THE APPLICATION OF STATISTICAL METHODS
TO THE
ANALYSIS OF SERVICE PERFORMANCE DATA
By PROF. IR. J. W. BONEBAKKER, Member9th March, 1951
SyNopsis-Two main points are advocated in this paper:
I. Improvement of ways and means for collecting reliable and accurate records
of engine output, propeller revolutions and ship's speed through the water, under varying service conditions.
2. The introduction of statistical methods to the analysis of such data, in order
to limit their amount and to improve the reliability and accuracy of the information deduced from them.
Ultimately, the correct relation between power, revolutions, speed and apparent slip is to be ascertained for any set of specific external conditions likely to be met in service. If this aim is to be achieved without recourse to model experi-ments, it would take a ship's lifetime to collect the mass of basic information required for computing a "generalized power diagram". Modern statistical methods enable us to limit the amount of this basic information, and to reduce the set of curves of the generalized power diagram to a single straight line, even if more jàctors than those mentioned above are brought into the picture (for instance, ship's draught).
Service performance data of three actual ships are analysed to illustrate the subject, and sample calculations are given.
In Appendix A, brief reference is made to some aspects of screw propulsion
theory. First principals of mathematical statistics are treated in Appendix B.
I.
SHIPS
are sailing the seven seas, their displacement, trim and
propeller revolutions varying
according
to circumstances.Displacement and trim depend upon the amount of deadweight
carried.
Propeller revolutions, or rather the power developed by the
main engines, depend upon schedules, weather conditions at sea, and
degree of fouling.
The shipowner wants to be sure that his ship, over
certain ranges of displacement and engine output, maintains her speed
under various weather conditions at the lowest possible fuel
con-sumption. He wants to know what he gets in return for his fuel bill.
Prior to the building of the ship, her model will have been tested in order
to get the best combination of ship's lines and propeller
design. Theseexperiments give the relation between power and revolutions over a certain range of speeds, but at one draught only, and under ideal conditions (tank conditions). The next step is to check the tank tests by carrying out progres-sive measured-mile trials, preferably under conditions closely approaching those of the model experiments.*
DB
See B.S.R.A. Report No. 7: Code of Procedure for Measured Mile Trials, and Standardization
Ofcourse, model experiments and their counterpartmeasured-mile trials-are indispensable and invaluable, but they have nothing to do with the ship's service performance. A ship may he quite good on the mile and under tank conditions, but rather poor in service. We simply cannot judge, unless we have service performance data as complete, accurate and reliable as those derived from model experiments and checked on measured-mile trials under similar conditions.
Some shipowners have their models tested at an average service draught and trim, at one average service speed, with progressive overloads. These tests will give some indication ofthe service allowance on trial horse-power, but this allowance can only be very roughly checked after the ship has been com-missioned for a long time. From practical considerations it is impossible to carry out measured-mile trials under conditions similar to those represented by the over-loaded model tests.
An opportunity might occur, by chance, to verify the overload tests while the ship is in actual service. For this purpose " endurance trials" might be run. Such trials would differ in two respects from measured-mile trials,
namely
They would be carried out without interrupting and only slightly
retarding the ship's voyage.
The ship's speed across the water would be measured by the log, or any other speed recorder installed on board, without the aid of land marks.
But the same basic information is to be collected in both instancesspeed through water, corresponding revolutions and powerand the same recom-mendations regarding engine control settings, time recording, simultaneous reading ofrevolution counter and log, course keeping, etc., are to be strictly adhered to.
If it is agreed that such "endurance trials' can be achievedprovided that
weather conditions are not too adverse, and despite the inconsistencies of the
existing speed and power recording instrumentsthen such trials could be
repeated at different speeds and under various external conditions, whenever there is an opportunity.
The results of several "endurance trials " can be
linked up and extrapolated by applying statistical methods, and tabulated or represented in a diagram similar to Prof. Telfer's generalized power diagram. The present procedure differs from Prof. Telfer's in the following respects
I. It is believed that the statistical methods advocated in the following paragraph, applied to less numerous performance data, will give more reliable and accurate results.
2.
These results are based on service performance data only, without
recourse to model tests for the ship in question, nor systematic propeller experiments or experiments for ascertaining wake valuesthe sea being the laboratory for experimenting on a scale of 1 1.
As stated above, the shipowner wants to know what service performance he gets in return for the ship's fuel bill, but he simply cannot judge unless he has speed, revolutions and power data as complete, accurate and reliable as those derived from model experiments and fine-weather loaded measured-mile trials. His fuel can be wasted in several, ways : by deficiencies of the propelling machinery, or by unfavourable qualities of the hull or the propeller.
Fuel consumptions and speeds can only then be adequately judged when
they are accurately known for specified powers and revolutions.
Speedsthrough the water, with their corresponding revolutions and powers, are to be related to the specific external conditions prevailing at the time (wind and sea, degree of fouling, draught and trim) if we want to judge the vessel's seagoing qualities. Only thus can detailed quantitative comparisons be made between different ships.
APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCE DATA 279
The crux of the matter is always
"What power do we get for the fuel
consumed, and what speed is attained with this power under specified external conditions?
We are concerned with service data only. From speed through the water, propeller revolutions and propeller pitch the apparent slip can be computed. Apparent slip has found favour with seagoing engineers since the early days of screw propulsion ; it adequately reflects external conditions.
In the following the computation of the empirical relation between power, revolutions and apparent slip is treated, with reference to several ship's models, and three actual ships.
II.
Theory and practice prove that the power (d.h.p.) delivered by the propeller of a ship or a self-propelled model varies with revolutions cubed (N3), provided that displacement and propeller slip remain constant. Some time ago seven single-screw and four twin-screw models (see Table 1) were tested at the Wageningen tank on ordinary runs at progressive speeds, and also at one speed but with progressive overloads. Delivered horse-power (d.h.p.) and apparent
slip(Sa) varied over wide ranges. For each model d.h.p./N3 values for all runs
were plotted to a base ofSa, the spots lying approximately on a straight line
represented by the equation
d.h.p.1'N = a.sa ± b (la)
D.h.p., N andSa values were taken from the model tests, and the values of the
constants a and b calculated by the method of minimum squares (vide Specimen Calculation I).
The values a and b being fixed, d.h.p. was plotted to a base of 1V3(a.sa ± b). Now the spots lie almost exactly on a straight 45-degree line passing through
zero. This straight line is represented by the equation
d.h.p. = N3 (a.sa + b) (lb)
where d.h.p. = horse-power, delivered at the tail shaft,
Sa
= apparent slip in per cent.,
N = propeller revolutions per minute,
a and b being constants computed from the experiments.
The equations la and lb are plotted in Figs. l-8 for the models B, F, G
and H. Equations la and lb are correct on the assumption that the torque-constant Km, plotted to a base of speed-torque-constant A, is a straight line over the slip interval with which we are concerned (see Appendix A), implying a constant wake fraction over this interval.
In actual ships, shaft h.p. or
indicated h.p. is recorded instead of delivered h.p.
Consequently shaftfriction, or shaft friction plus engine friction, comes into the picture. If it is assumed that in both cases the torque required to overcome this friction is constant for all practical purposes, we can write
s.h.p. (or i.h.p.) = N3 (a.s0 ± c) ± b.N
= N3 (a.sa + b.N2 + c)
(2b)and s.h.p./Nori.h.p./N3 = a.sa -f- b.N ± c
(2a)(See Appendix B for standard equations from which Calculations I and Il are
PIO DEL EXPERIHEPITS TABLE i tQ TYPE EqL/ATION ER F pows $tl TER VAL NEAR POWER V(''v) InTERvAl. REIf IRTER VAI. S
lIA TER
"AI-B TW.SCR. DfiF. (o.IN)'(O.06655,+ 3.6140) 25 65.0 I.o 3092 - 10646 6381 ts.. 18 so.q
15l.i + 2.o_ 20.6 (ACH MODEL WAS
TESTED AT 011E DRAUGHT ONLY.
