Propeller Design and
Two-Speed Gearboxes
. . . with partiGular reference to tugs and trawlers
byT. P. O'Brien, C.G.T.A.,
A.M.R.I.N.A., Ship
Divis-ion, National Physical
Laboratory.
This two-part article discusses the differences i n performance o f screws designed f o r free-running conditions and towing duty conditions, the f o r m e r when towing and the latter when running free. I t shows that sigdihcanf improvements i n performance SOT both types o f screw can be achieved by using two-speed gearboxes enabling the optimuiii rate o f rotation to be chosen f o r both free-running and towing conditions. Equations are derived and coefficients are given i n part one to enable design and operating con-ditions to be chosen to give o p t i m u m perfonnance.
1. Introduction
U n l i k e those f o r other vessels, screws f o r tugs and trawlers are dual purpose propulsion devices. since, i n addition to operating at free-running conditions, they are also required to run at low speed towing duty conditions. Some screws are designed to give best performance at free-running condi-tions and do not operate so efficiently when towing. Others designed to give best performance at towing duty conditions, suffer adverse performance when free-running.
For the former, the loss i n towing performance could be a 20 per cent reduction i n towing pull, while for.the latter the loss i n free-running performance could be a 15 per cent reduction i n ship speed. Some screws are, o f course, designed to operate at conditions that are a compromise between free-running and towing. . .
A marine screw can be designed to absorb a stipulated horsepower when running at a given rate o f rotation and speed o f advance i n propelling the hull. I f the screw is designed f o r free-running conditions, it has a moderate pitch ratio and operates at a moderate speed o f advance when running at its design condition. However, when the screw operates at l o w speed towing duty conditions, the maximum torque applied by the engine w i l l be reached at a low rate of rotation, consequently there will be a reduction i n delivered horsepower resulting i n low thrust and puU, i.e., f o r towing conditions the screw i s overpitched.
Conversely, i f the: screw, is designed f o r towing conditions, i t has a Tow pitch ratio and operates at a low speed o f advance when running at its design condition. However, when this screw operates at moderate speed free-running conditions, the maximum rate o f rotation w i l l be reached at a torque value substantially lower than the maximum. • Therefore, the engine w i l l n o t be able to apply maximum
torqiie, and there w i l l be a reduction i n delivered horse-power resulting i n l o w free-running speed, i.e., f o r free running conditions the screw is underpitched.
The foregoing restrictions apply i f the screw is driven either directly f r o m t h e engine or via a,single-speed gear box; however, significant improvements i n performance can be achieved by introducing a two speed gear box. For screws designed f o r free-running conditions^ a second gear can be .chosen to enable the screw to r u n at a higher rate o f rotation,
and so operate at maximum power when towing. Similarly, for screws designed f o r t o w i n g duty conditions, a second gear ratio is chosen to enable tjie screw to r u n at a higher rate o f rotation and so operate at maximum power when free-running.
2. Basic equations and (x-a coefficients
A f o r m o f chart convenient f o r designing and making performance estimates f o r both towing duty and free-running screws is the n-a chart given i n a paper by Troost.' Some o f the charts given by Troost are reproduced i n a book^and i n a report' by the present author, where worked examples are included illustrating practical applications. I n this chart, contours o f open water efficiency vjo, pitch ratio p and torque coefficient <j> are given on co-ordinates o f torque coefficient \i, and thrust-torque ratio a, as shown i n Fig. 1.. I n their basic f o r m , the coefficients are given by:—
( 1 ) # (2) | ^ = « (3) (4) vio = V Q O D T
' 7 ^
7:
pD Qo. 2™QOI f desired the thrust-torque ratio and screw efficiency can be linked by the advance coefficient J defined by •
(5) J = - K = K D a
where is the speed o f advance o f the screvy i n feet per second
n iis .the rate o f rotation, o f the screw i n revolutions per second
D is the screw diameter i n feet
Qo is the torque absorbed by the screw when n m n i n g i n open water i n pounds feet .
T is the thrust applied by the screw i n .pounds P is the mass density , o f the fluid i n which the screw
operates
(for freshwater? = 1.938, f o r sea water p = 1.988) F o r practical purposes i t is convenient to express speed o f advance i h knots; rate o f rotation i n revolutions per minute and thrust i n tons; moreover, it is desirable to apply the principle o f thrust identity as discussed i n Section 2.6
of the b o o k . ' , Accordingly, the coefficients are re-stated i n the f o r m •
(6) <!> = 1.689 V D
( 7 ) IJ. (8) (9) J -= N D ' /_pl 60 V S , ' .3S7DT„ 101.3V., pD Q 0-65 (10) V5„ = N D 602T„V.^ N S K Q
where is the speed o f advance o f the screw i n knots N is the rate o f rotation o f the screw i n revolutions
per minute
Tu is the thrust applied by the screw i n tons
£ R is the relative flow factor linking the screw efficiency 7)B when operating i n non-uniform flow behind the hull, and the screw efficiency TJO when operating i n u n i f o r m flow i n open water.
A p p l y i n g the principle o f thrust identity
( 1 1 ) SRQB = Q
I n applying the |A-<J coefficients i n designing a towing duty screw o f given diameter to absorb a stipulated delivered horsepovier D H P when running at given rate o f rotation N and speed o f advance V^, first, the torque Q is computed using the formula
33,000 D H P
( 1 2 ) Q
27rN
This enables torque coefficient ^ and \i to be evaluated, and the point on the (ji-o design chart defined by these values enables corresponding values o f pitch ratio p and thrust-torque ratio c to be determined." The thrust T^ is calculated using equation 8, and the related tow rope p u l l ? „ is derived f r o m the thrust by applying a pull-thrust ratio defined by the relation
(13)
A worked example following the above procedure is given i n Table 5 o f the report. =
The foregoing considerations apply i f the rate o f rotation is fixed. However, i f i t is possible to select a set o f gear ratios to give a range o f values o f rate o f rotation N i by applying a factor k to the basic value o f rate o f rotation N j and applying the condition that the power remains constant, the following relations can be derived:—
(14) N = / t N i
(15)
where Q i is the basic value o f the torque corresponding to the basic rate o f r o t a t i o n N j which, when substituted i n the equations f o r torque coefficients enable these equations to be re-stated i n the f o r m (16) ( 1 7 ) <f> = 1.689V^D fcND= ; pDfc ki ^1 60 1^1
where and are the basic values o f torque coefficient evaluated using basic value o f rate o f rotation N j and f o r which the coefficient k is equal t o unity. Pairs o f corre-sponding values o f pitch ratio p and thrust torque ratio a are determined using the n - o chart as before ( f o r fixed rate o f rotation) and thrust values are calculated using a modified f o r m o f equation f o r the thrust torque ratio given by
15-0
i
ISO soo
SATE OF ROTATION N
A B O V E : F i g . 2. Propulsion estimates (free-running) and
perfonnance estimates (towing) for varying rate of rotation
B E L O W : F i g . 3
10 lO'-i. II II'*
SPEED o r MIJLL V,
SCREW 2 - PROPULSION ESTIMATES' (FREE-RUNNING) FOP FIXED RATE OF ROTATION
Propeller Design and Two-Speed Gearboxes •
The results o f the calculations are plotted i n the f o r m o f value o f pitch ratio p arid thrust . T^ (on pull P^) o n a base o f rate o f rotation N , as shown i n Fig. 2.
