Research reports are published in English in two series: Series 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
Hy-2 PROHASKA, C. W. Trial Trip Analysis tor Six Sister Ships 6,00
Hy-3 lLOVl& V. A Five Hole Spherical Pitot Tube for 6,00
Three Dimensional Wake Measurements Hy-4 STRØM-TEjSEN, J. The HyA ALGOL-Programme for Analysis
of Open Water Propeller Test
6,00
Hy-5 ABKOWfTZ, M. A. Lectures on Ship Hydrodynamics - 20,00
Steering and Manoeuvrability
Series A:
No.: Author: Title: Price: D. Kr.
A-1 TEJLGARD JENSEN. A. An Experimental Analysis of a Pebble Bed Heat
Lyngby - Denmark
The HyA Program for Analysis of Open Water Propeller Test
by
J. Strørri-Tejsen
Hydrodynamics Department
Introduction i
Principles of Analysis Method 2
Formulae in the Calculation Procedure 3
Pairing Procedure 4
Degree of Polynomial 5
Elimination of Erroneous Points 8
Assessment of Accuracy 10
Application of the Program il
Input Data Form ii
Result Sheets 12
Conclusions 13
Recommendations 14
References 15
Appendix A: Calculation Example giving Data Sheet
The test data are faired by a polynomial, using the method of Least Squares. A fourth degree polynomial has been found adequate to define the open water curves for all non-cavitating propellers.
A statistical way of eliminating erroneous points has been introduced, which makes it possible to discard erroneous data without initially sketching the curves. It is found that the results from the analysis can be used directly without further manual checking or
fairing.
The Data Sheet and an example of the results is given.
INTRODUCTION
Propeller characteristic curves are obtained in the towing tank from the open water propeller test. The propeller is mounted on the shaft protruding forward from the propeller boat and is moved through an undisturbed homogenous velocity field. At Hydro- og Aerodynamisk Laboratorium (HyA) the experiment is carried out according to the
Standard Procedure [lJ with the propeller rotating at nearly constant revolutions, varying the speed of advance, and 25-35 measurements of revolution, speed, thrust, and torque are recorded for each experiment.
The analysis as hitherto carried out in the drawing office con-sists of plotting the non-dimensional coefficients in the propeller diagram and fairing of the small scatter in the plotted points by hand. The work involved is moderate and can be carried out in less than 4
hours.
The installation at HyA of the high-speed digital computer, GIER, has made it feasible to use a computer for this analysis work, and the program which has consequently been developed is described in the present report.
PRINCIPLES OF ANALYSIS METHOD
The following calculation procedure has been employed in the computer program for the handling of open water test data:
a. First the experimental data, which consist of measurements of revo-lutions, thrust, and torque for a certain number of speed values, are combined to give the non-dimensional coefficients:
advance coefficient:
J
= v/nD,thrust coefficient: KT = T/( 9fl2 s D4)
and torque coefficient: KQ
= Q/(9%nN
D5).All measured points are used, with no special treatment of zero
points.
The curves of the non-dimensional coefficients NT and KQ are there-after faired separately, using a polynomial equation in
J
which is fitted by the method of least squares, thus giving:KT - RT
[o] +RT [1] XJ+RT {2J*J2
+ RT [ni] m= EQ
[0] +RQ [l
* J+RQ [2]*J2
+ + RQ [m]o. A statistical method of eliminating erroneous points follows the fairing. The root mean square deviation, rms, is calculated from the faired KT_ and K -curves:
N
>(yi_fj)2
rms -N- (M+l) where N = number of points M = degree of polynomial y. = raw data f. = faired data iThe criterion for discarding raw data has then been taken as
y-f.
1 1
>2.7
rmsd. The remaining raw data are refaired and the above deletion pro-cedure is repeated until no more points are discarded. The final equations for KT and KQ are used for the calculation of the pro-peller characteristic curves at equal intervals of J. The
effi-ciency curve versus J will thus be derived from the final faired values of KT and KQ.
The cavitation number is not calculated, as the program is only intended for the analysis of propeller tests at atmospheric pressure.
Each step in the above calculation procedure is described in the ollowing chapters.
FORMULAE IN THE CALCULATION PROCEDURE
Certain corrections have to be made to the raw data from the experiment before the non-dimensional coefficients K, KQ and J are calculated. This is done in the program by means of the following expressions.
The thrust value, T, is calculated from the equation:
T = Trn+Tc+Td (kg)
whe r e
Tm = indicated thrust in kg as measured during the test. Pc = thrust correction in kg measured during the calibration
of zero thrust using a dummy propeller boss. Td = dynamic thrust correction calculated from:
Td =
-
V2 F = 5' X V2,( 0.000077; where F = area of propeller shaft in sq.metres.(Diameter = 11 mm at HyA)
= density in kg sec2/m4, (see below) V = speed of advance in rn/sec.
Tm and Tc are given in the data sheet, while Td is calculated in the program.
Each torque value, Q, is calculated as follows:
Q =Qrnxf+Qc
(kgxcm)whe r e
Qm = indicated torque (in kg ( cm) measured during the test.
