condition of steady symmetric flight in calm water at speed U, the x-axis is directed horizontally forward, the
z-axis vertically upward and the y-axis to port. The pitch angle O is positive for downward rotation of the txw.
Pitch: I O = E (-L.x. cos r. - D.z. + M. cos. Ï'.) - T (xsiny' - zTcos') (1)
y
ii
i
ii
i
i
Heave: m (w - U B) = E L. cos Ï'. + T sin - W (2)
o i i
Since dynamic pressure is constant L., D. and M. are functions of immersion depth (h) and angle-of-attack
()
alone. For an all-fixed Sideslip: m(v + Ur + gØ) = - E L. sin F.i i (4)Roll: I Ø = E L. (y. cos F. + z. sin F. (5)
X 1 1 1 1 1
Yaw: I r = E (D.y. - L.x. sin F. + M. sin F. (6)
z
ii
11
1 1 1L., D. and M. may be evaluated by the methods of References (9), (lO), (li) and (12).
Steady State PerfoLutance
In the steady state, equations (1) to (3) become
E (L.x. cos F. + D.z. - M. cos F. ) + (x cot y - z ) E D. = O (8)
11
111
1 1 T T iL. cos F. + cot y E D. = W (9)
1 1 1
where summation of lift (L.), drag (D.) and pitching moment (M.) is over all foil and strut elements, individually located at (x., y., z.). W is all-up-weight and the line of action of thrust (T) passes through
(xT, zT). The following sign convention is adopted for dihedral and
anhedral angles:
for a port dihedral foil of angle FDp r. =
for a stbd. dihedral foil of angle rDS, r.=
(7)
for a port anhedral foil of angle FAp Fi=
F9
for a stbd. anhedral foil of angle FAS r. =foil system, furthermore, knowledge of h and for a single foil element enables all other h's and
's
to be determined. Hence (8) and (9)contain only two unknowns: h and of a reference foil element. Because of the non-linear nature of these equations the solution must be obtained by an iterative technique.
Figure 11 illustrates the accuracy obtainable using the above
procedure. Predicted curves of BRAS D'OR trim, keel clearance and weight-drag ratio are presented, along with trials measurements of these quantities. Estimated measurement accuracies are ± ½° for trim, + 1 ft. for keel clear-ance and ± 1.5 for W/D. The accuracy of the resistance prediction is of particular importance; the fact that measured drag is higher than predicted is probably due largely to the one to three foot waves encountered during most calm water trials.
Calm Water Stability
Foilborne stability in calm water is most easily assessed by solving the linearized equations of ship motion. Linearization of (1) to (6) results in the following two sets of three coupled linear ordinary differential equations: Longitudinal Pitch: I P = M u + M z + M z + (M + U M ) 8 + e e Heave: mz = Z u + Z z + Z z + (Z + U Z ) e + ze e e Surge: m (u - ge) = x u + X z + X z + (X + U X ) e + xe e (10) (12)
Yaw: 13
-Lateral
Sideslip: m(vUrgØ)=YvYrY0+Yø
o y r Ø 0 Roll: I0 =
K y + K r +K0
+ K0Ø Xy
rIr=Nv+Nr+NØ+N0Ø
z y r where z = (w-Ii ) ätand the stability derivatives M, M etc. are listed in the Appendix.
The longitudinal modes of motion characteristic of passively-stabilized surface-piercing hydrofoil ships consist of a lightly damped oscillation governed by ship pitching characteristics, a heavily damped oscillation related to heave and a simple convergence arising from surge-heave-pitch coupling. These are termed the pitch, heave and coupled
subsidence modes, respectively. For canard configurations, the coupled subsidence mode is always stable, but in airplane configurations
instability may result from adverse heave-pitch coupling. Neither the pitch nor the heave modes are significantly influenced by surge.
Root locus plots showing the effect on BRAS D'OR's longitudinal modes of varying speed are presented in Fig. 12. Longitudinal dynamics
are dominated by the lightly-damped pitch mode in
which
the damping ratiodecreases and natural frequency increases with increasing speed; this
mode's characteristics are a direct result of the bow foil's design,
2
which combined high with low . Similarly, the characteristics of
the heave mode follow from the combination of low with high in the main foil.