In applying the (i-a coefRcients i n designing a free-running screw, a procedure similar to that used f o r towing duty screws as given above is followed. However, f o r free-running conditions the performance criterion is the screw efficiency pér cent instead o f the thrust T ^ used f o r towing conditions. Accordingly, values o f the advance coefficient J are calculated and the screw efficiency vjo is determined using equation 5. The results o f the calculations are presented i n a similar way as f o r towing conditions, but here the parameters are screw efficiency -^o (or propulsive effi-cier.cy ijp) on a base o f rate o f rotation N , as shown i n Fig. 2.
The towing performarce curves o f Fig. 2 show that optimum towing performance is associated with high rate o f rotation arid low pitch ratio, as might be expected. F r o m the free-running performance curves o f Fig. 2, the value o f trie rate o f rotation tp given maximum screw efficiency can be selected and the corresponding value o f the pitch ratio for a screw designed f o r free-running conditions can be determined. The optimum rate of rotation f o r this screw when operating at towing duty conditions, and the corre-sponding value of pull, can be determined f r o m the towing performance curve.
Towing duty
The performance data given i n Fig. 2 can also be applied i n designing towing duty screws and estimating their perform-ance at free-running conditions; since, having chosen the design rate o f rotation and pitch ratio, the optimum rate o f rotation and related value o f screw efficiency f o r free-running conditions can be determined f r o m the free-ruiming perform-ance data.
The performance data o f Fig. 2 do not give performance values f o r screws designed f o r free-running conditions, nor do they give free-running performance values f o r screws designed f o r towing duty conditions i f it is not intended to fit two speed gear boxes. For screws designed f o r free-running conditions, but operating at towing duty conditions, maximum torque is reached at a rate of rotation lower than the design value, and this needs to be estimated.
This can be done by first computing the torque coefficient ^ (equation 6) which is then plotted on the n - o chart at a point the position o f which is located by the intersection o f two contours, one o f j> the other o f the pitch ratio p of the screw. This enables corresponding values p f torque coefficient (i and thrust torque ratio CT to be read f r o m the chart, and.'values of screw rate of rotation N and thrust T^ to be derived using the equation given above f o r torque coefficient (i and thrust torque ratio (equation 8). A t the same time, the- dehvered horsepower D H P can also be evaluated"using equation 12.
As stated above, a towing duty screw operating at free-running conditions at the design rate o f rotation does so at reduced torque and delivered horsepower. I n making free-running performance estimates using the (i-<' coefficients, it is convenient to introduce a torque reduction factor K defined by the relation
(19) Q = K Q „ and D H P = K D H P „
where the suffix M denotes the maximum values o f torque Q and delivered horsepower D H P .
Incorporating the torque reduction factor K i n the equations f o r torque coefficient 4> and (x and thrust torque ratio CT (equations 6, 7 and 8) they can be re-stated, i n the f o r m
(20) ^ = 1.689 V . D y ^ - ^ ^ = ^
N D ' |iM
n-y\ n - 357T„D _ a» (22) " - - K Q7 - K
where ii.„ and CT„ are values o f the torque coefficients
<l> and n and the thrust-torque ratio CT computed using the
maximum value o f the torque Q „ .
I n making free-running performance estimates, a range o f values of torque reduction factor K is selected and a corre-sponding set o f values o f torque coefficient is evaluated. Values o f torque coefficient ^ and thrust-torque ratio a are read f r o m the (i-a chart at points the positions o f which are located by the intersection o f two contours, one o f torque coefficient n. the other o f the pitch ratio p o f the screw.
This enables the speed of advance V^ and the advance coefficient J to be determined using equations 6 and 9, respectively. The screw efficiency v)o is determined using equation 10, and the speed o f hull V j , the propulsive efficiency y)p and the efi'ective horsepower available' E H P i are derived using -the equations given i n the report,, which are reproduced below.
(23) Vs = V ^ ( I - ) v , ) (24) Yip = SpiQo (25) E H P i = v);7DHP where Vs is the speed o f the hull i n knots
Wf is the wake fraction T,p is the overall hull factor.
The values o f effective horsepower available E H P i are plotted on a base o f speed o f hull Vs, together with corre-sponding values o f effective horsepower on trial EHP^ derived f r o m the hull resistance experiment results, as shown i n Fig. 3. The value of the speed at which the hull w i l l be propelled and the corresponding value o f the effective horsepower are determined by the co-ordinates o f .the point o f intersection o f the curves o f effective horsepower.
I f desired, the value o f propulsive efficiency rjp can also be plotted i n Fig. 3, and diis enables the value o f propulsive efficiency at the t r i a l speed to be determined, f r o m which the delivered horsepower on trial D H P can be .derived using equation 25.
f^ r o o s t ! L . Open-Water Tests with Modern Propeller Forms. Trans. N.E. Coast Instn. Engrs. Shipb., Vol. 67, 1951.
