Holtrop, J. & Mennen, G.G.J.
An approximate power prediction method
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AN APPROXIMATE POWER PREDICTION METHOD by J. Holtrop* and G.G.J. Mennen*
1. Introduction
In a recent publication [ 1 ] a statistical method was presented for the determination of the required propulsive power at the initial design stage of a ship. This method was developed through a regression analysis of random model experiments and full-scale data, available at the Netherlands Ship Model Basin. Because the accuracy of the method was reported to be insufficient when unconventional combinations of main parameters were used, an attempt was made to extend the method by adjusting the original numerical prediction model to test data obtain ed in some specific cases. This adaptation of the method has resulted into a set of prediction formulae with a wider range of application. Nevertheless, it should be noticed that the given modifications have a tenta tive cha racter only, because the adjustments are based on a small number of experiments. In any case, the application is limited to hull forms resembling the average ship described by the main dimensions and form coefficients used in the method. The extension of the method was focussed on improving the power prediction of high-block ships with low L/B-ratios and of slender nava l ships with a complex appendage arrangement and immersed transom sterns. Some parts of this study were carried out in the scope of the NSMB Co-operative Research programme. The adaptation of the method to naval ships was carried out in a research study for the Royal Netherlands Navy. Permission to publish results of these studies is gratefully acknowledged.
RTR R A
addi tiona l pressure resistance of immersed transom stern model-ship correlation resistance.
For the form factor of the hull the prediction formula:
can be used. In this formula C P is the prismatic coefficient based on the waterline length L and lcb is the longitudinal position of the centre of buoyancy forward of 0.5 L as a percentage of L. In the form-factor formula L R is a parameter reflecting the length of the run according to:
The coefficient
c 12
is defined as:
In this formula T is the average moulded draught. The coefficient c 13 accounts for the specific shape of the afterbody and is related to the coefficient C stern according to:
For the coefficient C stern the following tentative guidelines are given:
2. Resistance prediction
The total resistance of a ship has been subdivided into:
where: frictional resistance according to the ITTC1957 friction formula 1+k 1 form factor describing the viscous resistance of the hull form in relation to R F R APP resistance of appendage s RW wave-making and wave-breaking resistance additional pressure resistance of bulbo us bow R B near the water surface RF
*) Netherlands Ship Model Basin, (Marin), Wageningen, The Netherlands.
After body form
C s tern
V -shaped sections Nor mal section shape U -shaped sections with Hogn er stern
– 10 0 + 10
The wetted area of the hull can be approximated well by:
In this formula C M is the midship section coefficient, C B is the block coefficient on the basis of the
W a t e r l i n e leng th L.
C WP
is the wate rpl ane area coef
f i c i e n t a n d ABT is the transverse sectional area of the
b u l b at th e posi ti on wh ere th e sti ll wat er su rf ac e in te r
sects the stem. The appendage resistance can be determined from:
wh er e ρ is the water density, V the speed of the ship, S APP the wett ed area of the appendages, 1 + k 2 the appendage resistance factor and C F the coefficient of frictional resistance of the ship according to the ITTC 195 7 for mula. In the Tab le belo w tent ativ e 1 + k 2 values are given for streamlined floworiented appendages. These va lu es were ob ta in ed fr om resi st an ce test s wi th bare and appended ship models. In several of these tests turbulence stimulators were present at the leading edges to induce turbulent flow over the appendages.
In these expressions c 2 is a parameter which accounts for the reduction of the wave resistance due to the ac tion of a bulbous bow. Similarly, c 5 expresses the in fluence of a transom stern on the wave resistance. In the expression A T represents the immersed part of the transverse area of the transom at zero speed. In th is figu re the transv erse area of wedges placed at the transom chine should be included. In the formula for the wave resistance, F n is the Froude number based on the waterline length L. The other parameters can be determined from:
Ap pr ox im ate 1 + k 2 values rud der behind skeg rud der beh ind stern twinscrew bala nce rudders shaft brackets
1.5 — 2.0 1.3 — 1.5 2.8 3.0
skeg strut bossings
1.5 — 2.0 3.0
hull bossings shaf ts stabilizer fin s dome bil ge ke el s
2.0 2.0 — 4.0 2.8 2.7 1.4
The coefficient c 15 is equ al to – 1.69385 for L3 / ! < 512, whereas c15 = 0.0 for L 3 / ! > 1727. For values of 512 < L 3 / ! < 1727, c 15 is determined from:
The equi valen t 1 + k 2 value for a combinat ion of appendages is determined from: The half angle of entrance i E is the angle of the waterline at the bow in degrees with reference to the centre plane but neglecting the local shape at the stem.
