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Requirements for Standard Harmonic Captive Manoeuvring Tests
Copyright IQ IFAC Manoeuvring and Control of Marine Criu't, Brijuni, Croatia, 1997
REQUIREMENTS FOR STANDARD HARMONIC CAPTIVE MANOEUVRING TESTS
M Vantorre1,l,l & K Eloof
1
University ofGhent (Department ofApplied Mechanics, Section Maritime Technology), Technologiepark Zwijnaarde 9. B 9052 Gent (Belgium) 2Fundfor &ientific Research - Flanders 3do Flanders Hydraulics. Berchemlei 115. B 2140Antwerpen (Belgium)
Abstract: In the scope of the detennination of a standard PMM testing procedure, a review of existing guidelines for the execution of harmonic captive manoeuvring tests with ship models is given, with emphasis on the selection of the oscillation frequency. These guidelines are discussed making use of the results of systematic PMM-t.est series, mainly carried out at low speed in shallow water conditions. In this way, the validity of rules of thumb in situations which are considerably different from design conditions can be assessed. Keywords: manoeuvrability, standards, ship control, models, tests
could be ascribed to amplitude limitations, were overcome by the development of mechanical and coIIlJUer controlled large amplitude oscillators in the 1970s.
1. IN1RODUCTION
Recently, research on ship manoeuvrability was intensified considerably due to several evolutions, such as the increasing use of manoeuvring simulation for waterway design and training, and the introduction of IMO Interim Standards for Ship Manoeuvrability (1993). For the development of reliable mathematical manoeuvring models, which takes an important place in this kind of research, the execution of captive model tests remains one of the main tools, in spite of the extensive efforts
As a result. a 30 years long experience exists in the cmrent experimental techniques applied for determin-
ing hydrodynamic manoeuvring coefficients. During this period, all tanks involved have developed their own practical method for executing captive manoeuvring tests, mainly based onl (semi-)empirical considerations. An increasing need for standard procedures was identified, in order to assess the quality of test results and, therefore, mathematical models; for this reason, the 21st lTIC Manoeuvrability Committee (1996) has formulated a Recommended standard PMM test procedure. As the latter intentionally has a rather qualitative character, an effort is required in order to provide quantitative guidelines for PMM tests. Such guidelines should lead to an optimal procedure, irrespective of the applied mathematical model, the range of kinematical conditions or the environmental parameters. The present paper intends to provide some background to the formu1ation of such guidelines: it contains a review of published guidelines for harmonic captive manoeuvring tests, and a critical analysis of systematic PMM-tests carried out at the Towing Tank for Manoeuvres in Shallow Water (cooperation Flanders Hydraulics - University ofGhent). Antwerp (Belgium).
and remarkable progress in the area of theoretical, numerical and semi-empirical prediction methods. During such tests, a ship model is forced by an extemal mechanism to undergo a prescribed trajectory in the horizontal plane; the measurement of forces acting on the model leads to numerical values for a number of coefficients or hydrodynamic derivatives occurring in the mathematical model. Captive manoeuvring test techniques started their development about fifty years ago with the application of oblique towing techniques in towing tanks and the construction of rotating arm facilities. A spectacular progress was made in the 19605 by the introduction of the so-called planar motion meclumism (PMM), which not only allows to obtain data about acx:eleration derivatives, but also offers the opportunity to investigate yawing motions in a relatively narrow towing tank. The shortcomings of first generation PMM systems, which
123
2.3. Restriction due to limitations of lateral motion
2. EXISTING GUIDELINES
Harmonic sway tests.ln a nondimensional notation, 2.1. Introduction
sway velocity and acceleration amplitudes depend on frequency 00' and lateral amplitude Y'OA = YOAIL:
Compared with stationary tests (e.g. oblique towing, rotating arm), the number of parameters determining a PMM test is rather large. Furthermore, the parameters cannot always be chosen independently, or the choice may be restricted by the concept of the mechanism or the tank dimensions.
v ~ L 2 vA A - -- Y'OA00' ' = ---A. = YO'AOO' ,.~'A -- - 2 U
Y'OA is restricted due to limitations of the mechanism, or in order to avoid wall effects; with respect to the latter, van Leeuwen considers half the tank width as an upper limit for the trajectory width. As a result, velocity and acceleration amplitudes can only be controlled by variation of the oscillation frequency.
If the model length L and the forward speed u are chosen, following parameters have to be determined: • oscillation frequency 00 or period T = 21t / 00 ; • number of cycles c; • amplitudes of sway/yaw velocity and acceleration; • static drift angle ~ (for PMM yawing tests); • control variables: rudder angle 8, propeller rate n. Ranges for ~, 8, n have to be selected according to the application area of the mathematical manoeuvring model. This is in principle also the case for the range of acceleration and velocity amplitudes, but frequency and motion amplitude cannot be combined without restrictions. The obtained combinations of accelerations and velocities should be realistic, which can e.g. be found by considering low frequency rudder actions, as was recommended by van Leeuwen (1969), although this author admitted that such an approach leads to unpractically low test frequencies. Moreover, such a criterion cannot always be applied to harbour manoeuvres, where yawing motions are not only determined by rudder action, but also by tugs, bow and stem thrusters, etc.
Harmonic yaw tests. Yaw velocity and acceleration amplitudes can be written in a nondimensional way:
For small yaw amplitudes, the nondimensional amplitude of the lateral motion of the ship model can be approximated by Y'OA:::: '¥A/OO', which yields :
so that, in a nondimensional notation, yaw velocity and acceleration amplitudes also depend on the frequency 00' and the lateral amplitude Y'OA. as is the case for PMM sway tests.
2.4. Restrictions due to nonstationary effects
Other restrictions for test frequency are related to: • the non-stationary character of PMM testing: as most mathematical manoeuvring models are quasistationary, memory effects in the experimental results should be avoided; • the tank dimensions.