2 O'Brien, T. P. The Design of Marine Screw Propellers. ' Hutchinson's Scientific and Technical Press, London, 1962. 3 O'Brien, T. P. Some Practical Aspects of Marine Propeller Design
with Particular Reference to Single-Screw Tugs N.P.L. Ship
Propeller Design and
Two-Speed Gearboxes
. . . with particular reference to tugs and trawlers
Part Two
I n this concluding article, the author gives worked examples, the results o f which show that f o r a screw designed f o r free-running conditions and driven via a single speed gearbox, the loss i n towing pull would be 22 per cent, but i f a two speed gearbox were f i t t e d the loss i n towing p u l l would be only three per cent. S i m i l a r l y , f o r a screw designed for towing conditions and driven via a single-speed gearbox, the loss in free-mnning speed would be 15 per cent, b u t i f a two-spet^d gearbox were fitted the loss i n free-ruiming speed would be only 1 | per cent.
by T. P. O'Brien, C.G.I.A., A.M.R.I.N.A., Ship Division, National Physical Laboratory.
I T is required to prepare the preliminary design calculations and make performance estimates f o r the propellers f o r a single screw tug.
The first is to be designed to absorb maximum power at a stipulated gear, ratio and rate o f rotation f o r free-running conditions. Towing performance estimates are to be made for zero speed o f hull f o r t w o conditions: (a) at sam.e gear ratio as f o r free-running conditions; (b) at a gear ratio selected to enable the screw to r u n at a rate o f rotation to absorb maximum power at towing conditions.
The second is to be designed to absorb maximum power at a stipulated gear ratio and rate o f rotation , for towing conditions. Propulsion estimates are to be made f o r two free-ruiming conditions (a) at same gear ratio and rate o f rotation as f o r towing conditions; (b) at a gear ratio selected to enable the screw to r u n at a rate o f rotation to absorb maximum power at free-ruiming conditions.
The computations are to be made using the n-a coefficients derived i n Section 2 above and the Troost B-4-55 series chart given i n Figure 1.
Design Data
Hull—Single-screw tug; length 100 f t . , breadth 28 f t . , draught (aft) 14 ft., rake o f keel 4 ft. aft, displacement (mid) 483 tons, block coefficient 0.502. Other particulars as Model 4033B, reference 4.
Hull speed (knots) V j 10 lOJ I I l l j 12 12V n Effective h.p. (model experiments) E H P „ 176 219 273 349 462 627 973 Effective h.p. (trial conditions) E H P T 194 241 300 384 508 690 960 EHPT = fMEHP„ = M O E H P M
Table 1 Screw 1—Design Calculations: Free-running Conditions Design Conditions DHP = 1,100, = 28,900 pounds feet Np = 200 RPM
D = 9 feet, Vs = 12.5 knots N , = 196 RPM Propulsion Factors w = 0.225, / = 0.206, SR = 1.0, = 1.02 (Ref. 3, Table 3)
Basic Torque Coefficients (equations 16 and 17)
k N ki k'l: 0 P a J (1) (2) (3) (4) (4) (5) (6) (7) 0.7 140 137 0.837 0.586 3.06 3.86 1.40 0.765 0.795 0.608 0.620 0.8 160 157 0.894 0.715 3.27 4.71 1.14 0.895 0.696 0.623 0.635 0.9 180 176i 0.949 0.855 3.47 5.62 0.97 0.995 0.618 0.615 0.628 1.0 200 196 1.000 1.000 3.66 6.58 0.82 1.090 0.556 0.606 0.617 1.1 220 215i 1.049 1.154 3.84 7.59 0.72 1.145 0.506 0.580 0.592 1.2 240 235 1.095 1.314 4.01 8.65 0.62 1.195 0.464 0.555 0.566 1.3 260 255 1.140 1.483 4.17 9.76 0.54 1.23 0.428 0.526 0.536
(1) N , = 0.98 N F (Wake scale effect, Ref. 2, Section 4.9); (2) ^ = /ci^, (equationl6); (3) (i = k'/.(i, (equation I T ) ; (4) Values from (i-CT chart (Fig. 1); (5) J = * (equation 9); (6) T),, = Jc7 (equation 10); (7) 7)j, = Sj,7?o (equation 24). For N F = 200, pitch ratio
p = 0.82, propulsive efficiency T/P = 0.617.
Table 2 Screw 2—Design Calculations: Towing Conditions Design Conditions DHP = 1,100, Q, == 28,900 pounds feet, N j = 200 RPM
D = 9 feet, V j = 0
Propulsion Data l'„ = 1.0, Pull-Thrust Ratio Xp = 0.975 (Ref. 3, Table 3)
N,D» / cD Basic Torque Coefficient (ij = ~~ / — = 6.71 (equation 17) V ^ Q i k N k'l. k'l. 4- 1^ P a Tu Tons Pu Tons k N k'l. k'l. 4-(1) (2) (2) (3) (4) 0.7 140 0.837 0.586 0 3.93 1.030 1.09 14.0 13.65 0.8 160 0.894 0.715 0 4.80 0.820 1.30 14.6 14.25 0.9 180 0.949 0.855 0 5.73 0.675 1.49 14.9 14.55 1.0 200 1.000 1.000 0 6.71 0.565 1.67 15.0 14.65 1.1 220 1.049 1.154 0 7.74 0.480 1.84 15.0 14.65
(1) ^ = k'l.n^ (equation 17); (2) Values from (i-o chart (Fig. I ) ; (3) Tu =
For N = 200, pitch ratio p = 0.565, pull Pu = 14.65 tons.
iSlkD (equation 18); (4) Pu = TpTu (equation 13).
Engine—Diesel. Delivered horsepower at screw d.h.p. = 1,100, engine speed 600 r.p.m., stipulated gear ratio 3:1 giving 200 r.p.m. f o r screw, corresponding maximum torque at screw = 28,900 pounds feet.
F o r free-running conditions N = 0.98 Np (2 per cent wake scale effect, see Section 4.9 o f Ref. 2).
= 196 R P M
For towing conditions N = N F = 200 r p m
Stern Details—Streamlined rudder, shaft immersion I = 7.7 f t .
Stipulations. Screw diameter 9.0 f t . , number o f blades 4. Design Conditions. Screw 1 to be designed to absorb
maximum power under trial conditions when running free at a trial speed o f 12^ knots.
Screw 2 to be designed to absorb maximum power under towing conditions at zero speed o f hull.
