Marine Technology, Vol. 20, No. 3, July 1983, pp. 209-226

Marine Technology

Twin-screw 5600-hp towboat pushing a barge train

River Towboat Hull and Propulsion

Bob Christopoulos ~ and Robert Latorre 2

With the growth of inland barge transport there is a continued interest in improving the design of the towboat hull and propulsion. Drawing from a large amount of experience in towboat hull and propulsion design this paper presents a review of recent European research in towboat hull form, summarizes the trends in tunnel stern design, and illustrates the design of a towboat propeller. The design concerns a twin-screw, 5600-bhp towboat pushing a 15-barge tow in deep (45 ft) and shallow (16 ft) water.

1 Manager, Naval Architecture and Marine Engineering, American Commercial Barge Line Co., Jeffersonville, Indiana.

2 Associate professor, Department of Naval Architecture and Marine Engineering, University of New Orleans, New Orleans, Louisiana. Presently, visiting scientist, Bassin d'Essais des Carenes, Paris, France

(formerly with The University of Michigan, Ann Arbor, Michigan). 3 Numbers in brackets designate References at end of paper. Presented at the January 28, 1982 meeting of the Great Lakes and

Great Rivers Section of THE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERS.

JULY 1983 0025-331618312003-0209500.6110 209

I n t r o d u c t i o n

TOWBOATS pushing multiple-barge tows such as shown in the frontispiece are a common sight on the inland waterways. Pres- ently about 12 percent of the intercity freight moves on the 25 000-mile inland navigation system. With continued emphasis on economy in transportation, use of coal, and export of grain and coal, it has been est imated tha t "barge traffic on the Missis- sippi-Ohio system would double by the end of the century, in- creasing from 624 million tons to 1.27 billion tons" [1]. 3

This growth was reflected in the shipbuilding on the inland waterways. The Annual Report of the Status of the Shipbuilding and Ship Repair Industry in the United States I980 confirms this growth. I t reports that inland shipyards capable of building barges deliver about 2200 units annually. The number of inland barges (hopper, deck and tank) was predicted to increase 24 percent from 23 000 (1980) to 28 500 (1990). The delivery rate of towboats has already increased from 100 vessels per year (1965) to 140 (1980). The present towboat fleet estimated at 3200 vessels (1980) may reach 4500 vessels by 1990 [2].

With this growth in inland waterway barge traffic there is a continual interest in improving towboat design. While the de- signer can refer to a number of published papers on the ar- rangement of towboat machinery and accommodations [3, 4], there is relatively litt le published material on contemporary high-power towboat hull form, tunnel stern, and propulsion system design [5, 6]. This is unfortunate since one of the main design requirements in towboat design is to deliver the thrust required for pushing the barge tow. Obtaining this thrust requires the designer to consider a number of factors, including:

• Propeller loading related to the operating conditions: 1. number of barges being pushed, 2. loading of barges, 3. water depth, and 4. current speed and direction. • Inflow into the propeller related to the preceding factors 1-4

and towboat hull: 5. hull lines, especially tunnel stern, 6. orientation of ahead and flanking rudders, and 7. propeller design. In many cases the relationship of each item to the towboat

propulsive efficiency may not be clear. Among the more critical factors is the waterway depth which limits the propeller diameter and reduces the propulsive efficiency. The use of systematic ducted propeller studies [7, 8], adopting tunnel stern hull forms to increase the propeller diameter (Fig. 17) [5, 6], and using twin, triple, and sometimes quadruple propellers [9] have allowed the designer to obtain a steady increase in propulsive power. Model test results similar to Figs. 3 and 11 have shown that a towboat pushing a barge tow has a propulsive efficiency 7o of 0.30 to 0.40:

Pu ~D - (1)

PD where

PE = ehp towrope hp = RV/550 PD = hp absorbed by propeller(s)

In contrast, oceangoing supertankers have values of 0.5 to 0.6, and typical high-speed containerships may reach values of 0.6 to 0.7. Volker at t r ibutes the low towboat rid to a "suction force" which appears as an increase in the thrust deduction t when the towboat propellers operate between tree running and push towing conditions [10].