Qm and Qc are stated in the data sheet, while f is chosen by the pro-gram corresponding to the dynamometer used.
Advance speed, V, is calculated from: V 1/time reading
where 'time reading" is the time recorded for the carriage speed. Rate of rotation, n, is calculated for each point from:
n = 25/time for 25 revs.
The propeller Reynoldst number is calculated for each point from the following formula:
Qc = torque correction measured during the calibration of zero torque with dummy propeller boss. As the revolutions are kept constant, Qc is a constant. f factor which depends on the dynamometer used.
The following factors are at present included in the program:
Mechanical dynamometer type 11: f 0.986 type 12: f = 0.988 Electronic dynamometer type 21: t' = 1.00
type 22: f = 1.00
Re = b07
0.7*%n xD)2/&
whe re
b0 = propeller section length at 0.7 radius. = kinematic viscosity (see below).
The mass density, 5 , and the kinematic viscosity,j) , are obtained in the program from the temperature by a second order degree interpolation in tabulated values.
FAIRING- PROCEDURE
A fairing process is in principle used to eliminate random rrors in the experimental data, and for this reason it should be applied to the raw data. In an open water test this would involve fairing thrust T and torque Q separately in terms of speed of advance
V for a constant rate of rotation n. In practice it is difficult to avoid slight changes in the nominally constant rate of rotation. Consequently it is desirable to apply the fairing process to
coeffi-cients combining the basic data, rather than to the raw data itself, and in the present program this has been obtained by fairing the non-dimensional coefficients KT and KQ in terms of the advance
coeffi-cient J.
For the above reason, it is found more logical to fair the experimental data at this step of the calculation, rather than to fair the more complicated end results, and therefore no fairing of the efficiency curve has been considered.
The above fairing principles are generally accepted [2]
The polynomial approximating to the faired curve is found by the Least Squares method as described in Ref. [3] . The method is programmed as a separate procedure [4] . The approximating polynomial will not coincide with the experimental points because they are sub-ject to random errors, but it rather seeks to fit a curve, which re-flects the general trend of the points without reproducing local fluctuations. For this reason the degree of the polynomial should be small compared with the number of points and not higher than necessary to give the correct shape of the curves.
It can be taken as a rough guide that the number of pcints, M, should be at least 3-4 times the degree of the polynomial in order to avoid any local fluctuations and for this reason the fairing process should only be used for an open water test with more that approximately 15 measured points.
In the program the KT_ and KQ-curves are faired separately, using the polynomials mentioned previously. The degree, N, of the polynomials are taken the same for and KQ, and the program allows any degree from 1-6 to be chosen.
DEGREE OF POLYNOMIAL
In order to find the degree of polynomial which should be used to give a satisfactory fit to the experimental points from open water
tests, 5 different propeller tests were analysed using polynomials of from 2nd to 6th degree.
The five propeller tests were all typical of results of open water tests made at HyA, which give 26-36 points covering the range from zero thrust to zero speed of advance.
The root mean square deviation between the faired curve and the measured points was calculated for each set of faired curves, and
Table 1 gives the results of' the examination using five different degrees of polynomial for each propeller.
Furthermore the propeller curves were compared with hand faired results.
Table i
Root mean square deviations x l0 for 5 sets of propeller
For the 5 propellers examined, the second order polynomial gave a far too rough approximation as can be seen from the table. It was
expected that the 3rd order polynomial would be sufficiently accurate and that hardly anything would be gained by using higher orders. The
examination clearly showed, however, that for some propellers the 3rd order curves did not become flat enough in the mid-region, while on the other hand the 4th order gave a very satisfactory fit in all cases. Higher orders gave no improvement in the range of the measured points, but introduced the risk that even the slightest extrapolation would be erroneous because of more strong fluctuations given by higher order polynomials.
curves as influenced by the degree of the approximating polynomial.
Propeller Degree of Polynomial Number of Number of
No. Measured Discarded
2 3 4 5 6 Points Points 6015-1 KT 65 57 31 31 32 28 1 KQ 67 62 45 44 44 6211-6 KT KQ 18 21 16 18 13 18 13 19 12 19 31 o 6211-7 KTKQ 9289 53 37 43 22 39 16 39 11 30 6109-1 KT KQ 36 83 35 49 33 22 31 23 25 23 36 2 6117-2 KT 23 9 9 8 12 26 2 KQ 81 49 32 33 40 Average KT 47 34 26 24 24 30.2 1.6 KQ 68 43 28 27 27
Thus the examination indicated that a fourth degree polynomial should be used for future open water tests following the present stan-dard practice.
The faired curves followed the shape of the measured points so accurately that no sketching is found necessary.
A further examination was carried out using results from atmos-pheric propeller tests made in an experimental Water Tunnel. In these tests the measured points were restricted to a smaller advance coeffi-cient range going from an advance coefficoeffi-cient of J»-' 0.2 to zero
thrust.