Screw I—Design Calculations—Free-running
conditions
I n making the design calculations given i n Table 1, first, the basic values o f the torque coefficients and jxi are calculated using the given screw diameter D and speed o f advance V^^ and the basic values o f delivered horsepower D H P , torque Qi and rate o f rotation N j . Next a series o f values o f torque coefficients ^ and n are derived covering a range o f screw rate o f rotation and applying the constant power condition. This enables a series o f corresponding values' o f pitch ratio p and thrust torque ratio o to be obtained f r o m the n - a chart shown i n Fig. 1. Finally, a set o f values o f screw efficiency TIQ are derived f r o m the chart values o f a. This enables a set o f values o f propulsive efficiency T], to be derived f r o m Vo, and these are plotted on a base o f rate o f rotation N , together with the values o f pitch ratio p, as shown i n F i g . 2,
Screw 2—Design Calculations—Towing Duty
Conditions
I n making the design calculations f o r this screw given i n Table 2, fhe procedure is similar to that followed f o r Screw 1. However, since the speed o f advance is zero the torque coefficients <j> become zero; consequently, the values o f pitch ratio p and thrust torque ratio a are read f r o m the
H-CT chart at points located by the contour ^ = 0 and the co-ordinate \i. A set o f values o f screw thrust Tu are derived f r o m the chart values o f c. A set o f values o f piül Pu are derived f r o m Tu and plotted o n a base o f rate o f rotation N , together with the values o f pitch ratio p, as also shown i n Fig. 2.
Screw I—Towing Performance Estimates
(a) Single Speed Gear Box. I n making the towing
performance estimates given i n Table 3, corresponding values o f torque coefficient (x and thrust-torque ratio are read f r o m the n-o chart at the point determined by the intersection o f the contours torque coefficient ^ = 0 and value o f pitch ratio p f o r the screw. The rate o f rotation N at which the screw is operating and the resulting delivered horsepower D H P are determined f r o m the torque coefficient [i. The thrust Tu is determined f r o m the thrust-torque ratio o and this enables the pull Pu to be derived.
(6) Two-Speed Gear Box. I n addition to giving the performance o f screws designed f o r towing duty conditions, the towing performance data shown i n Fig. 2 can also be
Table 3 Screw 1—Towing Performance: Estimates Operating Conditions: Maximum torque Q, = 28,900 pounds, feet at zero speed of advance V^ = 0, ^ = 0. Screw diameter D = 9.0 feet. p 1^
CT
N DHP Tu Pu p 1^CT
RPM DHP TONS TONS (1) (2) (2) (3) (4) (5) (6) (7) 0.82 4.79 1.305 143 785 11.75 0.971 11.4(1) Pitch ratio as determined for free-running condition
(Table 1); (2) Values from (X-CT chart (Fig. 1);
0)'i<='^J^
(equation 7); (4) DHP = (equation 12); (5) Tu-(equation 8); (6) PuU-Thrust'Ratio (Ref. 3, Table 3); (7) Pu = TpTo (equation 13); For two speed gear box N = 160, Pu = 14.25 (Fig. 2).
Table 4 Screw 2—Propulsion Estimates: Free Running Conditions Operating Conditions: Rate of rotation for stipulated gear ratio
N F = 200, N = 196 Propulsion Factors, w = 0.225, ZR = 1.0, = 1.02
(Ref. 3, Table 3)
Screw diameter D = 9.0 feet pitch ratio p = 0.565 (Table 2).
Basic Torque Coefficient [ji„ = —— / = 6.58 (equation 20).
6 0 V J-RQM K K' . (i (1) (2) 0 knots knots J Vo D H P E H P , (i (1) (2) (2) (3) (4) (5) (6) (7) (8) (9) 0.50 0.707 9.31 3.94 1.245 7.35 9,49 0.423 0.527 0.537 550 296 0.45 0.40 0.35 0.671 0.632 0.592 9.81 10.41 11.12 4.50 5.13 5.86 1.155 1.050 0.920 7.97 8.57 9.17 10.29 11.06 11.84 0.458 0.493 0.527 0.529 0.517 0.485 0.540 0.527 0.495 495 . 440 385 • 267 232 191
(I) (jt = /..„/K4 (equation 21); (2) Values from [x-a chart (Fig. 1); (3) V^ = , — t — / ^ R K Q M (equation 20); (4) V. = —
1.689D^ p D (1-w)
(equation 23); ( 5 ) 3 = ___-J? (equation 9); (6)7^0 = Jo (equation 10); (7) 7?j, = S^Vo (equation 24); (8) D H P = K D H P „ (equation 19);
(9) E H P I = Tij, D H P (equation 21). From Fig. 3, Vs = 10.6 knots, = 0.54. For two-speed gsar box, N = 253, 7)„ = 0.55 (Fig. 2).
E H P = T/j, D H P = 605 Vs = 12.3 (Fig. 3).
used to make towing performance estimates f o r screws designed f o r free-running conditions. I n applying the procedure, corresponding values of rate of rotation N and tow rope pull are obtained f r o m Fig. 2 f o r the value o f the pitch ratio p as previously determined f o r free running conditions. From the rate o f rotation N the values o f the second gear ratio f o r the gear box is derived.
Screw 2—Propulsion Estimates—Free-running
Conditions
(a) Single-Speed Gear Box. I n making the propulsion
estimates given in Table 4, first, the basic value o f the torque coefficient (x„ is calculated using the given screw
diameter D , the maximum value o f torque Q „ derived f r o m the maximum delivered horsepower D H P „ and the stipulated value o f the rate o f rotation N . Next, a series o f values o f torque coefficient [x are derived f r o m |x„ f o r reduced torque and power covering a range of values o f torque reduction factor K . This enables a series o f corresponding values o f torque coefficient <f> and thrust torque ratio o to be obtainfed f r o m the n-a chart shown in Fig. 1, at points the positions o f which are located by the co-ordinate o f y. and the contour o f the pitch ratio p of the screw. This enables a series o f values o f speed o f advance to be calculated f r o m ^ , and a series o f values o f screw efficiency ijo to be calculated f r o m o. Finally, a series o f values o f speed o f hull V are
Table 5 Screws I and 2—Comparisons of Free-Running and Towing Performance
Screw
Design Condition
Free-Running Towing (at Vs = 0) Gear Box Gear Ratios Screw Design Condition DHP N Vv Vs DHP N Pu RPM Knots RPM Tons (1) Free running 1,100 200 0.617 12.5 786 143 11.40 One Speed 3:1 Free running 1,100 200 0.617 12.5 1,100 160 14.25 Two speed 3:1 3.75:1 (2) Towing 470 200 0.54 10.6 1,100 200 14.65 One speed 3:1
1,100 253 0.55 12.3
1,100 200 14.65 Two speed 3:1 2.37:1
(1) % loss in towing pull - 22
One speed 3:1 3 Two speed 3.75:1 (2) % loss in free-running
speed 15 One speed 3:1
U Two speed 2.37:1
derived f r o m V^, and a series of values o f propulsive efficiency
Tp are derived f r o m rjo: the product Tjp D H P gives the
' effective horsepower available E H P i , the values o f which are plotted on a base o f speed o f hull V , together with the values o f the effective horsepower on trial E H P T obtained f r o m the hull resistance data, as shown i n Fig. 3 . The speed co-ordinate of the point o f intersection o f the two ' effective horsepower etudes determines the speed at which the hull w i l l be propelled. Similarly, the effective horse-power co-ordinate gives the corresponding value of the effective horsepower, and the propulsive efficiency curve gives the value o f the propulsive efficiency ijp f r o m which the delivered horsepower.PHP can be derived.