Generally speaking, three modes of lateral motion may be dìs-nguished for passively-stabilized surface-piercing hydrofoil ships
(Fig. 13): a rapid convergence of little importance, an oscillation governed by ship rolling characteristics, and a slow convergence arising from sideslip-roll-yaw coupling.
Simulation of Random Seas
In equations (1) to (6) a seaway acts as a forcing function through viriation of foil immersion depth and angle-of-attack with wave
elevation and orbital velocity. The simulation of these seaway variables is now discussed.
The Pierson-Moskowitz spectral form is chosen as a model of the
(l3)
The equation for the wave elevation power spectral density is:
4-'
(w) .008lg2 exp
-.74 (v)
E
w
where V is wind speed. Significant wave height is given by:
f
V'
h1/3 = 1.86-)
for y in knots.
Consider now the case where a hydrofoil ship is travelling at speed U into a head sea. The wave elevation spectrum, expressed in terms of frequency of encounter, is
15
-'' (w')
(w)
1±2U0 w g
with a similar expression holding for the transformed orbital velocity spectrum, (w').
/ w2Uc
w =
g
is the angular frequency of encounter. ' and '' are plotted in Figs.
14 and 15 for U = 50 knots and V = 24 knots (Sea State 5).
o
The white noise technique for simulating a random head sea will now be described. The basis of this method is that a signal with a prescribed
spectrum can be generated by passing white noise of spectral density through a linear filter so designed that the square of its frequency
response, H (w), has the desired shape. Filter output is, then,
(w) = 5H(w 2 (21)
J o
In particular, the generation of waves with spectrum ' can be accomplished using a filter network consisting of three high pass filters and two
integrators; the approximation to ' which is thus obtained is shown in Fig. 14. Taking the vertical orbital velocity to be the input to the last integrator multiplied by a suitable constant results in the approximation
to ' shown in Fig. 15. Proper phasing between wave elevation and
orbital velocity has been achieved, while also obtaining good approxima-tions to the spectra.
In head seas the waves seen by the main foil lag those at the bow foil by
(22)
g
where L is the foil base length. Over the frequency range of interest, can be very well approximated by a time lag and constant phase lead
(Fig. 16):
= Tw' - (23)
A block diagram of the head sea simulation system is shown in Fig. 17. Results derived from simulating BRAS D'OR foilborne motions
in rough water are presented in the next section; surge was neglected in this simulation in order to simplify the problem and also because it was felt that neglecting surge should give conservative results. (Consider the case where the bow foil encounters a steep high wave, leading to a rapid increase in bow foil immersion depth. In practice a speed reduction of several knots occurs, and the attendant dynamic pressure decrease results in lower lift and accelerations than on the simulated, constant speed ship.)
4. BRAS D'OR F'OILBORNE SEA-KEEPING TRIALS
BRAS D'OR rough water trials were less comprehensive than desired, but enough data were obtained to enable comparison of measured character-istics with predictions and to reach general conclusions about sea-keeping ability. Data will be presented for three key trials, two in Sea State 4 and one in Sea State 5. The wave elevation power spectral densities measured during these trials are shown in Fig. 18 and are compared with the Pierson-Noskowitz theoretical spectra for Sea States 4 and 5 (significant wave heights of 7' and 10' ). Wave measurements were made by a buoy equipped to
17
-measure vertical accelerations and are admittedly inaccurate, due partly to limitations of the buoy itself and partly to the practical difficulty of making a single measurement representative of rapidly changing conditions in a trials area close to the coast.
The variation of root mean square values of longitudinal ship motion parameters with heading to the sea is shown in Fig. 19 for an
average speed of 39 knots. These values do not exhibit the systematic increase with sea height that one would expect, probably because of
different sea energy distributions. For all three seaways there are similar trends with change of heading: vertical accelerations are highest in head and bow seas and lowest in following seas, while pitch angle shows the opposite trend.
The longitudinal distribution of vertical accelerations is indicated in Fig. 20, the points representing average root mean square values for the three sea trials. The most interesting feature of these plots is the comparatively small change in vertical acceleration along the length of the ship, illustrating the well-controlled pitch response of this canard
configuration, with its special bow foil.
