o
YDRO- 0G AERODYNAMISK
LABORATORI UM
Lyngby - Denmark
Hydrodynamics
Section
Report No. Hy-lO
.May 1967
The Reversed Spiral Test
A Note on Bech's Spiral Test
and some Unexpected Results of
its Application to Coasters
BY
L. WAGNER SMITT
1P4 COMMISSION:
SKELBAEKGADE4. COPENHAGEN
HYDRO- 0G AERODYNAMISK LABORATORIUM
is a self-supporting institution, established to carry out experiments for industry and to conduct research in the fields ot
Hydro- and Aerodynamics. According to its by-laws, confirmed by His Majesty the King of Denmark, it is governed by a council of eleven members, six of which are elected by the Danish Government and by research organzations, and five by the shipbuilding industry.
Research reports are published in English n two series: Sefies Hy (blue) from the Hydrodynamics Section and Series A (green) from the Aerodynamics Section.
The reports are on sale through the Danish Technical Press at the prices stated below. Research institutions within the fields of Hydro- and Aerodynamics and public technical libraries may, however, as a rule obtain the reports free of charge on application to the Laboratory.
The views expressed in the reports are those of the individual authors.
Series Hy:
No.: Author: Title: Price: D. Kr.
Hy-1 PROHASKA, C. W. Analysis of Ship Model Experiments
and Prediction of Ship Performance 5,00
(Second printing)
Hy-2 PROHASKA, C. W. Trial Trip Analysis for Six Sister Ships 6,00 Hy-3 ILOVR, V. A Five Hole Spherical Pitot Tube for 6,00
Three Dimensional Wake Measurements Hy-4 STR0M-TEJSEN, J. The HyA ALGOL-Programme for Analysis
of Open Water Propeller Test
6,00
Hy-5 ABKOWITZ, M. A. Lectures on Ship Hydrodynamics - 20,00
Steering and Manoeuvrability
Hy-6 CHISLETT, M. S., and
STR0M-TEJSEN, J.
Planar Motion Mechanism Tests and Full-Scale Steering and
12,00
Manoeuvring Predictions for a
MARINER Class Vessel
Hy-7 STR0M-TEJSEN, J.. and A Model Testing Technique and 12,00
CHISLETT, M. S. Method of Analysis for the Prediction
of Steering and Manoeuvring Qualities of Surface Vessels
Hy-8 CHISLETT, M. S., and BJÖRHEDEN, O.
Influence of Ship Speed
on the Effectiveness of a
12,00
Lateral-Thrust Unit
Hy-9 BARDARSON, H. R., WAGNER SMITT, L., and
The Effect of Rudder Configuration on Turning Ability of Trawler Forms.
20,00
CHISLETT, M. S. Model and Full-Scale tests with special Reference to a Conversion to Purse-Seiners
Hy-lO WAGNER SMITT, L. The Reversed Spiral Test. 10,00
A Note on Bech's Spiral Test
and some Unexpected Results
HYDRO- OGAERODYNAMISK
LA BORATO R I U M
Lyngby - Denmark
THE REVERSED SPIRAL TEST A Note on Bech's Spiral Test and some Unexpected Results of its Application to Coasters
by
L. Wagner Smitt
Hydrodynamics Department
TABLE OF CONTENTS
Page
ABSTRACT i
PREFACE i
BECH'S SPIRAL TEST i
SPIRAL TESTS WITH TWO COASTERS 2
The Ships 2
Test Equipment 3
Test Conditions and Results 4
MODEL TESTS 5
DISCUSSION s
Full Scale Tests B
Model Tests 9
CONCLUSION il
RECOMMENDATIONS 11
REFERENCES 12
APPENDIX:
Alternative Procedure for Carrying Out Spiral Tests,
by Mogens Bech 13
LIST OF TABLES
Table Page
I Principal Dimensions of Ship A and B 3
II Model and Ship Particulars 5
III Non-Dimensional Coefficients used to calculate the Stability Criterion C and the Slope of the
III
-LIST OP FIGURES
Figure Page
i Block-Diagram illustrating Full-Scale
8 Examples of r- ¿ Curves for both an Unstable
and a Stable Ship 15
2
3
Test Set-up
Full-Scale Tests. r- Curves for Ships A
andB
Model Test. Static Rudder Angle Test.
