DEPARTMENT OF DEFENCE
DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION AERONAUTICAL RESEARCH LABORATORIES
AERODYNAMICS NOTE 376
THE WAKE VELOCITY AND RUDDER FORCE
ON A TANKER SHIP MODEL
by N. MATHESON
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r L) A T Li M i SUMMARYA propeller tunnel had been fitted to a 33,000 t (32,500 ton) bulk carrier to cure
cavitation, vibration and noise problems occurring previously. However, the ship's masters reported that the propeller tunnel had reduced manoeuverability especially when operating at low speed in shallow water. From a series ofwind tunnel tests with a model, a set of
vortex generators was developed which improved the flow over the stern and increased the side force produced by the rudder. It is anticipated that fitting corresponding generators
to the ship, together with the propeller tunnel and a 03 m (Ift) extension to the rudder,
will improve the manoeuverability compared with the original hull, when the rudder is set
at an angle greater than 25° with a 0 9 m (3 ft) underkeel clearance, and greater than
12° in a deep sea.
POSTAL ADDRESS: Chief Superintendent, Aeronautical Research Laboratories, Box 4331 P.O., Melbourne, Victoria, 3001, Australia.
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CD DeiftCONTENTS Page No. NOMENCLATURE INTRODUCTION i EXPERIMENTS EQUIPMENT 2
EXPERIMENTAL RESULTS FOR THE MODEL 3
4.1 Bare hull 3
4.2 Model fitted with a propeller tunnel 4
4.3 Model fitted with vortex generators 5
4.4 Model fitted with larger rudder, vortex generators, and the propeller tunnel 6
4.5 Model resistance 6
4.6 Model yaw tests 7
APPLICATION OF MODEL RESULTS TO THE FULL SCALE SHIP 8
5.1 Scaling of the vortex generators and rudder extension 8
5.2 Additional power required 8
5.3 Predicted manoeuvering characteristics of the ship 9
CONCLUSIONS 9
REFERENCES 10
APPENDICES
li
FIGURES 31
NOMENCLATURE b Thickness of vortex generator CD D/(4pU2S) = Resistance coefficient Cy Y/(pU2S) = Side force coefficient
D Resistance
h Height of vortex generator Length between perpendiculars
¡ Length of vortex generator
PD Power delivered to propeller
PE Effective power R Radius of propeller
RN ULpp/v = Reynolds number
r
Radius from centre of propeller shaft, in the propeller plane,at which velocities were measured S Surface area of model (excluding rudder)
U Freestream velocity
u Axial velocity component of the flow in the propeller plane Y Side force
Angle of incidence of rudder measured from the centreline of the modelpositive when trailing edge of rudder is moved to starboard
ß Model yaw anglepositive when stern of model is moved
to port
Cy Increase in Cy
û Angular position in the propeller plane at which axial velocities were measured. (Origin at top dead centre and measured as positive in a clockwise direction when viewed from aft) y Kinematic viscosity
INTRODUCTION
Cavitation, vibration, and noise problems have occurred on a 33,000 t (32,500 ton) single screw tanker recently built in Australia for coastal operation. The ship is 173 m (566 ft) long,
has a 250m (820ft) beam and a 98 m (322 ft) draft when fully laden, and a service speed
of 16 kn. The problems were attributed to the propeller working in an uneven velocity distri-bution, and it was considered that they could be overcome by making the wake velocity more uniform. To do this, a propeller tunnel was designed and fitted to the ship. However, the ship's masters complained that under some conditions they now had difficulty in steering the ship. In particular, in the fully laden condition with underkeel clearances between approximately I m
(33 ft) and 4m (l3 I ft), difficulty was experienced in manocuvering at speeds between about
two and six knot. The loss of steerage was more severe when the ship was decelerating between
six and two knot under following or quartering sea conditions. Although procedures were developed which partly overcame these reported adverse steering characteristics it was feared that an accident might occur, especially during berthing, where these conditions commonly
exist and where maximum manoeuverability is usually required.
The Aeronautical Research Laboratories were asked by the owners of the ship to investigate the problem and to try and develop a simple method, possibly using vortex generators, to modify
the wake velocity and improve the steering characteristics of the ship without major structural
modifications.
EXPERIMENTS
The investigation was made using a reflex model of the hull tested in the low speed wind tunnel. The experiments were carried out in a number of separate parts. First, to determine the effects of the propeller tunnel, the axial velocity distribution of the flow through the propeller
plane and the forces generated by the rudder were measured with the hull as originally designed,
and then with the model fitted with the propeller tunnel. Second, a number of tests were made to try and develop a set of vortex generators which would improve the velocity of the fluid into the propeller and over the rudder. The vortex generators must create a velocity distribution of
the flow into the propeller which will produce satisfactory vibration and cavitation characteristics
as well as increasing the manoeuvering forces generated by the rudder.
The model tests were initially carried out in the 'deep water' condition, and then with
simulated underkeel clearances of 37 m (12 ft), and 09 m (3 ft). Deep water tests with vortex
generators were necessary in order to make sure that the velocity distribution of the flow into
the propeller would minimize cavitation and vibration. This was important because the ship
operates predominantly at its design speed in deep seas.
Surface flow visualization, wake surveys, resistance and side force (generated on the model by placing the rudder at incidence) measurements were made to investigate the steering, cavitation
and vibration problems. Some tests were also made with the model set at various small yaw angles to determine the effect of the propeller tunnel on stability. The wake survey, side force, and flow visualization tests were all made at a Reynolds number of approximately 10 based on model length. Yaw tests were carried out at a slightly lower Reynolds number of mately 8 x 106. Resistance tests were made over a range of Reynolds number from
approxi-mately 25 x 106 to 1 5 x 10v. The rudder was not fitted to the model during the resistance
or yaw tests. All of the experiments were made with the model corresponding to amaximum
draught of 98l m (322 ft) for the full scale ship, and without a propeller. Froude number
effects were not simulated since a reflex model of the below waterline section of the hull was
Manoeuvering and stability tests, such as Dieudonne's spiral manoeuvre, the zig zag
manoeuvre and the turning circle test, usually employed to demonstrate the steering charac-teristics of models tested in manoeuvering basins (or the full scale ship in a seaway), could not
be carried out since the model was rigidly mounted in the wind tunnel with its longitudinal axis
along the centreline of the working section. However, it was considered that the tests proposed
would be sufficient for present purposes.
3. EQUIPMENT
The investigation was carried out using a 1/5933 scale reflex model of the below-waterline
section of the hull mounted in a 27 m (9 ft) x 2 I m (7 ft) low speed wind tunnel on an external
mechanical drag balance.
The principal ship particulars from which the model was scaled are given in table 1. Section lines, and the stern arrangement with the propeller and rudder fitted are shown in figures 1 and 2
respectively. The propeller tunnel as originally designed is shown in figure 3. After the tunnel
had been fitted to the ship it was found that although the actual dimensions of the tunnel appeared
to be correct, the aft end of the tunnel was lower than originally intended as shown in figure 4.
TABLE i
Principal ship particulars
(a) Dimensions:
Length overall
l726 m (5660ft)
Length between perpendiculars136m (5365 ft)
Lengthsections 0 to 10 1628 m (5340 Lt)
Sections apart 1628 m (534ft)
Length at 9 15 m (30 Lt) draft waterline l668 m (5472 ft)
Breadth moulded 25O m (82O ft)
Depth moulded to upper deck l29 m (42.3 ft)
Load draft maximum
98l m (322ft)
Rise of floor 0.15 m(O.5Oft)
Radius of bilge 244 m (8M ft)
Load displacement at maximum draft 33,000 t (32,500 ton)
Wetted surface coefficient to 9 15 m
(30 ft) draft waterline 6 151 Block coefficient to 915 m (30 ft)
draft waterline
080l5
Type of bow Bulbous
(b) Machinery:
Two 16 cylinder turbocharged Crossley SEMI Pielstick PC2V. Maximum 8,000 BHP (Metric) at 520 R.P.M., coupled to a single
shaft.