{b) Two-Speed Gear Box. I n making these estimates, a
procedure similar to that used i n making the towing perform-ance estimates is followed, and corresponding values of rate of rotation N and propulsive efficiency nr are obtained f o r the value o f the pitch ratio p, as previously determined f o r towing duty conditions. From the rate o f rotation N the value o f the second gear ratio f o r the gear box is derived. Since the propulsive efficiency is lower than f o r Screw 1,
which had been designed f o r free-running conditions, the speed o f hull w i l l also be lower than f o r Screw 1 . The value of the speed o f hull is determined f r o m the hull resistance data given i n Fig. 3 , at the co-ordinate o f V j corresponding to the co-ordinate o f E H P determined by the product v)p D H P .
Comparison of Results
The results o f the foregoing calculations are compared i n Table 5. These show that there are significant advantages in fitting a two-speed gear box, as summarised below. For Screw 1, designed f o r free-running conditions and driven via a single speed gear box, the towing puU would be 2 2 per cent lower than f o r Screw 2 , designed f o r towing conditions; however, i f a two speed gear box were fitted the loss i n towing pull would be 3 per cent.
For Screw 2 , designed f o r towing conditions and driven via a single speed gear box, the free-running speed would be 1 5 per cent lower than f o r Screw 1, designed f o r free-running conditions; however, i f a two speed gear box were fitted the loss i n free-running speed would be 1 i per cent.
Reference
4. Parker, M . N . and Dawson, J. Tug Propulsion Investigation.
THe Effect of a Buttock Flow Stern on Bollard Pull, Towing and Free-Running Performance. Trans. Roy. Insm. Nav. Archit.,
Vol. 104, 1962.
Reprinted from Tug Supplement f e b . 1966 "Ship and Boat Builder International"
RESEARCH GN TUG PROPELLERS
by T. P. O'Brien, C.G.I.A., IVI.R.I.N.A., Ship Division, National Physical Laboratory
T N designing tug propellers and making estimates o f their performances a large amount o f basic data are required and numerous aspects need to be considered. These include: Propulsion data f o r free-running and towing conditions and performance data f o r altemative types o f propulsion machinery to enable preliminary propulsion estimates to be made; design charts, cavitation charts arid strength criteria to enable the overall geometric features o f basic screws t o be chosen; and correction factors to make allowance f o r variation i n particular geometric features (blade-section shape, blade thickness, number o f blades, blade-area ratio, blade outline and boss-diameter ratio) to enable the detailed geometric characteristics o f the screws to be selected.
These comments apply generally to a l l ' m a r i n e screws, but there are two factors affecting tug screws that are significant. F o r some classes o f vessel ( f o r example, tankers and cargo vessels) an extensive amount o f system-atic propulsion data are available, but f o r others (includ-ing tugs) there is a dearth o f published data. Moreover, owing to the d i f f e r i n g conditions under which tugs operate some tug screws are designed f o r free-running conditions and performance estimates are required f o r towing con-ditions, while others are designed f o r t o w i n g conditions and propulsion estimates are required f o r free-running conditions.
A summary of published data
What follows is a bibliography o f data comprising i n f o r m a t i o n which has proved useful i n designing tug screws and m a k i n g estimates o f their performances. Design topics and the particular publications in which they are discussed are listed in Table 1. The subject matter o f these publications relevant to tugs is summarised below.
1. A R G Y R I A D I S , D . A-, Modern tug design with par-ticular emphasis on propeller design, manoeuvrability and endurance. Trans. Soc. N a v a l A r c h . & M a r . Engrs., 1 9 5 7 , 65. '
Several types o f main propulsion machinery power plants are discussed and the merits o f each one are pre-sented. Propeller design is' discussed at some length.
Table 1. Design Topics ani Relevant Publications Item 1 2 3 4 5 6 7 Topic Aspects of screw design Propulsion data Propulsion machinery Design charts Cavitation Strength Variation features
Correction factors and formulae Worked examples in geometric Publications 1 , 2 , 3, 4 , 5, 6, 12, 1 3 1 , 2 , 3, 6, 7, 8 , 9 1 2, 3, 4 , 5, 12, 1 5 2, 3, 5 , 1 2 , 1 3 , 1 4 2, 3, 12, 1 3 2, 3 , 5 , 6 , 7 , 8 , 1 0 , 1 1 , 1 2 , 1 3 1, 2 , 3, 5, 6, 7, 8, 9, 10, 1 1 12, 13, 1 5 1 , 2 , 3, 5 , 1 2 , 1 3 , 1 5
Preliminary design formulae are given f o r both bollard pull and towing thrust. Comparisons between the different types o f propellers are made and a method f o r calculating the performance o f the propeller at any speed of the vessel is presented.
2 . O ' B R I E N , T . P. The design of marine screw pro-pellers, Hutchinson Scientific and Technical Press, L o n d o n , July, 1 9 6 2 .
Chart methods f o r the design o f screws and prediction o f screw performance are described in detail, and correc-tion factors given to enaible varying screws to be com-pared. M o d e m developments i n applied circulation theory, cavitation and its associated problems and Üie adaptation o f aerodynamic data to the design o f blade sections are a l l f u l l y and practically presented. Tiiere are chapters on model experiments, strength, design factors and screw geometry and a large number o f useful tables and charts throughout. A comprehensive set o f worked examples is given, ranging f r o m uses o f simple design charts to practical applications o f theoretical design methods.