Tank resonance. If the PMM frequency equals a natural frequency of the water in the tank, a standing wave system may interfere with the tests (StmmTejsen & Chislett, 1966; Smitt & Chislett, 1974; Goodman et al, 1977). This occurs if the wave length A. of the waves induced by oscillatory ship motions takes one of following values:
2.2. Restrictions due to tank length. The fraction eof the tank length covered during one oscillation cycle can be expressed nondimensionally: Af _ .(.
f. _ uT _ 21tU _ 21t L L Leo 00'
--------
A. = 2W, w,t W ..~ w, ...
00' = ooUu. Denoting the useful tank length by fT , the number of oscillation cycles c is limited to:
f.T
1
f.
21t
(6)
W being the tank width. A.=21t1k depends on the water depth h, as gk tanh kh = 00 2 ; the critical frequency according to A.=2W decreases with decreasing water depth. Stmm-Tejsen & Chislett (1966) have shown that frequencies higher than this critical value result into unacceptable scatter.
(I)
with
c~-=-f.ro'
(3)
U
Waves due to combined pulsation and translation. A pulsating source with frequency 00 moving at speed u in a free surface induces a wave system with a pattern depending on r=rou/g (Wehausen & Laitone, 1960). Ifr is small, the waves are located in a sector of 2xI9°28' 16" behind the source. The sector grows with increasing r , reaches 2x90o at r= 0.25 and decreases again at higher r . During PMM tests, r should be considerably less than 0.25 (van Leeuwen, 1964; Goodman et al, 1977; Smitt & Chislett, 1974).
(2)
Accuracy improves with increasing c, but this effect is rather restricted if c>3 (Vantorre, 1992).
124
• Theoretically, YvM and Nvjvj can be derived from the third harmonic of lateral force and yawing moment. However, very large errors are expected.
Nonstationary lift and memory effects. Taking account of the quasistationary nature of mathematical manoeuvring models, experimental data should not be affected by memory effects due to the application of nonstationary techniques. This requirement is generally formulated by a maximum value for ro'. Van Leeuwen's (1969) philosophy leads to optimal ro' for PMM yaw tests depending on the nondimensional yaw velocity amplitude. Most authors, however, recommend semi-empirical values for ro' : • ro' ~ 2-2.5, according to Nomoto (1975). • Smitt and Chislett (1974) recommend ro'=3 as a maximum. In a comment, Glansdorp states that for some derivatives (Yv', Nr') ro' should be limited to 1-l.5. The authors reply that ro'=3 is applied to yaw tests; a safer upper limit for sway tests, which are more sensitive to frequency, is ro'=2. • Milanov (1984) formulated, more qualitatively, a similar conclusion.
PlvfJvf yaw tests. The following was concluded: • The effect of heading angle fluctuations on the inertia terms of the yawing moment decreases with increasing ro'; the effect on the damping terms appears to be minimized at an 'optimal frequency' :
ro'opt =
(8)
3. EXPERIMENTAL OBSERVATIONS 3.1. Experimental program
Especially for harmonic sway tests, R. should not be too small, in order to avoid the model to move in its own wake. A minimum value of 2.5 for £', corresponding with ro'<2.5, seems reasonable, but may cause practical problems at very low and zero speed YOAfB should be sufficiently large, allowing the model to move laterally in 'unaffected' water.
Systematic captive manoeuvring tests were executed with several full form ship models at different draft and water depth, with special attention to very shallow water (h!f~1.2) and low forward speed. The selected conditions are summarized in Table 1. The PMM tests discussed in this chapter were carried out without propeller or rudder action; model speed, pulsation and motion amplitude were varied to assess their influence.
For harmonic yaw tests, swept paths covered during successive half cycles interfere with each other if ro' exceeds a value which depends on \IfA and BIL; ro'< 4 appears to be a realistic guideline.
3.2. Harmonic sway tests Acceleration derivatives. Figure I (EG, EH, AI) shows that in shallow water conditions a unique value for the acceleration derivative Y'v , obtained from a Fowler analysis, cannot be determined, due to the important influence of the test pulsation ro ' . Although less important, sway amplitude and forward speed also affect the results.
2.5. Influence o/trajectory errors. PMM sway tests. Vantorre's (1992) theoretical developments yield following conclusions: • With increasing frequency, the relative error on the damping component and, therefore, on Yuv, increases, while the relative error on the inertia terms decreases. At following optimal frequency, an equal accuracy is reached for both components:
Y'uv = Y\.-m'
I
taking values 2-4. However, the choice of ro' is not very critical, but should not be too small. • An accurate determination of Y ur and Y 'i- may be problematic due to the effect of heading angle fluctuations; for this reason, the yawing angle amplitude should not be taken too small.
Memory effects at larger ro' can be explained by interference between the model's swept path and its own (lateral) wake, leading to unrealistic flow. The interference pattern depends on ro', YOA' or \IfA, BIL.
, ro opt
N'uv-N'v N'ur -m'x'G
The frequency effect decreases with increasing ro ' ,which implies that more stable values for Y'v are obtained in a frequency range to be avoided from a point of view of quasi.-steadiness and wake interference (ro'> 3).
(7)
The test parameter dependency is clearly a shallow water problem: the effect decreases at larger underkeel clearance, and is of minor importance at hff ;:: 2.
as the components in phase with sway velocity and with sway acceleration are of the same magnitude. ro'opt takes very low values: 0.25 to 2.0 depending on hull shape and water depth. It therefore seems recommended to derive numerical values for the velocity derivatives from results of OT tests, so that the accuracy of the inertia terms can be improved by increasing ro', at least to some extend. • Similar conclusions can be drawn for the yawing moment. In this case, an 'optimum' is only reached at very large ro' (=10-20), so that an accurate determination of ~ might cause problems.
Table 1 Test conditions and model characteristics Test hff series AO 1.2 Al 2.5 C3 1.1 EG l.2 EH l.5
125
scale
Lpp(m) B(m) T(m) CB (-)
In5
259.2 259.2 220.0 325.0 325.0
In5 1/64 1185 1/85
43 17.34 0.854 14.6 0.844 43 32.24 12.25 0.811 53.0 21.79 0.829 53.0 21.79 0.829
o -10
•
r> -2O w
.+.
o
C.
~
phase I
+
phase 11
phase N
phase III
~
• -. • -40
• -so
o
3
2
I·.
