December 1983 Ship Research Institute
Tokyo, Japan
0,1 NOV, 1984
Lab. y. Sceepsboujpg7
Technische Hogeschool
Deli t
No. 73
PAPERS
OFSHIP RESEARCH INSTITUTE
Measurement of Cavity Thickness on a Full Scale Ship Using Lasers and a TV Camera
By
MEASUREMENT OF CAVITY THICKNESS QN A FULL SCALE SHIP USING LASERS AND A. TV CAMERA*
By
Yoshiaki KODAMÄ**, Yukio TAKEI**
Akira KAKUGAWA**
ABSTRACT
A new technique for meaifring cavity thickness on full scale ships has
been developed. This techúique, which uses laser light and a TV camera, is simple iñ prijiciple and has the advantage that it does not affect the
cavi-tation on propeller blades.
Full scale test was made twice.. The first test was made using CP (Con-ventional Propeller). The second test was made on the same ship using 11SF (Highly Skewed Pröpellet).
In the test with CF, the sea was rough and many of the instruments
broke down. Measuremens were restricted to two points on one blade. The measured thickness of the cavity increases with the increase of propeller re
volution The agreement with model expenments is good
In the test with HSP, the sea was calm and measurements were made
smoothly. Càvity thickness was measúred at blade angles 0=30, 40, 5ødeg,
at radiäl locations r/R=0.85, 0.90, 0.95, and at chord positións X/c=0.25, 0.50, 0.75, totalling 3x3x3=27 positions. The measured thickness distribu-tion agrees reasonably well with the model experiment data. The maximum thickness is about 80mm.
Through the above two tests, the validity of this new technique has been sucessfuily demonstrated.
1. INTRODUCTION
Recently, stern vibration problems of ships have become more important because of the new trend in ship design such as increase in engine power, lightening of hull weight, adoption of large diameter
propellers as eñergy sa'ing devices, and shallow-draft wide-body ships which tend to enhance the non-uniformity of wake distributions.
Stêrn vibration is caused predominantly by propeller excitation
forces Further, propeller excitation forces are caused mainly by pro-peller cavitation which is generated as a propro-peller rotates in a
non-uniform wake field' Propeller cavitation is unsteady cavitation, which
changes its extent and thickness with time Its volumetric change propagates pressure fluctuations and acts on the hull as surface forces, thus being the main cause of propeller excitation forces.
* Received on August 31, 1983 Ship Propulsion Division
Though unsteady cavitation has such an importance. on stern vi-bration problems, its theoretical study is not well developed in spite of several recent studies2'3>'4, due to the great complexity of the
phe-nomenon. In order to promote research in this area, it is essential to accumulate experimental data of high accuracy and reliability.
There are many experimental data on cavity extent, which are readily obtained through visual observations However, the data on cavity thickness which are needed for measuring cavity volume, are not many. In model tests, cavity thickness is usually measured by setting up pins with scales on a blade surf ace5. Though this method is simple, it has the disadvantage that cavitation ocóurs on the pins themselves and interferes with the cavity on the blade surface, causing
its deformation. Recently, a new technique has been developed at the Ship Research Institute of Japan for measurIng cavity thickness using
lasers6>. This technique utilizes the fact that the laser spot which is
caused by the emitted laser beam displaces in proportion to the thick-ness of the cavity There is no interference with cavity, and high
accuracy measurement is possible.
On the other hand, cavity thickness measurements with full scale ships are more scarce because of the difficulties unique to full scale tests, and only the measurement using 3-D photos has been reported
so far8>. With this method, a real-time measurement is not possible,
and the range of blade angles where the measurement is made is lithited.
- This paper introduces a new technique for measuring cavity
thick-ness on a full scale ship using lasers and a TV camera.. Full scale test
was made twice using "Seiun-Maru ", a training ship which belongs to
the institute of Sea Training of the Ministry of Transport of Japan.
The first test was made in May 1982 using CP (Conventional Propeller),
and the second test was made in December 1982 using HSP (Highly
Skewed Propeller).
2. MEASUREMENT PRINCIPLE
Fig. 2-1 shows schematically the measurement principle. Two small
boxes called émitters are attached on the starboard side of the hull, a few meters upstream of a propeller. A laser beam is emitted
to-ward the propeller, and laser spots are formed on the blade sutfacé. Underwater TV cameras, which are also attached on the hull side, are used for monitoring the spots on the TV screen.
In a noncavitating condition, in which there is no cavitation, the direction of the two laser beams is adjusted so that the two spots merge at the location on the blade where cavity thickness
is to be
Fig. 2-i Principle of Caviti Thicknes. Measurement
As cavitation occurs, the spot separates into two, whose distance is in proportion to the thickness of the cavity The distance is
meas-ured on the monitor TV screen and converted into cavity thickness by multiplying a suitable calibration constant obtained from geometrical
consideration.
In model experiments6, only one laser beam is. used and the dis placement of the spot due to cavitation is measured by viewing from the direction normal to the propeller axis In full scale experiments, however, a TV camera is placed at upstream of the propeller because it is used for cavitation pattern observ5tion as well. When viewed
from that angle, the displacement looks much smaller and the loss of
accuracy results. Therefore, in the present full scale experiments the number of laser béams are doubled, and the distance between the two
spots are measured The fact that the two spots appear on the TV screen at the same time makes the measurement more direct and easier, thus making this technique more practical and more suitable
for full scalè ship experiments.
3. SYSTEM COMPONENTS
The measurement system is shown in Fig. 3-1. Two laser tubes are placed in the cabin, and laser light is transmitted to the emitters
through optical fibers The video system has been based on the exist-ing one which is described in ref. 7).
3-1 Lasers and Optical fibeÑ
The lasers are the two sets of Argon ion laser with maximum
out-put of 4 watts Only the green light component with wavelength A 5145 A was used The maximum output of this component is 1 9 watts
Sea water has high transmission efficiency with green light (cf Fig
3.2).
2 .5 .2 .053 EMITTER 2 ROTATION PULSE DETECTOR AOM MODULATORS ESET COUNTER Ocean water .4 .5 .6 .7 .8
Fig. 3-2 Spectral Loss Characteristics of Sea Water (from ref. 9)) ARGON LASER I PTICAL FIBEI ARGON LASER 2 SIGNAL cONOmONER VTR, MONITOR TV
Fig. 3-1 Structure of Measurement System
used in order to allow the light to pass only during the moments when propeller blades are at a designated angle. Here, an AOM modulator,
which is a Bragg cell, was used as a chopper. It deflects an imping-ing light when a certain voltage is imposed, and works as a chopper by picking up the deflected light (cf. Fig. 4-2). The imposed voltage,
which is a pulse of rectangular shape, comes from a rotation pulse
detector through a signal conditioner.
The laser light coming out of the, modulator is focused into an optical fiber by a convex lens (f=30 mm). The optical fiber is a multi-mode fiber of SI (Step Index) type and is 50 m long. Though two fibers with different core diameters (600 pm and 200 um) were prepared,
only the former was used in the full scale tests }ecause the latter was found to réquire much more time for alignment.
3-2 Emitters
mitters emit laser light Onto a propeller blade surf ce where cavity
dB/m
EMITTER I BEAM AMOLE CONTROUSj
BEAM A.E INDICATOR
-COLQR
TV CAMERA
TvCAMcRACOR1mJ.-I VIDEO MEMORY
cJ
VIDEO CHARACTERSTR
ri
0 TV CAMERA8/W STROBOSTRÓBO CORTROLLER
POWER
SOURCE VIDEO TIMER
coastal water
.150 MIRROR
DRIVE
MOTOR
(PAN)
Fig. 3-3 Emitters (unit: mm)
The laser light which cornés out of the telescopic lens is reflected by two plain mirrors before going out of the emitter Each mirror is
connected to a DC motor and a rotary encoder The rotational axes of the two mirrors are normal to each other so that the laser beam is
controlled horizontally (pan) and vertically (tilt) Pan and tilt angles
are controUed with the accuracy of 1 min (= 1/60 deg)
The chamber where the two mirrors are housed is filled with dis-tilled water to cancel out the distortion due to the difference in re-fraction index between air and water.
5
thickness is to be measured (Photo 3-1). Fig. 3-3 shows its structue Laser light is transmitted to the emitters through optical fibers. The.
laser light which comes out of the fiber does not have coherency any more and spreads with a semi vertex angle of 24 deg This light is
collected by a convex lens having, a long focal length and focused into
a tiny spot on a propeller blade. Here a telescopic lens (f=75 mm) for TV cametas was ùsed.
n
3-3 Rotation Pulse Detector and Strobe
Th rotation pulse deteetör cönsits Of 180 piñs, which are equally
placed along the circumference of a propeller shaft, and a pulse
detec-tor which is made up of a light source and a receiver (seè Photo 3-2).
The change of the blade angle is detected at every 2 deg, and the pulse signal i generated The pulse signal is supplied to a strobe and an
AOM modulator through a pre-set counter and a strobe flash côntrôller.