(c) Propeller:
Four blade, controllable pitch, 6MO m (l969 ft) diameter, 140
R.P.M. at service speed.
(d) Speed:
Full load service speed 16 kn.
(e) Stern arrangement:
Closed aperture, semi balanced rudder, chord 396m (13 ft), span 648 m (21 25 ft).
To correctly simulate shallow water conditions experienced by the ship it would be necessary
to use a moving false floor and a moving false ceiling (moving ground boards) mounted in
the wind tunnel below and above the model respectively. However, since the tunnel is not equipped
with such a moving boundary system, a fixed false floor and ceiling were used to approximate underkeel clearances of 37 m (12 ft) and O9 m (3 ft). Each board was placed at a very small divergent angle to the flow in an attempt to allow for the boundary layer growth.
Vane type vortex generators were selected for the tests because they have been found to perform very well under the conditions likely to be experienced on a ship hull1'2'3'4'5. While these generators are effective over a wide range of conditions, a number of tests are usually
required to refine their design. All of the generators had a triangular planform and were attached at right angles to the surface of the model at about two-thirds of their length aft of the upstream tip. Local axial velocities in the plane of the propeller were measured with a rake of pitot probes
connected to a multi-tube manometer. The resistance of the model and the side force generated by the rudder were measured on an external mechanical drag balance. French chalk mixed with
kerosene was used for the surface flow visualization tests. Care must be employed in interpreting the resulting flow patterns because gravity forces can become significant.
4. EXPERIMENTAL RESULTS FOR THE MODEL
In the following sections, details of the test results are given for the model with and without
the propeller tunnel, and with various vortex generator systems. The results are given for the
model with simulated full scale underkeel clearances of O9 m (3 ft), 37 m (12 ft) and in a
deep sea. 4.1 Bare hull
Initially, the axial velocity distribution of the flow in the propeller plane, the surface flow pattern, the side force generated by the rudder, and the resistance of the model were found for
the hull as it was originally designed.
The axial velocity distribution of the flow into the propeller at four radius ratios of
nR = I
23, 096, 068 and 04l are shown in figure 5 for the deep sea condition, and in figures6 and 7 for simulated underkeel clearances of 37 m (12 ft) and 09 m (3 ft) respectively. The experimental results are tabulated in appendix I.
In the deep sea case, the axial velocity distribution of the flow through the propeller disc showed the usual low values near the top and bottom dead centre position associated with a
single screw ship which has a closed aperture. At nR = I 23 the velocity ratio varied from 026 at 0 = 00 to 093 at O = ± 100°, and then remained constant to 0 = ± 180°. Near the tip of the propeller disc at nR = 096 the velocity ratio varied gradually from 032 at 0 = 0° to 092 at O = ±120°, but decreased abruptly from 084 at 0 = ± 1600 to O24 atO = ± 1800. Further
towards the centre of the propeller disc at nR = 068 the velocity ratio variation was much
smaller but there were a number of 'humps' and 'hollows' in the distribution. Near the hub, at
nR = 04l the velocity ratio varied from 035 at O = 00 and increased to a maximum value of 040 at O = ±20° before decreasing through a number of small 'humps and hollows' to 008 at O = +180°.
There was little difference between the corresponding velocity distributions for the deep
sea and 37 m (l2ft) clearance conditions at radius ratios of l23 and 096. At nR = 068
differences in the velocity distribution occurred near the top dead centre where low values occurred for a 37 m (12 ft) clearance, and at O = +60° where a 'trough' in the velocity
distri-bution occurred in the deep sea condition. At r/R = 04l for O between +(0° to 60°) much
higher velocities were produced in a deep sea than with a 37 (12 ft) clearance, although similar
results were obtained for other values of 0. However, taken overall, the axial velocity distributioins for both cases were very similar.
Comparison between corresponding results in figure 5 and figure 7 indicates that the axial velocities with a 09 m (3 û) clearance are much lower than the axial velocities in a deep sea. Over the top segment of the propeller disc reverse flow or separation occurred with a 09 m
blade tip. However, the velocity of the flow over the lower segment of the propeller disc, for O between approximately +(160° to 180°) was somewhat higher for a 09 m (3 ft) underkeel clearance than in a deep sea.
Overall, the velocity distributions indicate that lower control forces will be produced by the rudder with a 09 m (3 ft) underkeel clearance compared with both a 3-7 m (12 ft) clearance and a deep sea where similar control forces are expected to be produced.
The surface flow patterns over the stern of the model shown in figure 8 confirm the relative
differences in the axial velocity distributions of the flow in the plane of the propeller. It should be noted that the patterns were formed on the upper section of the reflex model and that the
gravity force on the flow visualization fluid acts from the keel to the waterline. In all three cases
there appears to be some separation of the flow from the surface of the model. With deep seas, separation mainly occurs below the propeller shaft and produces low axial velocities in the propeller disc for O between +(160° to 180°). For a 3-7 m (12 ft) clearance the separation region is approximately equally located above and below the propeller shaft, but for a 0-9 m
(3 ft) clearance the separation area is greatest above the propeller shaft. In addition, the separation
region extends much further upstream with a 0-9 m (3 ft) clearance than with a 3-7m (12 ft)
clearance or a deep sea, and is the cause of the reverse flow found in the propeller plane.
The side force coefficients generated by placing the rudder at various angles of incidence are shown in figure 9, and tabulated in appendix 2. The results in figure 9 are the average coefficients
found by placing the rudder at equal angles of incidence to port and starboard. At a rudder angle of 20° the side force coefficient for a 3-7 m (12 ft) underkeel clearance was 6% greater than in a deep sea, but, with a 0-9 m (3 ft) clearance the side force coefficient was only 39% of that produced in a deep sea. This large reduction in side force coefficient caused by the rudder
working in a low velocity field might lead to manoeuvering problems in shallow Water. However, because of the interference effects caused by the boundary layer on the fixed ground boards, the
side force coefficients measured for a 0-9 m (3 ft) clearance may be lower than if the correct conditions had been simulated, for instance, by using moving ground boards. Comparable results between deep and shallow underkeel clearances therefore need to be interpreted with
caution.
4.2 Model fitted with a propeller tunnel
The axial velocity distributions for the model fitted with the designed propeller tunnel, and
with the propeller tunnel fitted to the ship are shown in figures 5, 6 and 7 for the deep sea, 37 m (12 ft) and 09m (3 ft) underkeel clearance conditions respectively. The experimental results are tabulated in appendix 3.
In a deep sea, and with a 37 m (12 ft) underkeel clearance there was little difference between
the velocity distributions for each propeller tunnel. However, with a 0-9 m (3 ft) underkeel clearance the velocity of the fluid through the propeller disc was slightly lower for the tunnel as originally designed. Slightly smaller sideforce coefficients were therefore expected with this tunnel fitted to the model.
The axial velocity ratios for the propeller tunnel fitted to the model in a deep sea, and with
a 37 m (12 ft) underkeel clearance were greater than those for the bare hull over the outer region
of the propeller disc for O between approximately ±(0 to 60°). Over the inner section of the propeller disc there was no improvement for O between ±10°. However, for a 0-9 m (3 ft) underkeel clearance, the reverse flow region which occurred near the hub in the upper segment of the propeller disc was virtually eliminated by fitting the propeller tunnel. In each case, there was little difference between the axial velocity distributions over the lower part of the propeller
disc with the propeller tunnel fitted compared with the bare hull. Overall, the velocity distributions were more uniform with the propeller tunnel fitted.