EG
4
w'
6
7 xJl(-)
EH
+
5
....
Fig. 1. Influence of pulsation hIT-ratios (EG, EH, AI).
ID'
A1
on Y'y for different
v
Y~v
c ~
o c. E o
-8
t<::::::::-: ,
- . -r - -
o
E
phase IIIlV
y(t) =
phase III
y(t)
· 16
!
I-
~
-40
in w
~
-80
o ,...
(EH)
.~
o
0.1
0.2
0.3
VA
•
o
1
(EG)
6
_.
o Fn=O.033
a (b)
~.1
0
• 0
r3(deg)
1.35 - 3.6 1.35 1.8
3
5
4
Fn=O.05O )(
+
Fn=O.065
2
• a
10
15
20
---
- --
.......•
2.5
3
3.5
4
5
4.5
EH
en.
-00·-
.......
Olr---.--.---.r---r--r--~
•
0.01
x- -
....... ..... ..... =tc-_
.., •...... .. ,
-500
a
0.015
+-
EG
.. ' 4!A = 35deg
;::::::: ~
3.6
.A
·
,
.....
-400
2.7
0.02
•
111
+
- -ljJA = 15 deg -ljJA = 25deg
.',
-
g -
(!l
W
v
in ,... -300
2- •
c
Fig. 5. Derivative N'r versus pulsation ID' (EG, EH).
w o
-15
;!(
•
2
-100
-20
IiI
hfT=1 .2
~
)(
o
0.1
-25
~
-1t
~
Fig. 2. First harmonic component of Y in phase with sway velocity versus nondimensional sway velocity amplitude (EG).
Z
~
hfT=1 .5
160
x 4
3
z -1L'
0.6
0.5
0.4
Cil = 2nutt.x
test.
)(
-20
-t.yl2 + (t.yl2n)(Cil(t-tlll )-sinCil(t-tm»
0
~
u::
=
+'- t.y/2
Fig. 4. Trajectory of an alternative nonstationary sway
8 y' 3rt vlvl
.~
~ -12
C
i
v'A
y(t) = t.yf2 • (t.yI2IT)(CIl(t-t) )-sinCll(t-t) »
with
--
-_.-r - - f - - - -
~ • ~
phase 1
ID o
-1OOIt-~-;----r----+---~~---+--~ iIi=:==-=_ I-
~L. >-
-2
,. .
25
~. 01
-OC~4~~-~:-~-~-~-~·c·~-=-=-=-:t:-==-~·l---~ : ............. . . ..
~. 015
3
3.5
4
4.5
W'
S(deg)
Fig. 3. Comparison between Y'(~) and N'(~) (C3).
2.5
2
~ . 02
•
or and PMM tests for
Fn=O.033
+
Fn=O.05O )(
Fn=O.065
Fig. 6. Derivative Y'j- versus pulsation ID' (EG, EH).
126
5
The values for the acceleration derivative N'v are characterized by very large scatter, especially at low Cl) '.
(figme 4). A constant forward speed is combined with alternating sway motions to port (phase I) and starboard (phase III), separated by so-called link periods (phases IT and IV), during which the model is kept in its ma'
Velocity derivatives. Principally, velocity derivatives (e.g. Y'uv,Y'vjvI,N' uv, N'.w or, in generaL relations between the drift angle ~ and the nondimensional lateral force and yawing moment can be derived from PMM sway tests. Such results can also be obtained by oblique towing (01) tests, offering the advantages of having a stationary character and allowing larger drift angles, which can only be realised by PMM tests with high oscillation frequencies and large lateral amplitudes.
Although the range of numerical values for Y'v can be reduced by 55%, the frequency dependency cannot be
eliminated completely. In addition, the link period should not be taken too short, as progressively decreasing oscillating lateral forces are measured both on fore and afterl:xxiy between two successive lateral motions.
PMM tests can yield velocity derivatives in two ways: (a) by regression analysis applied to the first harmonic component ofY or N in phase with sway velocity, measured during a series of tests executed at varying v'A = y'QA Cl)' (figme 2, EG); (b) by means of a regression analysis applied to Y or N measured during individual PMM tests. (a) can only be applied if a rather simple regression model is used for Y'(~) or N'(~), while (b) also allows more complicated mathematical models, such as a tabular representation for a discrete number of drift angles. The latter appeared to be preferable to a regression model. as was pointed out by a detailed analysis of drift induced forces and moments resulting from or tests in condition C3 (Vantorre & Eloot, 1996).
3.4. Harmonic yaw tests Acceleration derivatives. Variation of frequency and yaw amplitude yields no significant influence of these parameters on N'i (figure 5, EG, EH). However, at lower Cl)' the influence of yaw amplitude 'VA on Y'i cannot be denied. This influence becomes less important at increasing pulsation, and is less striking at larger underkeel clearance (figure 6, EG, EH). Velocity derivatives. If the lateral force and yawing moment due to combination of forward speed and yaw are formulated as follows:
A comparison between damping forces and moments derived from or tests and from PMM sway tests carried out with constant sway amplitude (Y;./B = 1) with 1.35 «0 '<3.61~ to following conclusions (figme 3, C3): • For 00'<2.7, Y'(~) and N'(~) do not change significantly with increasing frequency. Compared to or, Y' and N' are underestimated for all drift angles; only at very small ~, the fair agreement for Y' is observed • A significant difference is found between the Y'(~) and N'(~) curves obtained from PMM sway tests at relatively high frequency (Cl)'>2.7) compared to tests performed in the lower frequency range. • Even at low frequency it seems impossible to repr0duce steady drift forces by one single PMM sway test.
Y' (u' ,r' ,t') = (Y't -m'x'G )t'+(Y' ur -m')
N'(u' ,r' ,t') =(N't-1zz') t'+(N'
ur
-m'x'
r'+ Y' rlrl r' lr'l G
)r'+N'
* 1r' lr' l (9)
yaw damping coefficients Y'lr'Y'~,N'ur, N'~ can be derived from the first hannonic component ofY or N in phase with yaw velocity. The N-derivatives can be determined with satisfactory reliability, although some scatter OCCW'S at r'A <0.5 (figure 7, AO). Similar conclusions can be drawn for Ycoefficients, although the scatter is somewhat larger.