Non-Dimensional Side Force, Y', and Turning
3
4
4
Moment, N', as Functions of Rudder Angle,
Model Test. Pure Yaw Test.
6
Non-Dimensional Side Force, Y', and Turning Moment, N', as Functions of Non-Dimensional
Angular Velocity, r' 6
5 Model Test. Static Drift Angle Test.
Non-Dimensional Side Force, Y', and Turning Moment, N', as Functions of Non-Dimensional
Side Velocity
y' =
-sinf3Ship A and Mariner Data from Ref. [2] 7
6 Principal Characters of the r- Curve.
The Corresponding Handling Qualities with
Respect to Course Keeping are suggested 8
7 Full-Scale Test with Ship A and Predicted
ABSTRACT
Bech's method for making full scale spiral tests is described, and some extraordinary results
from its application to two coasters are given. A few preliminary model test results for one of the
ships are presented. It is suggested that the present trial trip codes be revised with respect
to the spiral test.
PREFACE
The author apologizes for the preliminary character of the
present report, but at the same time hopes that the unusual results presented may justify the publication.
The model tests of which a few preliminary results are given, will be continued, and a more complete report has been planned.
BEd'S SPIRAL TEST
The usual method for making spiral tests consists of
measurement of angular velocity, r, as a function of rudder
angle, ¿S:
r = f (Ç)
The rudder angle is varied in steps, and for each angle the corresponding rate of turn is measured. Por marginally stable or unstable ships this takes quite a long time and requires large
water areas. A lot of time is spent waiting for the angular
velocity to become steady for each angle, and no points can be
measured inside the loop for an unstable ship.
A faster and probably more accurate method which, further, can provide any point on the r- curve, also inside the loop in the
case of an unstable ship, has been developed by M. Bech.
Bechs method was presented at the
NSTMC)
1966 in Malmö, Sweden and a translation of his contribution appears in the Appendix.Mogens Bech, Electronical Engineer, Chief Development Engineer at A.R.K.A.S. (Dansk Automatisk Ror-Kontrol AIS, Copenhagen).
-2
According to Bech's reversed spiral test method, the rudder angle is measured as a function of angular velocity:
= 11(r)
Thus the angular velocity, r, measured by means of a rate gyro, is used as independent variable. S is then the
mean rudder angle necessary in order to maintain a given angular velocity, r.
Each point can be measured relatively quickly, because the ship is brought to the chosen rate of turn by active steering, and then balanced there by use of few and small
rudder movements. Even in the case of unstable ships, the
r- curve usually only needs to be measured coming one way, or
the points can be measured in any order. Points around zero rate of turn can thus be measured while essentially maintaining the
same heading.
Spiral tests according to this method can be made by hand-steering by an experienced helmsman. Instead of aiming at a certain compass course, the helmsman tries to maintain a certain deflection on the scale indicator of a rate gyro, corresponding to a certain angular velocity, while the observer judges the mean rudder angle from the rudder indicator. Figure 8 in the
appendix gives examples of this method, applied to both an unstable and a stable ship.
SPIRAL TESTS WITH TWO COASTERS
The Ships
Two coasters, A and B, have been tested using Bech's
method.
Ship A was reported by the captain to steer badly with respect to course-keeping, and in order to assess and possibly improve the steering characteristics, full-scale as well as model tests were performed.
Ship B, which is smaller, but of similar lines, was reported to steer well, and full-scale tests were carried out in order to classify the difference between the two ships.
Table I
Principal Dimensions of Ships A and B
Ship A Ship B
Length betw. P.P. m 73.30 66.25
Breadth moulded m 12.90 11.00
Draft to DWL m 4.70 3.70
Displacement m3 about 3030 1830
Block Coefficient about 0.68 0.68
Test Equipment
Besides the normal rudder angle indicator fitted on most ships, the equipment necessary for making the reversed spiral test need only consist of a rate gyro. However, in the present case the signal from the rate gyro was mixed with a signal from a potentiometer and fed to the ship's autopilot, which then
controlled the rudder action.
The rudder angle was recorded visually from a specially fitted, very accurate rudder indicator. The signal from the
rate gyro was also recorded visually. The autopilot was
adjusted so that the required rate o± turn could be maintained by use of few and small rudder corrections. The mean rudder angle could he estimated relatively easily.