C 3.6CR. 0HP (O.lr1)'(0.000925+0.I636) 22 18.14 ¿.0 1911 1438 661 8_12 115.1- 200.0 ...68.7-. aa .b 5.SCR. OkP. (0.1 Nf (0.0214 S2.l4S9) q 14.0 0.3 1850 5650 3608 II - is 90.2- l29.' - 0.4 ._.I6.9 E TW.SCA. DHP (O.1ff)'4'O.1311 5A +5.881) 32 122.0 15 3533. 22611 9540 15 _l3.5
156.5 + 2.0 - 21i5 0M All EVEN AE-L
EACH MODEL WAS All AT /'ROGPESßIVE 5PEE05 WITH /f.P, l?EQIÌIREO POE Sfb P4016/LSIOIP RUr.41.50 AT OrlE SPEED WITH iNCREASING HP
.c .SSCR. D4P (o.IN)'(O. 000395# 0.0451) 13 2.6 0.14 14110.. 951 686 10.5-12.6 2125-. ¿69.7-3.6 114.1 6 TMSCR. DHP (o.lt1)(o.0.986 SA+5.519) 19 11.3.0 1.2 5003- U41453 9828 iS -.195 9q.s.. 128.9 s l.a - 114.6 H 5.6CR. O/AP..(oIN)'O.1159 SA#19) 22 514.0 0.7' 3a36_13859 928_ 4866 114591\ t 7753* 13.518.5 II - IS 6o.7_ 92.5 120.2-150.4 -'1.2-111 - S.o_ 12.8 J 55CR. DHP (O.II)t(o.00115S,,t0426) 12 9.0 o.? R tI. Okp (o.ltlJ'(O.OI3OSA,o.62'7) g 455.0 4.6 2776- 18286 941414 46-25 157 -215.5 j.7.5-... 18.0 L 5.5(14.
û/IP= (o.,t')'o.io17 5A7')
20 l5IO Lo 3670- 42722 7494 44-49 402- II7.
-.44- lt6
M 5.5(14. ¿1fiP ÇalN)S'0.004L4.S#O.37d) 19 ¿1.8 0.5 321 - 1597 959 9-14 9q.6_ 157.5 -i.8_ 114.6SEA VICE PERFORfIA/ICE DATA. 5/MOLE SCREW
GEARED TURS/ME STEAMER .7
(I'ISTA/ITAMEOUS RECORDS)
SUP 8V TOR5/O'IETER /'IEAN ORAl/OHr iNTERVAL ,l'c,"_28',o'
r
.s.sj S(oJpi'(o.O1u1sA-44.m6 SHP.4o.lr)'(o.oeooS,fno8,-I-1+6.9144) 25 32 65 .1414 S.l 1.9 1210.. 2.720 1240_3000 ¿063 23145 9.2_133 9.0_l2.5 56.4 _19'.0 552....114.a 14.1 11.5 33.0 208 BALLAST LOADED T' SSCR.I T S.ScR.JsHP(olrY)'(oo'rn5S,,sI2soN'.O2tST45.2.l) 57 514 2.11 1210 _3000 2226 9.o_is.s 55.2.... 714-2. ...4.I - 20.8 SA&LASTI-LOAOEDSERVICE PERFORMANCE DATA.
TWIN SCREW MOTOR VESSEL ,,A
(INSTANTANEOUS RECORDS)
DERIVED FAO/I RECORDED
¡HP ay APPLYINQ
crr/Cl2wCIEs(",') ASCERTAI,IED ON THE TEST SED ORAl/ORT AFT'
INTERVAL Z3''.. 30'8' A TW.SCR. ¡RP=(OIN)1(O.0311S,,+ 214300N"A4.O78) 314 288 L? 7611. - 13350 loT 18 16.8_19 :05.0- 33.4 -+&41__..a1.2. A TW.SCR. (0.lI(O.0369S+ 89OOt'r+3.91Ll 514 266 3.1 5786_ 10966 5O i.8_i9 loSO- 135.14 +8.4-21.2.
SERVICE PERFORMANCE DATA, TWIN SCREW MOTOR VESSEL
,is'
(24 HOuRS' AVERAGES) DRAUIHT APT
irIrEE VAL
25'é'_ 316"
R TW.SCH.J IHP. (0.1fA,)1(0.0112O5,,f ra473/V'4.1.C)J
81 J 322 J 159 J '1483 -9020 ¡ 6522. j 42.17 89.1 ._ 441.2. ¡,u.q - 16.4]
APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCE DATA 281
Single-Screw Turbine Steamer T.
In 1923, accurate observations were made on board a single-screw turbine steamer, under average service conditions, both loaded and in ballast. Each set of observations comprised
S.h.p., based on torsionmeter readings, the instrument being placed in the thrust block recess.
Propeller revolutions per minute. Log miles.
From 2 and 3, and the propeller pitch, the apparent slip was calculated. Actually, the propeller's diameter and pitch were l8ft. 6m. N and Sa were computed from readings taken exactly simultaneously with an hour's interval, or taken as the mean value of several observations made during a longer period
while the engine torque was kept as constant as possible.
Torsionmeterreadings were taken regularly in the meantime, and average s.h.p. calculated for the corresponding time interval.
Applying multiple correlation calculus to these observations (vide Specimen Calculation II), the coefficients a, b and e of equation 2a are found. Finally, s.h.p. as recorded is plotted to a base of [a.s0 + b.N2 ± c] N, which might be called "s.h.p.-computed".
The results are shown in Figs. 9 and 10, and in Table 1, for ballast and loaded voyages separately.
In each case the spots should lie approximately on a
straight line under 45 degrees, passing through zero. Whether the approxi-mation achieved is more or less close can be appreciated numerically by com-puting the "mean deviation" F, expressed as a percentage of the average s.h.p.
F=
& being the difference between "s.h.p. computed" and "s.h.p. recorded ", and n the number of observations (i.e., the number of spots in the diagram).
TABLE 2-Single-Screw Geared Turbine Steamer "T"
N V N V G 7 s 6 6 7 8 40 11.3 1432 1478 I 525 1571 60 10.8 1480 1526 1512. 1619
I
11.5 1502 1551 1599 1648 6.1 11.0 1363 (601 f648 1699'a
11.7 1572 1623 1'76 1726 62 11.1 16.26 1677 1728 1179 63 11.9 1649 F103 f156 1810 63 11.3 1705 1759 1.3 ia 1866'4
2.1 1726 twa 1835 1896 1 LS f840 1896 1953 65 12.3 8 o 1868 1927 1986 65 11.7 1870 1929 1985 204 '1 6.6 12.5 1886 19 'ii 2009 2070 46 11.9 1950 2011 ¿073 2134 6.7 12.6 ISiS ¿040 2104 2169 67 12.0 ¿092 ¿loi ¿171 2236 68 12.8 2057 alas 2(92 2260 68 12.2 ¿127 2195 2262 2330 69 13.0 2153 ¿224 2254 2365 69 12.9 2227 2298 2368 ¿Ai 3$ 70 13.2 2242 ¿31G 2389 246.3 70 12.6 ¿319 ¿393 ¿q66 2540 71 I 3.4 2338 ¿415 2491 2568 7g l2.8 2418 ¿495 2512 2648 72 13.6 2q33 25132593 73
72 12.9 ¿516 2696 ¿6.77 ¿756. 73 13.8 2535 ¿GIS ¿704 2784 7 15.1 2706 2783 2872 7 14.0 ¿637 2811 2898 7 13.3 2727 ¿814 ¿900 2988 7 142 ¿746 283G 292G 3017 75 u,.s ¿835 2930 3020 3111 (a) (b)TABLE2-Single-Screw Geared Turbine Steamer
"T"-(contd.)