Fig. 3-4 Color TV Camera Photo 3-2 Rotation Pulse Detector
3-4 Color TV Camera
Fig. 3-4 and Photo 3-3 show a color TV camera. it is used to do cavitation obseavations and to measure cavity thickness on a monitor
Photo 3-3 Color TV Camera
TV screen. The zoom lens (f=16-.l6Omm) of the camera magnifies the images and increases the accuracy of the measurement
The picture caught by the camera is reverse because it is reflected by a plain mirror placed at the bottom of the vessel. It is electrically brought back to normal In the internal circuit. Pan and tilt are made
by rotating the mirror with two DC motors. The chamber which houses
the mirror is filled with distilled water in order to cancel the distortion of the pictures.
3-5 B/W (Black and White) TV Camera
A B/W TV camera was prepared as a spare for the color TV
camera.. It has a zoom lens, but no pan or tilt is possible. Though
it is inferior to the color camera with respect to the amount of infor-mation or the width of visual angle it is superior with respect to the resolution and the minimum i1lumination As will be shown later, cavity thickness measurement was made mostly by using the B/W
camera.
3-6 Monitor TV et al.
The picture obtained by a TV camera is intermittent because it comes only when a propeller blade is at a designated angle In order to make the observation easier, a video memory was used to store the picture and reproduce it continuously on the TV screen.
On the monitor TV screen, a video scaler dtaws scales which are used to measure the cavity thickness. A video ¿haracter generator
display necessary informations and time. Pictures are recorded by VTR (Vedeo Tape Recorder).
All made by Nippon Sheet Glass Co. Ltd., except SM-200 made by Dainichi
Nippon Cable Ltd.. SI-200H has a collimater lens. Cataloged values 4. PRELIMINARY STUDIES
Before constructing this totally new measuring system, many
technical problems had to be checked and solved. In this chapter the results of the technical studies and experiments made in ordèr to de-termine the specification of the system are presented.
4-1 Optical Fiber Test
As high power laser light is usèd in the system, a laser light
trans-mission test was made using five different large diameter optical fibers shown in Table 4-l. As will be shown later (see 4-3 and 4-4), the corè diameter of the fiber should be as small as possible to increase both
Table 4-1 Technical Data of Opticai Fibers
CAP JACKET
CLAD CORE
OPTICAL FIBER.
SI-200H QSF-200A QSF-400A QSF-600A SM-200
Core dia. rn 200 200 400 600 200 Clad dia. m 250 380 550 750 250 Jäcket dia. m 900 600 850 1060 1000 Power Loss (dB/krn) 2=8200 A 15 5 - 5 5 9 2=5i45A >30
-
16 16=
N.A. Design value 0.55 0.40 0.40 0.40 0.2 Steady value 0.50 0.27 0.27 0.27 Fracture Bending Radius (mni)-
3 i2 - Ï5 -MaterialCorè Glass Silica Siiica Silica Glass
Clad Glass Silicone Silicone Silicone Glass
Jacket Nylon Tefzel Tefzel Tefzel Nylon
Fig. 4-1 Optical Fiber Cap Photo 4-1 Optical Fiber Test
® Optical Fiber
Hole
Fig. 4-2 Transmission Path of Laser Light
Telescopic lens
9
illumination and measurement äccuracy. Photo 4-1 shows the test
ar-rangement.
Laser light of the wavelength 2=5145 A was used with maximum outpút power of L5 W. The laser light was focused with a single-layer
convex lens (f=30 mm) into the fiber end. The ends of the QSF-2Ó0A, QSF-400A, and QSF-600A fibers were obtained simply by snapping them
after scratching with a knife.
The QSF-400A and QSF-600A fibers kept their good conditions up
to the maximum power QSF-200A and SI-200H fibers failed to
trans-mit light because of the burning at the impinging ends. When the
optical alignment is incomplete, laser light impinges on the clad, where
it changes into heat and causes burning As a counter-measure, a cap shown Fig. 4-1 was attached on the SM-200 fiber. It has a hole of the same diameter as the core and prevents light from impinging on clad or jacket areas. With this device the SM-200 fiber can transmit light up to the maximum power without burning.
From the above test results, the SM-200 fiber with a cap and the
QSF-600A fiber have been selected. The QSF-600A fiber allows easy
optical alignment because of its large core diameter.
When a fiber is bent extremely, the output power drops to 1/2-1/3 but resumes its original value when it is made straight again. However, when it is bröken, the power drops to less than 1/1000 and
never recovers.
4-2 Laser Light Transmission Efficiency of Optical Fibers
The laser light at the exit of the tube is so strong that it can
penetrate a wooden board. However, when it finally reaches a propei
Table 4-2 Laser Light Transmission Efficiency of Optical Fibers
No mark - Measured
* Estimated based on measurement
** Estimated
Fròm catalog
of the accumulative loss in the intermediate steps. Fig. 4-2 shows the transmission path of laser light, and Table 4-2 shows the loss at
each step.
According to the table, the 1.9 W at the exist of the tube is re-duced to 67 mW at the final stage Efforts for improvement at each step are needed, especially at the hole (step ®) where the loss is the
highest.
4-3 Laser Spot Diameter
The laser light coming out of a fiber spreads with an angle which correspods to the NA (Numerical Aperture) of the fiber The emitted
light from a QSF-600A fiber whose NA is 0 40 spreads with a
semi-vertex angle of 24 de (= sin (NA)). The only wäy to collect the light
Lens y V ds: Spot dio. F
Fig 4-3 Laser Spot Size
dc Core diO.
Optical fIber
No. Name Loss
© Laser
-
1.9AOM Modülätör 0.32 1.29
© Lens O.05** 1.23
c Optical Fiber E1id (Imp.) - 0.135* l.Ò6
® Opticai Fiber (QS-6O0Á, 1= 50m) O.Ï59*** 0.893
® Optical Fibr End (Ernitt.) O.l3* O.773
Telescopiá Lens (Imp. End)
0.374* 0.483
®
-Telescopic Lens
® Holé 0.674 0.18
® Emitter Mirror Chamber 0.36 0.101
LOADING POINT
EASIJRING POINT
Fig. 4-4 Static Load Test of CP (unit: mm)
11 and föcus it into as small a spot as possible on a propeller blade is to focus it into a real image of the fiber core As shown in Fig 4-3,
yf
(4-1cL
f
As y is much greater than f in general, it is necessary to make f
large in order to make the spot diameter d, small. If f =75 mm, d0.6mm and y=3m, then d,23.4mm.
4-4 Static Load Test f CP and HSP
In the present method, cavity thickness 'is measuréd as the distance
between the blade surface of a propeller rotating slowly and the cavity surface on the propeller 'rotating fast. Therefòre, the displacement of
the blade due to loading is included as a part of the measured "cavity
thickness" This error is always positive
A static load test was made. using a full scale GP. Static loads
were imposed on a blade, and the displacement normal to the blade
was measured. The characteristics of GP ate shown in Table 6-1. (1) The Measuring Method
The propeller was fixed on a base as shown in Fig 4-4 Loads were imposed using an oil jack (power=10 tons, stroke= 100 mm) Loads
were. 0, 2, 4, and 6 tons. The measurement was made along the gen-erator line at 0.7R, 0.8R, 0.9R, and 0.95R radiál positiOns.
(2') Measured Results
corre-10.0 ao
-
6.0 E E C 4.0 o o. o ao o Fig. 4-5 X r/R=0.95 nR = 0.90 D n/RÔ.80 o n/R=0.70 2.0 4.0 6.0 6.0 Load (ton)Bending of Propeller Blade by 4-5 Lag in Blade Angles due to
Point Load Torsion of Propeller Shaft
As shown in Fig. 3-1, blade angles are measured by a rotation pulse detector attached on a propel-ler shaft. However, the torsion of the part of the propelpropel-ler shaft be tween the rotation pulse detector and the propeller causes lag in blade
angles. In full scale ship tests, as the next chapter shows, there is
difference in torque between a noncavitation condition and a cavitation
condition. Therefore, when the same laser angles are set on the emit-ters, the laser spots on a blade in the cavitation condition would be located closer to the leading edge than in the noncavitation condition. In addition to the error in iocating the spots mentioned above, the lag in blade angles causes positive error in measured cavity thickness. Following are the estimated values based on the data of "Seiu-Maru" with HSP (cf. chapter 6). Noncavitation condition is at 70 rpm. At
the propeller revolution of 163 rpm,
Lag in blade angle 0 66 deg
Spot movement toward leading
edge at 0.9R 19mm
Error in measured cavity thickness 5 mm
Therefore, this error in cavity thickness measurement can be neglected
with the same reason as that in the previous section.
The effect of the compression of the propeller shaft due to thrust
was also estimated. The compression in the entire length of the shaft was estimated to be only 0.6mm at 163 rpm
sponds to the thrust on one blade at MCR condition. The displace-ment at the tip, which is 6.5 mm, will increase to 10 mm if the load
is assumed to increase by 50%
due to the non-uniformity of the wake. This value is 10% of the
predicted maximum cavity thick-ness (= 100 mm) and, therefore,
can be neglected as a first
ap-proximation.