The surface flow patterns over the stern of the model with the propeller tunnel fitted are
shown in figure lO. No significant difference could be detected between the surface flow patterns
for the two propeller tunnels. The flow pattern for the model in a deep sea was similar to the corresponding pattern for the bare hull, but with a 37 m (12 ft) clearance there was a slightly smaller separation region above the propeller shaft. For a 0-9 m (3 ft) underkeel clearance, there was little difference between the flow patterns obtained for the bare hull and with the
propeller tunnel fitted. In this case the surface flow pattern did not reflect the significant
improve-ment in the axial velocity distribution of the flow in the propeller plane found from the wake
survey.
The side force coefficients found for the model with each propeller tunnel are plotted with the results for the bare hull in figure 9. The experimental results are tabulated in appendix 4. The percentage change in the side force coefficients is listed in table 2 for the model with the rudder at an angle of incidence of 200; the result with the "as fitted" propeller tunnel is used
as the basis for comparison for each underkeel clearance. In a deep sea the "as designed" model
propeller tunnel produces slightly greater side force coefficients than the "as fitted" tunnel however, the reverse occurs in shallow water. In each case fitting a propeller tunnel increases the side force coefficients compared with the bare hull. The greatest improvement occurs with
the 09 m (3 ft) clearance. This is in agreement with the wake survey results where a much greater
relative increase in velocity was produced in the propeller plane for a 09 m (3 ft) clearance than for a 37m (12 ft) clearance or a deep sea.
TABLE 2
Percentage change in the side force coefficients with the rudder at 200 incidence
(The results for the model with the propeller tunnel as fitted to the ship are used as the basis
for comparison)
4.3 Model fitted with vortex generators
The propeller tunnel was removed from the model and a series of tests were made with a number of different sets of vortex generators attached to the stern. The size and location of the
vortex generators was constrained so that they did not protrude beyond the maximum beam and
draught limits of the model. This reduces the possibility of accidental structural damage to the
generators on the ship especially when it is operating in shallow channels.
Increases in the side force coefficient of up to 45% were achieved (compared to the model with the propeller tunnel fitted) by increasing the velocity of the flow in the regions O
to 40°) and O = ±(160° to 180°). However, overall, the axial velocity distribution in the wake was less uniform than obtained with the propeller tunnel because large increases in the axial
velocity were also produced for O = +(50° to 150°). These high velocities could lead to increased
vibration and Cavitation. The use of vortex generators alone was therefore not considered
appropriate.
The propeller tunnel corresponding to that fitted to the ship was reattached to the model and further tests carried out with vortex generators fitted over the stern. While improvements
Model configuration % Change in Cy Deep sea 37 m (12 ft) clearance 09 m (3 ft) clearance Barehull
Designed propeller tunnel
Fitted propeller tunnel Fitted propeller tunnel plus
four vortex generators
Fitted propeller tunnel, plus
four vortex generators,
plus 03 m (I ft) addition to trailing edge of rudder
67
+25
Base (Cyzzzzl2OXlO4)+200
+3l6
9i
31
Base (Cyoo131X104)+153
+267
189
38
Base(Cy53x104)
+l69
±246
disc could be achieved, the overall effect was to make the velocity distribution less uniform. This increased non-uniformity was mainly caused by attempts to improve the velocity through
the upper section of the disc, Effort was therefore concentrated on using vortex generators to
increase the velocity of the flow through the lower section of the propeller disc. While a significant improvement in the axial velocity of the flow to the lower section of the rudder could be achieved
by using a free hanging (open aperture) rudder instead of a solepiece, this was not acceptable as it would involve major structural modifications. The axial velocity distributions for the most
suitable vortex generator system found are shown in figures II, 12, and 13, for the model corresponding to deep sea conditions, 37 m (12 ft) underkeel clearance and a 09m (3 ft)
underkeel clearance respectively. The experimental results are tabulated in appendix 5. The size and location of these vortex generators are shown in figure 14. The choice between the different vortex generator systems was based on a compromise between the uniformity of velocity
distri-bution of the flow into the propeller and the increase in side force produced by the rudder.
In all three cases, the low velocity over the lower segment of the propeller disc was significantly improved. It was considered that the changes in the velocity distribution produced by the vortex generators would not have any adverse effects on stern vibration or propeller cavitation.
The surface flow patterns obtained with the vortex generators fitted to the hull are shown in figure 15. These flow patterns show that the vortex generators have reduced the separation region over the lower section of the stern near the keel compared with the propeller tunnel alone as shown in figure 10. In addition, comparison of the flow patterns over the rudder in figures 10 and 15 shows that the vortex generators have reduced the large component of the
velocity of the fluid towards the keel which occurred when the propeller tunnel alone was fitted to the model.
The side force coefficients for the model fitted with vortex generators are shown in figure 9.
The experimental results are tabulated in appendix 6. As indicated in table 2, with the rudder set at 20° incidence, fitting the vortex generators produces a 20% increase in the side force coefficient in a deep sea, and 15.3% and 16.9% increase for underkeel clearances of 3'7 m (12 ft) and 0'9 m (3 ft) respectively. While a 17% increase in side force is significant for the most important case of 0'9 m (3 ft) underkeel clearance, it was not considered sufficient to
completely overcome the problem of lack of manoeuverability in shallow water. 4.4 Model fitted with larger rudder, vortex generators, and the propeller tunnel
To try to further increase the side force generated by the rudder an extension equivalent to 0'3 m (1 ft) full scale was added to the trailing edge of the rudder. For the ship, this would essentially consist of a flat plate welded to the rudder. A larger extension would have been
preferable, but could not be allowed for reasons of classification.
The side force coefficients for the model with the propeller tunnel, vortex generators, and the addition to the rudder are plotted in figure 9 with the previous results. The experimental
results are tabulated in appendix 7. Table 2 shows that the side force coefficient for the important
0'9 m (3 ft) underkeel clearance case is now 25% greater than for the model corresponding to the ship with the propeller tunnel. With a 37m (12 ft) underkeel clearance, and in a deep sea, the side force coefficients are now 27% and 31% greater than originally obtained.
4.5 Model resistance
The resistance of the model fitted with the propeller tunnel, and with vortex generators plus the propeller tunnel, was measured over a range of Reynolds number using a mechanical drag balance. The results were corrected for the interference effects of the shroud around the mounting column, blockage and the longitudinal pressure gradient in the tunnel. The resistance coefficients are plotted in figure 16 and tabulated ¡ri appendix 8.
The increase in resistance coefficient for each case, compared with the result for the model with the propeller tunnel corresponding to the tunnel fitted to the full scale ship, is given in table 3 for a Reynolds number of l0. There was virtually no difference between the resistance coefficients for the model with the propeller tunnel as designed and as fitted. However, adding the vortex generators produced a small increase in the resistance of the model which varied from 2% in a deep sea condition, to 1 3% with a 0'9 m (3 ft) underkeel clearance. As expected, the resistance of the model in shallow water was much greater than in a deep sea.
TABLE 3
Percentage change in the resistance coefficients for the model at RN = IØ7
(The results for the model fitted with the corresponding propeller tunnel on the ship are used
as the basis for comparison)
4.6 Model yaw tests
Fitting a propeller tunnel, or vortex generators, to the stern of the model will increase the directional stability since these appendages increase the effective area in the vertical plane through the longitudinal centreline. To determine this stabilizing effect the side force on the
model was measured at yaw angles from 00 to +8° in the deep sea case, and at yaw angles from
00 to ±40 with simulated full scale underkeel clearances of 3 7 m (12 ft) and 09 m (3 ft). Physical
constraints prevented the model being tested at higher yaw angles.