Fig. 21 compares predicted and measured root mean square vertical accelerations at the bow. The predictions were derived from analog simulation of pitch and heave motions in a theoretical head Sea State 5 with significant wave height of 10.7 feet, while the measurements were
obtained during head and bow sea runs in Sea States 4 and 5. Predicted acceleration levels are higher than measured, reflecting the higher
argument that neglect of surge is a conservative simplification of the simulation problem.
Fig. 22 presents typical power spectral density plots of vertical acceleration at the bow and pitch angle for head sea runs at speeds of 34 and 42 knots. Also given are the corresponding spectra for the
encountered seaway, derived from the nominal Sea State 5 plot of Fig. 18. There are two dominant seaway frequencies, and although the effects of both are clearly apparent in the pitch angle plots, pitching is associated mainly with the lower frequency. Pitch response falls off with increasing speed, particularly at the lower frequencies. Bow vertical acceleration peaks at the higher seaway frequency; the magnitude of this peak increases with speed and there is also a shift in the energy distribution toward
higher frequencies.
The response transforms of Figs. 23 and 24 quantitatively character-ize BRAS IJ'OR's pitch and heave response to random head seas at speeds of 35 and 40 knots. Although the experimental results are scattered, reflecting inaccuracy of sea state measurement, system non-linearity and limited
statistical confidence, they nevertheless furnish a reasonable indication of mean ship response, as given by the dashed lines in the figures. Pitch response peaks at approximately .2 Hz, in agreement with the prediction of pitch natural frequency obtained from linear stability analysis. Bow vertical acceleration response is fairly flat above .2 Hz, but falls off rapidly below this frequency.
Agreement between simulated and measured response transforms is
19
-pitch and heave motions in regular waves of small amplitude - a
procedure equivalent to linearization. The predictions of Fig. 21, on the other hand, were obtained by simulating ship motions in a random State 5 sea generated as described in Section 3. The regular wave technique was adopted for response transform prediction because it enabled more accurate modelling of the effects of circulation delay and wave orbital velocity on main foil angle-of-attack. Bow foil flow re-attachment and emergence of the main foil anhedral-dihedral intersections, both of which occurred occasionally during trials but never in the simulation, are probably the cause of the only notable discrepancy, under-prediction of pitch response below .3 Hz at 35 knots.
Roll and sway characteristics are presented in Fig. 25 in terms of rms values for lateral acceleration and roll angle, for the three seaways of Fig. 18. Lateral accelerations are given at two ship stations, the C.G. and the Control Information Centre, located comparatively high in the ship in the upper deck superstructure. As with the pitch-heave characteristics given earlier, there seems to be little effective difference between the state 4 and 5 seas. Roll angle is very dependent on direction to the seaway, increasing greatly for seas on and abaft the beam. The lateral accelerations exhibit a much smaller dependence because the roll frequency decreases for beam and stern seas.
The effect of heading on the frequency distribution is shown by the power spectral density plots of Fig. 26. These show lateral accelera-tion at the CIC for head and following sea runs at 39 knots in Sea State 5. The first peak is at the main rolling frequency and is due to accelerometer
tilt. For the head sea, in addition to the increase in frequency of the
main acceleration component, there is an increase in level in the 1 to 2 Hz range. This is significant because lateral "jerkiness" was considered the most uncomfortable feature of the ride, especially at higher speeds and for higher stations in the ship.
The effect of increased speed is shown in Fig. 27 by comparing lateral acceleration at the 010 for head sea runs of 34 and 42 knots in
the sanie Sea State 5. The effect of increased height within the ship is particularly marked and is illustrated by Fig. 28 which compares lateral accelerations at the 0.0. and CIC with the corresponding roll angle plot for 39 knots in head Sea State 5. A very small amount of roll angle energy above 0.5 Hz seems responsible for really significant lateral acceleration at the 010. The problem of lateral acceleration arnplifica-tion with height is clearly deserving of attenarnplifica-tion in large hydrofoil ship design.