In some of these tests only 14-18 points were measured, and the torque-measurements were not as accurate as desirable. The examina-tian of these tests showed that in this case nothing could be gained by going above the third order polynomial, and even the second order gave very accurate results. Furthermore, while a safe extrapolation could be carried out in the case with second or third order polynomial, this was not the case for the fourth order because of strong
fluctu-ations just outside the range of measured points. This effect is shown in Fig. 1, where the KQ-curves obtained for different degrees of poly-nomials are shown. It is seen that the lower order approximations maintain the correct shape of the propeller curve outside the range of measured points.
The following conclusions as to the degree of polynomial which has to be used can thus be drawn from the examinations:
For accurate measurements with more than 20-25 points, which cover the range from zero thrust to zero speed of advance,
a 4th order polynomial will give a fit which follows the natural and correct shape of the curve, and nothing can be gained by using a higher order polynomial.
In the case where there are less points, or the points are of lower accuracy, nothing will be gained by going above the 3rd order polynomial. Using the 4th order will only make extra-polation dangerous.
In the case where only 10-15 points are used or extrapola-tions far outside the measuring range is desirable, the 2nd order
offers advantages as it guarantees the correct trend of the
performed with normal propellers in the non-cavitating state. Super-cavitating, ventilated, and cavitating propellers give characteristic curves which might have bends and the program is not intended for these cases.
Open water tests for backing or reversing propellers will have to be sketched before analysis by the present program to make sure that the curves have a normal shape which might be approximated by a poly-nomial.
0.0 0.1 0.2 0.3 0.4 0.5
Figure 1. Polynomials of low order maintain the correct shape of the propeller curves outside the range of measured points and extrapolation can be performed with a certain accuracy.
ELIMINATION OF ERRONEOUS POINTS
Experimental values will diverge from the true values because of uncertainty in measuring technique, reading of scales, etc. These
errors in points will in principle be eliminated in the fairing process
J=VnD
012 0.10 -0.08 0.06 0.0* -0.02 IO' 12nd order polynomia2
order polynon)aZ +th order polynomi1Fair/ng of XQ-cvrve
and the faired curve should represent ±he true values with an accuracy dependent upon the number of points, accuracy of instrumentation etc. This is, however, only the case as long as the divergence of the points from the true values is due to random errors (errors whose average tend to zero as the number of points increases). Among the data might be test results which actually diverge from the truth, not because of random errors, but arising from mistakes (unintentional departures from the usual procedure) e.g. from misreadings of instruments, copy-ing mistakes, etc.
When fairing the points by hand, such a point will normally be recognized, as it clearly departs from the general trend of the points. By a check of the data the mistake might be found and the point correc-ted and used in the fairing. If the mistake cannot be found, the
point will be discarded.
When analysing experimental data by means of a computer, it is necessary to be able either to correct or to discard points which are erroneous. This treatment of erroneous points must be carried out by the computer, because if it should be necessary to do it by hand before the analysis, nothing would really be gained by the later use of the computer. A statistical way of eliminating erroneous points has there-fore been introduced in the present program.
The root mean square deviation is calculated using the curve ob-tained by fairing all the experimental points.
As long as the experimental points are distributed around the faired curve with a normal distribution, 75 per cent of the points should be situated within the root mean square distance from the faired curve, and 99 per cent within
2.5
times the root mean square.Then fairing a curve by hand it is found from experience that the eye would reject a point which diverge from the faired mean by more than say
2.5
times the root mean square. This principle for dis-carding points can easily be adapted for use in a computer program.Thus in the open water test analysis a point will be eliminated if the difference between the measured points and the faired curve ex-ceeds a certain factor times the root mean square deviation. After some tests with different propellers, where the factor was varied from
2.5
to 3.0, had been made,2.7
was found to be appropriate.The factor
2.7
will cause0.5
per cent of the true points to be outside the limit. This percentage is so small that very few nor-mally distributed points are discarded by the process.In the program a set of data for one run will be completely
discarded if a mistake is detected either in the fairing of the KT_ or of the KQcurve, as it has been found incorrect to let the point re-main in the curve where it is not detected. It has been found
im-possible to let the computer check and correct the data as can be done by hand when the mistake might be corrected.
After the first fairing and elimination of erroneous points, the process will be repeated. The mean curve will now be moved further away from the discarded points and the root mean square will be
re-duced. The process might be repeated several times, but using the
factor 2.7 it is found that the fairing process is carried out once or sometimes twice.
The above way of eliminating points has so far proved satis-factory and comparing the results with hand faired results it is found to be more consistent since personal judgment is not involved. In
fact it has been found that computer analysis of an open water test can confidently be carried out in full, and the final results used straight away after a perusal o± the root mean square deviations given in the results.
The factor 2.7 mentioned above is a value which is suggested as standard,but any value might be introduced on the data sheet.
ASSESSNT 0F ACCURACY
The calculation of the root mean square makes it possible to form an impression of the accuracy of the final propeller curves. Thus
the standard deviation of the mean curve can be judged from:
rms/\r
where n is the number of points.
In cases where different propellers are to be compared, it is of particular importance to be able to state from a statistical view-point whether one is superior to another.
The judgment of the root mean square values should also make it possible to detect unusual divergences caused by testing apparatus or careless test work.
a. Input Data Form
The results frais the open water test which is to be analyzed, are specified on an input data form as shown in Appendix A, page 17.