The appendage resistance can be increased by the resistance of bow thruster tunnel openings according to :
wher e d is the tunnel diameter. The coefficient C BT O ranges from 0.003 to 0.012. For openings in the cylindrical part of a bulbous bow the lower figures should be used. The wave resistance is determined from:
If iE is unknown, use can be made of the following formula:
This formula, obtained by regression analysis of over 200 hull shapes, yields iE values between 1° and 90°. The original equat ion in [1 ] sometimes resulted in
negative iE values for exceptional combinations of hull-form parameters.
wit h:
The coefficient that determines the influence of the
bulbous bow on the wave resistance is defined as:
168
wh ere h B is the positio n of the centre of the trans verse area A BT above the keel line and T F is the for war d dr au gh t of th e sh ip. The additi onal res istance due to the presence of a bu lbo us bo w nea r the su rf ac e is de te rm in ed fro m:
wh ere the co ef fi ci en t P B is a measure for the emer gence of the bow and F ni is the Froude num ber based on the immersion:
increase C A = (0.105 ks1/3 - 0.005579)/ L 1/3
In these formulae L an d k s are given in metres. 3. Prediction of propulsion factors
The statistical prediction formulae for estimating the effective wake fraction, the thrust deduction frac tion and the relativ erotative ef ficiency as presented in [ 1 ] could be improved on several point s. For singlescrew ships with a conventional stern ar rangement the following adapted formula for the wake fraction can be used:
In a similar way the additional pressure resistance due to the immersed transom can be determined:
The coefficient c 6 has been related to the Froude number based on the transom immersion:
The coefficient c 9 depends on a coeffic ient c8 defined as:
F nT has been defined as:
In this definition C WP is the waterplane area coeffi cient. The modelship correlation resistance R A with
is supposed to describe primarily the effect of the hull roughness and the stillair resistance. From an analysis of results of speed trials, which have been corrected to ideal trial conditions, the following formula for the correlation allowance coefficient C A was found:
In the formula for the wake fraction, C V is the vis cous resistance coefficient with C V = (1 + k ) C F + C A . Further:
In a similar manner the follo win g approximate for mula for the thrust deduction for singlescrew ships wi th a c on ven ti on al st ern c an be app lie d:
The coefficient c
10
is defi ned as:
In addition, C A might be increas ed to cal cu lat e e.g. the effect of a larger hull roughness than standard. To this end the ITTC1978 formulation can be used from wh ic h the in cr ea se of C A can be deriv ed for roughness values hi gh er th an th e st an da rd f ig u re of k 5 = ISOµm (mean apparent amplitude):
The
relativerotative
efficiency
can
be
predicted
169
w e l l by th e or ig ina l for mula:
Because the formulae above apply to ships with a conventional stern an attempt has been made to in dicate a tentative formulation for the propulsion fac tors of singlescrew ships with an open stern as applied some time s on slender, fast sailing ships:
These values are based on only a very limited num ber of mo de l da ta . Th e in fl uen ce of th e fu ll ne ss an d the viscous resistance coefficient has been expressed in a similar way as in the original prediction formulae for twinscrew ships. These original formulae for twin screw ships are:
c 0.75 is the chord length at a radius of 75 per cent and Z is the number of blades.