N O T E : Subsequent to publication i t was f o u n d that the design charts (pages 7 9 and 8 3 ) had been interchanged during printing. Consequently, the captions should read as foUows:
Page 7 9 , F i g . 3 . 1 6 Troost B . 4 - 5 5 Bp — 8 Chart. Page 8 3 , Fig. 3 . 1 3 Troost B . 3 - 5 0 Bp — S Chart.
Some small errors which have been f o u n d i n the text are listed i n an errata, copies o f which can be obtained f r o m the author.
3. O ' B R I E N , T . P. Design of tug propellers. SHIP A N D
B O A T B U I L D E R I N T E R N A T I O N A L , L o n d o n , A p r i l 1 9 6 5 IS
2 2 . , '
This article discusses general aspects o f propulsion and applications to t u g propellers operating at free-running and towing-duty conditions. I t describes charts f o r designing propeUers and making cavitation estimates, and It jpcludes a procedure f o r designing tug screws and making estimates o f their performance. Formulae f o r assessing blade stresses and estimating weight and moment of inertia are also given.
I t summarises single-screw tug propulsion data recentiy obtained at the N . P . L . , and it gives worked examples on the design aind performance assessment o f two tug screws, one designed f o r free-running conditions, the other f o r towing-duty conditions.
N O T E : A n improved f o r m o f cavitation chart used in making the design calculations discussed above is given i n an article mentioned below ( 1 4 ) . I t is reproduced i n F i g . l .
4. TROOST, L . Open-water test series with modern propeller forms. Trans. N . E . Coast Inst. Engrs. Shipb
1 9 5 1 , 67. y
This paper records the results o f experiments w i t h a systematic series o f two-bladed and w i t h two systematic
series o f five-bladed a e r o f o i l propeller models, designed in accordance w i t h practice i n 1950. Previously pub-lished results w i t h three- and four-bladed test series are completed w i t h results of tests w i t h propellers o f larger disc-area r a t i o and smaller pitch ratio. Charts of all series are extended by so called y.—cr design and analysis
diagrams.
. 5. W R I G H T , B . D . W . The N.S.W.B. standard series propeller data and their application, British Ship Research Assocn. T . M . 213, June, 1965.
T h e Netherlands Ship M o d e l Basin have extended the range of open-water tests on the Troost B-series propellers to include six- and seven-bladed propellers and have increased the range of blade-area ratios of the two-, three-, f o u r - and five-bladed series. I n this memorandum the results o f the whole series o f tests are presented i n the f o r m o f Bp—S and [i—a; design diagrams, t o g e ü i e r with a. selection o f w o r k e d examples illustrating the use o f these diagrams.
A brief discussion is included on (a) factors i n f l u -encing propeller design, (b) cavitation and (c) the usei of correction factors when departing f r o m standard series propeller dimensions.
6. H A R V A L D , S. A . Tug propulsion—wake, thrust deduction and rp.m., European Shipbuilding, Oslo, 1963, N o . 3.
T h e variation-of wake f r a c t i o n and thrust deduction co-efiicient w i t h speed, advance coefficient and thrust load coefficient has been determined on the basis o f model experiments published by different authors. The result is applicable f o r preliminary design of tugs. A diagram l i n k i n g wake fraction thrust deduction coefficient and block coefficient is given. Finally, the questions o f the most suit-able number o f revolutions and the propeller diameter are discussed.
7. P A R K E R , M . N . , and D A W S O N , J. Tug propulsion
investigation—the effect of a buttock-flow stern on bollard pull, towing and free-running performance. Trans. Roy. Inst. N a v a l Arch., 1962, 237.
A series o f model experiments was carried out to deter-mine the effect .of introducing buttock-flow stern lines on the performance of a tug under static (i.e., bollard trial), towing and free-running conditions. T h e models were tested w i t h a series of propellers, designed t o cover a range of revolutions f o r the same power absorption, correspond-ing to 1,100 h.p. f o r a 100-ft. full-scale tug.
F o u r model hiills were used: (1) Conventional f o r m A — this represented a t y p i c a l modern single-screw Diesel tug; (2) conventional f o r m B—^this was similar to conventional f o r m A , but the aperture was enlarged to enable a propeller of greater diameter to be fitted; (3) buttock-flow f o r m A — tilis had a buttock-flow afterbody, but was otherwise the same as conventional f o r m A ; and (4) buttock-flow f o r m B—^this had the same afterbody as buttock-flow f o r m A , but the forebody was redesigned on buttock-flow principles.
T h e results of the experiments indicated that the differ-ences i n the bollard and towing performances of the hull are small when they are fitted w i t h the same propeller, but, i n a l l conditions, f r o m static t o free-running, the con-ventional stem tends t o give a better performance than the buttock-flow stern. W h e n running free at a speed of 11 knots tiie buttock-flow f o r m s require 11 to 16 per cent more power than the conventional forms, depending upon the propeller fitted.
T h e results also show the advantage of a large-diameter propeller vritii l o w revolutions, particularly i n the static condition, b u t it is pointed out that i f the diameter is made
B L A D E A R E A C H A R T . M O D E R A T E L Y I X 3 A 0 E 0 S C R E W S . 4 B L A D E S .
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Va - SPEED OF KTMXX. IN KNOTS . ^ • EmaENCY IN OPEN WATER
0-2 0-3 0 - 4 0-5 0-6 0 ' 7 PROJECTED AREA RATIO Op
Fig. 1
too great there is the possibility that the propeller may "sing" when the tug is m n n i n g free.
8. D A W S O N , J. Tug propulsion investigation—the effect on performance of designing propellers for the free-running condition. Trans. Roy, Inst. N a v a l A r c h . , 1964, 106.
T h i s paper presents the r ö u l t s o f experiments carried out f o r the B.S.R.A. on a single-screw tug model, w h i c h had a conventional stem, to investigate the effect o n per-formance of designing projjellers f o r the free-running condition. T h e results are a continuation o f those given f o r bollard design propellers i n an earlier paper.
F o r many tugs speed is important, and it was considered that results f o r free-running design propellers, when com-pared w i t h those previously obtained, w o u l d t h r o w some light o n the perfonnance o f controllable-pitch propellers. Three p r o p e l e r s designed to cover a range o f revolutions f o r the same power absorption were used and the p r o p u l -sion experiments covered the static condition, towing at l o w speeds, and free r u n n i n g .