A similar test was made with HSP. The blade displacement of HSP was found to be smaller than
t
-Photo 4-2 Vibration Test of Emitters and TV Cameras
A sinusoidal vibration of 200 gal (peak to peak value) and 25 Hz
was applied for fiye minutes, during which the monitor TV screen and
pan. tilt controls of the emitters were checked. Nó malfunction was detected.
5. MÏLÄSUREMENT PROCEDURES ON A FULL SCALE SHIP The aótual measurement procedures are described belöw.
The locations of emitters and TV cameras attached on the hull side are measured while the ship is in the dock.
At sea, first the propeller is rotated slowly to realize the non
cavitation conditiOn. Pan and tilt angles of the emitters are con-trolled so that the two laser spots merge on the blade (cf. Appendix
3). Those pan and tilt angles are recorded. This procedure is
re-peated at each location where cavity thickness is to be measured
(ni) Next, the propeller is rotated fast to realize the cavitation con-dition. Pan and tilt angles are set at the values measured in the non-cavitation condition. When cavitation occurs, laser light is scat-tered at the cavIty surface and forms two spots (Photo 6-4) S,h,
which is the distance between the two spots, is measured using a video scaler on the monitor screen. The magnification rate of the screen is determined from the markings on the blade.
(iv) The spot distance S is then converted to cavity thickness t,, from
geometrical considerations such as the locations of the emitters and
13
4-6 Vibration Test of Emitters and TV Cameras
Emitters and TV Cameras, which are placed immediately upstream
of a propeller, will suffer from severe vibrations. Therefore, a
vibra-tion test was made using a large vibravibra-tion bed at the Nuclear Ship
Division of the Ship Research Institute The emitters and TV cameras
the TV camera, and the propeller geometry. That is,
(5-1)
where b is a calibration coefficient. It is calculated as shown in
Ap-pendix 2.
6. FULL SCALE SHIP TISTS
6-1 Tested Ship and Propellers
Full scale ship test was made tWice. The first test was made
us-ing CP. The second test was made using HSP with 45 deg skew, which
was newly designed by the SR 183 Research Panel aiming at reducing stern vibration and noise Principal characteristics of the two propel-lers are shown in Table 6--1. Offset tables are shown in Tables 6-2
and 6-3. Blade configurations are shown in Figs.. 6-1 and 6-2. Pitch distributions of HSP, which is tip-unloaded, is shown in Table 6-4.
The tested ship is "Seiun-Maru" in both tests It was completed in 1968 and belongs to the Institute of Sea Training'° Principal char-acteristics of the ship is shown in Table 6-5. The general arrangement
is shown in Fig. 6-3. The engine exercise room on the upper deck
was used for rneasúrement.
The emitters et aL were attached on the starboard side of the hull, 3-4m upstream of the propeller (Photo 6-1). Their measured
locations are shown in Table 6-6. They were attached at the same
Tab1 6-1 Principál Characteristics of CP and HSP
Type CP HSP
Diameter (mm) 3600
Pitch Ratio (Mean) 0.95Ó 0.920
Expanded Area Ratio 0.650 0.700
Boss RatiO 0.1972
Number of Blades
Blade Thickness RatiO 0.0442 0.0496'
Méan Blade Width Ratio 0.2465 0.2739
Skew Angie (deg) 10.5 - 45.0
Rake Angle (deg) 6.0 3.03
Blade Section ' MAU Modified SRI-B
Table 6-2 CP Offset Table r/! 1 2 3 4 5 6 7 8 9 10 11 12 .13 14 15 16 17 &__Q.. _1. ...2O....L_2..ì. ..JQ.,i. 1LD. ?1LQ U.a LQ_ ìkQ_. ?L_1Q _u,o __ì.g1.g. 0,20 vO 44.6 66,1 76.1 84,3 96,9 108.6 111.5 127,1 121,4 124,5 114,6 99,6 ßo,5 5),6 32,2 19.1 5,1 YlI_ .. ..3._19..1__12.i....?. ...Q-_Q.Q _..0,Q ...O,Q_9,Q.. _Q.0 QJ OQ 9,0 0,Q 0I11 3)Q 82.i
14.0 1.0.
LQ ?L0 QQ_ illtQ_ _11.Q _6'h.Q .I.2.Q .JO.IQ 0.30 yO 39.0 57.8 66.6 13.8 84.8 99.1 102,8 111.3 111.5 109,0 100,3 87,1 lo,4 50,5 28,2 16,1 5.0 27,0 21,2 16.1 11,1 6.0 2,6 0,0 0,Q 0.0 __j,0 Q___Q.
0.0 0.0 0.0 0,0 __o..o 3L.O ...33..5. _92..Ì 1i9,.Q 18.0 Z1LQ. 29.0 ¿10..Q... a..a_i..a. _ l.0._i9..Q _8.0. _818.0 .28,0. 0.40 YO 33.5 49.6 57,1 63,2 72,7 81.5 88.1 95,4 95.6 93,4 86.0 14,1 60,4 433 242 14,3 4,3 th_ .23..2 J.fl1__18..J.. _.6..3.2
..2.2 _0.Q 0.0 0_.._0..0_ .1L0 __û..O ....0.O _Q.0 ._.._0..0 .._..0.0 x 9.0 2Q 40.6 6L0 12,0 lfl.O QLL95.OQ_QiQ_21&. 1o.o J.Q,2._.29?.o
.J9.Q9P_ 0,50 YO 25,7 38.4 44.6 49,9 58,7 66.7 72,9 19,4 19.6 17.8 11.6 62,3 50,4 36,0 20,3 12.2 4,0 19.Q.. ,j 3.2
t4
00 0,9 0,0 0,0 0,0 Ì),0 O O 0 0,0 0.0 _Q..0_LL
.J.. ELL UL. 12.LQ fl!...Q. LQ 7,Q ".1.9. .Q _80.9. _QQ 1001.9 1Q1.Q. 0,60 YO 18.5 28,6 34,0 38,6 46,0 53,1 58,1 63,9 64,0 62.6 57,7 50,2 40,8 29,5 16,9 10,4 4.0_1t2__L..i _.1.9. _2..9 _O..L _a.o _n,.o.
0,, _Q...0... __.0...O _(hO __00 .J1L ..__Q.L0.. ..î1.Q. L0!9.9 __QQ__0Q_. 0b9_ X Q.L9 _.L .13.2 J2LL 229 ?,Q. 9L9 12L9_ íL0_ .Jfl.,Q 0.70 YO 11,5 19.6 24.5 28,5 35,1 41,1 45,7 50,7 50.8 497 45,8 40,0 32.7 23,8 141 9,2 4,4 vu __Lb.. iii ..J_LL._4 ._.Q.Q ..Q1 Q..Q _09 Q.Q .. 9.9... &__.flL 2L.Q. _.6...0_8i..L , H0.I.O UOLQ 2.8Q,L tîQ1Q H.,.fl. 19LQ. .J.H..O _JL.9. .iQL..a. .ÌJ9. _,Q_ 0,80 YO 4,8 11.7 15,7 18,9 24,5 29,8 33,8 37.8 31,9 37,1 34,3 30,1. 24,7 18,4 11,7 8,3 5,0 Y.1j_ _2..i .2.O.._..i.,3. _..Q.,.L ._Jh _Q,2 .0.0.... 0,0 .. 0.0 .0.0 .. 0.0 _.0..0 .._0,9 __0.0. .__0.0 X 0..0. 24,3 j8.5 _iL,LI2L...82L9. 2.,Q ILO LQ.. i30 7..Q _Th.9 _l.,Q. 0.90 YO 2,5 1,3 9.8 11,9 15,6 19,4 22,1 24,8 24,9 24,6 23.3 21.L 18.0 14.3 10.1 7,8 5.5 ..o..0 u.n a..n 0.0 0.0 0.0. .ft.0. .ILO _0.. _0...0
O...0 ..0..0. ....0...0. ..0..O __o,o...
X OLQ_ ....111L ..1lI... LLLQ 18.,.P. L9 QQ,LQ. .fl.iQ _LLQ. j12,.9. i1 .9 Ó.95 YO 1.9 5.6 7.5 9.0 11,1 14.4 16,5 18,4 18.5 18,3 17,5 16,1 14,1 11,6 8.8 7,2 5,6 _0..O _0...fl ...o,.L 0.0 ...O,9... 0,o O.,p ..O..O _0.0_ ._0.0.. .._0.0 _.0.O. ._0.Q 00 .._0,0 . 0,0
Table 6-3 HSP Offset Table nR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
it9
..k1LI.J3.1
i o .1 :A. 6. L.Jt'-?''j-f?
n.a ?' a a o..aa
t2 . 9 ____i .'.'i-,:l
.1 6. : 1 '1___rt1_l
¿L' t A+
q naû..9..ì_2.&4L_6L..4
!Q39...i
:i tL?':
Q, Y.U
:-:4'
23.1:
,.6:.J'9
60ü Xn QL) i
? tial ìJ.6Q.9_21&LjLB.A29.. '36_l9 6._929
IL 0.ß_.I26.. A.!. Y' . 5.4 2.4 .1 34. 42.0 4 .b 5.0 b4. 143 80.1 81.9 19.'. 11.i 51.4 i9.1 fl.9.:
' 6!t:i. Y°QLl9f_l6l.
i_t.H_l_lt:_l6_3;1
2i&ia3?_LQ ° 2 va 1OE1 .9ia .Traffin. Ed.. 1L 0.3R
-i.