The side force coefficients for the model at various constant yaw angles both with and without
the propeller tunnel, and with the propeller tunnel and vortex generators attached to the stern, are plotted in figure 17 and tabulated in appendix 9. The results in figure 17 are the average
coefficients found by placing the model at equal yaw angles to port and starboard.
The results show that the sideforce coefficients for the model with the propeller tunnel, and with both the propeller tunnel and vortex generators, are approximately the same for each of the three underkeel clearance cases tested. This indicates that fitting vortex generators has
little effect on the directional stability of the model. However, fitting the propeller tunnel
increases the sideforce coefficients compared with the bare hull. Within the rather narrow limits
of the tests it appears that above about one degree yaw the increase in side-force coefficient caused by fitting the propeller tunnel is approximately constant with angle of yaw for each
underkeel clearance. These sideforce increments are listed in table4. As shown in figure 17, the
side force coefficient is much greater with a small underkeel clearance than in the deep sea
condition.
TABLE 4
Increase in sideforce produced by fitting the propeller tunnel to the model
7 Model Configuration % Change in CD Deep sea 3 .7 m (12 ft) clearance 09 m (3 ft) clearance Fitted propeller tunnel
Designed propeller tunnel
Fitted propeller tunnel plus
four vortex generators
Base (CD=O.00404)
00
+20
Base (CD=O 00552)04
+1 8 Base (CD=O 00602)00
±13
Underkeel clearance Increase in model sideforce (Cy) Deep sea37m(l2ft)
09m(3ft)
25 X l0
28 x l0
32x 10
Assuming that the increase in sideforce produced by fitting the propeller tunnel acts at the
propeller tunnel, then an additional stabilizing moment will be produced which resists any
change in heading. There is also a stabilizing effect caused by the increased resistance with the propeller tunnel fitted. However, at a yaw angle of 4°, this latter effect is only about 5% of that produced by the increase in sideforce, and is neglected in the following discussion.
To counter the increased stabilizing moment created by the propeller tunnel an additional force, or disturbing moment, must be produced by the rudder to maintain the same turning ability. This, of course, can be achieved by increasing the rudder incidence. For example, in the worst case, with a 09 m (3 ft) clearance, figure 9 indicates that a rudder incidence of 20°
produces a sideforce coefficient of 43 x When the propeller tunnel is fitted the sideforce
coefficient produced by the rudder at the same incidence is increased to 53 x 10, an increase
of I 0 x l0-. However, the propeller tunnel has a stabilizing influence on the vessel, and table 4
indicates that the sideforce coefficient produced by the rudder must be increased by 3 2 >< l0 to maintain the same turning moment. From figure 9, this larger sideforce coefficient of 75 x 1 O
can be achieved by increasing the rudder incidence to 28°. Corresponding increases in rudder incidence of only 24° need to be applied for both the deep sea, and 3-7m (12 ft) clearance cases. A similar analysis for other rudder angles can be made using the results in figure 9.
By fitting vortex generators, and adding an equivalent of U-3 m (I ft) full scale to the
trailing edge of the rudder the increase in rudder incidence can be reduced. Again, for example,
consider the 09 m (3 ft) clearance case with an initial rudder angle of 20°, then the sideforce
coefficient is now 66 x 10. To produce the required coefficient of 7-5 x l0- the rudder
would need to be set at only 22°. Rudder angles greater than 25° produce increased sideforce, and hence greater turning moment, than originally obtained for the model without the propeller
tunnel. Likewise, for the deep sea, and 37 m (12 It) clearance cases, increased turning moments will be produced for rudder angles greater than 12° and 14° respectively.
It should be remembered that the previous discussion neglects the dynamic effects of
manoeuvering, such as yaw velocity, yaw acceleration, and cross coupling effects, which can be
important in certain manoeuvres.
5. APPLICATION OF MODEL RESULTS TO THE FULL SCALE SHIP
The results of the model tests presented in the previous sections must now be applied to
the full scale ship. This involves determining the size and location of the vortex generators to be fitted to the ship, the increase in power required in fitting the generators, as well as the
manoeu-vering characteristics produced by fitting the generators and the extension to the trailing edge of the rudder.
5.1 Scaling of the vortex generators and rudder extension
Differences in the flow over the model and ship exist because the ship operates at a Reynolds
number which is approximately one hundred times greater than the Reynolds number at which the model could be tested. Both hull fouling and structural roughness cause differences in the flow over the ship compared with the flow over the smooth model tested in the wind tunnel. In addition, other factors not represented in the model tests, such as propeller action,
wave-making, and ship motions also influence the real flow. Taking all of these factors into account3'5, it was nevertheless estimated that the vortex generators and the size of the addition to the trailing
edge of the rudder should be geometrically scaled from the model to the ship. The location and
size of the most suitable set of vortex generators described previously in sections 4.3 and 4.4 are
shown in figure 18 for the full scale ship. In addition to the vortex generators, as described in section 4.4, the trailing edge of the rudder should be extended aft by 0-3 m (1 ft) on the ship.
5.2 Additional power required
Fitting vortex generators to the hull will require an increase in power to be delivered to the
propeller to maintain the service speed of 16 knot. Unfortunately, the propulsion factors
necessary to determine this increase in power cannot be found from tests in the wind tunnel. However, in order to gain some indication of the extra power required, a very simple approach
was adopted, where it was assumed that the alteration in the wake fraction, and the increase in resistance coefficient produced by fitting the vortex generators, were the only factors contri-buting to the increase in power5. In addition, it was assumed that these factors remain constant
and that they are directly applicable to the ship fitted with vortex generators. Using this method,
it was estimated that fitting the vortex generators to the ship with the propeller tunnel would require an increase in delivered power of 3% to maintain 16 knot in a deep sea.
5.3 Predicted manoeuvering characteristics of the ship
The actual turning characteristics of the ship cannot be predicted from data obtained
from the wind tunnel tests. However, the changes in manoeuverability which occur when the ship is modified in the same way as the model can be estimated from the wind tunnel data. A
complete picture of the changes which occur cannot be obtained since the dynamic effects (yaw velocity, yaw acceleration, and cross coupling effects) could not be simulated in the model tests.
Nevertheless, after considering the effects that these factors are likely to have on manoeuver-ability, it was estimated that the addition of the propeller tunnel, vortex generators, and the
extension to the rudder, would produce the same percentage changes in the side force coefficient on the ship as on the model. Therefore, fitting the propeller tunnel, vortex generators and rudder
extension to the ship can be expected to improve manoeuverability, compared with the bare hull, when the rudder is set at an angle greater than 25° and the underkeel clearance is 09 m (3 ft). In a deep sea, and with a 37 m (12 ft) clearance, increased manoeuverability can be
expected for rudder angles greater than 12° and 14° respectively.
6. CONCLUSIONS
The following conclusions are drawn from the wind tunnel tests.
Compared with the bare hull, fitting the propeller tunnel to the model produced a more
uniform axial velocity distribution of the flow into the propeller by increasing the velocity
in the upper region of the propeller disc. In addition, the tunnel increased the side force coefficients generated by the rudder by approximately 7% for a simulated deep sea,
10% for a simulated underkeel clearance of 37 m (12 ft), and by 23% with a simulated clearance of 09 m (3 ft).
For small underkeel clearances, the side force coefficients for the model fitted with a propeller tunnel as fitted to the ship were slightly greater than those produced with the
propeller tunnel as originally designed. However, the reverse occurred in simulated deep
waters. Both propeller tunnels produced similar axial velocity distributions of the flow in the propeller plane.
A set of vortex generators was developed for use with the model fitted with both the propeller tunnel and an addition to the trailing edge of the rudder of 03 m (1 ft) full scale. Compared with the model fitted with the propeller tunnel alone, the addition of
the vortex generators and the extension to the rudder increased the side force coefficients produced by the rudder by 32% for a simulated deep sea, 27% for a simulated underkeel
clearance of 37 m (12 ft), and by 25% for a simulated clearance of 0-9m (3 ft). The vortex generators also slightly improved the uniformity of the velocity distribution of
the flow through the propeller disc.