SAS 5% 5A 10% N V 6 TA N V TA 7 e s 6 7 8 3 60 1528 167 1 1621 7667 60 44.7 ¡576 1622 r6 69 1715 61 70.44 16044 1652 7699 1744 7 61 9.9 16544 1703 7751 ¡800 62 10.6 7679 1730 1781 7832 62 70.0 1731 182 18344 ¡335 67, 10.8 1 761 1816 1868 i9a2 63 ¡o-2 1876 1870 *925 ¡977 644 10.9 ¡8443 1899 ¡955 ¿01f GLi 0.3 ¡90* ¿951 ¿015 20705
11.1 1932 1991 2050 2109 65 70.5 1993 2052 2110 2,70 66 11.3 ¿0144 ¿075 2131 ¿198 66 70.7 ¿017 ¿738 ¿20° 2262 61 17.4 alo g ¿ I 744 2238 2305 67 *0.8 2776 22441 ¿505 2570 68 11.6 2797 2265 ¿532 24400 66 7.0 22'7 ¿335 2902 ¿4469 69 11.8 2300 2311 ¿44 ¿4 1 25la 69 II2 ¿373 ¿44 1 'i 25I4 2685 70 ¡ ¡.9 2596 a5qa ¿'16 70 11.3 24471 ¿5445 2618 2692 71 12.1 24497 ¿5744 ¿'SI 2728 71 IL 5 2571 ¿731 2601 72 12.6 2599 261.9 ¿760 28'i o 72 1L6 ¿682 ¿762 ¿8443 2922 73 12.5 ¿709 ¿792 2816 2969 73 ¿1.8 2795 ¿878 2962 00445 744 12.6 2518 2905 ¿991 3078 7L 72,0 ¿907 29941 3080 3168 75 12.8 2933 3024.1 37144 3205 75 12.7 3027 3716 3208 3299 (c) (d) SA IS % = 20% 11 V N V TA 6 7 8 9 6 7 B 90
9.2 16244 1670 ¿777 ¡763 60 8.6 1612. 7718 1765 ¡8711
9.3 I-705 175'i 7802. 1851 61 8.8 7155 78044 ¿352 190f2
9.5 1785 836 i888 1939 62 8.9 831 I 888 15410 19975
g. & 1872 7926 1979 2033 63 3.1 1928 1982 2035 2089 44 9.8 1959 2016 2072 2128 644 9.2 2017 2073 2130 2186'ç
99 ¿o s 2111 2172 ¿237 65 9.3 ¿ils 21744 2233 27.92 66 10.7 ¿1441 2202. 2264 2326 66 9.5 a ¿os 2266 2328 2389 67 70.2 22443 2308 2372 2967 67 9.6 ¿7,10 2375 2459 25044 65 70.44 2337 24472. ¿5440 68 9.8 ¿4407 24475 2542 26109
0.6 24144G 251 1 2587 ¿658 69 9.9 ¿519 2590 2650 ¿731 70 ¡0.7 25448 asaz ¿695 ¿769 70 10.1 ¿62M ¿698 2771 259G 7* 10.8 2657 213f 2810 2887 71 10.2 273G ¿813 ¿389 2966 72 11.0 2766 28445 2926 3005 72 10.3 2848 ¿928 s002 3089 73 7.7 ¿882 ¿Sos 3153 73 10.5 2962 3052 3135 3219 744 1.3 2398 5085 1172 3259 744 10.6 3 aSS 3115 3262 33449 75 ¡1.5 3*21 3212 3302 3395 .75 70.8 3215 33o6 3396 34487 (e)(f)
The equations for the single-screw turbine steamer under consideration are for loaded voyages :
s.h.p. = [00600 Sa + 1108 N2 + 6946] (0 i N)
the mean deviation being i 9 per cent.;
and for ballast voyages :
s.h.p. = [00417
Sa+ 80N2 ± 6736] (0 i N)3,
the mean deviation being 3 i per cent.
APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCEDATA 283
Substituting in these equations any combination of N and Sa likely to occur in actual service, the corresponding s.h.p.'s and speeds can be calculated, and the results either tabulated or represented in a generalized power diagram.
This example shows what can be achieved if the observations are taken accurately and in the right way. Revolutions ranged from 55 2 to 74 2, s.h.p. from 1210 to 3000, slip from 4 1 per cent. to + 208 per cent.
With single-screw ships, especially those with large slow running propellers,
the ship's draught has a marked influence on
performance. Hence thedifferent equations for loaded and ballast voyages.
However, they can be
combined by writings.h.p./N
=
(a.sa ± b.N ± c.T-+- d)
The coefficients a, b, c and dare again found by applying multiple correlation
calculus. It should be noted that in this case the "mean deviation is
repre-sented by
F=
Actually the equation becomes
s.h.p. = L°°445 a
+ 1250 N ± 02l45 T ± 52l8] (0 1 N),
T being the mean draught, and F=
24 per cent.(see Fig. 11, Table 1, and Table 2 a tof).
The deviations can also be appreciated from Table 3
TABLE 3Total Number of Sets of Observations (Each Set Comprising Simultaneous Values of s.h.p., N, Sa and T) 57
=
100 per cent.Twin-screw motorship A, log abstracts. (No model experiments with progres-sive overloads were carried out.)
V
=
l375 to 19 knots;
T
=
23ft. 8m. to30ft. 8 in.;
D
=
propeller diameter 4 800 metre, pitch 4 900 metre. Number of observations per engine 17, or 34 total. i.h.p.=
7600 to 13360 ; mean ± 10800 (metric units). Equation00371
24,300 N2 ± 408.
(Table I and Fig. 12).Number of Observations Range of Differences Between Minus and Plus Absolute In per cent, of Total
21 36.8 20 s.h.p. 31 54.4 40 42 73.7 60 49 86.0 80 53 93O 100 57 100.0 120
The engine efficiency = b.h.p. /i.h.p. was ascertained on the test bed over a wide range of powers. 1.h.p. can be converted into b.h.p. as follows
TABLE 4
The equation becomes b.h.p.
(0-1 N)3
00369 Sa ± 8900 N ± 3-91.
(Table I and Fig. 1.)The percentage differences between i.h.p. (recorded) and i.h.p. (computed) can be summarized as follows
TABLE 5Total Number of Observations 34
Number oJ Observations Absolute In per cent of Total
lo 24 33 29 71 97 Range of Differences Between Minus and Plus
i per cent. 3 per cent. 5 per cent.
+ 5.4 per cent.
Twin-Screw Motorship B.
L Model experiment r, carried out at the Wageningen tank Self-propelled tests
V = 13 to 18 knots.
P = 3100 to 10,000 delivered h.p. (tank conditions). Overload tests
V = 16 knots
P
4200 to 10,700 delivered h.p. (tank conditions). Total number of observations 23d.h.p. (mean) = 6380 Equation:
(0 iN)3 -
0 0665 a ± 3-64, see Figs. I and 2.Power Developed
(metric units) Logbooki.h.p. B.h.p.
maximum
..
..
13,360 0.82 10,960mean ..
..
..
10,800 0.80 8,660APPLICATION OF STATISTICAL MSTHODS TO ANALYSIS OF SERVICEPERFORMANCE DATA 285
2. Log abstracts:
V = 12 to 17 knots; Ta = 23 ft. 6 in. tO 31 ft. 6 in.
D = propeller diameter 4' 588 metre, pitch 4- 761 metre. Number of observations 81 (mean values ofF and SBengine)
i.h.p. = 4200 to 9000; mean ± 6500 (metric units). Equation:
= 0O42 Sa 12473 N2 + 4'366 (Table 1 and Fig. 14).
The percentage differences between i.h.p. (recorded) and i.h.p. (computed) can be summarized as follows:
TAB LE 6Totai Number of Observations 81
-Comparison between model experiments and log abstracts, twin-screw
motor-ship B.