T h e marked effect o f whether a propeller is designed f o r ' the bollard or the free-running condition is clearly shown, and this indicates the possible advantages o f a controllable-pitch propeller. I n the range 130 to 270 r.p.m. covered by the Investigation, free-running speeds have been improved by approximately 14 to 17 per cent, compared w i t h the performance o f corresponding bollard design propellers.
T h e results also show that the original bollard pulls, w i t h
screws designed f o r the static condition, are f r o m 43 t o 19 per cent better than those obtained w i t h the corresponding free-running design propellers. The performance at l o w .«ipeeds could also be improved i f the propellers were designed specifically f o r the towing condition or, i n the case o f controllable-pitch propellers, i f the pitches were adjusted to intermediate positions.
9. M O O R , D . I . An investigation of tug propulsion,. Trans. Roy. lost. Naval A r c h . , 1963, 105.
This paper presents the results o f a series of tests carried out on a model o f a single-screw tug i n an investigation of its propulsive characteristics.
Resistance experiments were conducted over a range o f speed-length ratios o f 0.40 t o 1.30. Propulsion experi-ments, both free-running and w i t i i various towing pulls, were made over the same speed range and i n the bollard condition, with three difl'erent propeller designs. The results are presented f o r a 100-ft. ship.
On the average, the m a x i m u m towing h.p. is available at 0.64 o f the running-free speed attainable, and is 0.45 o f the d.h.p. The corresponding r.p.m. are 0.93 o f those when the vessel is running free at the same d.h.p.
The bollard p u l l w i t h the propeller revolving ahead is 1.66 of the towrope p u l l corresponding to the m a x i m u m towiing h.p., and the corresponding r.p.m. are 0.81 of the running-free r.p.m. F o r a given towing puU, with the propeller revolving astern, d.h.p. and r.p.m. are, on the average, respectively 1.92 arid 1.25 o f those obtained w i t h the propeller revolving ahead.
10. O ' B R I E N , T . P. Some effects of blade-tliickness
varia-tion on model screw performance, Trans. N . E . Coast Inst.
Engrs. Shipb., 1957, 73. 405.
Calculations and experiments have been made f o r t w o groups o f screws, one having N . P . L . sections and the other ' having segmental sections, each o f varying blade thickness. Performance values have been calculated f o r non-cavitating conditions by alternative methods and the results com-pared w i t h those obtained by testing model screws i n open water. The calculations have been extended i n a simplified f o r m to cover the range o f a four-bladed model screw series so as to provide thickness correction factors f o r pitch, power and efficiency. Some o f tiie model screws have been tested i n the Lithgow water tunnel.
I n an appendix some calculated results are given to enable the increase i n blade area f o r a given increase i n blade thickness to be estimated.
11. O ' B R I E N , T . P. Some effects of variation in number
of blades on model screw performance. Trans. N . E . Coast
Inst. Engrs. Shipb., 1965, 81, 233.
This paper gives the results o f calculations and experi-ments f o r two groups o f model screws, one o f standard . type and the other of non-standard type, both comprising
screws having three, f o u r and five blades. I t includes comparisons o f performance under non-cavitating and cavitating conditions based on calculations, open-water experiments and water-tunnel experiments.
For standard type screws, correction factors are derived and design data are given which enable three- and five-bladed screws to be designed using four-five-bladed standard series data as the bases. • For non-standard type screws, correction factors a d d i t i o n a l to those applied i n m a k i n g the basic design calculations are given, enabling closer agreement to be obtained i n the performance o f three-, four^ and five-bladed screws designed using detailed calculations.
12. O ' B R I E N , T . P. De.<:ign of lug
propellers—per-formance of three-, four- and five-bladed screws, S H I P AND
B O A T B U I L D E R I N T E R N A T I O N A L , L o n d o n , N o v e m b e r and
December 1965, 18, and January 1966, 19.
This group o f articles discusses differences between the performance o f three-, f o u r - and five-bladed screws both under non-cavitating and cavitating conditions. I t summarises N . P . L . model experiment data, and i t com-prises correction factors and design, data which enable three- and five-bladed screws to be designed, and comparative performance estimates to be made, using f o u r -bladed standard series data as the bases. I t gives ex-amples on designing additional three- and five-bladed screws f o r a singlescrew t u g ' f o r which data f o r f o u r -bladed screws are available.
The results o f the calculations show that reducing the number o f blades f r o m f o u r to three results i n improved performance, but that increasing the number o f blades f r o m f o u r to five generally results i n adverse performance. For a three-bladed screw designed, f o r free-running con-ditions the increase i n efficiency would be 2^ per cent, and at towing conditions the increase i n p u l l w o u l d be H per cent. F o r a three-bladed screw designed f o r towing conditions the increase i n p u l l w o u l d be 1 per cent, but at free-running conditions there w o u l d be no change i n per-formance. F o r a five-bladed screw designed f o r free-r u n n i n g conditions the free-reduction in efficiency w o u l d be 4 per cent, and at towing conditions the reduction i n p u l l w o u l d be 5, per cent. F o r a five-bladed screw designed f o r towing conditions the reduction in p u l l w o u l d be 5 per cent, but at free-running conditions there would be an increase i n speed o f i per cent.
13. O ' B R I E N , T . P. Design of tug propellers—optimum
screw diameter and rate of rotation (not yet published).
This discusses the results o f varying the screw diameter and the design rate of rotation and the effects on per-formance under both non-cavitating and cavitating con-ditions. I t describes a procedure f o r m a k i n g allowance f o r variation f o r d ^ a r t u r e f r o m basic blade-area ratio and blade-thickness ratio. I t comprises worked examples f o r tug screws designed f o r both free-running and towing conditions.
The results show that f o r the free-running screws small improvements i n performance can be achieved i f the design rate o f rotation can be selected, and that significant improvements i n performance can be achieved i f also the screw diameter can be increased w i t h i n practical limits of aperture size ( f o r single screws) or tip clearance ( f o r twin screws). F o r these screws operating at towing conditions, the change i n rate o f rotation results i n adverse per-formance, but the change d f both rate o f rotation and diameter results i n improved performance.
For the screws designed f o r t o w i n g conditions the change i n rate o f rotation results i n adverse performance, but the change i n both rate o f rotation and diameter results in improved performance. F o r tiiese screws operating at free-running conditions botii the change i n rate o f rotation only and the change i n rate o f rotation and diameter result i n improved performance.