Fitting the propeller tunnel to the model produced an increase in directional stability
which was countered to a limited extent by an increase in side force coefficient generated
by the rudder. However, within the range of yaw angles tested, adding to the rudder and fitting vortex generators to the model with the propeller tunnel, increased the side force coefficient (or turning moment) compared with the bare hull, provided the rudder incidence was greater than 25° for a simulated underkeel clearance of 09 m (3 ft), or
14° for a simulated clearance of 37 m (12 ft) and 12° for a simulated deep sea. A similar situation is expected to occur when the vortex generators and the addition to the trailing edge of the rudder are directly scaled and fitted to the ship with the existing propeller tunnel.
The addition of vortex generators to the ship with the propeller tunnel is expected to require an increase in delivered power of 3% for a fully laden ship to maintain 16 knot
REFERENCES
Lachman, G. V. (Editor)"Boundary layer and flow control". Pergamon Press, Oxford,
London, 1961.
Clements, R. E."The control of flow separation at the stern of a ship model using vortex generators". Trans. R.I.N.A., Vol. 107, 1965.
Matheson, N."Wind tunnel studies of a ship model using vortex generators to improve
wake velocities". Department of Supply, Australian Defence Scientific Service, Aeronautical Research Laboratories, Aerodynamics Note 347, April 1974.
Chang, P. K."Control of flow separation: energy conservation, operational efficiency, and
safety". Hemisphere Publishing Corporation, Washington, London, 1976.
Matheson, N."Further studies on a ship model fitted with vortex generators to improve
the velocity distribution of the flow into the propeller". Department of Defence, Australian
Defence Scientific Service, Aeronautical Research Laboratories, Aerodynamics Note 359, 1975.
APPENDIX i
Axial velocity component ratios of the flow in the propeller plane of the model (without propeller tunnel or vortex generators)
1.1 Deep sea e (°) u/U
nR = 1 23
r/R = 096
r/R = 068
r/R = 04l
O026
032
038
035
12039
0.45044
038
24 O53 051044
040
48067
061031
033
72082
076
038
024
96091
088
060
026
120093
092
069
026
144094
093
068
019
168093
068
031010
180094
024
015
009
12
042
042
039
038
24
056
048
0'42032
48
069
0-50 0-25 0-2872
0-83 0-68 o-32 0-1996
0-93 0-85 0-55 O-19120
0-94 0-91 0-66 0-20144
0-94092
0-58 0-13168
0-94080
0-30007
180
0-95 O-24 0-15 0-08APPENDIX i (Continued) 1.2 37m (12 ft) Underkeel clearance 12 o (°) u/U r/R = 1-23 r/R = 0-96 nR = 0-68 r/R = O-41
O O-26 O-27 O-26 O-12
12 0-48 0-49 0-40 0-23 30 0-68 0-61 0-48 0-26 48
076
0-68 0-53 0-24 66 0-81076
0-60 0-24 84 0-87082
0-68 0-25 102 0-94 0-88 0-73 0-27 120 0-98 0-93 0-76 0-26 138 1-00 0-95 0-73 0-22 156 1-01094
0-59 0-15 168 1-00 0-74 0-35 0-10 180 0-96 0-28 0-17 0-0912
0-46035
0-25 0-1030
0-71 0-58 0-40 0-1848
0-80 O-68 0-49 0-2166
0-86 0-75 O-58 O-2284
0-90 O-81 0-65 0-23102
0-95 0-87 0-70 0-25120
0-98 0-91 0-74 0-23138
1-00 0-93 0-71 0-19156
1-01 0-92 0-58 0-15168
O-99 0-86 O-39 O-il1.3 0-9 m (3 ft) Underkeel clearance APPENDIX i (Continued) 6 (0) u/U nR = 1-23 r/R = O-96
r/R = 068
r/R = O-41 O 0O9ve
ve
ve
12Oi3
ve
ve
ve
24 0-26 0-07ve
ve
36 0-38016
ve
ve
48 0-44 0-25 0-05ve
60 0-59037
013
ve
72 0-63046
023
O-03 84 0-63 0-52 0-31 0-06 96 0-59 0-55040
0-10 108 0-53 0.55 0-45 0-14 120046
0-53 0-48016
132 0-40 0-51 0-46 0-17 144 0-36 0-50 0-42 0-16 156 0-36 0-42 0-37 0-14 168 0-44 0-40 0-28 0-14 180 0-49 0-38 0-30 0-1612
0-23ve
ve
ve
24
0-38 0-16ve
ve
36
054
0-31 0-10ve
48
0-65 0-47 0-24 0-0260
0-70 0-59 0-36008
72
0-71062
0-44 0-1484
0-69 0-62 0-49 0-1996
0-64 0-59 0-52 0-23108
0-55 0-54 O-53 O-26120
O-47 0-49 0-52027
132
O-38 O-45050
O-27144
03!
0-41 0-47 0-26156
O31 O-40 O-43 O-24168
0-40 0-41 O-37 O-20APPENDIX 2
Side force coefficients for the model (without propeller tunnel or vortex
generators) fitted with the standard rudder
Deep sea 3 7 m (12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy x 1O x (°) Cy X lOE' (°) Cy X 10
00
Oil
00
007
00
014
46
253
92
559
76
139
76
423
l54
-882
123
250
l23
656
219
1313
170
353
170951
286
1588
219
467
2I9
1255
92
520
286
609
286
l584
154
907
76
16146
228
2l9
1382123
278
76
392
286
179717O
370
123
643
219
478
170
935
286
620
219
1218286
1568APPENDIX 3
Axial velocity component ratios of the flow in the propeller plane of the model fitted with a propeller tunnel.