For this vessel, the regression equations are
d.h.p. = (O' i N)3 (0 0665 Sa ± 3 640), from model experiments, and i.h.p. = (01 N)3 (0'042 Sa + 12473 N2 H- 4-366), from service data.
1f we substitute, for a range of speeds, the values of N and Sa from the model experiments in both equations, a comparison can be made between d.h.p. (delivered horse-power) and i.h.p. (indicated horse-power), both under tank conditions:
TABLE 7
Neglecting scale effect (if any), the figures in column (6) represent the total mechanical efficiency, including shaft friction.
Number of Observations Range of Differences Between Minus and Plus Absolute In per cent, of To tal
9 11 1 percent. 20 25 2 per cent. 39 48 3 per cent. 52 64 4 per cent. 58 72 5 per cent. 65 80 6 per cent. (1) V (2) N (3) Sa per (4) d.h.p. (5) i.h.p. (6) d.h.p./i.h.p. (7) s.h.p. (8) s.h.p./i.h.p. cent. 13
904
8-3 3,092 4,612 0670 3,390 0735 14966
7-6 3,727 5,426 0.687 4,046 0.745 15l028
69
4,443 6,338070l
4,782 0755 161l08
79
5,654 7,771 0728 6,020 0775 17 12O499
7,486 9,845 0760 7,883 0-800 1813l4
126 10,142 12,745 0796 10,576 0830Assuming about 400 h.p. for shaft friction at 17 knots, or shaft friction
h.p. = 33 N, columns (7) and (8) can be computed :
(7) = (4) + 33 N.
The figures in the last column represent the mechanical efficiency of the main engines at various revolutions ; these figures are in close agreement with those ascertained on the test bed for the engines of ship A.
The assumption about the absence of scale effect requires qualilication. Probably there will be some scale effect between model screw and full-size propeller the latter may have some 5 per cent. higher efficiency, but the roughness of the full-size propeller's surface will counterbalance this gain.
For twin-screw vessels there will be no question of scale effect affecting wake, because the screw discs lie outside the frictional wake belt.*
It will be noted that there is an appreciable difference between the coefficients preceding a, i.e., 00665 (model) and 00420 (ship). This may be due to the slip interval in the A Km diagram (Fig. 15) not being the same for model and ship (cf. Appendix I), but this is a mere conjecture.
IV. Concluding Remarks
From the three examples it is apparent that the best results were obtained in the case of the turbine steamer's log abstracts of 1923.
This is due to the
following:
The observations were made by experts and carried out with greatcare and accuracy ; the torsionmeter and the ship's log of 1923 were in no way superior to those of to-day.
The observations were made simultaneously ; if 24 hours' mean values
of r.p.m. and log readings had been combined with haphazard torsion-meter readings, these observations would not have fitted together" so
nicely.
It would be best to register continuously both r.p.m. and distance by log to a time basis, and to time accurately the moments when torsionmeter readings or indicator diagrams are taken. Revolutions per minute can beand should
berecorded with an accuracy of 05.
At the present time log readings maybe less exact, but their influence on the results of the calculations is small.
Nevertheless it will pay to improve the accuracy of the ship's log and the
torsionmeter.
It is advisable to reproduce the basic data in diagrams. i.e., power/Ne to a
base of Sa. Observations whose spots wander rather off the mark should be re-examined, and often the causes rendering them useless will become apparent. This sorting out before the statistical calculations are started should be done by someone well acquainted with the intricacies of ship propulsion.
In the second example giventwin-screw motorship Athe number of sets
of observations was only seventeen per engine, or thirty-four in all. It seems probable that the required basic information could be substantially restricted provided that the observations are collected by experienced men using reliable and accurate instruments. It might be good practice to run a few "endurance trials" within a wide range of speeds, powers and revolutions; for instance, at 05, 075 and l0 normal service h.p., and at apparent slip values between 10 and 20 per cent. Similar runs could be carried out with ship's models in the experimental tank, and the resulting equations compared. Measured-mile
triaisexpensive in time and moneymight be dispensed with altogether.
For it will be easier to predict a vessel's fair-weather performance from her generalized power diagram, than to predict her performance undera particular set of external conditions from her fine-weather measured-mile trials.
APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCEDATA 287
It is believed that the procedure as advocated is the best way
of" calibrating"
a ship and her propelling machinery.This means that the exact relation
between speed, power and revolutions can be computed from a limited amount of service performance data, provided that these are collected in the correcway. As the ship is calibrated without reference to modelexperiments a fair
comparison can now be made between her tank tests or fine-weather measured-mile trials, and her actual performance under any particular set of external conditions. Hitherto such comparisons were mainly restricted to average conditions over long periods. It is essential to be sure about the exact relation between speed, power and revolutions under any particular set of external conditions if the vessel's sensitiveness to adverse weather conditions, her sea-kindliness, the merits of dillerent propellers, alternative rudder designs, etc., are to be assessed fairly.
Acknowledgement
The Author wishes to acknowledge, with thanks, the assistance received from the Delfts Hogeschool Fonds*, which enabled him to get the investigation started. He further enjoyed the valuable co-operation of several shipowners, the staff of the Wageningen Tank, Mr. Erlee of the Statistical Department of the Organization T.N.O., and the Author's assistant, Mr. Gerritsma.
Further investigations will be carried out under the auspices of the Studie-centrum T.N.O. voor Scheepsbouw en Navigatie," the Dutch equivalent of the B.S.R.A.
APPENDIX A
Notation: I.
Km = torque constant of the screw
M = torque on the screw D = screw diameter
N = revolutions per minute of th& screw
n = revolutions per second of the screw
H = face pitch of the screw
= nominal slip of the screw (calculated by using face pitch) Sa = apparent slip of the screw
wake fraction
A = velocity coefficient
p = density of fluid V ship speed in knots
V, = intake velocity for the screw in m sec' P = propeller horse-power
lt is assumed that a linear connexion exists between
M
Km
pD5 n2
and
A =
represented by the equation
Km = - a
A +bWhether this assumption holds good can be verified by considering the diagrams of the Wageningen B-series of screw propellers. The slip interval with which we are
concerned in actual practice is small in comparison with the total range of the diagrams. Generally speaking, the curve is almost straight, as illustrated by propeller B 3.50. But there are exceptions, as shown by B 44Ø*
The following deduction proves our case:
V v,H
H
A=
= nDH
=(l -
s,7)--consequentlyK,n(ls,,)+b=(s,,+l)a
or [C = (s,, + p)q, bD aHp =
- I and q =
D being constants.On the other hand
Sn Sa (1 - i,') + SO
Km = Esa(l - )+ 'fr +pq = (Sa +
(1 -
)q.or Km (Sa + p') q'
p'
and q/ = (1 - iJi) q being constants.APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCE DATA 289
In metric units we can write
M 75F pD5 n2 2np Dò 4 or
-
2iïpD5N3Km - C Km N3,6Ox75
Hence: P = CN3 (Sa +p')q'
= c' N3 (Sa ± p')I'.
In actual ships, shaft horse-powers or indicated horse-powers are recorded instead of P. This leads to the following extensions of the last formula:
i.h.p. = P + P(shafting) + F(engjnes) and s.h.p. = P + P
P3 and F9 being the power required to overcome shaft and engine friction.
We assume that the torque required to overcome friction is constant. This will be almost true over the range of revolutions with which we are concerned in practice.
When this constant torque is represented by Q, then we may write (metric units):
2iQ.N
fnction horse-power = P5 + P? = 60 x 75 = b N,
b 2ir being a constant.