There are indications that damping forces are affected by memory effects in the frequency range Cl) '>2.7, which can be ascribed to wake interference. This is confirmed by figme 2, illustrating method (a): the application of
As the mathematical model (9) does not lead to satisfactory results for larger r', a more general formulation for the damping forces is considered:
higher frequencies may cause scatter of results at higher drift angles in shallow water. Besides, sway tests at higher Cl)' result into a relationship between measured drift induced force and moment and drift angle ~ which is not characterized by a single curve but by a loop.
Y'(u' ,r' ,t') = (Y't-m'x'G )t'+Y'(r)- m' r' N'(u' ,r' ,t') =(N't -I zz ')
(10)
t'+N'(r) - m'x'G r'
with y = arctan(rUlu). Y'(y) and N'(y) can be derived from an individual PMM sway test by means of (10), in which acceleration derivatives Y'i and N'i are based on harmonic analysis. Figme 8 (EG) shows that the relationship Y'(y) is dominated by a loop which in general increases with Cl)', comparable with the drift induced force Y'(~) derived from individual sway tests. If the yaw amplitude is kept constant, the slope of Y' (y) increases slightly with increasing Cl) '. Again there are indications that nonstationary phenomena due to interference with the model's swept path affect the test results.
3.3. Alternative nonstationary sway test
A dilemma occurs when the test frequency of PMM sway tests has to be chosen: acceleration derivatives can be obtained more accurately and with less scatter by increasing frequencies; on the other hand, this leads to an increasing interference of flow patterns generated by the model's fore and afteIbody. To avoid wake interference and impose a more realistic motion to the ship model, an alternative nonstationary sway test is introduced
127
Stmm-Tejsen, l and M.S. Chislett (1966). A model
4. CONCLUSIONS
testing technique and method of analysiS for the prediction of steering and manoeuvring qualities ofsurface vessels. Rep.No. Hy-7. HyA, Lyngby. Vantorre, M. (1992). Accuracy and optimization of captive ship model tests. In: (5th Int. Symposium on) Practical Design of Ships and Mobile Units, Newcastle upon Tyne (lB. Caldwell and G. Ward (Bd». Vol. 1, pp. 1.190-203. Elsevier Applied Science, LondonlNew York. Vantorre, M. and K. Eloot (1996). Hydrodynamic phenomena affecting manoeuvres at low speed in shallow navigation areas. In: Proceedings of the 11th Int. Harbour Congress (H. Smitz and G. Thues (Ed», pp. 535-546. KVIV, Antwerp. Wehausen, lY. and E. Laitone(1960). Surface Waves. InHandbuch der Physik.Band IX: Stromungsmechanik rn, p.446-778. Springer Verlag, Berlin.
Guidelines for the selection of P:rvIM test parameters, such as motion amplitude and frequency, should lead to an optimal reliability of test results. The selected test conditions should therefore not only guarantee an accurate measurement of all resulting coefficients, but also avoid unrealistic situations due to interaction between ship model and tank walls or to artificial interference patterns between the model and its own wake generated by the imposed oscillatory motions. For some hydrodynamic derivatives (e.g. Y'v, N'v), a compromise between accuracy and realism appears not to be feasible, so that reliable data can only be obtained by extrapolation to realistic conditions or application of alternative techniques. It was also found that memory effects cannot always be recognized by classical Fourier analysis techniques, but sometimes require alternative methods. It should be mentioned that many of these difficulties are tYPical for test conditions with limited underkeel clearance, and are less important in deep water. On the other hand, standard procedures should be applicable to all environmental conditions.
N'ul"-m'x'G
2
C .,
-4
c::
o
~
o
u u
C o
REFERENCES
-6
- t - - -1 - - - -_.-
I-
~ I .. .-
8 N' rlrl
r'
~ ~.3n:
-8
7<
E
~
~ -1
Goodman,A, M.Gertler and RKohl (1977). Experimental techniques and methods of analysis used at Hydronautics for surface-ship maneuvering predictions. In: Eleventh Symposium on Naval Hydrodynamics, London, 1976 (R Bishop, A Parkinson, W. Price (Ed», pp 55-113 . Mechanical Engineering Publications Limited, London/New York. Leeuwen, G. van (1964). The lateral damping and added mass of an oscillating shipmodel. Publ. No. 23, Shipbuilding Laboratory, Technological University, Delft. Leeuwen, G. van (1969). Enkele problemen bij het ontwerpen van een horizontale oscillator. Rap. No. 225, Lab. Scheepsbouwkunde, Technische Hogeschool Delft. Manoeuvrability Committee (1996). Final report and recommendations to the 21st ITTC. In: 21st International Towing Tank Conference, VoU, pp. 347-398. NTNUlMarintek, Trondheim. Milanov, E. (1984). On the use of quasisteady P:rvIMtest results. In: International Symposium on Ship Techniques, Rostock. Nomoto, K. (1975). Ship response in directional control taking account of frequency dependent hydrodynamic derivatives. In: Proceedings of the 14th International TOwing Tank Conference. Vol. 2, pp. 408413. National Research Council Canada, Ottawa. Smitt, L.W. and M.S. Chislett (1974). Large amplitude P:rvIM tests and maneuvering prediction for a Mariner class vessel. In: Proceedings of the 10th Symposium on Naval Hydrodynamics, pp. 131-157, Boston.
~ '-•
f!
u:::
-12
o
0.5
I•
2
1.5
Fn=O.034 +
Fn=O.052
x
-.....:: 2.5
Fn=O.069
Fig. 7. First harmonic component of N in phase with yaw velocity versus nondimensional yaw velocity amplitude (AO). 0.04
.-
... -...... 0.03
)r'
0.02
-.oX
~. 03
_. _____ _ lIt --
.X
~ . 04
'Y (deg) - Y ' ( 11, 1', 1') (-)
··.. ··m - m'x'G) i' (-)
- - m'r(-)
--+-YTY)
Fig. 8. Loop observed during individual yaw test (EG: Fn= 0.033, (1)'= 4.4 and'VA= 25 deg) for Y'(y) .