In the column to the left is stated data identifying the calcu-lation (order and propeller nos. as. well as date), data for the pro-peller, particulars about the test (temperature, depth of propro-peller, dynamometer no.), and the thrust and torque corrections found from the calibration. It is important that none of the !tframesl are left empty us in this case the data would become mixed up in the computer.
Further-!ore the figures stated have to be consistent with the units indicated, e.g. the torque correction, Qc, must be given on the data sheet in kg g cm, etc.
The dynamometer number stated determines the correction factor which will be applied when calculating the final torque value (see page
The measurements made on the carriage should be stated directly without aoplying any corrections in the five columns to the right in the dato sheet. The input values for carriage speed and number of revolutions thus have to be given as the average of the time reading and of the time for 25 revolutions, which are recorded directly on the
carriage. The values for thrust and torque are the uncorrected values which can be taken directly from the records.
Then filling out the data sheet, the following restrictions have to be remembered:
Number of measured points must be less than 42. If more than 36 points are taken, the remaining points should be stated on
another data sheet which should be carefully attached to the first one.
The temperature of the tank water must be within the follow-ing limits:
8.0°Ctemp <20.0°C
The propeller curve should be of normal type.
b. Result Sheets
The results from the calculation are given on 4 or more pages, the number of pages depending upon how many fairings have been carried
out.
The first result sheet designated OWT-1 (page 18) gives a read out of all the input data stated on the input data sheets making it possible to check the data preparation. (There will be no risk of errors arising from the input equipment of the computer as one out of the eight channels on the paper tape is used solely for checking).
Page OWT-2 gives the raw unfaired data for propeller curves, which is normally used in the drawing office when plotting the points and fairing the curves by hand. Reynoldst number for 0.7-blade section as well as data describing the propeller and test conditions are also
given.
The following page, OWT-3, shows the results from the first fairing. In the present example 4th degree polynomials have been used for the fairing of the K_ and KQ_curves and the coefficients for the polynomials are given at the top of the page. Thus e.g. for the KT_curve the equation is as follows:
KT = 0.29764 + 0.080066 x J - 2.5489 x J2+ 4.5138 x J3- 2.6992 J4 Por each point the raw and the corresponding faired value and the difference in between them is stated making it easy to assess the correctness of the fairing process. The differences have been used for the calculation of the root mean square deviations which are given below the columns of differences, and which are subsequently used in the elimination process.
The efficiency is not faired in the program and the values given for the raw and faired efficiency on this page are the values, which can be calculated from the corresponding raw and faired values of KT and KQ respectively. It has, however, also been found convenient to be able to appraise the efficiency differences as those differences
show any tendency toward reduction or increase in efficiency by the fairing process. Thus in the present example the faired efficiency curve has been raised by the error in point no. 15 (which is subse-quently eliminated).
When any of the points are situated far away from either the KT_ or the KQ_curve, they will be eliminated as described previously. In
the present calculation point 15 is clearly defective and for this reason has been typed out in the bottom of the page.
The fairing process will be repeated until no more points are discarded and the result from the final (second) fairing is given on page OWT-4. This page corresponds exactly to page OWT-3 except that the faired data has new values. It can be clearly seen by examining the efficiency curve that it does not go above or below the raw effi-ciency values in the working region.
As no further points have been discarded after the second fairing, this fairing becomes the final one and the polynomials can be taken as representative of the and KQ_curves obtained from the test.
The accuracy of the test can be estimated by judging the root mean square deviation.
The final results which will be inserted in the report are final-ly typed out as shown on page 0WT-5. Apart from data for propeller and test condition it gives all the propeller curves for rounded J-values starting with J O and ending with the first J-value which gives a negative KT_value.
CONCLtJSIONS
It has been found advantageous to carry out the analysis of open water tests on the HyA-digital computer. The experimental data can be faired by means of a least squares polynomial representation of the non-dimensional KT_ and KQ_curves.
A 4th order polynomial is found to give as good a fit to the ex-perimental points as any hand fairing (for a test with 20-25 points). In cases with less points or less accurate experimental data a third order polynomial is proposed.
It is not necessary to make a sketch of the experimental points as the elimination of erroneous test data can be carried out by com-paring the root mean square deviation with the difference between each experimental point and the faired curve. A point will be eliminated
when the difference is greater than 2.7 times the root mean square. The final result can be used directly in reports, and the poly-noinial representation of KT and can further be used in the program for analysis of self propulsion tests.
The use of the computer for the analysis has lead to several advantages, among them the virtual elimination of drawing office time,
the elimination of personal bias and judgment in the analysis work, and the ability to derive additional information regarding accuracy from a given experiment.
RECOENDATIONS
The calculation of the root mean square deviation makes it possible to assess the accuracy of the open water test. It is recom-mended that these values be stored for comparison with future tests. This will enable errors due to the human element or the instrumentation to be detected. Furthermore it should form a basis for a more correct planning of experiments as to the necessary number of experimental points.