3.1 Propeller tunnel as designed
3.1.1 Deep sea 0 (°) u/U
r/R = i 23
r/R = 096
r/R = O68r/R = 041
O-
04O035
O30 12-
049
047
O35 24053
051
040
48065
060
042
040
72081
O70036
O3l 96091
O86057
028
120094
091063
026
144094
O92051
O12 168 O84050
O24006
180093
025
021008
12
-
046
044
032
---24053
051 04O48
066
059
043
042
72
083
068
033
032
96
093
085
055
030
120
095
092
065
030
144 0.95092
055
020
168
09l
074
030
004
180
093
026
021009
APPENDIX 3 (Continued) 3L2 3-7 m (12 ft) Underkeel clearance 16 o (°) u/U
r/R = 123
r/R = O-96 r/R = O-68 r/R = O-41O
-
O-42 O-31016
12
-
0-49 0-42 0-2330
-
o-63 0-52 0-3348 0-77 0-68 0-55 0-35
66 0-80 0-73 0-55 0-32
84 o-86 O-80 O-59 O-30
102 0-94 O-86 O-63 O-29
120 0-98 0-90 0-62 0-25 138 1-00
091
O-56017
156 1-00088
O-43 0-11 168 0-96 O-62 0-29 0-10 180 0-93 0-28 0-23 0-1012
-
O-46 0-40 O2030
-
O-64 O-52 O-3148
0-81 0-70 0-55 0-3366
O-86 0-74059
O-3284
0-90 0-80 0-62 0-30102
0-94 0-86 O-66 O-30120
0-99 O-90 O-68 O-27138
1-00 0-92 O-62 O-19156
1-01 0-89 0-48 0-11168
0-97 0-68 0-34 0-08APPENDIX 3 (Continued) 3J.3 O-9m (3 ft) Underkeel clearance
8 (0) u/U
r/R=1-23
r/R=0-96
r/R=0-68
r/R=O-41
O-
O-32 O-19ve
12 0-33 0-23ve
24-
0-36024
0-09 36 0-39 0-21 0-13 48 0-60 0-38 0-21 0-13 60 0-60 0-43 0-26 0-15 72 0-64 0-50 0-31 0-15 84 0-63 0-55 0-36014
96 0-59 0-57 O-38 O-11 108 0-52 0-55 0-39 0-08 120 0-45 0-53 0-38 0-07 132 0-39 0-51 0-37 0-09 144 o-38 0-49 0-33 0-10 156 0-40 0-43 0-31 0-11 168 0-43 0-36 o-26 o-12 180 0-47 0-26 0-22 O-1312
0-39 0-26 0-0924
-
0-43 0-24 0-1536
-
0-45 0-24 0-1548
0-65 0-48 0-28 0-1560
0-66 O-54 0-35 0-1572
0-69 0-60 0-43 0-1884
O-67 0-62 0-48 0-2096
0-61 0-60 0-49 0-20108
0-54 0-56 0-49 0-20120
0-46 0-52 0-49 0-19132
0-37 0-48 0-46 0-19144
0-32 0-46 0-44 0-20156
0-33 0-46 0-37 0-19168
0-43 0-42 0-32 0-16180
0-46 0-27023
0-14APPENDIX 3 (Continued) 3.2 Propeller tunnel as fitted
3.2.1 Deep sea 18 û (°) u/U
r/R = i 23
nR = 096
nR = 068
nR = 041
O-
043
037
029
12-
050
047
O33 24054
051
O39 48066
060
043
041 72082
068
036
031 96093
086
057
O28 120094
092
062
027
144094
092
O48009
168081
O47023
006
180093
027
022
006
12
-
045
045
034
24
-
053
052
041
48
068
061045
043
72
082
069
036
034
96
093
086
055
031
120
095
093
067
032
144
095
094
o-56023
168
0-88 0-76 0-31 0-02180
094
0-28 0-23005
APPENDIX 3 (Continued) 3.2.2 3-7m (12 ft) Underkeel clearance û (°) u/U r/R = 1 -23 r/R = 0-96 nR = 0-68 nR = 0-41 O
-
0-44 0-31015
12 0-51 0-43 0-24 30-
0-64 0-53 0-34 48 0-77 0-68 0-55 0-35 66 0-81 0-73 0-54 0-32 84 0-87 0-80 0-58 0-30 102 0-94087
0-62 0-29 120 0-96 0-87061
0-25 138 1-00 0-91 0-54 0-15 156 1-0! 0-89 0-46011
168100
0-77 0-34 0-11 180 0-94 0-29 0-23 0-1012
-
0-46 o-42 o-2030
-
0-67 0-54 0-3248
0-79 0-72 0-58 0-3566
0-87075
0-59 0-3484
091
081
0-62 0-32102
0-95 0-87 0-67 0-31120
099
0-91 0-68028
138
1-00 0-92 0-62 0-19156
1-01089
0-48 0-10168
0-96 0-70 0-34 0-09180
0-93 0-28 0-23 0-11APPENDIX 3 (Continued) 3.2.3 0-9 m (3 ft) Underkeel clearance 20 0 (°) u/U r/R = 1-23 r/R = 0-96 r/R = 0-68 r/R = 0-41 0
-
O-32 O-21ve
12-
0-34 0-23ve
24-
0-36 0-26009
36-
039
0-23012
48 0-60 0-39 0-24014
60062
0-43 0-28014
72 0-63 0-51035
0-15 84 0-63 0-56 0-39 0-13 96 0-59 0-57 0-40 0-12 108 0-53 0-56 0-40 0-08 120 0-46 0-54 0-41 0-08 132 0-42 0-52040
0-10 144 0-42 0-49 0-38012
156 0-40 0-43 0-32012
168 0-43 0-36 0-28 0-14 180 0-48 0-26 0-28 0-1612
-
0-39 0-27 0-1324
0-44 0-26 0-1736
0-47 0-26 0-1748
0-64 0-50 0-29 O-1660
0-68 O-55 O-36 0-1772
0-69 0-60 O-44 O-1884
0-66 0-62 0-48 0-2096
O-61 0-60 0-50 0-20108
0-54 0-56 0-50 0-20120
0-46 0-53 0-50 0-22132
0-38 0-49 0-46 0-20144
0-33 O-47 0-44 0-20156
0-35 0-46 0-38 0-19168
0-45 0-42 0-32 0-18180
O-48 0-28 0-28 0-174.2 Propeller tunnel as fitted
APPENDIX 4
Side force coefficients for the model fitted with a propeller tunnel and the standard rudder.
4.1 Propeller tunnel as designed
Deep sea 3 7 m (12 ft) Underkeel clearance 0 9 m (3 ft) Underkeel clearance (0) Cr X 10 (0) Cy X 10 (0) Cy X 10 0.0
014
00
O2O
00
021
46
312
92
53l
l73
76
503
154
907
123284
123
757
2l9
1438
17O426
l70
1021
286
1917
219
551
219
1371
92
492
286
704
286
1709
154
943
T6
209
46
225
2l9
1380123
320
76
442
286
1828170
440
123
726
219
5'56170
1054286
718
219
1380286
1791 Deep sea 3 7 m (12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy X 10 (0) Cy X 104()
Cy X 1000
018
00
023
00
015
46
309
92
576
76
156
76
462
154
1026
123275
123720
219
l494
170426
170
957
286
1989
219
548
219
1293
92
551286
747
286
l675
154
943
76
203
2312L9
1399123
35l
76
426
286
l850
170
490
123
7.45219
620
170
1043286
768
219
1293286
1725APPENDIX 5
Axial velocity component ratios of the flow in the propeller plane of
the model with the propeller tunnel as fitted and four vortex generators.
5.1 Deep sea o (°) u/U
r/R= l-23
r/R=096
r/R=0-68
r/R=0-41
O-
0-42 0-35 0-28 12048
0-45 0-32 24-
0-53052
0-38 48066
0-59 0-49 0-48 72 0-80063
O-34 0-33 96 O-91 O-66 0-29 0-27 120 0-94 0-79 0-43 0-15 144 0-95 0-93 0-72 o-28 168 0-95 0-91072
0-44 180 0-96 0-52 0-56 0-4612
-
0-47 0-48 0-3424
-
0-54 0-52 0-4248
-
O-60 0-42 0-4272
0-83 0-66 0-34 0-3596
0.93 0-73 0-30 0-31120
0-96 0-81 0-38 0-17144
0-95 0-93 0-70 0-22168
0-96 0-92 0-72 0-45180
0-96 0-53 0-56 0-46APPENDIX 5 (Continued) 5.2 3-7m (12 ft) Underkeel clearance
û
(°)
u/U
r/R = 1-23 r/R = O-96 r/R = O-68 r/R = O-41
o
-
0-45 0-32 0-1712
-
0-52 0-43 0-2430
-
U-65 O-54 U-3436
-
O-67 o-55 U-3648 0-76 0-68 0-56 U-36 66 0-80 0-72 0-55 0-34 84 0-86 0-77 0-51 0-30 102 o-93 0-73 0-34 0-22 120 o-97 0-71 0-30 0-02 138 1-01 0-90 0-54 0-21 156 1-01 0-95 0-80 U-43 168 1-00 0-91 0-77 0-54 180 0-97 0-54 0-54 0-53
12
0-54 0-42 O-2230
-
0-67 U-53 O-3148
0-79 0-72 0-56 0-3466
U-85 O-74 U-56 O-3384
U-89 O-79 U-56 O-30102
0-94 0-81 0-47 0-23120
U-96 O-76 O-32 O-03138
U-99 O-84 U-43 O-12156
1-UI O-93 U-68 O-32168
1-UO O-92 U-71 O-45APPENDIX 5 (Continued) 53 09 m (3 ft) Underkeel clearance 24 e (°) u/U nR = 1-23 r/R = O-96 r/R = O-68 r/R = 0-41 O O-33 O-19
ve
12 0-34 0-24ve
24 0-40 0-26 0-12 36 0-40023
0-14 48 0-60 0-39 0-25 0-16 60 0-59 0-42 0-26 0-16 72 0-62 0-48 O-30 O-1484 0-63 O-52 O-29 O-IO
96 0-59 0-53 0-26 O-04
108 O-54 O-51 O-20 O-02
120 0-48 0-49 0-22 0-04
132 O-43 0-50 0-28 0-16
144 0-40 O-49 O-38 o-22
156 O-38 0-48 0-43 O-26
168 0-43 0-48 O-41 0-31
180 0-49 O-42 0-36 0-34
12
-
039
0-26 0-1424
-
O-43 O-26 O-1836
-
0-46 0-26 O-1848
0-64 0-48 O-29 O-1860
0-65 0-53 0-34 O-1872
0-68 0-59 0-37 0-1884
0-67 0-62 0-37 0-1796
0-61 0-59 O-36 0-13108
0-55 0-55 0-34 0-11120
O-48 0-51 0-36 0-15132
0-40 0-47 0-43 0-23144
0-33 0-47 0-48 0-32156
0-32045
0-48 0-38168
0-44 0-46 0-43 0-38180
0-49 0-43 0-37 0-35APPENDIX 6
Side force coefficients for the model with the propeller tunnel as fitted, four vortex generators, and the standard rudder.