128
REQUIREMENTS FOR STANDARD HARMONIC CAPTIVE MANOEUVRING TESTS
M Vantorre1,l,l & K Eloof
1
University ofGhent (Department ofApplied Mechanics, Section Maritime Technology), Technologiepark Zwijnaarde 9. B 9052 Gent (Belgium) 2Fundfor &ientific Research - Flanders 3do Flanders Hydraulics. Berchemlei 115. B 2140Antwerpen (Belgium)
Abstract: In the scope of the detennination of a standard PMM testing procedure, a review of existing guidelines for the execution of harmonic captive manoeuvring tests with ship models is given, with emphasis on the selection of the oscillation frequency. These guidelines are discussed making use of the results of systematic PMM-t.est series, mainly carried out at low speed in shallow water conditions. In this way, the validity of rules of thumb in situations which are considerably different from design conditions can be assessed. Keywords: manoeuvrability, standards, ship control, models, tests
could be ascribed to amplitude limitations, were overcome by the development of mechanical and coIIlJUer controlled large amplitude oscillators in the 1970s.
1. IN1RODUCTION
Recently, research on ship manoeuvrability was intensified considerably due to several evolutions, such as the increasing use of manoeuvring simulation for waterway design and training, and the introduction of IMO Interim Standards for Ship Manoeuvrability (1993). For the development of reliable mathematical manoeuvring models, which takes an important place in this kind of research, the execution of captive model tests remains one of the main tools, in spite of the extensive efforts
As a result. a 30 years long experience exists in the cmrent experimental techniques applied for determin-
ing hydrodynamic manoeuvring coefficients. During this period, all tanks involved have developed their own practical method for executing captive manoeuvring tests, mainly based onl (semi-)empirical considerations. An increasing need for standard procedures was identified, in order to assess the quality of test results and, therefore, mathematical models; for this reason, the 21st lTIC Manoeuvrability Committee (1996) has formulated a Recommended standard PMM test procedure. As the latter intentionally has a rather qualitative character, an effort is required in order to provide quantitative guidelines for PMM tests. Such guidelines should lead to an optimal procedure, irrespective of the applied mathematical model, the range of kinematical conditions or the environmental parameters. The present paper intends to provide some background to the formu1ation of such guidelines: it contains a review of published guidelines for harmonic captive manoeuvring tests, and a critical analysis of systematic PMM-tests carried out at the Towing Tank for Manoeuvres in Shallow Water (cooperation Flanders Hydraulics - University ofGhent). Antwerp (Belgium).
and remarkable progress in the area of theoretical, numerical and semi-empirical prediction methods. During such tests, a ship model is forced by an extemal mechanism to undergo a prescribed trajectory in the horizontal plane; the measurement of forces acting on the model leads to numerical values for a number of coefficients or hydrodynamic derivatives occurring in the mathematical model. Captive manoeuvring test techniques started their development about fifty years ago with the application of oblique towing techniques in towing tanks and the construction of rotating arm facilities. A spectacular progress was made in the 19605 by the introduction of the so-called planar motion meclumism (PMM), which not only allows to obtain data about acx:eleration derivatives, but also offers the opportunity to investigate yawing motions in a relatively narrow towing tank. The shortcomings of first generation PMM systems, which
123
2.3. Restriction due to limitations of lateral motion
2. EXISTING GUIDELINES
Harmonic sway tests.ln a nondimensional notation, 2.1. Introduction
sway velocity and acceleration amplitudes depend on frequency 00' and lateral amplitude Y'OA = YOAIL:
Compared with stationary tests (e.g. oblique towing, rotating arm), the number of parameters determining a PMM test is rather large. Furthermore, the parameters cannot always be chosen independently, or the choice may be restricted by the concept of the mechanism or the tank dimensions.
v ~ L 2 vA A - -- Y'OA00' ' = ---A. = YO'AOO' ,.~'A -- - 2 U
Y'OA is restricted due to limitations of the mechanism, or in order to avoid wall effects; with respect to the latter, van Leeuwen considers half the tank width as an upper limit for the trajectory width. As a result, velocity and acceleration amplitudes can only be controlled by variation of the oscillation frequency.
If the model length L and the forward speed u are chosen, following parameters have to be determined: • oscillation frequency 00 or period T = 21t / 00 ; • number of cycles c; • amplitudes of sway/yaw velocity and acceleration; • static drift angle ~ (for PMM yawing tests); • control variables: rudder angle 8, propeller rate n. Ranges for ~, 8, n have to be selected according to the application area of the mathematical manoeuvring model. This is in principle also the case for the range of acceleration and velocity amplitudes, but frequency and motion amplitude cannot be combined without restrictions. The obtained combinations of accelerations and velocities should be realistic, which can e.g. be found by considering low frequency rudder actions, as was recommended by van Leeuwen (1969), although this author admitted that such an approach leads to unpractically low test frequencies. Moreover, such a criterion cannot always be applied to harbour manoeuvres, where yawing motions are not only determined by rudder action, but also by tugs, bow and stem thrusters, etc.
Harmonic yaw tests. Yaw velocity and acceleration amplitudes can be written in a nondimensional way:
For small yaw amplitudes, the nondimensional amplitude of the lateral motion of the ship model can be approximated by Y'OA:::: '¥A/OO', which yields :
so that, in a nondimensional notation, yaw velocity and acceleration amplitudes also depend on the frequency 00' and the lateral amplitude Y'OA. as is the case for PMM sway tests.
2.4. Restrictions due to nonstationary effects
Other restrictions for test frequency are related to: • the non-stationary character of PMM testing: as most mathematical manoeuvring models are quasistationary, memory effects in the experimental results should be avoided; • the tank dimensions.