While the relationships of the other items to the propulsive efficiency may not be clear, it is worthwhile to a t tempt a summary of the large amount of experience in towboat hull and propulsion design. The authors felt it t imely to review recent European re- search in towboat hull design, characterize recent high-powered

towboat tunnel stern designs, and present an example of the propeller design for a 5600-hp, twin-screw towboat pushing a 15-barge tow in deep (45 ft) and shallow (16 ft) water.

S t u d i e s o n t o w b o a t h u l l f o r m [ 11-14]

Recently several papers [11, 12, 13] were published in Germany summarizing research on the propulsion of towboats pushing barge trains in shallow water. These studies were done with 1:16 scale models in the shallow-water tank of the Versuchanstalt fur Binnenschiffbau e.V., Duisburg, West Germany (VBD).

The appearance of twin-hull catamaran towboats pushing barge trains on the inland waterways of the Soviet Union prompted a VBD research project to compare the performance of a conventional twin-screw towboat and the catamaran towboat [12]. The principal particulars of the towboats are summarized in Table 1. The lines of the towboat and barge models used are shown in Fig. 1.

In the tests four barges were arranged stern to stern in two rows (2 X 2) in front of the towboat. The self-propulsion tests were conducted in shallow-water conditions representat ive of a 5-m water depth. The results of the self-propulsion tests are sum- marized in Figs. 2 and 3. I t is clear that the catamaran towboat when tested without rudders or nozzles has about 10 percent lower power than the conventional towboat for the same speed at barge drafts of Tc = 3.2 and 2.8 m. Later tests with dueted propellers and rudders were inconclusive. This was due to the rudders not being set optimally to the incoming flow. In Fig. 3, the riD-Values are in the range of 0.3 to 0.35 typical of towboats operating behind a barge train in shallow water. Figure 3 indicates that the advantage of the catamaran towboat hull is in the lower values of the thrust deduction t which contribute to a higher hull efficiency ~H:

(1 - t ) ~H - (1 - w) (2)

where

w = wake fraction; Va = (1 - w)V t = thrust deduction; R = (1 - t)T

R = total resistance T = propeller thrust V = tow velocity

Va = local velocity seen by propeller

Detailed measurements of the wake behind the barge train with and without the towboat were also reported. The ratio of the

Table 1 Comparison of conventional and catamaran towboat and barge particulars [12]

Catamaran Conventional Barge

M 799 Length LWL, m 35.00 Beam, B, m 14.00 Beam hull, m 5.00 Draft, T m 2.00 a Displ., w m 3 541.78

M 771 35.OO 76.00 14.00 11.33

517.08 2528.83 (TL = 3.2)

2195.00 (TL = 2.8)

PROPELLER DESIGN Diameter, D, m 2.1 2.1 Pitch/dia, P/D 1.052 1.052 Area, Ae/Ao 0.710 0.710 Blade No., z 4 4

NOTES: Model scale 1:16. a Catamaran hulls have deeper draft to obtain equivalent displace-

ment.

210 MARINE TECHNOLOGY

O 1 2 3 4 5 G 7 8, 9 15 1G 17 18 19 20

7.5 m iSETWEEN SHAFTS 1.55mFROM B.L. TO TRANSOM BOTTOM

a) CONVENTIONAL TOWBOAT VBD M-771

, , , , , , , i , , , , i , , , , , , , , , , ' ' ' l l " I ' I I z / I

SHALLOW WATER TESTS

h = 5 . 0 m 4 B A R G E S

T = 2 . 8 m a n d 3 . 2 m

~WLII!I ~. . - -d~l l 2 20

9.0 m BETWEEN SHAFTS 1.55m EROM B.L. TO TRANSOM BOTTOM

O 1 2 3 4 5 G 18 19 20

b) C A T A M A R A N TOWBOAT VBD M-799 Fig. 1

LW L ~ --

V B D M 7 5 1 - 7 6 2

O 1 1G '17 18 19 20

c) S T A N D A R D "EUROPA H" BARGE Hull lines of VBD towboat and barge models [12]: (a) conventional towboat model M771; (b) catamaran towboat model