Hence:
i.h.p. = C1 N3 (Sa ± p1) + b N and s.h.p. = c1 N3 (Sa + p') + b' N
The original equation was P = C1 N3 (sa + pl),
aH
c1 being = Ca! = c(l - fr)q = c(l - t)
bD
and p' =
± '
, pbeing a constant =- i.
consequently, C' and p' are constants whensfris constant.Neglecting the influence of fouling (which means neglecting variations in r on
account of variations in frictional wake), s/c varies with T. This gives an opportunity to bring draught T into the picture.
aH
cl=c(ly)
D=(l!fr)A
bD bDIs/c
ÏI
B-
l
l_+l__l_fr
A[lfr(Sa+
BA(l)Sa±ABA(ls/i)
A(l
s/i)Sa±ABA+A!f
A'Sa+A'fr+C
CABA
Km 2ir pD C = x 75 being a constant.Variations in A (I - SIr) can be neglected, because the relative influence of the term A (I - /I)Sa is small. Hence we may assume A (1 - = A' constant.
At constant ship speed, P will vary with draught T; but variations in P involve variations in propeller load and in effective 'r. We cannot record variations in
effective t(r, but we canrecord variations in draught T. Substituting T (or Ta in particular) for 1,we can write
i.h.p. (or s.h.p.)
= cash) + yTa + 8'.
N
, y and 8' being constants.
8' can sometimes be split up to advantage into ßN'- + 8 (see formulae III and IV in
the text).
APPENDIX B
Derivation of the multiple regression formula
Given is a set of n observations y being empirical values of a variable y*:
vax+bz+c
(1)The values x, z are given (observed).
The coefficients a, band c are to be calculated in such a manner that the values of y calculated from the formula differ as little as possible from the empirical values y.
"As little as possible" is mathematically specified by the postulate thatE (y y*)
= E (y* - y)2 be minimum; the summation is to be made over the n observations. Substituting formula (I) in our postulate we find
V =E (ax + bz + c -y)2 be minimum. This reduces to
V=
Ea2x2 + Eb2z2 + Ec2 + Ey9+ 2Eabxz+2Eacx+2Ebcz
[2Eax.v+2Ebzy+2Ecy]
or
V= a2 Ex2 + b2Ez2 + nc2 + Ey'
+2abExz + 2acEx + 2bcEz
- 2aExy +bEzy
+ CEy] (2)This formula can be simplified by measuring the variables about a convenient zero point, viz., the arithmetic mean.
So
Ey=0
Ex = O
Ez =0
Formula (2) then reduces to
V=a2Ex2 +b2Ez2 + Ey2+
nc2APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCE DATA 291
During the computation a, b and e are to be considered as variables, because we must satisfy the minimum condition by choosing these coefficients. For this it is
necessary that the partial derivatives with respect to a, h and c be zero, thus
a X2 + b
xz -
xy = O=axz±bz2 -
yz=O
2cn=0
c=O
This gives two linear equations which are to be solved for a and b. i.h.p.
= aSA + bN + C.
In our case (O IN)
Substituting the mean values of i.h.p.
SA and N-2 gives C (O.IN)3'
(namely, Specimen Calculation II). A similar derivation can be given for the general equation.
y1 = a + a1x1 + a2x2 +
The standard equations are then
etc.
The Specimen Calculations I and II are special cases derived from these standard
equations. a1 x1 + a2 x1x2 + a3 x1x3 + :: x1y a1 x1x2 ± a2 x7-1 ± a3 x2x3 + x2y a1 x1x3 + a2 x2x3 + a3 x32 + x3y 3V ôa 13V
p =y
(o.IN)l 5Ak!±Y
rl s =x ft. n r1a ¿ n X _X n a = Z x 1. xLbics
F 1? aSA4b COIN SPECIMEN CALCULATION IF Zy Z,zacztbz2
c? _ci.-b
SPECIMEN CALCULATION I DHP ECOl-IP) nflj
_(Ie-4P) n DHP i a 3 ¿1 5 6 7 6 9 lo ii ta 13 i'i 's0:0
®.1?®-®a 0h ®® ox® ®b Ox® 0-0 0'
NO DJ.IP (oIN)3 Y c y'-q5 0S,b DHP1 £ 6'-pl (OHP) V( Z) ZY'- Ix'-Ixy r 3 5 6 7 8 9 10 II IL IS ¡5 IS Ii 18 20 ®-g ®h ® O'-®A® ®*® 0*0 ax® bx® Ox® ®® O'--'10 Il-tP (0th)1 5% N'-j z y'-x1 j1 ix yz xi q5 br-IHP, L n lOuP)
IY
IX IZ
lyx Iyz
Zxz F' f4P
n-APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCE DATA 293 Z.t .onass..ss,a CC Fig. I Fig. 3 Fig. 5
/
Fig. 2 Fig. 4 Th.(Oflf(O S&s.ts,S) Fig. 6 M-./
jjjjï
Fig. 9Loaded
Fig. 10Ballast
jjjjj.
!III1IIIII
APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCE DATA 295
Fig. 11Ballast and Loaded
SHP.(O. N)'(O.ø395_ 8gOOM,S.S!'
Fig. 13 Fig. 12 P.)tlNf)&O4Sk.IZ5OH*OJl(5T* 521e) oP.(o.0 10.037,S, S00fl-.. 010) P :
-Fig. 14
'L
The PRESIDENT (Sir Philip B. Johnson):
We are all agreed that the analysis of
actual ship performance in service as
corn-pared with the information we are able
to obtain from model experiments is of the
greatest importance, and any paper
con-tributing to this subject is of great interest to us. ¡ was interested
to note that
Professor Bonebakker makes a point in his paper which is confirmed by my own
experience, namely, that one of the greatest difficulties in analysing actual performance
is to get really accurate basic data. I gather that in his experiments he has found
this to be the biggest stumbling block. A
study of his paper and the methods which
he has employed will be of great interest
to those whose special business it is to make
a study of this problem, but for myself I wish that in the course of explaining his paper he had given us a more complete
description of the application of his methods to the diagrams which he includes. Possibly
during the discussion somebody may ask
questions which will elucidate them more fully.
Prof. L. C. BURRILL, Member of Council: I am entirely in agreement with the aims
set forth by Professor Bonebakker at the beginning of his paper. The analysis of service or trial data is to me the correct
means of assessing propulsive performance, and my experience has been that if sufficient information is available, and it is carefully analysed, a great deal can be learned from
these ship data. Those who would reject
the ship data on the ground that they are not sufficiently accurate are, I think,
rejecting the criterion by which they are
ultimately judged. It is of no use to say that a good result was obtained on the
model if the ship is not doing well. In my
view, therefore, any effort which can be
made to reduce the question of dealing with
the rather scattered type of data obtained
from ships' logs to a routine method is well worth while.
Paper by Prof. Ir. i. W. Bonebakker, Member. (See p. 277 ante.)
22
DISCUSSION ON "THE APPLICATION OF
STATISTICAL METHODS TO THE ANALYSIS
OF SERVICE PERFORMANCE DATA"
*There is in this connexion one fortunate circumstance. It is the propeller, and only the propeller, which determines the
relation-ship between power and revolutions at a given speed, and therefore a study of the behaviour of the propeller is sufficient to
correlate the power records, under different conditions of slip. It is usually accepted
by engineers that the is constant, and
I would use that relationship as a first approximation for determining, say, the i.h.p. for the day, from the indicator card
records, when the revolutions for the card,
and the revolutions for the day differ slightly, on the grounds that the slip for the day is likely to be constant. Un-doubtedly, as the slip changes thenthe1 will undergo a corresponding change, which can readily be ascertained from the normal
propeller diagram in which KQ is plotted
V
to a base of J =nd
Professor Bonebakker has chosen appar-ent slip rather thanf for his investigations. but this dces not materially affect the issue.
It is evident that which is a function
N3'
KQ, diminishes linearly with slip, and diminishes as - increases.