Tank resonance. If the PMM frequency equals a natural frequency of the water in the tank, a standing wave system may interfere with the tests (StmmTejsen & Chislett, 1966; Smitt & Chislett, 1974; Goodman et al, 1977). This occurs if the wave length A. of the waves induced by oscillatory ship motions takes one of following values:
2.2. Restrictions due to tank length. The fraction eof the tank length covered during one oscillation cycle can be expressed nondimensionally: Af _ .(.
f. _ uT _ 21tU _ 21t L L Leo 00'
--------
A. = 2W, w,t W ..~ w, ...
00' = ooUu. Denoting the useful tank length by fT , the number of oscillation cycles c is limited to:
f.T
1
f.
21t
(6)
W being the tank width. A.=21t1k depends on the water depth h, as gk tanh kh = 00 2 ; the critical frequency according to A.=2W decreases with decreasing water depth. Stmm-Tejsen & Chislett (1966) have shown that frequencies higher than this critical value result into unacceptable scatter.
(I)
with
c~-=-f.ro'
(3)
U
Waves due to combined pulsation and translation. A pulsating source with frequency 00 moving at speed u in a free surface induces a wave system with a pattern depending on r=rou/g (Wehausen & Laitone, 1960). Ifr is small, the waves are located in a sector of 2xI9°28' 16" behind the source. The sector grows with increasing r , reaches 2x90o at r= 0.25 and decreases again at higher r . During PMM tests, r should be considerably less than 0.25 (van Leeuwen, 1964; Goodman et al, 1977; Smitt & Chislett, 1974).
(2)
Accuracy improves with increasing c, but this effect is rather restricted if c>3 (Vantorre, 1992).
124
• Theoretically, YvM and Nvjvj can be derived from the third harmonic of lateral force and yawing moment. However, very large errors are expected.
Nonstationary lift and memory effects. Taking account of the quasistationary nature of mathematical manoeuvring models, experimental data should not be affected by memory effects due to the application of nonstationary techniques. This requirement is generally formulated by a maximum value for ro'. Van Leeuwen's (1969) philosophy leads to optimal ro' for PMM yaw tests depending on the nondimensional yaw velocity amplitude. Most authors, however, recommend semi-empirical values for ro' : • ro' ~ 2-2.5, according to Nomoto (1975). • Smitt and Chislett (1974) recommend ro'=3 as a maximum. In a comment, Glansdorp states that for some derivatives (Yv', Nr') ro' should be limited to 1-l.5. The authors reply that ro'=3 is applied to yaw tests; a safer upper limit for sway tests, which are more sensitive to frequency, is ro'=2. • Milanov (1984) formulated, more qualitatively, a similar conclusion.
PlvfJvf yaw tests. The following was concluded: • The effect of heading angle fluctuations on the inertia terms of the yawing moment decreases with increasing ro'; the effect on the damping terms appears to be minimized at an 'optimal frequency' :
ro'opt =
(8)
3. EXPERIMENTAL OBSERVATIONS 3.1. Experimental program
Especially for harmonic sway tests, R. should not be too small, in order to avoid the model to move in its own wake. A minimum value of 2.5 for £', corresponding with ro'<2.5, seems reasonable, but may cause practical problems at very low and zero speed YOAfB should be sufficiently large, allowing the model to move laterally in 'unaffected' water.
Systematic captive manoeuvring tests were executed with several full form ship models at different draft and water depth, with special attention to very shallow water (h!f~1.2) and low forward speed. The selected conditions are summarized in Table 1. The PMM tests discussed in this chapter were carried out without propeller or rudder action; model speed, pulsation and motion amplitude were varied to assess their influence.
For harmonic yaw tests, swept paths covered during successive half cycles interfere with each other if ro' exceeds a value which depends on \IfA and BIL; ro'< 4 appears to be a realistic guideline.
3.2. Harmonic sway tests Acceleration derivatives. Figure I (EG, EH, AI) shows that in shallow water conditions a unique value for the acceleration derivative Y'v , obtained from a Fowler analysis, cannot be determined, due to the important influence of the test pulsation ro ' . Although less important, sway amplitude and forward speed also affect the results.
2.5. Influence o/trajectory errors. PMM sway tests. Vantorre's (1992) theoretical developments yield following conclusions: • With increasing frequency, the relative error on the damping component and, therefore, on Yuv, increases, while the relative error on the inertia terms decreases. At following optimal frequency, an equal accuracy is reached for both components:
Y'uv = Y\.-m'
I
taking values 2-4. However, the choice of ro' is not very critical, but should not be too small. • An accurate determination of Y ur and Y 'i- may be problematic due to the effect of heading angle fluctuations; for this reason, the yawing angle amplitude should not be taken too small.
Memory effects at larger ro' can be explained by interference between the model's swept path and its own (lateral) wake, leading to unrealistic flow. The interference pattern depends on ro', YOA' or \IfA, BIL.
, ro opt
N'uv-N'v N'ur -m'x'G
The frequency effect decreases with increasing ro ' ,which implies that more stable values for Y'v are obtained in a frequency range to be avoided from a point of view of quasi.-steadiness and wake interference (ro'> 3).
(7)
The test parameter dependency is clearly a shallow water problem: the effect decreases at larger underkeel clearance, and is of minor importance at hff ;:: 2.
as the components in phase with sway velocity and with sway acceleration are of the same magnitude. ro'opt takes very low values: 0.25 to 2.0 depending on hull shape and water depth. It therefore seems recommended to derive numerical values for the velocity derivatives from results of OT tests, so that the accuracy of the inertia terms can be improved by increasing ro', at least to some extend. • Similar conclusions can be drawn for the yawing moment. In this case, an 'optimum' is only reached at very large ro' (=10-20), so that an accurate determination of ~ might cause problems.
Table 1 Test conditions and model characteristics Test hff series AO 1.2 Al 2.5 C3 1.1 EG l.2 EH l.5
125
scale
Lpp(m) B(m) T(m) CB (-)
In5
259.2 259.2 220.0 325.0 325.0
In5 1/64 1185 1/85
43 17.34 0.854 14.6 0.844 43 32.24 12.25 0.811 53.0 21.79 0.829 53.0 21.79 0.829
o -10
•
r> -2O w
.+.
o
C.
~
phase I
+
phase 11
phase N
phase III
~
• -. • -40
• -so
o
3
2
I·.
EG
4
w'
6
7 xJl(-)
EH
+
5
....