It is difficult to relate seakeeping data directly to habitability or to compare the capability of different systems, other than subjectively. The behaviour of the BRAS D'OR canard system was well up to expectation in seaways encountered, both for straight runs arid turns. There was a complete absence of slamming and motions were modest, particularly in pitch and heave. Motions were almost certainly greater for BRAS D'OR than for a comparable fully-submerged system but less than for other types of craft with surface-piercing foils. There were no particular problems for the crew when seated. Personnel moving about and standing, tired quickly,
21
-mainly because of the roll motions, but this situation would not arise in an operational ship.
For BRAS D'OR, a deciding factor in the choice of foil system was the exceptional hullborne seakeeping offered by the canard surface-piercing arrangement. For the tasks envisaged, the habitability is more important under huliborne cruise conditions than for short periods of foilborne operation. Experience with BRAS D'OR supports the contention that foil-borne motions are acceptable for continuous periods of several hours and has confirmed the promise of exceptionally good hullborne
seeeping2.
5. CONCLUSION
The Canadian hydrofoil program has significantly advanced both the performance and the fundamental understanding of surface-piercing hydrofoil systems designed for open ocean operation; the development of a successful super-ventilated bow foil unit is especially noteworthy. As regards
simulation, the extension of aerodynamic methods into the hydrofoil field has proved reasonably successful, yielding satisfactory predictions of both steady state and dynamic performance; of particular importance is the good characterization of BRAS D'OR pitch and heave response derived from a linear mathematical model.
CD drag coefficient CL lift coefficient
CM pitching moment coefficient
D drag
H frequency response
I rolling moment of inertia
X
I pitching moment of inertia
yawing moment of inertia K rolling moment
L lift
M pitching moment
N yawing moment S immersed foil area
T thrust, also time lag
U ship steady state speed
V wind speed
W ship all-up weight
X surging force
Y swaying force
Z heaving force
o chord
g acceleration due to gravity
h1/3 significant wave height £ foil base length
-
23 -q dynamic pressure r yawing velocity u surging velocity y swaying velocity w heaving velocity(x., y., z. )
i
i
foil coordinatesJ_
z heave
F dihedral angle constant phase lead phase lag
spectral density
A sweep angle angle-of-attack
y inclination of thrust line to horizontal
Ø roll angle fl wave elevation P density e pitch angle W wave frequency w' frequency of encounter
REFERENCES
1. Eames, M. C. and Jones, E. A.: HNCS BRAS D'OR - An Open Ocean Hydrofoil Ship. Journal R.I.N.A., Vol.1, No. 1, April, 1971.
1. Eames, M. C. and Drurnmond, T. G.: HNCS BRAS D'OR - Sea Trials
and Future Prospects. Presented at R.I.N.A. Spring Meeting, April, 1972.
Richardson, J. R.: Hydrofoil Profiles with Wide Cavitation Buckets. Engineering Research Associates, Toronto (Prepared for
DeHavilland Aircraft of Canada Ltd.) September, 1961.
Jones, E. A.: Rx Craft, A Manned Model of the RCN Hydrofoil Ship "BRAS D'OR". J. Hydronautics, Vol. 1, No. 1, July 1967.
Tulin, M. P. and Burkart, M. P.: Linearized Theory for Flow about Lifting Foils at Zero Cavitation Number, David Taylor Model Basin Report, C-638, February, 1955.
Oates, G. L. and Davis, B. V.: Hydrofoil Motions in a Random
Seaway. 5th Symposium on Naval Hydrodynamics, Bergen, August, 1964. Schmitke, R. T.: Longitudinal Simulation and Trials of the Rx
Hydrofoil Craft. CAS Journal, Vol 16, No. 3, March, 1970. b. Schrnitke, R. T.: A Computer Simulatii of the Performance and
Dynamics of I-U1CS BRAS D'OR (FHE-400). CAS Journal,
Vol.
17,No. 3,
March, 1971.
9. Diederich, F. W.: A Plan-Form Parameter for Correlating Certain Aerodynamic Characteristics of Swept Wings. NASA Tech. Note 2335, April, 1951.
25
-Wadlin, K. L. and Christopher, K. W.: A Method for Calculation of
Hydrodynamic Lift for Submerged and Planing Rectangular Lifting Surfaces. NASA Tech. Report R-14, 1959.