Selecting a typical 9 ft.-diameter screw designed to operate at 200 r.p.m. as the basis, it was f o u n d that tiie o p t i m u m rate o f rotation w o u l d be 160 r.p.m. and the resulting increase i n efficiency w o u l d be 2 per cent. M o r e -over, i f the rnaximiim diameter consistent w i t h aperture size ( D = 10.25 f t . ) were selected, the optimum rate o f rotation would be 140 r.p.m. and the resulting increase i n efficiency w o u l d be 8 per cent. A t towing Conditions tiie change i n rate o f rotation would, result i n a reduction i n p u l l o f 4 per cent, but the change in both rate o f rotation
and diameter w o u l d result i n an increase in p u l l o f 6^ per cent.
For a 9 ft.-diameter screw designed t o operate at 160 r.p.m. at towing conditions there w o u l d be a reduction in puU o f 2i per cent, but at free-running conditions there would be an increase i n speed o f 4 per cent. F o r a 10.25 ft.-diameter screw designed to operate at 140 r.p.m. at towing conditions there would be an increase i n p u l l of 7 per cent, and at free-running conditions there w o u l d be an increase i n speed o f 3 per cent.
14. O ' B R I E N , T . P.' Graphs and contour charts and
applications to propeller design, European Shipbuilding,
Oslo, M a r c h 1965, 14, 2. •
. This note describes simple graphs relating two variables and contour charts comprising three variables. I t describes methods f o r constructing contour charts, and it gives two examples; one where the relation between the variables is of a simple mathematical f o r m , and the other where it is of an empirical f o r m .
15. O ' B R I E N , T . P. Propeller design and two-speed
gearboxes with particular reference to tugs and trawlers.
S H I P A N D B O A T B U I L D E R I N T E R N A T I O N A L , L o n d o n , N o v e m
-ber 1964, 17, 41 (reprinted i n Ship Division Tech. M e m o . 79, February 1965).
This article discusses the differences i n performance o f screws designed f o r free-running conditions and towing-duty conditions, the f o r m e r when towing and the latter when r u n n i n g free. I t shows that significant improvements in performance f o r both types o f screw can be achieved b y using two-speed gearboxes enabling the optimum rate o f rotation to be chosen f o r both free-running and towing conditions. Equations are derived and coefficients are given to enable design and operating conditions to be chosen to give o p t i m u m performance.
W o r k e d examples are given, the results o f which show that f o r a screw designed f o r free-running conditions and driven via a single-speed gearbox the loss in t o w i n g p u l l w o u l d be 22 per cent, but i f a two-speed gearbox were fitted the loss in towing pull would only be 3 per cent. Similarly, f o r a screw designed f o r towing conditions and driven via a single-speed gearbox the loss i n free-running speed w o u l d be 15 per cent, but i f a two-speed gearbox were fitted the loss in free-running speed w o u l d only be H per cent.
Research in Progress at the N.P.L.
In addition to t h e list o f data already mentioned, t w o research projects at present being undertaken at the N . P . L . are listed below. The first (16) is a continuation o f an investigation into the effects o f varying the geometric features o f a series of model screws (10 and 11 above). The second (17) w i l l provide both propulsion data and screw design data f o r tug propellers. I t f o r m s two parts— (I) o n tug propulsion and ( I I ) on propeller design. T h e preliminary work f o r Part I is i n h a n d : the items com-prising Part I I , some o f w h i c h have been published (3, 12 and 15), are Ibted in Table 2. A synopsis o f the first project and an outline o f the second project are summarised below.
16. O ' B R I E N , T . P. Some effects of variadon in blade
area, blade outline and boss diameter on model screw performance.' (Completed—awaiting publication.)
This paper gives the results o f experiments f o r three groups of model screws, covering variations i n blade area, blade outline and boss diameter. I t includes comparisons of performance under non-cavitating and cavitating
con-Table 2. Design of Tog Propellers—Proposed Outline of Work, January 1966
Item Topics Remarks
1 Aspects o f propulsion I>esign considerations Design charts. Cavitation
charts.
Stress calculations. Weight and moment o f inertia Worked examples
Published April 1965 (Reference 3)
2 Comparison of three-, four-and five-bladed screws
Published November 1965 (Reference 12) 3 Effects of variation in diameter
and rate of rotation
Not yet published
4 Effects of variation in blade shape and boss diameter
Preliminary work in hand
.5 Comparisons o f ahead and astern performance. Design of astem-duty screws 6 Controllable-pitch screws 7 Nozzle screws
8 Altemative propulsion units (steam, Diesel, Diesel-electric)
9 Two-speed gearboxes Published November 1964 (Reference 15) 10 Overall comparisons, optimum
combination o f screw and propulsion unit
ditions based on open-water experiments and water-tunnel experiments. Correction factors are derived and design data are given which enable screws of different blade area, blade outline and boss diameter t o be designed, and c o m -parative estimates o f their performance to be made using data f o r a standard screw as the bases.
17. O ' B R I E N , T . P. A thesis on tug propulsion and
pro-peller design. ( I n preparation.)
Part I—^Propulsion: Analysis o f N . P . L . resistance and propulsion data f o r tugs, derivation o f basic screw design data. Proposed outline is as f o l l o w s : Analysis o f propul-sion experiment results. Assessment o f basic data, includ-ing geometric features o f screws, values o f wake f r a c t i o n and h u l l f a c t o r at free-running conditions, a n d values o f pull-thrust ratio and p u l l at towing conditions. D e r i v a t i o n of design data comprising charts f o r estimating propulsion factors f o r free-rimning screws and pull criteria f o r towing-duty screws.
Part II—Propeller Design: Dissertation on general aspects o f propulsion, application to t u g screws operating at free-running and towing conditions, design charts, cavita-tion charts, strength criteria. W o r k e d examples on design-ing screws and makdesign-ing performance estimates at free-run-ning and towing conditions. Investigation i n t o effects o f variation i n number o f blades, blade shape, boss diameter, screw diameter and rate o f rotation. Comparisons o f per-formance o f fixed-pitch, controUable-pitch and nozzle screws. Propulsion estimates f o r astern conditions. Altemative propulsion units and two-speed gearboxes. For proposed outline see Table 2.