The second approach, therefore, for a
small variation in revolutions is to assume
that . x = constant, at the normal
n3 n
working slip. As a third approximation,
the proposal made by Professor Bonebakker takes the matter a step further, as he obtains an expression for - in terms of a linear
equation using apparent slip and N-2 as variables, the constants being determined
by means of statistical methods.
The question which arises is, whether he can obtain a better result in this way, than
an informed naval architect or engineer can obtain by judgment, in plotting against _!. In fact, I think the "nub" of
this paper lies in the sentence which appears on p. 286, where he says that it is advisable
that the sorting Out must be done by someone who is well acquainted with the
intricacies of ship propulsion. This remains to be proved by experience.
One advantage of adopting the plotting of KQ against " j" (or
against_) is
that it readily gives the analysis-wake, andmy own experience has been that the
analysis-wake factors obtained in this way from the examination of ship data are much more consistent than the tank wake values,
and can be used satisfactorily for design
purposes.
The analysis wakes obtained from a
number of readings are usually very steady,
and I feel that the determination of the analysis wake factors is, if anything, a
better means of controlling the final result
than the statistical analysis method.
In the above, I have made no reference
to the frictional torque in the shafting, as a figure of something like 97 per cent is used to determine the d.h.p. from the recorded b.h.p. values. Professor
Bone-bakker has made no such allowance, and,
as a consequence, he obtains a term in N-2.
I should be interested to know whether from the constant he obtains he can work
back to the shafting efficiency, or whether on the other hand the use of d.h.p. instead
of b.h.p., making an allowance of say 3 per cent for frictional torque, would
eliminate the N_2 term.
This paper is an attempt to introduce statistical methods in place of the usual procedure adopted in this country of plotting curves through a seiies of spots, and if it can be shown that this leads to more consistent results, or can be applied
when few spots are available, it represents a
definite advance, and I am sure it
is a
method that will be of great interest to those who are analysing ship data as part
of their daily task. It is a very unfortunate
fact that by the time a man becomes
competent to analyse ship data, and is fully acquainted with the intricacies of
ship propulsion," he has probably reached such a position that he is wasting his time
financially to do this kind of work. Any
method that would lend itself to a routine procedure which can be carried out by
less fully-trained personnel would therefore be of considerable value.
Mr. J. W. COMMON, Associate A: I am not a technical man and, therefore,
cannot possibly judge the merits of the
various methods of ascertaining the
technical efficiency or economy of one
vessel as against another.
There is, however, one point brought
out by Professor Bonebakker which interests me and about which I have some knowledge. He insists that the data
obtained must be accurate and reliable, as
accurate and reliable as that taken for
model test and trial trips. Now, I would
suggest that these data cannot be obtained
by shipowners from their sea-going
per-sonnel. I am afraid that it is a fact that most sea-going personnel are indifferent to this sort of thing. Our experience as shipowners has taught us that many of the
technical data asked for are inaccurately
supplied and of little value.
I would suggest, therefore, that if these technical data are to be really accurate
and reliable they should be taken either by shipbuilders' technical
staff or in
this country by such institutions as the B.S.R.A.or National Physical Laboratory. I have no doubt that there are many difficulties in the way of this, but, nevertheless, I am sure that it is the only way of getting the
information required.
Mr. W. MUCKLE; Member of Council; The subject of this paper is an interesting one to all naval architects and it is pleasing
to know that the Author is in favour of using actual full-scale data in assessing performance. With regard to the use of statistical methods for analysing the data, is this only intended to correct for errors in the observed data? In other words, if
the observations were all taken with a very high degree of accuracy, would they all lie
on a single line or would there still be a
scatter of the spots? This is a point upon
which I am not clear but it would seem possible that for given revolutions and measured power the propeller may work at different slips depending upon the external conditions such as the state of the
sea and the motion of the ship. This brings me to the question of the
relation of model experiments to the actual full-scale results. It is noted that the
over-load model tests gave different results from the full-size observations. Were the model
tests made in still water or amongst
artificially created waves? If the former, then it would appear that the model and ship would be working under different
conditions and the motion of the ship may account for the different results.
The Author's method establishes a
APPLICATION OF STATISTICAL METHODS TO ALYSIS OF SERVICE PERFORMANCE DATA Dl 17
slip for a particular ship and presumably
the relation will hold good for that ship in
a particular condition of loading, for all
external conditions. How does the Author
relate the performance of the ship to the
external conditions? It would seem neces-sary to have records of weather as defined by the state of the sea and the wind speed, etc. so as to determine the weather intensity and then relate this tod.h.p/N3or to slip.
Dr. O. KANTOROWICZ,
Associate Member:
The analysis of any set of correlated readings is greatly helped by plotting on double logarithmic paper. This is due
mainly, I think, to its property that equal
percentage variations appear as equal distances. Therefore, when denoting a
reading not by a mere dot but by an area the height and breadth of which corre-sponds to the estimated percentage of the probable error of abscissae and ordinates it will often be possible in drawing inter-pretation curves to draw a best fitting curve without going outside the range of
error of any reading. Furthermore, if the
law which the readings should obey is
already known, then it is also known what
slope an interpretation curve should have when drawn on log-log paper, and this
helps in fitting curves, or indeed makes it
possible to draw them when the range through which a parameter is varied is
small.
A further trick, useful particularly if the law is not known accurately, is to tag each
observation by a number, a letter, or sorno other symbol and to seo whether different
interpretation curves would fit a different kind of observation better. In this way
very complex observations, with many and
often ill-defined variables can be broken
down economically and rationally in
successive stages of approximation until
the law is revealed.
Numerical analysis as used by the Author is in my experience only rarely required in engineering research. Before doing a full,
rigorous analysis I usually try to restrict myself to the use of probability paper,
which not only shows at a glance the most
probable mean value and the degree of certainty attaching to it, but may also
reveal parameters which are hidden in the general scatter.
VOTE OF THANKS
The PRESIDENT (Sir Philip B. Johnson):
I think we owe our thanks to Professor Bonebakker for giving us a paper which describes a new approach on a subject
which is of the greatest interest to us. As
Professor Burrill has said, it is a paper of a highly technical character and will be
primarily of interest to those people whose
particular job it is to make an analysis of
ship performance. I am quite sure when such people have had an opportunity of making a full study of the paper they will consider it of very great value and a most
important contribution to the Transactions of our Institution.
Mr. K. C. BARNABY, Member:
It would be most unfortunate if Professor Bonebakker's remarks at the top of p. 278
were to be taken seriously. They imply that service performance cannot be estimated
from model experiments, but can only be
ascertained from actual service results. If
this were true, few shipowners would think model experiments worth-while. Fortu-nately Professor Bonebakker's remark that "model experiments . . . have nothing to do with the ship's service performance "is com-pletely wide of thc mark. Unless the ship is a rather exceptional type, Tank authori-ties can, and do, predict with very consider-able accuracy the service performance. In fact, if there is a considerable discrepancy
we should first examine the reported
service performance as being far more likely to be adrift. Were the speeds and powers properly recorded? Was all the fuel really being burnt under the boilers
or was there a "disposable" surplus?
Even the revolutions are sometimes suspect, instances of incorrect gearing to the counters not being unknown.The types that are most likely to show divergence from tank scale to ship scale
are vessels of very full block coefficients, say O75 and over, and small ships running at high speeds in rough weather. If,
however, the models of such types are
tested not only in smooth water but also in
waves (many or most tanks now have some form of wave-making apparatus) there should be little discrepancy.
I do not think it can be too strongly emphasized that we can, and do, predict
service performance from model trials
with a very real accuracy. Dr. J. F. G. CONN, Member:
This is an interesting and welcome paper, although the application of statistical methods is limited in scope. The Author
has not convinced me that measured-mile
trials, admittedly expensive in time and
money, can be dispensed with altogether.