4V. - -. 41!! ImiIi
dUuIEJWIIJJ .14III_vrmr.
i ..i ..3CG d.__IIWI
Ft Datonc LinaFig. 6-1 CP Blade Configuration
92.2 Generator Line
Fig. 6-2 HSP Blade Configuration
locations in both tests.
The tests were made on the east side öff
Ohshima, Hachijojima, and Miyakejima islands;
The clarity of the
water was good.
6-2 First Test (CP)
(1)
Test ConditionsThe sea was rough because of the passing of the cold front. Maìy 17
2.0
w
nl
Dato,,, Line i83 ed Cantone
i,
L1;.i_'
1E Macin, n, Thicknena Line
1L
_uhi____________________________ax-i. L.14tL1F
Table 6-4 HSP Pitch Ratio Dstributi9n
Table 6-5 Principal Characteristics of
Seiun-Märu
of the instruments attached on the hull side broké downs It was found
later that the most of the damage was due to insufficient protection of the cables attached along the hull side.
Cavitation Observations
Fig 6-4 shows cavitation patterns of CP The explanation for the
patterns is given in Fig 6-5
The observations were made in theblade angle range of 35Odeg-9ødeg. The color TV camera made wide range and detailed observations possible through pan, tilt, and zoom Photos 6-2 (a), (b), and (c) show the cavitation patterns observed on
the TV screen.
The pitching of the ship was considerable during the observation,
and the cavity extent varied accordingly. The figures show their
aver-age extent The observation was made on the A blade, but the dif-ference among the blades AE was nominal
Sheet cavitation which is not likely to cause erosion is dominant. The extent of the cavity reaches maximum at the blade angle of 30
deg. Only the TVC (Tip Vortex Cavitation) is seen at around 90 deg. Cavity Thickness Measurement
The measurements are not many because of the breakdown of the
instruments One of the laser tubes did not work well, so the laser light was supplied by a single tube to the emitters in .a time-sharing
manner.. The measurement was restricted to two points on the blade,
nR Pitch Ratio nR Pitch Qatio
0.200 0.945 0.700 0.944 0.300 0.987 0.800 0.871 Ò.400 1.010 0.900 0.78Ò 0.500 1.015 0.950 0.727 0.600 0.993 1.000 0.668 Length b.p 105.00 m Breadth 16.00 m Depth 800m DÑft 5.80 m C0 0.576 Displacement 5,781.3 ton Maine Engine Diesel 5,400 PSx 176 RPM
u
1'
's . r' i-_ Iiu1
-- i :
.i: --:.r CàSCD - flU e Fig. 6-3General Arrangement of "Seiun.Maru
kL.
'-
fti
E[L
I ' IOU
* Estimated value
Photo 6-1 (a), (b) Emitters and TV Cameras Attached
on Hull Side (HSP)
Tablé 6-6 Location of Emitters and TV Cameras
;i ør
44
FULL SCLE TEST 149 RPM, 4.6 KTS
(a)
(c)
Fig. 6-4 Cavitation Patterns (CP) 149rpm, 14.6kts 163rpm, 15.5kts 170rpm, 16.3kts
From A.P. From B.L. From Cnter Plane
Emitter 1 518g (On Fiame 8) 4500 1452
Emitter 2 « ( # ) 2800 713
Color 1'V Camera 5793 (On Frame 9) 4000 1260
B/W TV Camera 6405 (On Frame 10) 3800 1300*
-1
(a)
Fig. 6-5 Cavitation Pattern Explanation
(c) Photo 6-2 Cavitation on CP (163 rpm) (a) 0=200, (b) 0=400, (c) 0=60° (a) r (b) (b) u p (c) Photo 6-3 Cavitation on HSP (163rpm) (a) 0=20°, (b) 0=50°, (c) 0=80° 21
i.e., (0.85R, 0.10e) and (0.85R, 0.25e), both at the blade angle of 30deg.
The test was started at the propeller revolution of 90rpm, where there
was no cavity. Then the revolution was increased step by step to 172 rpm and was decreased to 90 rpm again to check the reproducibility of
SHEET CAVITATION
/ / / / -IO Emitter I ¡ SPOT OF EMITTER IO X SPOT OF EMITTER 2
-
CALCULATED BEAM PATHio xi
-S
Emittàr 2
mm 'I
Fig. 6-6 Movement of Laser Spots on CF
the merging of the two spots. Fig. 6-6 shows the movement of the
laser spots x and y coordinates show actual length The origin
corre-sponds tó the point where the two spots merge at 90rpm. The figure
also shows the calculated laser beam path along which the spots should
move. However, there is considerable discrepancy between the observed
movement of the spots and the calculated path. Its reason is ñot yet
clear The flexibility of the hull, which is not taken into account in
the present analysis might be responsible for it
The figure also shows the measured spot size (29 mm dia.), which is somewhat larger than the estimated value of 23.4 mm (cf. 4-3). By
comparing the spot size with the spot distances, one can see that the spot size should be further decreased in order to make the measure-ment more accurate and easier.
Fig 6-7 shows the measured cavity thickness which is obtained from the data in Fig. 6-6. The thickness increases as the propeller revolution increases and shows reasonable agreement with the model
test results'.
The reproducibility of the merging at .90 rpm is good,SHIP MODEL POSITION
O (Q85R,O.IOC)
8 300 A £ (O.85R O.25C)
mm
.
3
4#Øf
FULL SCALE TEST (49RPM, I5JKTS
(a)
FULL. SCALE TEST 171RPM, 16.6 (<IS
(c)
FULL SCALE TEST (63RPM, I63KTS
(b)
Fig. 6-8 Cavitation Patterns (HSP) 149rpm, 15.lkts 163rpm, 16.3kts
171 rpm, 16.6 kts
23
resulting in the error of 10mm, which agrees with the estimated ac-curacy of the present measurement system The accuracy estimation
has been based on the following factors: the distance between the emitter or the TV camera and the blade, the accuracy of the pan and tilt angle controls, magnification rate and the resolution of the TV
camera.
6-3 Second Test Test Conditions
Though it Was winter, the sea was c.lm, and the tests were made
smoothly. Steel pipes (SGP) were used to protect the cables Which were attached along the hull side.
Cavitation Observations
Fig 6-8 shows the cavitation patterns of HSP The blade angle range where the observation was made js 350 deg-80 deg. The
obser-vation was made mainly on the A blade.
TVC is thick though sheet cavitation is dominant. The extent of the cavity is maximum at 40 deg TVC is thick at around 80 deg The comparison with the CP result shows that the extent of the cavity is greater on CP in the blade angle range of 350-3Odeg, but it is
1 mm. lOO LE T-mm nR = 0.95 T 50 0LE nR =0.90 (a) MC u.,' \ N TE 500 mm MC TE 500 1000 mm 9 = 30 mm mo T 50 mm 50
t
mm 100 nR 0.95t'
t'
r' LE MC TE 500 mm nR = 0:90 -r.
t'
t t Il, t LE MC ' TE nR = 085 500 mm' luuumm LE' MC TE °LE 500 e 4o (b)Fig. 6-9 Measured: Cavity Thickness (HSP)
'(a) O=3O (:b) 4ØO (c) O=5O 1 mm 100 50 cnn -, mm LE -MC_ TE 'nR = 085 ' s' 't marks marks: marks,: N =163RPM
o--- measured by Laser (ship)
N = 163 RPM
o--- measured by Laser(ship)
N = 163' RPM measired by Laser(ship). measured. by,Laser(model) measuredby Laer(model) -- mêasured byLaser(rrtodel) MC 500 50 (c) TE 1000mm
25
greater on HSP in the range of 40-70 deg. No harmful cavitation
was observed on HSP.
(3)
Cavity ThIckness MeasurementCavity thickness was measured at blade angles O = 30, 40, 50 deg, at radial locations r/R= 0.85, 0.90, 0.95, at chord positions X/c=0.25, 0.50,
0.75, totalling 3x3 x3=27 positions. All the measurements were made at 163rpm. The B/W TV camera was used because the color TV cameraj
somehow could not produce pictures of good quality. The SM-200
fibers were not used because they needed much time for alignment.
The non-cavitation condition was at 70 rpm.
The, measured cavity thickness distribution is shown in Fig. 6-9
(a), (b), and (c). Ten readings Of the measured values were averaged at each measuring point. The standard deviation is also shown. The scattering of the measurements is considered to reflect the actual
thick-ness fluctuations because the estimated measurement error is 10 mm,
which is considerably smaller than the scattering. The data show that the cavity is thin and stable near the leading edge of the blade, and it is thick and unstable near the trailing
edge. The same tendency is observed in the model experiments">.
The figure also shows the cavity thickness measüred in the model
ex-perimens">, where the estimated wake
distribution of a full scale ship was
used (Fig. 6-10).. The agreement be-tween the model and full data is very good, considering the difficulty in the scaling of the wake distribution.