The HyA-open water propeller tests are carried out according to the standard specifications for ship model experiments fi], with a constant rate of rotation and speed of advance varying from zero to the negative thrust condition. The tests are normally carried out with the carriage speed increasing from run to run. It is felt that this testing practice can introduce a time dependent effect, which it is impossible to recognize. It is therefore suggested that open water tests be carried out with randomisation of all other factors than those which are kept constant, thus giving a more correct background for the statistical elimination of erroneous points. The advance speed should thus be chosen in a random way, e.g. by means of a
sta-tistical table.
No correction for scale effects on the model propeller charac-teristics caused by Reynoldst number, change of friction coefficient, etc. have been taken into consideration in the present program.
This omission of corrections seems only to be permissible if the model propeller has been tested above a critical Reynoldst
number of approximately 5 X 10 [5], at a sufficient depth of immer-sion, and if the full scale propeller is smooth [6]. Normally the
propellers are investigated in the supercritical range and at a sufficient depth, but only very little is known about the roughness
of full scale propellers, and it has been found difficult to intro-duce a correction for roughness. When more accurate data regarding propeller roughness become available, a correction should, however, be introduced in the program.
REFERENCE S
[i] Moor, D.I. and Silverleaf, A.: "A Procedure for Resistance and Propulsion Experiments with Ship Models", Proceedings of the
Symposium, Zagreb 22-25 September 1959, Paper 19.
Moor, D.I. and Silverleaf, A.: "Pairing of Data from Resistance and Propulsion Experiments with Ship Models", N.P.L. Seminar
on Computers in Ship Research and Design (Nov. 1962). Mime, W.E.: "Numerical Calculus", Princeton University Press,
(1949) pp242-25O.
1]
Strøm-Te.jsen, J.: "An ALGOL-60 Procedure for Polynomial Approxi-mation to a Function of a Single Variable by Least Squares", HyA Report No. 6289F-1, (October 1962).Beveridge, J.L.: "Propulsion Characteristics of a Submerged Model as Affected by Reynoldst Number", TMB Report 1454, Dec. 1960. Bussler, M.: "Die Berechnung des Reibungsbeiwertes und des
Rei-bungsmasstabseinflusses von glatten und rauhen Propellern", Schiffstechnik,
\Tol.
3, No. 17, June 1956, pp.254-26l.Appendix
ACalculation Example giving Data Sheet
and Result Exainp1e
Page
Data Sheet 17
Result Example 18
Input Data 18
Unfaired Data 19
Paired Data ist fairing 20
2nd Pairing . 21
der no. Uno
Data for full scale propeller
Results fra the test
6289
6015
oC rs kg kgxcmOPER WATER PROPELLER TT INFVT DATA Rur no. TL' reedlrg 1/speed Ti for 25 revs Thrust uncorr Torque uncorr sec kg k.xCin 2 9.804- 1.3369
15.4U
/
36.318 34902
1.3f5815965 3767/
4. 3.226 1.3151 16.051 37.709 52.488
1,302115511 3&683
61984
1.280f/5.305
36.409 71647
1.2768/5 f86
36.391 81420
1.2927 1+210 35165
9 1.2201.282/
13.470 33.262/0
1.1071.280/
12.74.0 32.072
1/0.9950 1.2768 /2.316 31030
120.9033
1.2639f1.197 28.916
13 0.5313 1.2639/0.582
28 f11
1+0.7657 12607
9.948
2704-9 150.7123 1.2880
10.1512434f
160.6662 12840
8129 23.500
170.6274 1280/
7470 22.365
180.5882 1.2768
6.8322/.177
1905559 1.2768
6.1+320.042
20
0.5258 1.274.2
5.538
18.980 21 0.5000 1.29134.600
16.950
220.4.764 1.2639
4.4.38
17.096 230.4550 1.2620
3.81/
/5.870
24