Deep sea
37m (12 ft)
Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy X lO (°) Cy X 10 (°) Cy X 1O00
_Ø.Ø300
012
0'O011
76
.._5.3792
673
76
214
123887
l54
1l99
123354
1701223
219
1733
ITO540
2l9
1549
286
2292
219
726
286
2064
92
604
286
971
76
49O154
103576
242
123
873
2l9
1577123
376
170
1246286
2156l70
492
219
1647219
687
286
2172
286
915
APPENDIX 7
Side force coefficients for the model with the propeller tunnel as fitted, four vortex generators, and an equivalent addition of O3 m (1 ft) full scale to the trailing edge of the rudder.
26 Deep sea 3 7 m (12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy X 1O (°) Cy X lO (°) Cy X lOi 0O +OO2 0O
007
00
O07
5.5356
82
662
68
234
110
815
I52
l238
138
473
1661307
224
1939
195
645
224
19O0
284
259O
254
851
284
247O
82
568
3l6
1038
5.5 3.31152
119668
184
110
812
224
1919138
412
l66
1299284
252O195
643
224
l803
254
868
284
24123l6
1129APPENDIX 8
Resistance coefficients for various configurations of the model.
8.1 Propeller tunnel as fitted
Deep sea
37m (l2ft)
Underkeel clearance09m (3ft)
Underkeel clearance RN x 10-6 CD >< l0 RN x 10-6 CD x 10 RN x 10-6 CD x l0239
472
1071549
234
690
328
483
1154544
3'36683
568
439
1128 541464
660
743
42!
1O3O 55O527
649
869
412
1114547
629
634
930
410
lI88
544
711623
988
407
1262539
804
618
248
478
904
609
3.57 4.74 9.93603
4l9
460
1076598
487
451 1161 591547
4.44 1220 591610
4.35284
698
664
4.31376
674
823
417
4.75653
883
413
576
640
9.47406
672
629
9.67 4'07 7.53622
918
409
859
613
791
4i8
708
424
632
431
566
442
505
448
4.54458
394
468
307
488
1047403
APPENDIX 8 (Continued)
8.2 Propeller tunnel as designed
8.3 Propeller tunnel as fitted plus vortex generators
28 Deep Sea 37 m ((12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance RN x106 CD >< 1O RN x 106 CD x 1O RN >< 106 CD >< 1O
585
438
lO73546
1057 5.97652
429
1146544
ll78
593
727
423
l224
54O 1265588
859
413
1037547
933
6O6705
4.74ll89
5.39 1001604
789
417
1258538
1128594
849
412
9l4
408
986
4'04 Deep Sea37m (l2ft)
Underkeel clearance09m (3ft)
Underkeel cleara nce RN >< l06 CD >< l0RN x106 CD x 10
RN >< 106 CD X 10823
422
1103558
1072602
887
418
1l80
555
II78
598
9.454l4
1259549
l264
5.94796
4-24 10-57559
9-98 6-09 8-59 4-20Il-44
5-53 11-33 6-01914
416
12-22552
12-25 5-95973
413
12-95 5.49 10-02409
9.2 3-7m (12 ft) Underkeel clearance APPENDIX 9
Side force coefficients for the model at various fixed yaw angles.
9.1 Deep sea
p
(°)
Cy X 10 Bare hull Propeller tunnel
as fitted
Propeller tunnel as fitted plus vortex generators
8
9-77 10-20 9-986
4-68 5-28 5-204
1-98 2-32218
2
0-89 1-05 1-05 00-02
004
004
20-84
0-99
129
42-26
236
2-58
65-55
5-54
5-62
810-67
1084
10-82
B (°) Cy X 10Bare hull Propeller tunnel as fitted
Propeller tunnel as fitted plus vortex generators
4
9-78 10-72 10-653
6-95 7-56 7-572
4-04486
4-921
142 2-28236
O002
0-02 0-032-22
2-12
2-08
24-44
4-26
4-20
37-26
7-06
7-04
41070
1018
10-10
APPENDIX 9 (Continued) 9.3 09 m (3 ft) Underkeel clearance 30 ß (°) Ci' X l0
Bare hull Propeller tunnel as fitted
Propeller tunnel as fitted plus vortex generators
4
14'62 1472 1470 9.44 1030985
2
551546
510
1
279
298
254
o I245
292
324
2523
582
640
3930
956
9.55
41438
l462
1480
Upper deck FIG. i
SHIP SECTION LINES
93;/'
7
/
91/4 14.64 m (48 ft) 12.20 m (40 ft) 9.81 m (32.2 ft)- L,WL.
3.32 m (24 ft) 4.88 m (16 ft) 2.44 m (8 ft)10.99 m (36 ft) 9.81 m (32.2 ft)
LW. L.
7.32 m (24 ft) 3.66 m (12 ft) Base lineFIG. 2
PROPELLER AND STERN ARRANGEMENT
I
3.50 m (11.5 ft)A.RO
1/2 3I Station no.10.99 m (36 ft) 9.81 m (32.2 ft) L.WL.
I
L
7.32 m (24 ft)3.66m(l2ft)
p Base line--,-
--J
j 'I I' t I t I J I p I i iI---r
'TI,
-,
p1
Upper intersection with shell LowerinterSe°.