The set-up is illustrated by the block-diagram Fig. 1.
POT E N 110M E T E R it RATE GYRO RUDDER INDICATOR
-3
AUTO PILOT STEERING ENGIN E ISENSORI RUDDERFigure 1 - Block Diagram illustrating
Test Conditions and Results
The tests were in all cases carried out in a wind-force below 2 Beaufort, and in calm seas. The water depth varied
between 25 and 14 meters.
The tests were made at full power corresponding to a straight course speed of 13 knots. The draughts fore and aft are given in Fig. 2, which also shows the results of the tests.
It should he noted that the angular velocity, r, corresponds to the horizontal axis contrary to the usual presentation. This has been done as a consequence of the reversed method.
P 1.0 1.0 0.5 5 SB 5 DA (95m 9.. 0F ¿75m SB
Figure 2 - Full Scale Tests. r- ¿ Curves for Ships A and B.
SHIP A P o s 5 SB 4 L deg 8o SB L deg SHIP A DA 3.60 m DF 2.20 m 0.5 5 SHIP B °A 3.51m 0F 2.52m 0.5 ¿ deg SHIP B 3.L0 m DF 340m 05 0.5 to r deg/sec SB 1.0 r deg/sec SB 10 r deg/sec SB 1.0 r deg/s.c SB 0 o
5
MODEL TESTS
Model Tests with a model of Ship A have been carried out using the HyA-Planar Motion Mechanism to measure hydrodynamic
forces and moments. A complete description of the measuring technique is given in Ref.
[i]
X) Some preliminary results,which imply a similar phenomenon as found during the full scale tests, are presented below. The model was made of paraffin-wax and had the main dimensions shown in Table II below:
Table II. Model and Ship Particulars
The results of a static rudder-angle test and of a pure-yaw
test are given in Figs. 3 and 4 respectively. In order to show the difference between Ship ! and a "normal ship" the results
of two sets of static drift-angle tests for the model of Ship A and the corresponding results for a Mariner class vessel are
given in Pig. 5.
x)
Numbers in square brackets [ ] indicate references listed
on page 12
Model Scale 1:12.59 Model Ship A
L m 5.822 73.30 LWL m 5.995 75.48 B m 1.025 12.90 DA m 0.373 4.70 D in 0.373 4.70 L.C.E. (pos.for'd of stn.5) in -0.029 - 0.36 Displacement in3 1.522 3037 Block Coefficient 0.68 0.68 Speed in/sec 1.885 knots 13
Figure 3 - Model Test.
Static Rudder Angle Test.
Non-Dimensional Side Force, Y', and Turning Moment, N', as Functions of Rudder Angle,
L
Figure 4
Model Test.
Pure Yaw Test.
Non-Dimensional Side Force, Y', and Turning Moment, N', as Functions of Non-Dimensional Angular Velocity, r'.
-20° -10° 0° 10° 20° 0.04 0.08 0.12 0.1 6 Rudder Angles in deg. Non-Dimensional Angu'ar VeLocity , r
5 Q
>-4
3 2 O 2 3-'
-5 7 VI - SIfl(3Figure 5 - Model Test. Static Drift Angle Test.
Non-Dimensional Side Force, Y', and Turning Moment, N', as Functions of Non-Dimensional
Side Velocity, y' =_sinf3
Ship A and Mariner Data from Ref. [2]
The Mariner results are taken from Ref. [2] and have been faired
by a polynomial of the form y = a0 + a1x + a3x3. The results for Ship A have been faired by hand.
Non-dimensionalizing is by means of and
fL3U2
for side force, Y, and turning moment, N, respectively. Station
5 at half L has been used as reference point.
pp
When comparing the results for Mariner and for Ship A it thould be noted that the length/draft ratios are very different.
y o O o Ship A
-MARINER -Side Force Moment Side Force Moment Y N Y N V O.