0.434-2 1.2960 2.84.6 14-.20525
0.4167. 1. 2967
f. 954. 12.010 26 0.3994 1.29601275 10.592
27
03842
f. 2513 1.270 1/, / /3 28 0.3704. 1.26200.535
9.4/2
290.356+ 1.2639 -0.773
7966
Date of te st day : = nth:= year:-28
12/962
Water tersj temp ath
the tank 14-ô Depth of pro)el-le? centerlii depth:-belc'w water surface 0.180Dynaw.*e ter no Dno : a
Dno:-11 r 12 for ica1 nnd 21 or 22 for the
alec-tronic dynansetere
/2
Thruet Te :-correction0.053
?orque
Qe
:-correct ion 0.301 No of rasured.runs in the col- N
:-r to the right N < L4
28
Degree of approx. poiyncial M:-W
6. Use norrsally M4-Factor used for statistical deletion of points rinef :=
rmef-2.7 isa
standard value2.7
Number of blades Z:-
4. Dia ter D2.450
m Pitch at c.7 R E-:-
f. 730
Zn Propeller blade length et 0.7 R b07:. 1. 4.20 m Developed area AD: - 3. 150 2Model scale 1/sc
sc:-
12.5PnoI : Prio2 :
run 1/speed 1/v sec/rn time for 25 revs 25/n sec thrust thrust measured corr Tkii Tc kg kg dyn thrust Td kg torque torque measured xfact f=0.988 ux.02 Qjnx102xf kgxm kgxm torque corr Qcx02 kgxm 2 9.80)40 1.3369 15.48)4 0.053 0 36.318 35.882 0.301 3 )4.9o2o 1.3158 15.965 0.053 0 37.671 37.219 0.301 L. 3.2260 1.3151 16.051 0.053 0.001 37.708 37.256 0.301 5 2»4880 1.3021 15.511 0.053 0.001 36.683 36.2)43 0.301 6 1.9840 1.2801 15.305 0.053 0.002 36»4c9 35.972 0.301 7 1.6)47o 1.2768 15.186 0.053 0.003 36.391 35.95)4 0.301 8 1.L2OO 1.2927 1)4.210 0.053 0.00)4 35.165 3)4.7)43 0.301 9 1.2200 1.2821 13.)470 0.053 0.005 33.262 32.863 0.301 10 1.1070 1.2801 12.7)40 0.053 o.006 32.072 31.687 0.301 11 0.9950 1.2768 12.316 0.053 o.008 31.030 30.658 0.301 12 0.9033 1.2639 11.197 0.053 0.010 28.916 28.569 0.301 13 0.8313 1.2639 10.582 0.053 0.011 28.111 27.77)4 0.301 1)4 0.7657 1.2607 9.9)48 0.053 0.013 27.0)49 26.72)4 0.301 15 0.7123 1.2880 10.151 0.053 0.015 2)4.3)41 2)4.0)49 0.301 16 0.6662 1.28)40 8.129 0.053 o.o18 23.500 23.218 0.301 17 0.627)4 1.2801 7.)470 0.053
o.o
22.365 22.097 0.301 18 0.5882 1.2768 6.832 0.053 0.023 21.177 20.923 0.301 19 0.5559 1.2768 6.1)43 0.0530.5
20.042 19.801 0.301 20 0.5258 1.27)42 5.538 0.053o.ß
18.980 18.752 0.301 21 0.5000 1.2913 )4.600 0.053 0.031 16.950 16.7)47 0.301 22 0»476)4 1.2639 )4.)438 0.053 0.035 17.096 16.891 0.301 23 0.4550 1.2620 3.811 0.053 0.038 15.870 15.680 0.301 2)4 0.)43)42 1.2960 2.8)46 0.053 0.0)42 1)4.205 1)4.035 0.301 250»467
1.2967 1.95)4 0.053 0.0)45 12.010 ii.866 0.301 26 0.399)4 1.2960 1.275 0.0530.c9
10.592 iO.465 0.301 27 0.38)42 1.2513 1.270 0.053 0.053 11.113 10.980 0.301 28 0.370)4 1.2620 0.535 0.053 0.057 9.412 9.299 0.301 29 0.356)4 1.2639 -0.773 0.053 0.062 7.966 7.870 0.301Order no. : 6289 Propeller no.: 6015 1
Model scale : 1/12.50 No of blades :
Dynamometer no.: 12 Diameter : 2.)450 m
Temperature : i 4 8 oC Pitch at .7E : 1.730 in
Submerged : o.i8o rn Pitch ratio : 0.706
Length at.7R : 1.)420 in
Develop area : 3.150
Density : 101.87 kgxsec42/n.4)4 Disc area :
run speed y rn/sec revs n 1/sec thrust T kg torque Q102 kgxm advance coeff. J thrust coeff. KT torque coeff.
KQx1
effici- reynolds ency number Ef f Re 20.102
18.700 15.537
36.183
0.0278
0.2955
0.3512
0.0373
7.985
3 0.201419.000
i6.oi8
37.520
0.051480.2952
0.3527
0.0730
8.115
140.310 19.010
16.105
37.557
0.0832
0.296140.3527
0.1113
8.125
5o.14
19.200
15.565
36.51414o.1068
0.2809
0.33614 0.114198.20.5
60.504
19.530
15.360
36.273
0.1317
0.2679
0.3228
0.1739
8.355
70.607
19.580
15.242
36.255
0.1582
0.2614140.3209
0.2075
8.385
80.704
19.339
14.267
35.0LJ40.1858
0.2537
0.3180
0.2359
8.285