Fig. 1. Influence of pulsation hIT-ratios (EG, EH, AI).
ID'
A1
on Y'y for different
v
Y~v
c ~
o c. E o
-8
t<::::::::-: ,
- . -r - -
o
E
phase IIIlV
y(t) =
phase III
y(t)
· 16
!
I-
~
-40
in w
~
-80
o ,...
(EH)
.~
o
0.1
0.2
0.3
VA
•
o
1
(EG)
6
_.
o Fn=O.033
a (b)
~.1
0
• 0
r3(deg)
1.35 - 3.6 1.35 1.8
3
5
4
Fn=O.05O )(
+
Fn=O.065
2
• a
10
15
20
---
- --
.......•
2.5
3
3.5
4
5
4.5
EH
en.
-00·-
.......
Olr---.--.---.r---r--r--~
•
0.01
x- -
....... ..... ..... =tc-_
.., •...... .. ,
-500
a
0.015
+-
EG
.. ' 4!A = 35deg
;::::::: ~
3.6
.A
·
,
.....
-400
2.7
0.02
•
111
+
- -ljJA = 15 deg -ljJA = 25deg
.',
-
g -
(!l
W
v
in ,... -300
2- •
c
Fig. 5. Derivative N'r versus pulsation ID' (EG, EH).
w o
-15
;!(
•
2
-100
-20
IiI
hfT=1 .2
~
)(
o
0.1
-25
~
-1t
~
Fig. 2. First harmonic component of Y in phase with sway velocity versus nondimensional sway velocity amplitude (EG).
Z
~
hfT=1 .5
160
x 4
3
z -1L'
0.6
0.5
0.4
Cil = 2nutt.x
test.
)(
-20
-t.yl2 + (t.yl2n)(Cil(t-tlll )-sinCil(t-tm»
0
~
u::
=
+'- t.y/2
Fig. 4. Trajectory of an alternative nonstationary sway
8 y' 3rt vlvl
.~
~ -12
C
i
v'A
y(t) = t.yf2 • (t.yI2IT)(CIl(t-t) )-sinCll(t-t) »
with
--
-_.-r - - f - - - -
~ • ~
phase 1
ID o
-1OOIt-~-;----r----+---~~---+--~ iIi=:==-=_ I-
~L. >-
-2
,. .
25
~. 01
-OC~4~~-~:-~-~-~-~·c·~-=-=-=-:t:-==-~·l---~ : ............. . . ..
~. 015
3
3.5
4
4.5
W'
S(deg)
Fig. 3. Comparison between Y'(~) and N'(~) (C3).
2.5
2
~ . 02
•
or and PMM tests for
Fn=O.033
+
Fn=O.05O )(
Fn=O.065
Fig. 6. Derivative Y'j- versus pulsation ID' (EG, EH).
126
5
The values for the acceleration derivative N'v are characterized by very large scatter, especially at low Cl) '.
(figme 4). A constant forward speed is combined with alternating sway motions to port (phase I) and starboard (phase III), separated by so-called link periods (phases IT and IV), during which the model is kept in its ma'
Velocity derivatives. Principally, velocity derivatives (e.g. Y'uv,Y'vjvI,N' uv, N'.w or, in generaL relations between the drift angle ~ and the nondimensional lateral force and yawing moment can be derived from PMM sway tests. Such results can also be obtained by oblique towing (01) tests, offering the advantages of having a stationary character and allowing larger drift angles, which can only be realised by PMM tests with high oscillation frequencies and large lateral amplitudes.
Although the range of numerical values for Y'v can be reduced by 55%, the frequency dependency cannot be
eliminated completely. In addition, the link period should not be taken too short, as progressively decreasing oscillating lateral forces are measured both on fore and afterl:xxiy between two successive lateral motions.
PMM tests can yield velocity derivatives in two ways: (a) by regression analysis applied to the first harmonic component ofY or N in phase with sway velocity, measured during a series of tests executed at varying v'A = y'QA Cl)' (figme 2, EG); (b) by means of a regression analysis applied to Y or N measured during individual PMM tests. (a) can only be applied if a rather simple regression model is used for Y'(~) or N'(~), while (b) also allows more complicated mathematical models, such as a tabular representation for a discrete number of drift angles. The latter appeared to be preferable to a regression model. as was pointed out by a detailed analysis of drift induced forces and moments resulting from or tests in condition C3 (Vantorre & Eloot, 1996).
3.4. Harmonic yaw tests Acceleration derivatives. Variation of frequency and yaw amplitude yields no significant influence of these parameters on N'i (figure 5, EG, EH). However, at lower Cl)' the influence of yaw amplitude 'VA on Y'i cannot be denied. This influence becomes less important at increasing pulsation, and is less striking at larger underkeel clearance (figure 6, EG, EH). Velocity derivatives. If the lateral force and yawing moment due to combination of forward speed and yaw are formulated as follows:
A comparison between damping forces and moments derived from or tests and from PMM sway tests carried out with constant sway amplitude (Y;./B = 1) with 1.35 «0 '<3.61~ to following conclusions (figme 3, C3): • For 00'<2.7, Y'(~) and N'(~) do not change significantly with increasing frequency. Compared to or, Y' and N' are underestimated for all drift angles; only at very small ~, the fair agreement for Y' is observed • A significant difference is found between the Y'(~) and N'(~) curves obtained from PMM sway tests at relatively high frequency (Cl)'>2.7) compared to tests performed in the lower frequency range. • Even at low frequency it seems impossible to repr0duce steady drift forces by one single PMM sway test.
Y' (u' ,r' ,t') = (Y't -m'x'G )t'+(Y' ur -m')
N'(u' ,r' ,t') =(N't-1zz') t'+(N'
ur
-m'x'
r'+ Y' rlrl r' lr'l G
)r'+N'
* 1r' lr' l (9)
yaw damping coefficients Y'lr'Y'~,N'ur, N'~ can be derived from the first hannonic component ofY or N in phase with yaw velocity. The N-derivatives can be determined with satisfactory reliability, although some scatter OCCW'S at r'A <0.5 (figure 7, AO). Similar conclusions can be drawn for Ycoefficients, although the scatter is somewhat larger.