A n ofl:95
7554
n -7.5 -9.Sdeg. y- ° D D -0.2 -0.1 O 01 0.2 1.0 r)o
X 0.8 z C 4) E o 0.6 I' C 0 u' C 0.4 C o z 0.2 o 0.2 0.4 0.6 0.8 1.0DISCUSSION
Pull Scale Tests
The unusual r- curves for ships A and B are characterized by the steep part around zero rate of turn and the adjacent flat
parts. These ships are thus very stable around zero rate of turn and approach marginal stability at larger rates of turn. This
phenomenon has previously been reported by Nomoto in Ref. [3] , but
for models only. Nomoto suggests that a qualitative discrepancy exists between models and ships, however, the results presented here indicate that carefully accomplished full-scale spiral tests, may, in some cases, reduce the discrepancy to a quantitative one.
8-.
The phenomenon may be more or less pronounced, the steep part being more or less steep and extending over a larger or smaller range of
rudder angles. In Fig. 6 the
principal characters o± the r-curve have been sketched and the corresponding handling qualities with respect to course keeping are
suggested, based on reports from
captains and crews.
Some influence on the handling qualities for the "super-stable" ships is probably related to the regions outside the steep part of
the r- curve, which may be of stable, marginally stable or
unstable character. Trim by the
stern will in most cases make a ship more stable, and it should be noted that Ship B, which for one of the full-scale tests was loaded to zero trim, normally trims 3 ft. by the stern even in fully loaded
condition. This may partly account for the better reputation of Ship B with respect to course keeping.
Figure 6 - Principal Characters
of the r- Curve.
The Corresponding Handling Qualities with Respect to Course Keeping are suggested.
Handling: Bad o Ordinary Unstable Mnally Stable ír Good Stable Good or Fair Super' Stable
Bad Infinitely Stabte
Very Bad J "Reversed Loop '
-9
Model Tests
The preliminary model test results for Ship A presented in Figs. 3, 4 and 5 have been used to calculate the stability criterion C:
c = y (N - u)-N (y -mU)
y r G y r
and the slope of the r-cÇ curve
L
C pp
NY
NY
U secv v
where the coefficients Y N etc. are the slopes
V V
Vt Vt etc..
As both the rudder angle test and especially the static
drift angle test gave non-linear results, two sets 0±' coefficients
have been used, one taken from the curves around zero, and the other from the adjacent parts of the curves. The results of these calculations are given in Table III below.
Table III Non-dimensional Coefficients From curve around zero Average from adjacent par-V of curve Coefficient from Fig. No. Y x 10 -2880 -2590 5 N
x105
-316
-715
5 x 1O -1097 -1097 4 } Corrected to (N -mx u) x 10 r CxiO
- 370 351 - 370 361 3 J ship massN_x105
-173
-175
3 C x 10 7.19 1.74 (sec) -12.9 -2.45 . r nIi U 13 knots = 6.70 rn/slo
-In Fig. 7 the full scale test for Ship A at DA = ni
and DF = 4.75 ni, which comes nearest to the model condition,
has been replotted, and the slopes calculated from the model
tests are indicated. Though some difference exists between the prediction and the full scale test the trends are the
same.
Predicted Slope From "Around Zero".
U ti ti uAdjacent Parts". SHIPA DA (95m : -e.. 0F 475m 1.0 --0.5._.... s 5 1.0 r deg/sec O -___ SB
Figure 7 - Full-Scale Test with Ship A and Predicted Slopes from Table III.
Each point shown in Figs. 3 and 5 represents the average of at least 25 seconds run, and although the average values plot nicely and the repeatability is very good (see Fig. 5), considerably more scatter than usual existed within the 25 seconds, indicating some unsteady flow phenomenon.
In the pure yw test the angular velocity varies
sinusoidally, and each point represents the average amplitude
of four complete periods from O to 2 hoe . However, the usual
assumption of quasi-steady conditions may not be correct in this case, where unsymmetrical separation or unsteady flow
apparently exists. Thus large scatter existed between the four individually integrated values which have been averaged to
obtain each point.
It is not unlikely that rotating arm tests would show similar effects for Y and N as functions of r, to those found here for Y and N as functions of
/3
, thus further improving the correlation between model and ship.CONCLUSION
Bech's reversed spiral test method has proved a useful
tool when detailed knowledge of the r- curve is required. A certain phenomenon associated with coasters has been revealed
by the use of the method. The nature of this phenomenon is such that these ships are very stable around zero rate of turn and approach marginal stability at larger rate o± turn.