Apart from contract requirements, trials
are necessary for various reasons. Given
good weather, progressive speed trials over a measured course provide a yardstick
of performance which is not otherwise
readily obtained. Even where strong winds
are blowing during trials, much useful
information can be obtained; for example, when the wind is straight up and down the mile, two sets of performance data, corre-sponding to relatively still air and to strong head winds, can be worked out.
As the Author suggests, simultaneous
readings (preferably registered
autographic-ally) of speed, r.p.m., torque, thrust and
CORRESPONDENCE
helm angle are most desirable, and this. applies to all ship-performance
measure-ments. There are now available ship logs
based on the pitot-tube principle which,
when previously calibrated during measured-mile trials, can be relied upon for accurate
values of the all-important speed through
the water.
The Author's methods for the analysis of data appear to be sound and he has
presented them clearly. I suggest that the
application of statistical methods should be
extended to a more general analysis of voyage records, as has already been done
by Dr. Lehmann* and by Dr. J. Lockwood Taylorf. The examination of service logs is difficult owing to the simultaneous operation of various factors
such a
weather, displacement, season, fouling, etc. Lehmann's method can give useful resultswhen "net probability" is employed. Slip-frequency diagrams, for example, can
be prepared and plotted together with the
values derived from Gauss frequency curves.
Good use can be made of arithmetical
probability paper in examining the varia-tion of speed, wind strength, r.p.m., power, fuel consumption, etc. The "probable"
values so derived may differ sharply from the values of arithmetic means. The extension of Prof. Bonebakker's methoth
to the general problem, as outlined above,
and his findings, would form another
welcome paper.
Prof. C. W. PROHASKA, Member:
Everybody will agree with the Author that the analysis of service data is a most important subject and that it is essential that better methods be developed than those ordinarily used. The idea of treating a huge amount of data statistically is not
new. The use of the Gauss curve and of probability paper in such investigations was introduced many years ago, but has
probably not found wide application.
The method of
least squares heresuggested seems rather complicated when the number of data is great and when more
than three numerical coefficients (a, b, c) are used in the equation for HF/N3.
The Author suggests four such coefficients and writes: s.h.p. = (O 1 N): (a.Sa + b. N-2 + cT + d).
The correctness of this expression can
be doubted for different reasons:
1. The wake is supposed constant,
irre-spective of slip, which is not correct. Slip and frictional wake both mcrease *Schjffbao, Vol. 39. 1938.
APPLICATION OF STATISTICAL METHODS TO ANALYSIS OF SERVICE PERFORMANCE DATA o! 19
with time since last docking. The introduction of Sa instead of s:
there-fore represents an approximation. 2. The introduction of draught T in the
formula instead of wake is rather
daring, as there very rarely is a linear relation between the two quantities.
For these reasons it is not obvious that
the method suggested will be of such value that it would be wise to dispense with
the trial trip.
The numerical results obtained also
seem to indicate that the method is not
sufficiently accurate. For ship T, for
in-stance, the frictional losses are found to be 108-N h.p. for loaded voyages, and only
0080'N h.p. for ballast voyages. When
T is introduced in the equation the fric-tional losses amount to I 25N. Which of these figures should be taken as the correct
one?
For ship B the Author's estimate of
frictional losses in the shafting is more than
5 per cent of the total h.p. This figure is probably much too high for modern ships.
The question: "What power do we get for the fuel consumed, and what speed is attained with this power under specified external conditions?" on top of p. 279
is not answered by the straight-line diagrams alone, as speed corresponding to a certain power can only be derived if the shipowner can predict both slip and revolutions (and
can he ?), and as fuel consumption is not
dealt with.
As the Author intends to continue his
investigations, it will probably be possible to improve the method. A reliable
method would certainly be welcomed by all shipowners. The present attempt
de-serves appreciation.
Prof. E. V. TELFER, Associate Member: in this interesting paper Prof. Bonebakker
gives an extremely valuable method of analysing ship-performance statistics. Underlying the method, however, is the
basic assumption that the data are without
consistent errors and that related data are
indeed capable of being correlated. 1f the data do not satisfy this test, then the method
fails and can lead to quite unacceptable
conclusions. For example, a Plate voyage
with indicator cards taken at high power and current with on the outward passage
in association with low power and current against on the homeward passage, will lead
to completely falsely high engine friction
and a falsely low rate of increase of torque
absorption with apparent slip.
Prof. Bonebakker's basis equation 2a is,
of course, acceptable and is the basis of
23
power diagram construction, one means of
calculating the a term being given in my
1934/35 paper.* The b term is the engine
and shaft friction term and its behaviour
in the examples given is extremely interest-ing. For example, in the turbine steamer
T, the loaded shaft friction is proportional to 1,108 whereas the ballast is proportional to 80. One of these figures is clearly wrong
and it is probably the loaded, Its high value obviously confirms that our oid friend the torsion-meter zero-error is not
eliminated by statistical methods and here at once we see the weakness of the method.
Again, consider motorship B for which model experiments and service data are
available: if there were perfect correlation between model and ship, the a and c terms would be identical and the inclusion of the b term would suffice to convert d.h.p. into i.h.p. Generally, however, the model
wake is higher than the ship's; and this means that the ship a term is greater than the model's, while the c term will be less.
This is the very reverse of what Prof. Bone-bakker finds, and he could probably reply that his analysis shows that the ship wake
is much more than the model's, but he is denied this explanation as he disclaims
wake scale-effect. 1f the explanation were propeller scale-effect, it would influence the a and c terms in the same manner and not in the opposite as is actually found. In all probability the true explanation of the difference is the erroneous taking of
the indicator cards. If the cards were taken
at higher revolutions than were averaged for the day and these latter were used for the statistical correlation, the difference
between model and ship coefficients will be completely explained. Even with Diesel
engines, engineers evidently boost the power
to show the lb/i.h.p./hour values which the "office" expect.
In view of the foregoing, Table 7, I regret
to say, does not prove anything. If the statistical analysis is correct then for the ship, d.h.p. = (0.lN)3 (0042 Sa -F 4'366)
and
i.h.p.=(O IN)3 (0042 Sa+12473N-2 +4 366)
Accepting the shaft losses suggested by Prof. Bonebakker, we have
b.h.p.=(0' IN)3 (0.042 Sa+3,300N-2 +4366)
Now, taking a representative slip of 10 per cent the mechanical efficiency becomes
bh
'h
4786N2 + 3,300 - 4'786N2 + 12473 and this for 904 r.p.m. gives 821 per cent*" The Reduced-Speed Running of Merchant Ships." Vol. 51.
against the Authors 73 5 per cent efficiency; while for 131 4 r.p.m. the efficiency is 904
per cent against 830 given by the Author. As the Author states that his results are endorsed by the test-bed data, it follows
that the ship regression equations must be wrong.
So far I appear to have dealt somewhaL harshly with the Author's work. This,
however, is only apparently so. He can rightly claim that if a statistician is let loose on ship performance data he will be forced to produce the regression equations
as found by the Author. The mere fact that because I happen to have had some
experience in the subject I have been able
to point out that the basic data are faulty, and because of this experience be able to
say with some certainty just where and why it is faulty, shows that, given the necessary
control of those taking the original data,
the intrinsic value of the Author's method can be greatly increased.
To this end I would like to offer one
constructive suggestion. First, the Author's
use of the expression s.h.p. ¡N is perhaps
unfortunate. The expression is not
dimen-sionless and this fact prevents the
im-mediate appreciation of the significance of each regression equation. Instead of this,
I would use the torque constant which I published in discussing Sir Amos Ayres'
1945* paper in the form
c
- pn2D3H1l0O.Q which can be shown to equal945x108
PC_DH1
xor as Prof. Bonebakker prefers revolutions in tens per minute
9.45 x10 P
D
H'
(OlN3)In this expression D is the propeller diameter
and H the mean face pitch, both in feet. If Prof. Bonebakker's regression equations are multiplied by the factor 945 x lO/ D H1, the slip and constant terms would
greatly stabilize. It is not possible to carry
out this calculation for all of the cases considered by the Author, but if he could give us the diameter, face pitch, and area, ratio for all the models tested in Table I and the area ratio for all the other
pro-pellers, it would be possible to make much
greater use of his interesting work.