There are indications that damping forces are affected by memory effects in the frequency range Cl) '>2.7, which can be ascribed to wake interference. This is confirmed by figme 2, illustrating method (a): the application of
As the mathematical model (9) does not lead to satisfactory results for larger r', a more general formulation for the damping forces is considered:
higher frequencies may cause scatter of results at higher drift angles in shallow water. Besides, sway tests at higher Cl)' result into a relationship between measured drift induced force and moment and drift angle ~ which is not characterized by a single curve but by a loop.
Y'(u' ,r' ,t') = (Y't-m'x'G )t'+Y'(r)- m' r' N'(u' ,r' ,t') =(N't -I zz ')
(10)
t'+N'(r) - m'x'G r'
with y = arctan(rUlu). Y'(y) and N'(y) can be derived from an individual PMM sway test by means of (10), in which acceleration derivatives Y'i and N'i are based on harmonic analysis. Figme 8 (EG) shows that the relationship Y'(y) is dominated by a loop which in general increases with Cl)', comparable with the drift induced force Y'(~) derived from individual sway tests. If the yaw amplitude is kept constant, the slope of Y' (y) increases slightly with increasing Cl) '. Again there are indications that nonstationary phenomena due to interference with the model's swept path affect the test results.
3.3. Alternative nonstationary sway test
A dilemma occurs when the test frequency of PMM sway tests has to be chosen: acceleration derivatives can be obtained more accurately and with less scatter by increasing frequencies; on the other hand, this leads to an increasing interference of flow patterns generated by the model's fore and afteIbody. To avoid wake interference and impose a more realistic motion to the ship model, an alternative nonstationary sway test is introduced
127
Stmm-Tejsen, l and M.S. Chislett (1966). A model
4. CONCLUSIONS
testing technique and method of analysiS for the prediction of steering and manoeuvring qualities ofsurface vessels. Rep.No. Hy-7. HyA, Lyngby. Vantorre, M. (1992). Accuracy and optimization of captive ship model tests. In: (5th Int. Symposium on) Practical Design of Ships and Mobile Units, Newcastle upon Tyne (lB. Caldwell and G. Ward (Bd». Vol. 1, pp. 1.190-203. Elsevier Applied Science, LondonlNew York. Vantorre, M. and K. Eloot (1996). Hydrodynamic phenomena affecting manoeuvres at low speed in shallow navigation areas. In: Proceedings of the 11th Int. Harbour Congress (H. Smitz and G. Thues (Ed», pp. 535-546. KVIV, Antwerp. Wehausen, lY. and E. Laitone(1960). Surface Waves. InHandbuch der Physik.Band IX: Stromungsmechanik rn, p.446-778. Springer Verlag, Berlin.
Guidelines for the selection of P:rvIM test parameters, such as motion amplitude and frequency, should lead to an optimal reliability of test results. The selected test conditions should therefore not only guarantee an accurate measurement of all resulting coefficients, but also avoid unrealistic situations due to interaction between ship model and tank walls or to artificial interference patterns between the model and its own wake generated by the imposed oscillatory motions. For some hydrodynamic derivatives (e.g. Y'v, N'v), a compromise between accuracy and realism appears not to be feasible, so that reliable data can only be obtained by extrapolation to realistic conditions or application of alternative techniques. It was also found that memory effects cannot always be recognized by classical Fourier analysis techniques, but sometimes require alternative methods. It should be mentioned that many of these difficulties are tYPical for test conditions with limited underkeel clearance, and are less important in deep water. On the other hand, standard procedures should be applicable to all environmental conditions.
N'ul"-m'x'G
2
C .,
-4
c::
o
~
o
u u
C o
REFERENCES
-6
- t - - -1 - - - -_.-
I-
~ I .. .-
8 N' rlrl
r'
~ ~.3n:
-8
7<
E
~
~ -1
Goodman,A, M.Gertler and RKohl (1977). Experimental techniques and methods of analysis used at Hydronautics for surface-ship maneuvering predictions. In: Eleventh Symposium on Naval Hydrodynamics, London, 1976 (R Bishop, A Parkinson, W. Price (Ed», pp 55-113 . Mechanical Engineering Publications Limited, London/New York. Leeuwen, G. van (1964). The lateral damping and added mass of an oscillating shipmodel. Publ. No. 23, Shipbuilding Laboratory, Technological University, Delft. Leeuwen, G. van (1969). Enkele problemen bij het ontwerpen van een horizontale oscillator. Rap. No. 225, Lab. Scheepsbouwkunde, Technische Hogeschool Delft. Manoeuvrability Committee (1996). Final report and recommendations to the 21st ITTC. In: 21st International Towing Tank Conference, VoU, pp. 347-398. NTNUlMarintek, Trondheim. Milanov, E. (1984). On the use of quasisteady P:rvIMtest results. In: International Symposium on Ship Techniques, Rostock. Nomoto, K. (1975). Ship response in directional control taking account of frequency dependent hydrodynamic derivatives. In: Proceedings of the 14th International TOwing Tank Conference. Vol. 2, pp. 408413. National Research Council Canada, Ottawa. Smitt, L.W. and M.S. Chislett (1974). Large amplitude P:rvIM tests and maneuvering prediction for a Mariner class vessel. In: Proceedings of the 10th Symposium on Naval Hydrodynamics, pp. 131-157, Boston.
~ '-•
f!
u:::
-12
o
0.5
I•
2
1.5
Fn=O.034 +
Fn=O.052
x
-.....:: 2.5
Fn=O.069
Fig. 7. First harmonic component of N in phase with yaw velocity versus nondimensional yaw velocity amplitude (AO). 0.04
.-
... -...... 0.03
)r'
0.02
-.oX
~. 03
_. _____ _ lIt --
.X
~ . 04
'Y (deg) - Y ' ( 11, 1', 1') (-)
··.. ··m - m'x'G) i' (-)
- - m'r(-)
--+-YTY)
Fig. 8. Loop observed during individual yaw test (EG: Fn= 0.033, (1)'= 4.4 and'VA= 25 deg) for Y'(y) .
128