Auslaender, J.: The Linearized Theory for Supercavitating Hydrofoils Operating at High Speeds Near a Free Surface. Hydronautics Technical Report 001-5, June, 1961.
Johnson, V. E.: Theoretical and Experimental Investigation of Super-cavitating Hydrofoils Operating Near the Free Water Surface. NASA Tech. Report R-93, 1961.
Pierson, W.J. and Moskowitz, L: A Proposed Spectral Form of Fully
Developed Wind Seas Based on the Similarity Theory of S. A. Kitaigorodski. J. of Geophysical Research, Vol. 69, Novembe 1964.
using the sign convention of equation (7). Summation of a given
expression over all foil elements gives the total ship stability derivative. Longitudinal X
= -
QU SCDx
= q (CD +ScosF(C
-c
2\D
L X -w -q =[c
(zT+ 2z.) + x.
cosr
(c0
-
cL)] Z = pu0 SCL COSr
u z = -q (-
+ S
cosr
z
Lh
z
=-
s(C
cos2rc)
w 2 L DS)x
cosF
Ze(C
h) i
2s
[2
C z. cos
r
+ x
Ccos
F + C
Li
i(L
D 2 ... 2= -pU0 SC z. - Z D i ( M (cS) ) r M = X z. - Z x. - q cS + CM h z
zi
zi
= X z. - Z X.Wi
Wi
qx
(CS
N (cS)) M = X z. - Z x. + eei
ei
Mh
jcosr
2.
S [2 C z. + x. cosr(cD
- C z. - Zx.e-
2Di
UI i
e1
where the derivation of X and X assumes constant thrust horsepower. e Lateral = - (CL
Sifl
r +
CD)
pU s ( CL .sin r + C z. - CLY. tan A)
Ø 2
Di
s ( 2 C y. sin r - C x. sin2 r - C x.Li
L iDi
Y=_qsinF(CL
+S
)K = -Y z. + s (CLY. tan A
+ CL
y. sin F cos FV
Vi
= -Yz. - S
(2
C y + C y.z tan A + C cos F2
Di
Lii
LKr =
_YrZi
+ S [CLXIYj + (CLx
sin F
-
2CLY)]
=
+ q
[.
cos
r
(CL -+ s --) +
SCLN=Yx._.2-Qsysinr(cL_cD
VVi
=
Yx. +
s
(CL
-CD
N = Y
x.
-
S Y
[Çc
-
C 'ix.sin
r
2 CDYiL
Du
r
ri
0
01
DiØ
Ji
N =Yx.+qC
y +where S is imersed foil area, A is sweep angle
and= .
r
+ .r
FIG. 3
DELAYED CAVITATION
HORIZONTAL FOIL DATUM
MID-BACK SPOILER
FIG. 5
SUPERVENTILATED
1.4
1.2
1.0
0.6
0.4
0.2
-0.2
o
6.6
D
9.0
13.5
o
16.5
19.5
TEST SPEED 40
FPSfr
/
-o
'Lt
,,,A
/
/ LV
-E3
/
'
cz-E1°
/
i
/
a
-6
-4
-2
0
2
4
6
RAKE
(DEGREES)
0.4
0.3
L
0.2
0.I
SYMBOL
DRAFT - INS
o
6.6
D
9.0
13.5
o
16.5
9.5
TEST SPEED 40 FPS
s
I I I i I-6
-4
-2
0
2
4
6
RAKE (DEGREES)
-6
-4
-2
0
2
4
RAKE (DEGREES)
6
24
OFHE 400
TRIALS
CALCULATED
FROM
NPL '4 SCALE TESTS
CALCULATED FROM
LUMF '4
SCALE TESTS
/
C.
FIG. 9
BRAS D'OR BOW FOIL LIFT
COEFFICIENT
30
40
50
60
LU
H
o
p'
LL-i
U
-J
LU LUo
to
6
O TRIALS DATA
- PREDICTION
O
FIG.