The reproducibility of the merging
of the two laser spots was checked at
(0.70R, 0.75c), where there was no cav-ity. The blade angle was 40 deg. First the two spots were made to merge at 70 rpm. When the same pan and tilt
angles were set at 156rpm, the two
Spots merged. However, their location
shifted by 17mm toward the leading
edge. The shift may be caused by the
lag in blade angles due to the torsion or the propeller shaft described in Section 4-5. The estimated shift of the spot due to the lag is 13 mm, which
reason-ably agrees with the observed value.
Fig. 6-10 Estimated Wake
Distribu-tion of a Full Scale Ship
7. FUTURE TASKS
The measurement of cavity thickness on a full scale ship uiftg lasers was made for the first time iñ the world. Though the measure-ment was successful, there are several points which need to be
modi-fied. They are listed below.
7-1 Impróvemeút of Méasureinent Accuracy
Increase of the Sensitivity of Color TV Camera
Laser spots could not be seen through the color TV camera in the test with HSP Use of a color TV camera with higher sensitivity is
recommended.
Increase of Transmission Efficiency on Laser Light
As pointed out in 4-2, the transmission efficiency of the system on
laser light is very low Modification at each step is needed Reduction of the Laser Spot Size
Laser spot illuminatiön increases as the spot size is reduced,
assum-ing that the laser power is constant The smaller the spot size, the higher the measurement accuracy The most effective way to reduce the spot size is to use a fiber with a smaller core diameter Though
it was unsuccessful, the use of 200 pm dia. (or less) fibers is
recom-mended.
Further, if the use of a single mode fiber becomes possible, as it
is with LDV, the spot size will become minimum because the coherency is maintained. At the same time, the transmission efficiency will in
crease because the telescopic lens and the hole become unnecessary
7-2 Speedup of Measurement
(1) Computerized TV Screen Data Processing
The laser spots on the screen, as is shown in Photo 6-4, is fitted for computer processing. The measurement accuracy will increase,
Photo 6-4 Láser Spots n Propeller Blade (HSP) 163 rpm, =4O0, (O.95R, O.75c)
27
while the measurement time will decrease.
(2)
Computer Control of Pan añd Tilt Angles of Eînittei'sThe automation of the measurement will become possible by - coth bining the computer control of pan and tilt angles and the computerized screen processing.
7-3 Others
Light Source
An Argon ion laser needs large power (maximum 35 kW) and
cool-ing water The work required for installation is not nominal The
system will be greatly simplified if a semiconductor laser is used as a light source. and is installed in the emitter. The use of a normal strobe as a light source should also be considered
Measurement of Propeller B.ade Bending
By increasing the measurement accuracy of the system, the meas-urement of the blade bending of a full scale propeller working behind
a ship will become possible. -8. CONCLUSIONS
A new technique for measuring cavity thickness on a full scale propeller using lasers and a TV camera has been developed and
suc-cessfully applied. This technique is an optical one, which uses the fact
that a laser spot on a propeller blade displaces in proportion to the
cavity thickness.
The test using a full scale ship was made twice. In the first test, the sea was rough and many of the instruments broke down. Only a few measurements were made In the second test, the measurement
went smoothly The measured cavity thickness shows a reasonable distribution and agrees with model test results.
Through the above two tests, it has been established tiat the cay.-ity thickness of a full scale propeller can be accurately measured with the present technique.
ACKNOWLEDGMENTS
This research project was conducted as a part of the project "Study
on Propellers and Stern Hull Forms Aiming at Reducing the Stern Vi-bration and Noise" by the SR 183 Research Panel of the Japan
Ship-building Research Association
The authors are especially grateful to Mr Hajime Yuasa and Mr Hikaru Kamiirisa of Akishima Laboratory of the Mitsui Engineering
with the authors on this research project. Mr. Hirotaka Kubo of the Nakashima Propeller Co., Ltd. and Mr. Yuzo Kuróbe of the Ship Re-search Institute were also helpful in conducting this reRe-search.
The authors are grateful to the members of the SR 183 Research
Panél. Professor T. mu1 of Tamagawa University showed
understand-ing and encouragement on this project as the head of the panel
Pro-fessor H. Kato of Tokyo University made valuable suggestions during the course of the work as the head of the No. 2 Sub-Researe Panel. Thanks are extended to Dr. Hai ime Takahashi of the Ship Research Institute, who was the head of the No. 4 Sub-Research panel.
The authors also thank the Institute for Sea Training, which pro-vided the tested ship "Seiun-Maru".
REFERENCES
Takahashi, H.: "Study on Propeller Vibratory Forces (2nd Report)Effect of Cavi-tation on Surface Forces", Abstract of Autumn Meeting of SRI (1968), or "Investi-gation into the Effects of Cavitation on Fluctuating Pressures around a Marine Pro
peller ", Paper of SRI, No. 33 (1970).
Kodama Y The Growth of an Attached Cavity on a Two dimensional Nonlifting
Body ", J. of the SociCty of Naval Architecture of Japan, vol. 148, November 1980.
Isshiki H and Murakami M On a Theoretical Treatment of Unsteady Cavitation
(3rd report) ", Transactions of the West-Japan Society of Naval Architects, No. 64, Aug. 1982.
Tulin, M. P. and Hsü, C. C.: "New Applicatiòns of Cavity Fow Theory "; 13th Symposium on Naval Hydrodynamics, October 1980.
Hoshino, T.: 'Estimation of Unsteady Cavitatiòn on Propeller Blades as Base for
Predicting Propeller Induced Pressure Fluctuations J of the Society of Naval Archi tects of Japan, vol. 148, December l980.
Ukon, Y. and Kurobe, Y.: "Measurement of Cavity Thickness Distribution on Marine Propeller by Laser Scattering Technique ", Report of Ship Research Institute, vol. 19,
No. 1, 1982.
Kamiirisa H et al Full Scale Observation of Propeller Cavitation and Model Test ing ", Mitsui Zôsen Technical Review, No. 119, July 1983:
Holden, K. and SçSntvedt: "On Stability and Vôlume of Marine Propeller Cavitation and Corresponding Spectral Distribution in Hull Pressure Fields Symposium on High
Powered Propulsion of Large Ships, Publication No. 490, Netherland Ship Model Basin
1974.
Harvey, A. F.: "Coherent Light ", pp. 1107, Wiley Interscience 1970.
Institute for Sea Training Ministry of Transport Training Ship Sein MaruFrom Its Design to Completion", Seizan-do, 1969.
Kurobe, Y. et al.: "Measurement of Cavity Volume and Pressute Fluctuation on a Model of the Training Ship "SEIUN-MARU" with reference to Full Scale
A.R
Fig. Al-1 Propeller Coordinates
x axis: Propeller axis. Positive in downstream diectiòh..
y axis Port-starboard Positive in starboard direction z axis : Orthogonal to the above two axis. Positive in upward
direction.
Origin Crosspoint of Propeller axis and the propeller
gener-ator line.
The parameters h, i, r which indicate the relation between Propel-ler Coordinates and BL or AP, which have the values h=2.00 m, 1=
2 135 m and r = 0 579143 deg for "Seiun-Maru" The propeller rotation is clockwise seei from downstream.
Al-2 Conversion of Offset. Values to (z, ,z)
Fig. Al-2 shows the relatiòn among the propeller coordinates, the generator line, and a spiral The symbols are explained below
Fig. Al-2 Generätor Linê and Spiräl
29
APPENDIX
Appendix 1 Calculation of Propeller Coordinates (x, y,. z) from Propel-1er Offsets
Al-1 Propeller Coordinates (x, y, z)
Fig. Al-3 Distance X along a Spiral and Angle O
xQ=ço(r)--LH(r)
yQ=r sin O (Al-3)
zQrcosOï
..
s=w(r)O wherew(r)J(_)2+r2
(Al-2) At the blade angle O=O, the coordinates (XQ, yQ, ZQ) of the pointQ whose distance from the leading edge along the spiral of radius r is X, are (cf.. Fig Al-8),
r
Radius of the spiral.H(r) Pitch of the spiral In general, function of r
Rake Of the spiral.
s : Pistaiçe along the spiral.
Angle between z axis and a point on the spiral See
the figure.
( y, z) coordinatès of the point on a spiral with radiu r are,
I x=cp(r)_±.H(r)
2ir
(Al-1) z=r còs O
The relation between O ànd s, distance along the spiral, is,
where o.
XL X
(Al-4)w(r)
X :
Listance along the spiral to Q from the leading edge.XL : Distance along, the spiral to GL from the leading edge. This X concides with X in the propeller offset tables shown in Tables
6-2 and L-3.