6.10 m (20.01 ft) Station no. FIG. 3PROPELLER TUNNEL AS DESIGNED (a)
Location of propeller tunnel
7.90 m (25.91 ft) 3i
II
J I 1/5 1/4 1/2 5í o A'F'.0.705 m (2.31 ft)
-l.185m(3.89ft)
-w-I View A on Fig. 3a FIG. 3 cont.(b) Plan view of propeller tunnel
o
0.743m(2.44ft)
Station no. 0.652 m (2.14 ft)__
1/8 1/4 1/2 3/4Angle of side plate over length of propeller tunnel
h'-230 (1590m (1.94 ft) 4 6.145m'i
(20.l6ft) I
'
'
I L 1 6.450 m )i'
(21.l6ft
4'I
/1
0.60m/
/ p
(1.97 ft)i/1'
0.90 m (2.95 ft) $/
tt
11.100m 3.74m (36.41 (12.27ft)/
5.78 m(18.96ft) 1/8 1/4 3, 1/2 5i 3/4/
/ / /
/
/r/
/
Station in way of propeller 13.715 m (44.99 ft) 15.103 m (49.54 ft) Base line 14.400m (47.23 ft.) Station no. 6.100m (20.01 ft) 7.900m (25.91 ft) T0.610m (2.00 ft.) 1.08 m (3.54 ft)
L
4-0.153m (0.50 ft) Rudder 0.318 m (1.04 ft)t
Rudder Propeller tunnel(a) Propeller tunnel as designed
Base line
(b) Propeller tunnel as fitted
Base line
Propel ter tunnel
Lower intersection with shell
Lower intersection with shell
FIG. 4 DIFFERENCES BETWEEN THE PROPELLER TUNNELAS DESIGNED AND AS FITTED
1.0 0.8 0.6 0.4 0.2
O
FIG. 5
AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL IN A SIMULATED DEEP SEA
(a) r/R= 1.23
-/
I
/
/
/
/
/
tunnel as fitted tunnel as designed
-'
1li
I
/
/
/
Propeller _____ Propeller-
Barehull - 160 -120-80
-40
O 90 40 80 120 160FIG.5cont.
(b) r/R=O.96
-F
i
,.
j
y
-
- - :flTj1uI
160120
- 80 - 40 O 40 BO 120 160 00 1.0 0.8 u/U 0.6 0.6 0.2 O1.0 0.6 0.4 0.2 O FIG. 5 cont. (c) r/R = 0.68 Propeller Propeller
tunnel as fitted tunnel as designed
hull
--- Bare
_
NI
I
\d
'
t\
d/
/
/
/
Ib t t t -I k I I I I II
Ib - 160120
- 8040
O 60 80 120 160 00 0.81.0 0.6 0.4 0.2 O - 160 -120 -80
-60
O 00 FIG.5cont. (d) r/R=O.41 40 80 120 160Propeller tunnel as fitted Propeller tunnel as designed Bare hull
-s,.
/
/
/
4/
-_% 'I.._--,
/
's. s.. s. -.-..--s..-J
---I I I L I -I s. 's.. 0.8 u/UT
I
I
/
I
/
/
-t t I I I I g aI
I
tunnel as fitted tunnel as designed
% -g g
/
Propeller ---iPropeller Bare hull
I t I
-8
-60
O 60 80 120 160 00 FIG. 6AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODE,L WITH A SIMULATED FULL SCALE UNDERKEEL CLEARANCE OF 3.7 m (12 ft).
1.0 0.8 u/U 0.6 0.6 0.2 FIG.6cont.
(b) r/R0.96
/
F-
.-%% s' 's'.' -f'
/
---.
t'
s 5.. ... 0/
-./
/
p'7
t%V
f i ii
i i a -as fitted as designed I ¡ I Propeller tunnel .5 I I/
g LPropeller tunnel Bare hull
I i i I - 160
120
80
- 60 O 00 60 80 120 160- 160 -120 -80
-60
O 00 FIG.6cont.(c) r/R0.68
40 80 12I
- -
/
-s s s s s/
-/
/
/
-. .s. I/
I
\
s ¼,/
/
1 -t L t I t I'
-J
/
/
/
I IPropeller tunnel Propeller tunnel Bare hull i
I
as fitted as designed
1.0 0.8 u/U 0.6 0.6 0.2 - 160
120
80
40
o Q0FIG.6cont.
(d) r/R=O.41 60 80 12 6Propeller tunnel as fitted
as designed
-Propeller tunnel---Barehull
--
-
/-- /-- a
-I I
W,
/
I I iN
I00
FIG. 7
AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL WITH A SIMULATED FULL SCALE UNDERKEEL CLEARANCE OF 0.9 m (3 ft).
(a) r/R = 1.23
/
/
/
I
/
/
I
I/
g I//
h I II
I
/
I
tunnel as fitted tunnel as designed
Propeller Propeller Bare hull
I .
I
/
\ .1
i - 160120
- 80 - 40 O 40 80 120 160 1.0 0.8 0.6 0.4 0.2 O1.0 0.8 u/U 06 0.4 0.2 o 40 O 00 FIG.7cont.
(b) r/R=O.96
40 80 120 160 -as fitted as designedPropeller tunnel Propeller tunnel Bare hull
-1.0 0,8 0.6 0.4 0.2 O - 160
12
B
- 40 O 00 FIG. 7 cont. (c) nR = 0.68 40 BO 120 160 as fitted as designed tunnelPropeller tunnel Propeller
-
--Bare hull
//
-.0
I
/
/
1
,.
J I I I -I/
Ii
/
/
/
L/
I -t1.0 0.6 0.4 0.2 o 00 FIG. 7 cont.
(d) nR
0.41Propeller tunnel as fitted
as designed
-Propeller tunnel Bare hull
-- 160
120
80
60
o 60 BO 120 160 0.8 u/U> Cu
o
FIG. 8
FLOW PATTERN OVER THE STERN OF THE MODEL WITH BARE HULL
FIG. 8 cont.
FIG. 8 cont.
cyx
20 15 lo5 o
vortex generators and rudder extension
Propeller tunnel as fitted plus
o 5 10 15 20 25 30 FIG. 9
SIDE FORCE COEFFICIENTS FOR THE MODEL
(a) Simulated deep sea
Bare hull
O
Propeller tunnel as fitted
+ Propeller tunnel as designed
A
Propeller tunnel as fitted plus vortex generators25
cyx
20 15 10 5 o lO p u Bare hull QPropeller tunnel as fitted
+
Propeller tunnel as designed
A
Propeller tunnel as fitted plus vortex generators Propeller tunnel as fitted plus vortex generators and rudder extension
D 5 lo is 20 25 30 o FIG. 9 cont.
k
1OBare hull
o Propeller tunnel as fitted
-f-Propeller tunnel as designed
A
Propeller tunnel as fitted plus vortex generators
D
vortex generators and rudder extension
Propeller tunnel as fitted plus
5 lo 15 20
a°
25 30 FIG. 9 cont.FIG. lo
FLOW PATTERN OVER THE STERN OF THE MODEL WITH THE PROPELLER TUNNEL AS FITTED
-n P Q o cf) CD o- o- CD -I CD CD CD D) C) CD o 4,
p
()
Gravity force00
FIG. 11
AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL IN A SIMULATED DEEP SEA.
(a) r/R = 1.23
L'
-L I I i I itunnel as fitted tunnel as fitted generators
I i I Propeller Propeller - _____ I I plus vortex I I - 160 -120 - 80
-60
O 40 80 120 160 1.0 0.8 u/U 0.6 0.4 0.2 O0.6 0.4 0.2 O 00 FIG. 11 cont. (b) r/R = 0.96
/
j
j
as fitted as fitted generatorsI
N
/
A7
I _1zf I_lnt
I nA iPropeller tunnel Propeller tunnel
I I --plus vortex i I I ILV LU 80 120 160
1.0 0,8 (1/U 0.6 0.4 0.2 O FIG. 11 cont. (c) nR = 0.68
tunnel as fitted tunnel as fitted
vortex generators
/
/
'\
/
Propeller Propeller plus
/
/
\
/
/
\
/
w
I I I -I f I I o 00 40 80 120 1601.0 0.6 0,2 90 HG. 11 cont. (d) nR = 0.41 as fitted as fitted generators
-Propeller tunnel Propeller tunnel plus vortex
-
>Ti'T
- ILU 40 80 120 1601.0 0.8 u/U 0.6 0.4 0.2
0
FIG. 12
AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL WITH A SIMULATED FULL SCALE UNDERKEEL CLEARANCE OF 3.7 m (12 ft.)
(a) nR = 1.23 I I I t I I
Propeller tunnel as fitted
tunnel as fitted generators
i I
-Propeller -I I plus vortex i I