Captive model tests have been carried out showing effects which imply a similar phenomenon in model scale.
RECONDATIONS
The time saved and the more detailed knowledge to be gained from the use of the reversed spiral test are believed to more than compensate for the larger initial cost of
equipment.
The method is especially recommended in case of unstable or marginally stable ships or ships which otherwise show bad course-keeping ability. It is suggested that present trial trip codes are extended to include the reversed spiral test method as an alternative to the usual method.
Captive model tests enable one parameter to be investigated at a time, and are thus well suited for a study of phenomena such as the one found here for coasters.
Information on any non-linearity of side force, Y, and moment,
N, as functions of angular velocity, r, can probably be obtained
12
-REFERENCE S
i Strøui-Tejsen, J. and Chislett, M.S.: "A Model
Testing Technique and Method of Analysis for the Prediction of Steering and
Manoeuvring Qualities of Surface Vessels". Hydro- og Aerodynamisk Laboratorium,
Report Hy-7, September 1966.
2 Chislett, M.S. and Strøm-Tejsen, J.: "Planar Motion
Mechanism Tests and Full-Scale Steering and Manoeuvring Predictions for a
Mariner Class Vessel".
Hydro- og Aerodynamisk Laboratorium,
Report Hy-6, April 1965.
3 Nomo-tu, K.: "Unusual Scale Effects on Manoeuvrabilities
of Ships with Blunt Bodies".
Written Contribution to the 11th International Towing Tank Conference, 1966.
13
-APPENDIX
Alternative Procedure for Carrying out Spiral Tests
by
Mogens Bech, ABKAS
The r- curve of a vessel, as measured by a spiral test, provides extremely useful information about the steering
qualities of the ship.
In practice, however, such tests are normally abandoned, which no doubt is caused by the rather long time required and
by the fact that the test necessarily must take place in a large water area.
In the following, a measuring method is described, which eliminates these two inconveniences, and which furthermore
m.kes it possible unambiguously to measure the r- curve through the unstable area for a dynamically unstable ship.
The linearized equation connecting rudder angle and rate
of turn for a ship is:
r1
T2[3
+-1- [+]
where \jr is the rate of turn and ¿ the rudder angle. The terms k
q1,
2 and T3 are constants.
If is constant, the equation will be reduced to:
f C
c13ö
o
=Lij
(2)As is known, the ship's steering characteristics are non-linear outside a limited area. As, however, the rudder effect generally is a linear function of the rudder angle, the non-linearity is due to the forces acting on the ship's hull as a consequence of the ship's turning.
14
-Consequently, equation (2) must be rewritten as follows:
¶3
=H(4i)
If the ship is being steered to a certain rate of turn,
,
measured on a rate gyro, then will only indicate the small steering movements which are necessary in order to maintain this
condition. Then
4
(T3
(t)+(t)) dt
for T oo (3)o
where is the mean value of the observed rudder deflection.
From this is obtained:
S0
=H(s)
(4)Thus H('4i) indicates the rudder angle, , as function of
rate of turn, tji , i.e. the rudder angle necessary in order to
balance the forces acting on the ship's hull as a consequence of
the ship's turning.
This definition of the r- ¿ curve makes ¿ a single valued function of r also in case of unstable ships. It further means
that a spiral test will need only one run instead of two as
previously, and at the same time it ensures that the individual points are obtained considerably faster than by the previous
method. This difference is due to the fact that the helmsman brings the ship into the desired rate of turn by active steering instead of passively waiting for the ship to stabilize its rate
of turn at a fixed rudder angle, which in case of marginal stability theoretically will take an infinite time. Thereafter it is only a question of maintaining an already obtained balance and of reading the rudder angle.
In Fig. 8 are given the results of some practical
measurements, which have all, separately, been carried out within a period of about 30 minutes.
It is my hope that this measuring method will contribute to the more general application of the spiral test on trial trips.
P P 20 i 1J 05 P
-
15 -SHIP I loaded r deg /5cc 00 iO 15 20 r deg /sec s 2,0Figure 8 - Examples of r- Curves for both an Unstable and a Stable Ship.
SB SB r deg /scc 10 SB SHIP I ballast 0.5 10