The spiral t has the the same radius r and intersects orthogonally with the spiral s. ts pitch R' is, from Fig. Al-4 (a),
(a)
The relation between
similarly to eq. (Al-2), t=w'(r)e'
Fig. Al-4 (a), (b) Spirai t Orthogonal to Spiral S
H' (27rr)2
H(r)
(b)
31
(Al-5) The angle O' is defined as shown in Fig. Al-4 (b). Then the (x, y,
z) coordinates of a point on the spiral t are,
x=xQ__H'(r)
2ir(Al-6)
y=r sin (OsO') z=r cos(O-O')
O' and the distance t along the spiral t is,
where ei(r) }2±r2 (Al-7)
coordinates of tie point P*(x, ) which has distance X from the leading edge and thickness Y (i e distance along the spiral t) at radius r is obtained by ubstituting the following value into O' in eq. (Al-6).
co'(r) (Al-8)
This Y coincides with YO or YU in the propeller offset table shown in Tables 6-2 and 6-3.
Let P(x, y, z) be the point where P* is shifted in case 5*O
y,=y cos OG+z' Sfl 8G (Al-9)
z=y; sin O±z cos 8
From the above arguments, the propeller coordinates (xv, y, z) may be obtained by using eqs (Al-2) through (Al-9), in case the blade angle 0G and X and Y are given as shown in Tables 6-2 and 6-3.
For the case when the given X or Y does not coincide with the value given in the table, it is interpolated by using quadratures.
Appendix 2 Calculation o the calibration coefficient b for Cavity
Thick-ness
In Chapter the calibration cofficiént b is defined tO convert the
spot distance S to the cavity thickness t.
(5-l)
In this appendix, the calculation method of b s presented.
A2-1 Definition of Cavity Thickness
Cavity thickness is normally shown together with a blade section of r/R=const as shown in Fig A2-1 In this case, the cavity
thick-r/ =Const
Fig.. A2-2 Locäl Orthogonal Coorinates (, ¿2, ¿8) on Blades Surface
Point of origin P. : Point of Laser spot on the blade. (nR,
x/c) values are obtained through observations on TV screen, and the coordinates (x,, y8 z,) are calculated by the method shown in Appendiì 1.
¿ axis This axis is parallel with the tangential line of the spiral t at the above (r/R, x/c) position. The
thick-ness of the blade and the cavity is approximately
along this axis.
¿ axis This axis is parallel with the tangential line of the spiral s at the above (r/R, x/c) position
¿ axis: Orthogonal to the above two axes.
¿,
¿2, ¿3 axes are regarded as the chordwise, radial, and normal-toblade-surface directions approximately Let , , be the unit
vec-tors along ¿1, ¿2, ¿ axes.
is the tangential vector to the spiral s, and positive in the
di-rection of decreasing s Using thé equations (Ahi) and (Al-2),
-_(.dx
dy ds---,
--ds ds dz e=ox.
33
ness t. at a certain (nR, x/c) position is defined to be the length along a spiral t from the back surface to the cavity surface The spiral t is perpendicular to the pitch surface spiral s at that radial position (c.f.
Fig. A1-4 (a)). This definitIon is adopted in the présent paper.
A2-2 Local Coordinates (' ¿, ¿) on Blade Surface
rcos rsmO1 (A2-i)
\ 2irw(r) w(r) w(r) /
¿ is the tangential vector to the spiral t Using the equations
(Al-6) and (Al-t),
_(x dy
dt'\ ' e'=o-
( H'(r) r cos O r sin 6 2irw'(r)' öl(r) ' w'(r) TV Camera (A2-2)- Fig. A2-3 Laser Angles a ß
a: The angle between ' axis and either of the Laser beam
path or the observation path.
¡9: The angle betweeñ: ¿ axis and the projection of the Laser
beam path on ¿C2 plane Positive in counterclockwise di-rection
The subscripts e1, e2 and u represent Emitter 1, Emitter 2, and
Under-water TV camera, respectively
A2-4 Calibration Coefficient b
Following two approximations are introduced to simplify the cal-¿2 is perpendicular to both and axes.
= e3X¿1 (A2-3)
A2-3 Laset Angles a, ¡9
Fig A2-3 shows the geometrial relation when the Laser spots from
the two emitters merge on the blade surface and are observed by the
culation.
[Approximation ii The cavity thickness t is approximated by
the distance along e3 axis from the blade surface to the cavity surface
[Approximation 2] The cavity surface is approximated by the
at plane in the vicinity of the region
where the two Laser spots
exist. Thisplane is called a cavity pláne.
Fig. A2-4 (a), (b) show the arrange ient near the point. P. under the
approxlmatiòns listed above.
(ç) e3 Cavity Plane -Pc
-j-(b)Fig. A2-4 (a), (b), (c) Càvity Plane and
Cavity Thickness
35
Let be the unit vector Íi6rmal to the cavity plane.
i(n1, n2, n3) (A2-4)
Let P. be the point of interséction of axis and the cavity plane.
Then,
P=(O,O, t) (A2-5)
The point P. denotes the Lasr spot on the blade under the
non-cavitating condition The points P,1, P2, P denote the positions of
P3 and P3 are the Laser spots under the cavitating condition, that is,
the points of intersection M the cavity plane and P3P31 or PsP32.
Let PP
41 and P3P then the coordinates of the pointsP3. (i=1, 2) are,
J ¿, \ ( . sin a. cos
P=
E2) where 2.sin o. Sjfl ße. (A2-6)¿l=COSaC, (i=1, 2)
The cavity plane is expressed by,
n1C1 + n2Ç2 + nICI = n3t3 (A2-7)
The points P31, and P3., are on the cavity plane. Substituting eq. (A2-6) into the above equation,
4l =
where k1 niCjj ± ne12 + fl3ej3k1 n3,
le2_
where k2 fiCzi+fl222±'IhCza (A2-8)k2 n3
As shown in Fig. A2-4 (c), the. spot distance S observed by the
TV camera is,
SHIsnO=I&xI
Substituting eqs. (A2-9) and (A2-1O) into the above eqùation results,
finally., .
Let be the vector between the two
I Si
s( s2 =2F81=t3
\ s3 spots. Using & \ 21 11the above equation,
(A-9) k2 E22 --k1 E12 k2 e23 k1 e13 k2 k1.
A unit vector ,. in P3P1. direction is,
/e\
( e2J'=/sina3CoSß
( sin sin ß (A2-1O)
37
Once i, is determined, the ,cavity thickness t, is calculated by eq.
(5-1).
In the case when the measurements are made at many points, it is possible to obtain the cavity thickness without assuming the cavity
plane slope. That is, first the cavity thickness distribution is obtained
under [Approximation 3], and the vector i, is estimated, based on that
thickness distribution Then, the cavity thickness is calculated again This iteration is repeated until it converges.
Appendix 3 Calculation of Pan, Tilt Angles of Emitters
As described prevÏously, in noncavitation conditions two Laser spots
from the emitters need to be located on the blade where the cavity
thickness measurement is to be made. This operation is made by
con-trolling pan, tilt angles of the emitters while monitoring TV screen, and may reqüire much time. In order to shorten the time required, a method is developed for calculating the pan, tilt angles from given
(O, nR, X/c) values.
A3-1 Equation for Laser Beam Emitted from Emitters
The structure of the emitter is shown schematically in Fig A3-1 An upper mirror is called Mirror 1, and the lower mirror is called
Mirror 2. Mirror i rotates with an axis normal to the paper plane.
where b2-'-( eL2I + + f 23 tc=+.su \ / cil
e
I Ç22 & Ç12 (5-1) (A2-11) k2 {eU3(-k1 / U3\ k2 \ f e 23 k1 i13 k1)uk2
e 12 e 21 k1 cil k1) u2\\k k1The slope of the caVity plane cannot be obtained from a single
measurement. Therefore the third approximatiòn is adopted.
[Approximation 3] The cavity plane is assumed to be parallel with the 12 planeé That is,
This rotation angle is called a tilt angle .. It is positive when the
emitted Laser beam is directed upward Mirror 2 rotates with an axis which aligns with top-to-bottom direction in the paper The rotation
angle is called a pan angle It is positive when the mirror rotates to the left as shown in the figure.
'7'
'73 MIRROR I
-4i
.1IRROR 2
Fig. A3-i Pan Angle O, and Tilt Angie ,.
The emitter coordinates are defined as follows.
Origin O: Point of intersection of the Laser beam and Mirror
.2 plané when O e 0.
axis Direction of the emitted Laser beam when 0p=0T=° axis Axis of the Laser beam between Mirror i and
Mir-ror 2 when O=O.
7z axis : Orthogonal to the above two axes.
Mirrors i and 2 are both installed with an inclination angle of 45
deg. The distahce i,,. bétWeen the mirrors is defined as shown in the
figure.
Let . be a unit vector normal to the Mirror 2 p1ane In case &,=0: L=(sin 450,Ø, cos45°)
(A3-i)
Tn case v3,*n Ø. (coser sin O i
. ,
r-Let ê be a unit vector along thø Laser beam impinging on Mirror 2.
ê=(sineT, 0, cosO.)
(A3-2) Let r be a unit vecor along the Laser beam reflected from Iiro2. According to the law of réflection, (ë,.j)IIiim
(A3-3)
(j)Xiim0
1 78=371cot 8+l '72=O i lcosO
(''
' s +cot O, cos 39/
r1\/
cos O cos sin281- sin O,r2
J=( sin O.(cos O,+cos Osin O.)