90.820
19.149913.528
33.1614 0.211450.2367
0.2960
0.2729
8.365
10
0.903
19.530
12.799
31.988
0.2360
0.2232
0.28146 0.291468.385
111.005
19.580 12.377
30.959
0.2619
0.2147
0.271400.3266
8.1415
121.107
19.780 11.260 28.870
0.2856
0.19114 0.25014 0.3147148.515
13
1.203
19.780
10.614628.075
0.3103
0.1810
0.214350.3670
8.525
i141.306
19.8)0
1o.o114 27.5
0.3360
0.169140.2)32
0.388148.565
15 1.14014 19.141010.219
214.3500.3690
0.180140.2193
0.148318.14o5
161.501
19.14708.200
23.519
0.3933
0.114)90.2105
0.14278 8.14145 171.594
19.530
7.514322.398
0.1416140.1315
0.1993
0.1437148.1485
181.700 19.580
6.9o8
21.2214 0.1414300.1198
0.1879
0.1414988.525
191.799
19.580
6.221
20.102
0.146870.1079
0.1779
0.1452520
1.902
19.620
5.619
19.053
0.1491460.0971
o.i68o
0.145508.585
212.000 19.360
14.6814 17.01480.5271
o.c831
0.15144 0.145188.5o5
222.c99 19.780
14.52617.192
0.5141140.0769
0.11491 o.14141468.695
232.198
19.810
3.902
15.981
0.5660
o.o661
0.1382
0.143118.735
2142.303
19.290
2.9141 114.3360.6091
0.0526
0.1307
0.3898
25 2.140019.280
2.052
12.167
0.6351
0.0367
0.1111
0.331418.565
26 2.501419.290
1.377
10.766
0.6622
o.146
0.0982
0.261428.6o5
272.603
19.979
1.376
11.281
0.66147 o.29 0.0959
0.2529
8.915
28
2.700 19.810
0.61459.600
0.6953
o.oio
o.c83o
0.114588.875
292.806
19.780
-0.658
8.171
0.7237 -0.0112
0.cITC90.1819
8.895
KIDRO- 0G AERODYNAIVflSK UNFAED DATA FOR OPEN WATER TEST
LAB0RARIUM
L.yngby Denmark28-12-1962
Page -Owr-2 Order no.6289
Model scale1/12.50
Propeller no.: No of blades6015
14 1Dynamometer no.: 12 Diameter : 2.1450 in
Temperature 114.8 oC Pitch at .7R :
1.730
inSubmerged
o,i8o
Pitch ratio :0.706
Length at.7R 1.1420 in
Develop area :
3.150
Density
101.87
kgxsec,42/z4J4 Disc area : 14.7114Order no.:
6289
Propeller no.:6015
Fairing no.: i
Lyngby Denmark
28-12-1962
OWT-3run advance thrust coefficient
coeff.
J
raw raw faired dif
torque coefficient
KQx01
raw faired dif
efficiency
Eff
raw faired dif
2
0.0278
0.2955
0.2980
-2140.3512
0.3535
-23
0.0373
0.0373
-1
3 0.051480.2952
0.2951
10.3527
0.3515
130.0730
0.0732
-2
140.0832
0.296140.2891
730.3527
0.31461 660.1113
o.iio6
7 50.1068
0.2809
0.2823
-114 0.336140.3396
-32
0.11419 0.11413 6 60.1317
0.2679
0.2735
-56
0.3228
0.3311
-83
0.1739
0.1731
8 70.1582
0.2614140.2627
18
0.3209
0.3206
140.2075
0.2063
la. 80.1858
0.2537
0.2503
350.3180
0.3081496
0.2359
0.21400 -14o 9 0.211450.2367
0.23614 30.2960
0.29148 120.2729
0.2737
-8
10
0.2360
0.2232
0.2255
-215 0.28146 0.28142 14 0.291460.2980
-35
110.2619
0.211470.2122
26 0.271400.2713
28
0.3266
0.3260
6 120.2856
0.191140.1998
-814 0.25014 0.25914-90
0.3147140.3501
-27
13
0.3103
0.1810
0.1869
-59
0.21435 0.21471-36
0.3670
0.3735
-65
1140.3360
0.169140.1736
-1420.2332
0.23146-13
0.388140.3958
-714 150.3690
0.180140.1569
236
0.2193
0.2190
3 0.14831 0.14206625
160.3933
0.11439 0.114149-10
0.2105
0.2081
25 0.14278 0.14358-81
17 o.14i6140.1315
0.1338
-22
0.1993
0.1981
12 0.143714 0.141476 -10218
0.1414300.1198
0.1214
-15
0.1879
0.1870
9 0.141498 0.14576-78
19 0.146870.1079
0.1097
-18
0.1779
0.1767
12 0.145250.14631 -106
20
0.1491460.0971
0.0983
-12
o.i68o
o.i668
12 0.14550 o.146140-90
21
0.5271
0.0831
o.o81414-12
0.15414 0.15147-3
0.14518 0.14575-57
22
0.5141140.0769
0.0783
-13
0.11491 0.114914-3
o.1414146o.14i14
-68
23
0.5660
o.o66i
0.0678
-17
0.1382
0.11403-21
0.14311 0.14355 -1414 2140.6091
0.0526
0.01492 3130.1307
0.1238
70
0.3898
0.3856
14125
0.6351
0.0367
0.0376
-8
0.1111
0.1131
-20
0.331410.3357
-i6
26
0.6622
o.146 o.146
00.0982
0.1009
-27