In this formula t/c is the thickness— chordlen gth ratio an d k P is the propeller blade surface roughness . For this roughness the value of k P = 0.00003 m is used as a standard figure for new propellers. The chord length and the thicknesschordlength ratio can be estimated using the following empirical for mulae:
The blade area ratio can be determined from Keller's formula:
In this formula T is the propeller thrust, pO + ρgh is the static pressure at the shaft centre line, pV is the va po ur pr es sure an d K is a constant to which the following figures apply: 4. Estimation of propeller efficiency
For the prediction of the required propulsive power the efficiency of the propeller in openwater condition has to be determined. It has appeared that the charac teristics of most propellers can be approximated well by usin g th e results of test s wit h sy st em at ic pro pelle r series. In [2] a polynomia l represen tation is given of the thrust and torque coefficients of the Bseries propellers. These polynomials are valid, however, for a 6 Reynolds number of 2.10 and need to be corrected for the specific Reynolds number and the roughness of the actual propeller. The presented statistical pre diction equations for the modelship correlation al lowance and the propulsion factors are based on Reynolds and roughness corrections according to the ITTC1978 method, [3]. According to this method the propeller thrust and torque coefficients are cor rected according to:
K = 0 to 0.1 for twinscrew ships K = 0.2 for singlescrew ships
For sea water of 15 degrees centigrade the value of 2 pO p V is 99047 N / m . The given prediction equations are consistent with a shafting efficiency of
-
and reflect ideal trial conditions, implying: — no wind, waves and swell, 3 — deep water with a density of 1025 kg/m and a temperature of 15 degrees centigrade and — a clean hull and propeller with a surface roughness according to modern standards. The shaft power can now be determined from:
5. Numerical example
Here ∆ C D is the difference in drag coeffic ient of the profile section, P is the pitch of the propeller and
The performance characteristics of a hypothetical singlescrew ship are calculated for a speed of 25 knots. The calculations are made for the various resistance components and the propulsion factors, successively. The main ship particulars are listed in the Table on the next page:
170
Main ship characteristics length on waterline 205.00 m L length between perpendiculars 200.00 m L PP breadth moulded 32.00 m B draught moulded on P.P. 10.00 m T F draught moulded on A.P. 10.00 m T A displacement volume moulded 37500 m 3 ! longitudinal centre of buoyancy 2.02% aft of ½ Lpp transverse bulb area 20.0 m2 A BT centre of bulb area above keel line h B 4.0 m midship section coefficie nt 0.980 C M waterplane area coefficient 0.750 C WP 2 transom area 16.0 m AT 2 wetted area appendages 50.0 m S APP stern shape parameter propeller diameter number of propeller blades clearance propeller with keel line ship speed
C stern D Z V
10.0 8.00 m 4 0.20 m 25.0 knots
The calculations with the statistical method resulted into the following coefficients and powering charac teristics listed in the next Table: F n
= 0.2868
F nT
C P
= 0.5833
RTR
= 81.385 m = – 0.75%
c4 C A R A
L R
lcb c12 c13 1+k 1 S C F RF 1 + k 2 R APP c7 i E c1 c3 c2 c5 m l c15 m2
References
λ
1. Holtrop, J. and Mennen, G.G.J., 'A statistical power prediction method', International Shipbuilding Progress, Vol. 25, October 1978. 2. Oosterveld, M.W.C. and Oossanen, P. van, 'Furth er comput er analyzed data of the Wageningen B-screw series', International Shipbuilding Progress, July 1975. 3. Proceedings 15th ITTC, The Hague, 1978.
R W P B F ni RB
= 0.5102 = 1.030 = 1.156 2 = 7381.45 m = 0.001390 = 869.63 kN = 1.50 = 8.83 kN
= 0.1561 = 12.08 degrees = 1.398
= 0.02119 = 0.7595 = 0.9592 = –2.1274 = 1.69385 = –0.17087 = 0.6513 = 557.11 kN = 0.6261 = 1.5084 = 0.049 kN
R total PE C V
c9 c11
C pi w c 10 t
T A E / A O η R c0.75 t/c0.75 ∆CD
= 5.433 = 0.00 kN = 0.04 = 0.000352 = 221.98 kN = 1793.26 kN = 23063 kW = 0.001963 = 14.500 = 1.250 = 0.5477 = 0.2584 =0.15610 = 0.1747 =2172.75 kN =0.7393 = 0.9931
= 3.065 m = 0.03524 = 0.000956
From the Bseries polynomials:
K Ts n K Qo η 0 P S
= = = = =
0.18802 1.6594 Hz 0.033275 0.6461 32621 kW