\r3/
\cose-sine
An equation for the Mirror 2 pIane in the case OO is now
ob-taÏned. Let the point on the Mirror 2 plane be denoted by Ï('7, 72' 73),
thén,
I
37jCOS 51,±,72sin ±373=0 (A3-5)
The equation for the Laser beam impining on Mirror 2 is,
(A3-4)
(A3-6)
The point P*(37', ') which is the point of intersection of the Mirror 2 plane and the impinging Laser light is, by solving the above
two equations,
(A3-7)
The equations for the emitted Laser beam is therefore using t as an arbitrary parameter,
72= '7' + r2 t - (Ä3-8)
where (r1, r2, r3) are given by eq. (AS-4).
In full scale measurements, lm=45mm, &pmax=25°, O,.=23.3°,
I7Mmax15mm, and the distance between the emitter and the blade
'surface is about 3 m. Therefore (, '7g', ,7') components are negligible, and will be neglected, in the subsequent calculations. That is,
r2t (A3-9)
77 r3t
Fig. A3-2 shows plotting of the points of iriterseçtion of the = i
plane and the emitted Laser beam by using eq (A3-9) The scanned area 'is cOnsiderably distored from 'a rectange.
-ii
5° 0.5u.
"I.
"u
50 8î-23° 50 loo 'IO. I50 -20° -23.3°Fig. A3-2 Laser Spot Movement due to Pan and Tilt
A3-2 Relation between Propeller Coordinates and Emitter Coordinates
The emitters are attached on the hull side with some inclination
angles. The relation between propeller coordinates and emitter coordi-nates is expressed as follows.
/ x \
/
, \ / x, a1, a12 a,, \y J.A( '72 y
where A=
a,1 a,, a2,J
(A3-].0)
z ¡ \ ,, / \ z a,1 a,, a,, /
The point P3(X3 y, z3) denotès the location of the emitter on the hull' side and is measured at the dock. It is the origin of the emitter
co-ordinates. The matrix A expresses inclinations of the emitter and is
obtained by moving the Laser spots at sea.
First the spot location P31(x31, ye,, z31) at O=t9,.=O is obtaiñed (Fig.
A3-3). A unit vector ä1 in
.E,
direction is a. unit vector along , axis,and has components (a11, a,,, a,).
Next, spot locations Ph,,. . ,, P. are obtained by changing C,. while
keeping O,,=O. As the points P3,..., P. are on plane, a unit
vec-tor i(a,,, a,2, a,,) in '22 axis direction. is calculated. by the least squares
9p°25°
Let the pòint of intersecti6n of the Laser beam and ml plane
havé côordiñates (n', , ). Theíi,
I
7il
'72
(A3-i3)
The
The coodinates (m '72' m) of the point of intersection of the Laser
beam añd =1 plane is, by using eq. (A3-9),
'2' 1
Fig. A3-3 Detection of Emitter Inclination Angles
method.
Finally, a unit vector 1(a3, a23, a33) is obtained by simply,
(A3-11) A3-3 Calculation of Pan, Tilt Angles
In this section a method is shown for calculating pan, tilt angles in case (O, nR, X/c) values of a Laser spot are given
Propeller coordinates (x8, , z8) of the point P. are calculated from
(O, nR, X/c) values The coordinates are transformed into Emitter
co-ordinates (, ,, m) by üsing eq (A3-1O), that is,
-
+cos O38 sin O)'22
cosO38eosOsin2838sinO
- COSOS, I! Or
co O cos ,:.iÌi2 &, sin 9,.
41
(A3-12)
From eqs. (A3-13) and (A3-14), pan, tilt angles 01,, O are obtained by
solving eq. (AS-14) when (2' ) values are given by eq. (AS-13).
The eq. (AS-14) is nonlinear with respect to O, O, and is not easily
solved. Taking advantage of thé fët that O= constant lIne in Fig. A3-2 is linear, eq. (A3-14) is rearranged so that,
COSE O
cos O,, (A3-15)
sin. O
Finally,
tan o = '22COS O
(AS-16)
'
When (22v ) are given, O,,, is obtained by solving the above equation
through iterations. The first approì1imation is,
22
28±1
The O value thus obtained is substituted into RHS of eq. (A3-16), and
the second approximation is obtained from LHS, nd so on.
Once Or,, is obtained, 0r is obtained by the third equation of eq
(A3-14), that is,
O.=tan1 (
cos (A3-18)\.cosO1,±'2,,sin2O1,/
A3-4 Comparison of Measured and CalcuÎated Results
Table AS-1 shows the comparison of measured and calculated values.
Measurements were made both with CP and HSP The agreement is
very good with pan angles, and fairly good with tilt angles.
Table A3-1 Comparison of Measured and Calculated Pan, Tilt Angles
(AS-17)
Emitter
No. Propel-1er
Blâde Angie
Ù (deg)
Position Pan AngleO (mm) Tilt Angle
°T (mid)
nR X/c Meas. Cal. Meas. Cal.
1 CP 30 0.67 0.53 0 0 0 0 /F if if 0.85 0.40 0 0 329. 306 /1 if if 0.60 0.60 0
28
95
109 if n « 0.92 030 06
455 431 'i if 20 0.90 0.50 368 357 300 305 if if 30 0.85 0.25 101 123 347 305 if if if 0.85 0.10 .241 251 352 295 1 HSP 40 0.90 0.50 457 433 259 197 if if 70 0.80 0.50 591 556 283 375 2 40 0.90. 050 342 337 426 466 if 70 0.80 0.50 578 579 166 149PAPERS OF SHIP RESEARCH INSTITUTE
No. 1 Model Tests on Four-Bladed Controllable-Pitch Propellers by Atsuo Yazaki,
March 1964.
No. 2 Experimental Research on the Application of High Tensile Steel to Ship Struc-tures by Hitoshi Nagasawa Nontaka Ando and Yoshio Akita March 1964
No 3 Increase of Sliding Resistance of Gravity Walls by Use of Projecting Keys under
the Bases, by Matsuhei Ichihara and Reisaku moue, June 1964.
No. 4 An Expression for the Neutron Blackness of a Fuél Rod after Long Irradiation,
by Hisao Yamakoshi, August 1964.
No. 5 On the Winds and Waves on the Northern North Pacific Ocean and South Ad-jacent Seas of Japan as the Environmental Condition for the Ship, by Yasúfúmi Yamanouchi, Sanàe Unoki and Taro Kanda, March 1965.
No. 6 A code and Some Results of a Numericál Integration Method ôf the Photoñ Transport Equatión is Slab Geometry, by Iwao Kâtaoka and Kiyoshi Takeuchi,
March 1965.
No. 7 OÍi the Fast Fission Factor for a Lattice System, by Hisao Yamakoshi, June 1965;
No 8 The Nondestructive Testing of Brazed Joints by Akira Kannö November 1965
No; 9 Brittle Fracture Strength of Thick Steel Plates fòr Reáctor Pressure VesseÍs, by
Hiroshi Kihara and Kazuo Ikedä, January 1966.
No. 10 Studies and ConsideratiOn On the' Effects of Heaving änd Listing upon
Thermo-Hydraulic Performance and Cntical Heat Flux of Water Cooled Manne Reactors by Naotsugu Isshiki, March 1966.
No 11 An Expenmental Investigation into the Unsteady Cavitation of Marine Propel
1ers, by Tatsùo Ito, March 1966.
No. 12 CavitatiOn Tests in Non-Uniform Flow on Screw Propellers of the
Atomic-Power-ed Oceanographic and Tender ShipComparison Tests On Screw Propellers
De-signed by Theoretical and Conventional Methods; by Tatsuo Ito, Hajime
Takahashi and Hiroyuki Kadoi, March 1966.
No. 13 A Study on Tanker Life Boats, by Takeshi Eto, Fukutaro Yamazaki and Osamu
Nagatá, Màrch 1966.
No. 14 A Proposal on Evaluation of Brittle Crack Initiation and Arresting Temperatures
and Their Application to Design of Welded Structures, by Hiroshi Kihara and
Kazuo Ikeda, April 1966
No 15 Ultrasonic Absorption and Relaxation Times in Water Vapor and Heavy Water Vapor, by Yahei Fujii, June 1966.
No 16 Further Model Tests on Four Bladed Controllable Pitch Propellers by Atsuo
Yazaki and Nobuo Sugai, August 1966. Supplement Nô. 1
Design Charts for the Propulsive Perfòrmañces of High Speed Cargo Liners with CB=
0 575 by Koichi Yokoo Yoshio Ichthara Kiyoshi Tsuchida and Isamu Saito August 1966.
No. 17 Roughness of Hull Surface and Its Effect on Skin Friction, by Koichi Yokoo,
Akihiro Ogawä, Hideo Sasajima, Tefichi Terao and Michio NakatO, September
1966.
No. 18 Experiments on a Series 60, CB=O.7O Ship Model in Oblique Regular Waves,
by Yasúfumi Yamanouchi and Sadao Ando, October 1966.
No. 19 Measurement of Dead Load in Steel Structure by Magnetostriction Effect, ,by
Juùji Iwayanagi, Akio Yoshinaga and Tokuharú Yoshii, May 1967.