0.26142 0.25714 69 27 0.661470.0229
0.02314-5
0.0959
0.0997
-38
0.2529
0.2485
14528
0.6953
0.0109
0.0075
350.0830
0.08141-10
0.114580.0983
14x14 290.7237
-0.0112 -0.0099
-23
0.0709
0.06714 35-0.1819 -0.1525 -293
Root messi square deviation : Discarded poits after fairing:
15
0.3690
0.180140.1569
21560.2193
0.2190
3 0.14831 0.14206 625 Degree of Polynomial : Coefficients 0 2.97614-1
3.51914 10-1 18. oo66
-2
1.3158
-1
2 2.51489 -2.814214 13 14.51385.3050
L4.-2.6992
-3.2877
LABORAIJRIUM
Lyngby Denmark
28-12-1962
OWT-14run advance thrust coefficient
coeff. KT
J
raw raw faired dif
torque coefficient KQ101
raw faired dif
efficiency
Eff
raw faired dif
2
0.0278
0.2955
0.2970
-14
0.3512
0.5535
-23
0.0373
0.0372
1 15 0.051480.2952
0.2953
-1
0.3527
0.3515
13
0.0730
0.0735
-3
140.0832
0.2964
0.2900
65
0.3527
0.31461 660.1113
0.1109
14 5o.io68
0.2809
0.2832
-214 0.336140.3396
-32
0.11419 0.11418 1 60.1317
0.2679
0.2743
-6140.3228
0.3311
-8140.1739
0.1736
3 70.1582
0.2614140.2631
13
0.3209
0.3206
140.2075
0.2067
8
80.1858
0.2537
0.2501
370.3180
0.3081496
0.2359
0.2398
-39
9 0.211450.2367
0.2355
120.2960
0.29148 120.2729
0.2727
210
0.2360
0.2232
0.22141-9
0.28146 0.28142 14 0.291460.2962
-16
110.2619
0.2147
0.2101
146 0.271400.2712
28
0.3266
0.3229
37
120.2856
0.19114 0.19715-58
0.25014 0.25914-89
0.314714 0.3145717
13
0.3103
0.1810
0.1839
-29
0.21435 0.21471 -.350.3670
0.3677
-6
1140.3360
0.169140.1703
-9
0.2332
0.23145-13
0.38814 0.388140
160.3933
0.11439 0.11415 2140.2105
0.2080
25 0.14278 0.1425820
17
0.1416140.1315
0.1306
90.1993
0.1980
13 0.143714 0.14371 1418
0.144300.1198
0.1185
130.1879
0.1870
9 0.141498 0.14147127
19 0.146870.1079
0.10714 60.1779
0.1767
15 0.14525 0.451514-8
20
0.1491460.0971
0.0966
50.1680
o.i668
12 0.14550 0.14559-8
210.5271
0.08151 0.08314 -15 0.151414 0.15147-3
0.14518 0.14525-7
22 0.5141140.0769
0.0777
-8
0.11491 0.114914-3
0.1414146 0.141482-36
230. 5660
0.0661
0.0679
-17
0.1382
0.11403-21
0.14311 0.14358 -146 240.6091
0.0526
0.0501
250.1307
0.1238
690.3898
0.15921 -214 250.6351
0.0367
0.0386
-19
0.1111
0.1131
-20
0.33141 0.314149 -108 260.6622
0.021460.0255
-9
0.0982
0.1009
-27
0.261420.2667
-25
27 o.66L4.70.0229
0.02143 -1140.0959
0.0997
-38
0.2529
0.2576
-47
28
0.6955
0.0109
0.0076
3140.0830
o.0814i
-10
0.114580.0995
1462 290.7237
-0.0112 -0.0102
-9
0.0709
0.0673
1550.1819 -0.1753
-66
Root mean square deviation : T5T LL
No points have been discarded
Order no.: 6289 Propeller no.:
6015
Fairing no.: 2 Degree of Polynomial 14 Coefficients O 2.91465i
1.6755
2-3.11493
35. 8117
14-3.5708
_1-1
1.152733.5190
-2.8503
5.3220
-3.2992
-1
Order no. : 6289 Model scale : 1/12.50 Dynamometer no.: 12 Temperature : i4.8 oC Submerged : 0.180 m Density : 101.87 kgxsec42/iw414 Viscosity : 1.1147_6 n42/sec advance coeff.: J thrust coeff.: NT = torque coeff.: KQ = efficiency : Eff= v/(nxD) T/ ( rhoxn,2xD4.14) Q/(rhoxn,.2xD45) (J/2xpi)x (IT/KQ)
Lyngby Denmark 28-12 -1962 OWT- 5
Propeller no.: 6015 1 No of blades : Diameter : 2.1450 m Pitch at .7R : 1.7150 m Pitch ratio : 0.706 Length at.7R : 1.1420 m Develop area : 5.150 Disc area : 14.7114
rea ratio : o.668
thrust torque ist 2nd
load load basic basic
coeff. coeff. coeff. coeff
aT aQ bT bQ 15.1467 1.921 9.812 1.2148 6.505 0.851 14.1414 o.6o5 5.1014 0.1459 2.201 0.526 1.577 0.2148 1.154 0.190 0.812 0.1148 i.18o o.14i14 0.571 o.ii6 0.715 0.259
thrust load coeff. torque load coeff. ist basic coeff.: 2nd basic coeff.: 0.582 0.090 0.226 0.069 0.089 0.051 -0.038 0.0514 advance coeff. J thrust coeff. torque coeff.