An Approximate and Simple Formula Con-cerning Four-Bladed Propellers of Single-Screw Cargo Ships." Vol. 61.
DISCUSSION ON "THE APPLICATION OF
STATISTICAL METHODS TO THE ANALYSIS
OF SERVICE PERFORMANCE DATA"
*AUTHOR'S REPLY
In preparing his paper, the Author was
handicapped in two respects:
Statistics have become an autonomous science, rooted in pure mathematics, applic-able to phenomena to be investigated from observations which are neither complete nor
exact. A lecture on this subject could hardly be expected from the Author, who believed that the members of the
North-East Coast Institution
wereif
notacquainted withat least aware of the
existence of this new tool and its achieve-ments in other fields: insurance, economics, agriculture, meteorology, etc. The numberof textbooks and the amount of literature on mathematical statistics, particularly in
English, is overwhelming. The Author
was convinced that he could restrict himself
to the application to one particular case-the analysis of service performance data-of a procedure known in principle to his
audience.
The statistical calculations are in no way
more intricate than those required for the preparation of stability curves.
Calculat-ing machines will greatly reduce the time
required for treating a mass of figures. This
is demonstrated by the specimen calcula-tions I and II, their mathematical back-ground being treated in Appendix B.
To sum up the argument: mathematical
statistics are essentially a new tool, designed
and improved by specialists, to be under-stood and handled by every one who can
benefit by applying it to his own particular
problems. We can drive a motorcar,
without being an expert motorcar designer. Compared with the United Kingdom,
the number of shipping companies in Holland is restricted, and there is nothing
like the numerous profession of consulting
naval architects which flourishes in Great
Britain. It will thus be readily understood
that there were not many sources from which service performance data could be expected, and the information which was put at the disnosal of the Author was, for the greater part, too incomplete to be of
any use. Consequently, the Author could
only produce the three examples given in
his paper: he lacks the experience in dealing with service performance data, in one way
or another, which his British colleagues have gaineda lack of experience, more
particularly, in detecting faulty basic information.
* Paper by Prof. Ir. J. W. Bonebakker, Member. (see p.277 ante).
24
Nevertheless, it was considered worth while to focus the attention on modern statistical methods, and to illustrate their
merits and possibilities with a few examples, just to show how the procedure works and
that it does work.
The procedure itself isas stated before quite simple and should become mere
routine. Some understanding of the principles of mathematical statistics is desirable,
but a
full knowledge is notrequired.
The Author could only hope that those
who have reliable service performance data
at their disposal would care to apply the procedure advocated in the paper to these data, and compare the results with their
own analysis.
There is a certain mistrust of statistical methods among professional engineers, and it takes some time before it is dispelled;
but it is becoming apparent that many technical problems of to-day require an
inductive rather than a deductive approach,
leading from incomplete and inexact data to a very close approximation of the true
quantitative relation between two or more factors. Obviously, the experimental data
to be collected should not be chosen at random, but are to be selected on the
ground of basic assumptions which should be physically sound.
It seems to be advisable to include the fundamentals of the statistical method in the courses of every technical college or
university. This is recommended by the
Royal Statistical Society in a report to the
Council and published in its Journal, vol. 110, part I, 1947, and by the (U.S.A.) Institute of Mathematical Statistics in its report to the (U.S.A.) National Research
Council.
One of the biggest stumbling blocks in analysing actual performance is to get
really accurate basic data. Incidental
inaccuraciesplus and minuswill counterbalance each other, provided that
numerous observations are available.
Consistent errors are far more difficult to
detect. Clearly the sifting of the basic data
is of primary importance, and should be
!eft to people well acquainted with the practical and theoretical intricacies of ship propulsion. This point is the keynote of
the paper, but no endeavour has been made
to expatiate on this part of the subject,
mainly because the ship-performance data
Finally, the analysis of service perform-ance data is not a goal in itself, but only a way to fair comparisons between ship and
model, or between one ship and another. What can be achieved in this respect has been briefly indicated in the concluding paragraphs of the paper. Ultimately it
should lead to a well-founded verdict on a
vessel's seakindlinesst and her fuel
con-sumption. Moreover it may foster the
investigation of the influence of scale effect on the factors governing propulsive efficiency.
Reply to Sir Philip Johnson
The President's remarks are greatly
appreciated, and his and the Author's
opinions agree. His final question asks
for a more complete description of
statist-ical methods, of their application, and of
the representation of the results in diagrams
like those included in the paper. The
answer to the first part of the question is
included in the preceding general remarks,
and the Author hopes that Sir Philip will excuse him for referring him to that part of the discussion. It
is of the utmost
importance to get the right grasp of the statistical method, which is rightly called a new tool; but the Author is not entitled to give authoritative information in this
respect.
As to the second part of the
question, he can only ask Sir Philip to havethe application of the method and the representation of the results tried. He is
sure Mr. Barnes would have given a similar
answer, some ninety years ago, to similar questions on his method for calculating stability curves. The proof cf the pudding
is in the eating.
Reply ro Professor Burri/I
Professor Burrill sums up very aptly some of the papef s main points, and the Author
is particularly grateful for his final
state-ment. Indeed, it will be a definite advance
when the analysis of service performance
data can be carried Out by an expert on ship
propulsion and a statistician with an elementary training, the former only sifting the data, and the latter submitting them to a routine procedure.
Professor Burrill, in discussing his first approximation. rightly states that it is irrelevant whether we plot (power)/(N) to a base of V/N, or to a base of apparent slip.
Sa is preferred because it characterizes in a simple and familiar way whether the
external conditions under which the ship is sailing are favourable or not irrespective of the speed.
Our ways divide when Professor Burrill refers Io the normal propeller diagram, in
which KQ is plotted to a base of J. to get
the corresponding change in (power)/(N)3 as slip changes, and to obtain the analysis
See Mr. J. L. Kent's paper in the Transactions of this Institution, vol. 66 p. 417 and f159.
wake. It is a feature of the paper not to
infiltrate service data with model data. On the other hand the analysis wake might be very helpful in detecting faulty data;
however, that does not imply that the analysis wake would be a better means of
controlling the final result than the statistical method.
Professor Burrill's second approach,
assuming
P V
X
to be constant, at the normal working slip, for a small variation in revolutions, can be
Titten as follows:
P C
N3 VJÑ
This relation is represented by a hyperbola.
If it is agreed that the influence of variations in = wake fraction (ship) is small, then a wider range of variation in revolutions can be taken into account by
writing:-= f
(Sa)or = f (V/N). Both equations are represented by astraight line, which is borne out by actual
service performance figures.
It remains to be proved by experience whether a better result can be attained by
statistical methods than an informed naval
architect can obtain by judgment. The
Author can only appeal to Professor
Burrill to try for himself: the best results
should, of course, be achieved by an
informed naval architect applying statistical methods after using his judgment in sifting the basic data.The
equation:-P C
P
C=
or =where C = a constant
n = revolutions per second
y = ship speed in feet per second is similar to Professor
Telfer's:-P C'
N 15a,
because
c_c'
C'v/n
v/nH -
fi.This formula, and the Author's
P
= Q Sa + b
were both applied to the results of the eleven series of model tests mentioned in
section 2 of the paper. The superiority of the latter proved to be evident.
As to Professor Burrill's remarks on
frictional torq ue. he is referred to the reply to Professor Telfer.
!["Un testament latin per aes et librám de 142 après J. С.", O. Guéraud, P. Jouguet, "Etudes de Papyrologie", VI, 1940 : [recenzja]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)