No. 20 Acoustic' Response of a Rectangular Receiver to a Rectangular Source, by
Kazunari Yamada, June 1967.
No. 21 Linearized Theory of Cavity Flow Past a Hydrofoil of Arbitrary Shape, by
Tatsuro Hanaoka, June 1967..
No. 22 Investigation into a Novel Gas-Turbine Cycle with an Equi-Pressure Air Heater,
by Kosa Miwa September 1967.
No. 23 Measuring Method for the Spray Characteristics of a Fuel Atomizer at Various
Conditions of the Ambient Gas, by Kiyoshi Neya, September 1967.
No 24 A Proposal on Criteria for Prevention of Welded Structures from Brittle Frac
ture, by Kazuo Ikeda and Hiroshi Kihara, December 1967.
No 25 The Deep Notch Test and Brittle Fracture Initiation by Kazuo Ikeda Yoshio
Akita. and Hiroshi Kihara, December 1967
No 26 Collected Papers Contributed to the 11th International Towing Tank Conference
January 1968.
No 27 Effect of Ambient Air Pressure on the Spray Characteristics of Swirl Atomizers by Kiyoshi Neya and SeishirO SatO, February 1968.
No 28 Open Water Test Series of Modified AU Type Four and Five Bladed Propeller
Models of Large Area Ratio, by Atsuo Yazaki, Hiroshi Sugano, Michio
Takahashi and Junzo Minakata, March 1968.
No. 29 The MENE Neutron Transport Code, by Kiyoshi Takeuchi, November 1968.
No. 30 Brittle Fracture Strength of Welded Joint, by Kazuo Ikeda and Hiroshi Kihara,
March 1969.
No. 31 Some Aspects of the Correlations between the Wire Type Penetrameter
Sensi-tivity and thé Hole Type Penetrameter SensiSensi-tivity, by Akira Kanno, Júly 1969.
No. 32 Experimental Studies on and Considerations of the Supercharged Once-through
Manne Boiler by Naotsugu Isshiki and Hiroya Tamaki January 1970
Supplement No. 2
Statistical Diagrams on the Wind and Waves on the North Pacific Ocean, by Yàsufumi Yamanouchi and Akihiro Ogawa, March 1970.
No 33 Collected Papers Contributed to the 12th International Towing Tank Conference
March 1970.
No 34 Heat Transfer through a Horizontal Water Layer by Shinobu Tokuda February 1971.
No. 35 A New Method of C.O.D. Measurement --Britt1e Fracture Initiation
Character-istics of Deep Notch Test by Means of Electrostatic Capacitance Method, by
Kazuo Ikeda, Shigeru Kitamura and Hiroshi Maenaka, March 1971.
No 36 Elasto Plastic Stress Analysis of Discs (The ist Report in Steady State of
Thermal and Centrifugal Loadings), by Shigeyasu Amada, July 1971.
No. 37 Multigroup Neutron Transport with Anisotropic Scattering, by Tornio Yòshimura,
August 1971.
No. 38 Primary Neutroù Damage State in Ferritic Steels and Correlation of Charpy
V-Notch Transition Temperature Increase with Frenkel Defect Density with
Neutron Irradiation, by Michiyoshi Nomakuchi, March 1972.
No 39 Further Studies of Cracking Behavior in Multipass Fillet Weld by Takuya
Kòbayashi, Kaziirrii Nishikäwa and Hiroshi Tamura, March 1972.
No. 40 A Magnetic Méthod for the Determinatioñ of Residual Stress, by Seiichi Abuku,
May 1972.
No 41 An Investigation of Effect of Surface Roughness on Forced Convection Surface Boiling Heat Transfer, by Masanobu Nomura and Herman Merte, Jr., December
1972.
Nô. 42 PALLAS-PL, SP A One Dimensional Transport Code, by Kiyoshi Takeuchi,
February 1973.
Nô. 43 Unsteady Heat Transfer from a Cylinder, by Shinobu Tokuda, March 1973.
No. 44 On Propeller Vibratory Forces of the Container Ship Coti-elation between Ship
and Model, and the Effect of Flow Control Fin on Vibratory Foces, by Hjime
45.
No. 45 Life Distribution and Design Curve in Low Cycle Fatigue, by Kunihiro lida and
Hajime moue, July 1973.
No. 46 Elasto Plastic Stress Analysis of Rotating Discs. (2nd Report: Discs subjected to
Ïransient Thermal and Constant Centrifugal Loading), by Shigeyasu Amada and Akimasa Machida, July 1973.
No. 47 PALLAS-2DCY, A Two-Dimensional Transport Code, by Kiyoshi Takeuchi,
November 1973.
No. 48 On the Irregular Frequencies in the Theory of Oscillating Bodies in a Free
Surface, by Shigeo Ohrnatsu, January 1975.
No. 49 Fast Neutron Streaming through a Cylindrical Air Duct in Water, by Toshimasa
Miura, Akio Yarnaji, Kiyoshi Takeuchi and Takayoshi Fuse, September 1975.
No 50 A Consideration on the Extraordinary Response of the Automatic Steering Sys tern for Ship Model in Quartering Seas, by Takeshi Fùwa, November 1975.
No 51 On the Effect of the Forward Velocity on the Roll Damping Moment by Iwao
Watanabe, February 1977.
No 52 The Added Mass Coefficient of a Cylinder Oscillating in Shallow Water in the
Limit K - O and K-. , by Makoto Kan, May 1977.
No. 53 Wave Generation and AbsorptiOn by Means of Completely Submerged Horizontal
Circular Cylinder Moving in a Circular OrbitFundamental Study on Wave Energy Extraction, by Takeshi Fuwa, October 1978.
No. 54 Wave-power Absorption by Asymmetric Bodies, by Makoto Kan, February 1979.
No. 55 Measurement of Pressures on a Blade of a Propeller Model, by Yukio Takéi,
Koichi Koyama and Yuzo Kurobe, March 1979.
No. 56 Experimental Studies on the Stability of Inflatable Life Raft, by Osamu Nagata,
Masayuki Tsuchiya and Osamu Miyata, March 1979.
No. 57 PALLAS-2DCY-FC; A. Calcùlational Method and Radiation Transport Code. in
Two-Dimensional (R, Z) Geometry, by Kiyoshi Takeuchi, July 1979.
No. 58 Transverse Pressure Difference between Adjacent Subchannels in a Square Pitch
Nuclear Fuel Rod Bundle, by Kaki Okumura, November 1979.
No. 59 Propeller Erosion Test by Soft Surface Methodusing Stencil Ink proposed by
the Cavitation Committee of the 14th ITTC, by Yuzo Kurobe and Yukio. Take,
March 1980.
No. 60 Plastic Deformation Energy and Fracture Toughness of Plastic Materials, by
L. I. Ma1slov, March 1980.
No. 61 Performance of Fireproof Lifeboats of Reinforced Plastics, by Osamu Nagata
and Kazûhiko Ohnaga, March 1980. Supplement No. 3
Winds and Waves of The North Pacific Ocean, by Yoshifumi Takaishi, Tsugio Matsu-moto and Shigeo Ohmatsu, March 1980.
No. 62 Elasto-Plastic Stress Analysis of Rotating Discs (The 3rd Report: Application
of Perturbation Method), by Shigeyasìi Amada, August 1980.
No. 63 On the Fatigue Damage of Standing Wire Ropes Multiple Step Testing Loading,
by Takahisa Otsuru, Hisao Hayashi, Shoju Okada, Yoshihisa Tanaka and Isao Ueno, December 1980
No. 64 Low Speed Wave Making Theory by Slender Body Theory, by Hiroyuki Adachi,
February 1981.
No 65 Une Méthode Simple. pour Générer une Houle Arbitràire dans ün Bassin d'Essais, by Shigeo Ohmatsu, September 1981.
No. 66 An Experimental Study on Broaching of a Small High Speed Boat, by Takeshi
Fuwa, Kazuô Sugai, Taihëi Yoshino and Tokutaro Yamamoto, April 1982.
No 67 An Application of a Reliability Analysis to the Emergency Sea Water Cooling
System of the Nuclear Ship Sàvannah, by Takeshi Matsuoka, May 1982.
the Bottom Profile, by Bernard Mohn,. May 1982.
No 69 Numerical Investigation into Nonlinear Water Waves by Means of the Boundary
Element Method by Hiroshi Tornita and Katsuji Tanizawa June 1983
No 70 A New Simple Method to Eliminate the Irregular Frequencies in the Theory of
Water Wave Radiation Problems, by Shigeo Ohrnatsu, July 1983.
No 71 Measurements of Wake Flow and Hydrodynamic Force Distribution on a Num
erical Ship Hull Form with Drift Angle by Takeshi Fuwa Koji Nonaka and Tadashi .Nirnura, October 1983.
No. 72 Studies on Void Fraction and Flow Pattern for Countercurrent Gas-Liquid
Two-Phase Flow by Katsuji Yamaguchi November 1983
In addition to the above-mentidned. ïepofts, the. Ship Resèafth Institute has another senes of reports entitled Report of Ship Research Institute The Report is published