II
BRAS D'OR TRIM,RISE AND W/D
30
40
50
60
RAPID CONVERGENCE
35 60
4
r(SEC')
FIG. 12
BRAS
D'OR LONGITUDiNAL ROOT
LOOt, 35-60K
i-60
PITC7
50351
COU PLED SUBSIDE NCE 4 SLOW ¡CONVERGENCE
35 60 :325
¡54
0
' (SEC)
FIG. 13
BRAS D'OR
LATERAL ROOT LOCI,
I
Cl)z
w ÓIo
W'(RAD/SEC)
FIG.
15WAVE ORBITAL
VELOCITY SPECTRUM
,HEAD
SEA
STATE
5
,50 K
5w' (RAD/sEc)
FIG.
14
WAVE ELEVATION SPECTRUM
,HEAD SEA
STATE
5, 50K
WHITE
NOISE
GEN.
HIGH PASS FILTERS
o
5
UI'
(RAD/SEC)
FIG. 16
PHASE
LAG
PHASE DI FE NET TIME LAG PHASE D 1FF. N ET TIME LAG
- Wa
30
o
30
t-420
N30
20
Io
o
THEORETICAL
S.S. 4
NOMINAL Sß.4
(A)(SIG. HT. 6.4 FT.)
N
THEORETICAL
S.S. 4
NOMINAL
S.S. 4 (B)
(SIG. HT 6.4 ET)
THEORETICAL
S.S. 5
NOMINAL
S.S. 5 (SIG. HT.
10.0FT.)
f
(HZ)
HG. 18
TRIALS
WAVE ELEVATION SPECTRA
0.5
70
60
0.2
e
o
£
QSEA STATE 4
(B)BOW
2
O
e
C.G.45°
900
1350
1800
HEADING TO SEAWAY
FIG. 19 PITCH ANGLE AND VERTICAL
ACCELERATIONS,
39 KNOTS
o
45e
900
1350 1800 (Dw
o
w
(Dz
I
o
I
Q-C!) cr LO0
/0
HEAD /'
-
o---BEAM
L
-o
LONG.
POS'N
AFT
OF
F.P.
(FT.)
FOLLOWING
FIG. 20
LONGITUDINAL
DISTRIBUTION
OF VERTICAL
ACCEL--ERATIONS, 39 KNOTS
o
40
80
120
z
w
o o
o
PREDICTION
O
TRIALS DATA
FIG.
21
VERTICAL ACCELERATION AT
BOW - PREDICTED
AND MEASURED
30
40
SPEED (KT)
N
cjJ (Dw
o
3
2
'o
s' \ s' \ \ s'36 KTS
42 KTS
BOW VERTICAL
ACCELERATION
PITCH ANGLE
ENCOUNTERED WAVES
FIG. 22 POWER SPECTRAL
DENSITIES,SEA STATE 5
o
*5f (HZ)
M
I
IL
o
w
o
w
-j
z
o
F-cL OD
f (HZ)
I.0FIG. 23
BRAS D'OR HEAD SEA RESPONSE
H
LLz
-J
w
o
o
-J
o
f-w
>
o
s-Lu-J
(Dz
o
j- o-O SIMULATED- FAIRED
CURVE THROUGH DATA
0
.5
8
E
\
O
O\
DE
O Of (HZ)
I.0
FIG. 24
BRAS D'OR
HEAD SEA RESPONSE
o
z
w
o
o
-J
w
F--J
(I)
(Dw
o
(I)o
A
A
OA
45
9Q0135°
1800HEADING TO SEAWAY
FIG. 25
ROLL ANGLE AND LATERAL ACCELER
--ATIONS, 39 KNOTS
O
O
OSEA STATE 5
(B)Cic.
o
o
O
2
/
CGM
t
c'J (D>
F-(f)z
w
.01o
r
'I ,' _iHEAD SEA
FOLLOWING SEA
f (HZ)
2
FIG. 26
C.LC.
LATERAL ACCELERATION
NJ
=
t-(I)
z
w
c:3-J
t-o
w
3-U)f (HZ)
FIG. 27
C.LC.
LATERAL ACCELERATION
M
(9
.004
4
LATERAL ACCELERATION AT
C.I.C.LATERAL ACCELERATION AT
C.G.ROLL ANGLE
O I