M799; (c) Europa standard barge models M751-762

TRIM FORWARD

5 6 7 15 V TRIM & S NKAC,4~-'9,'- ~--'-'~----~-----~ "- "-- --'K------7" ' - - ' - - ~ . ~ T RIM

cOl._ TOWBOAT / / 7--r--7~- ~T PROPULSION TESTS / ] / I I I t

S I NKAGE RESISTANCE AND PROPULSION TESTS WITH BARC4E TRAIN

PD WPS

n

4000 (2o

3 0 0 0 -2OO

5O

2 0 0 0 !100 (10oo)

1OOO

0

Fig. 2

c: : l I I M-771 WATER DEPTH h: 5Ore or M-799 TOWBOAT WITHOUT

RUDDERS AND NOZZLES

CONVENTIONAL TOWBOAT DRAFT T :1 .75 m

. . . . CATAMARAN TOWBOAT DRAFT T : 2 . 0 0 m

, ?oo

/

¢ ~ / / 1OOO

L TL= 3 20

I 4 5 G 7 8 9 10 11 12 13 14 kVm/h

Comparison of resistance and propulsion tests [ 12], conventional and catamaran towboats pushing a barge train

Fig. 3

TOW BOA T ~ C O N V E N TIONAL . . . . CATAMARAN . ~....~ TLz 3-20 m

]CL - l - W I W A K E [ ~ J - - ' T L ' - 2.8Orn o.41 ~ I W M~-ASURE'DWlTHOUT .

-_~. d ' - ' ~ "~.~T'L: ~.s0,~ • F [ ~ I - ~V;;IRDOEMNTIHTRyU ST -

°.11 J - "

0.3Tc3.2o ~ " - - " - _ . . . . . m : .

QU,ASI-PROP ULSIVE CQEFFICIENT I

02 ' '

EFFICIENCY ,"~";

1,2 I - - "~ '"° '" '"" CO,r, TL: 3.20m~.. . . . . ~ " ' ~ ' = =

1.1

~ F F I ~

10[ 80m

I j TL: BARGE TRAIN DRAFT i I I i

9 10 11 12 13 14 V km.~

Self-propulsion test results [12], conventional and catamaran towboats pushing a barge train

JULY 1983 211

i M E A S U R E M E N T

P L A N E

TOW £

3 . 7 5 m 4 . 5 0 m

- - -o.~s L 4 ;] % ~ , r , ? ~,

- -" T I "; 't// i ' " ; ? I , , :

")5.f :°~-s,. : ' ~ ' o / I V~//v = O, 7

Fig. 4

h : 5.O0 m TL: 2 . 8 O m

CONV. CAT. V : 12 .78 km/h

PROP. PROR BARGE & &

LWL

A.4~b.Yl ,,, , ~' . . - p .2s - ~ ? I(/! r-; '. i 1,' ~ - - - - M ' :O,80 t . .4

,.', )1".1 ; I f l * ~ ° ~ . " I

Wake field V a / V o f barge train without towboat measured at 0.4D ahead of propeller plane [12]

I t P L A N E h= 5 . 0 0 rn M 771 TL= 2 . 8 0 m

Fig. 7

p-

Change in wake field ( Vpro Vn o - - V for conventional towboat ~t2]

M E ASUREM ENT P L A N E M 7 7 1 i ~ I h : 5 . 0 0 rn

TL: 2 . 8 0 m

• V -- 12.78 km/~

Fig. 5 Wake field V a / V o f conventional towboat pushing a 2 X 2 barge train--measured without propeller at 0.4D ahead of propeller plane

[12]

' , i ~ . . ~ - . J - ~ ~I . .Z..____J~..=,,," M E A S U R E M E N T

i L I I I I I I P L A N E ~ ~ I h = 5 . 0 0 m M 7 9 9 TL= 2 .SOm

V = 12,78 kmjh

,", :,, ' , : I :

' - ' Z , ' 7 ~ 0 . 2

Change in wake field ( Vpro[o12] Vno prop)/Vfor catamaran towboat

LWL

--~,1-I X • - O . 1 5 _t l

2 ~ 1 ""1 / /, 1 > O,1--

I I :~f y ,,,x

Fig. 8

, , ~ - - - ~ . . . . . . . ~ ~ M E A S U R E M E N T

P L A N E M 799

Lw

VJv o.~ 0.7

Fig, 6 Wake field Va/V of catamaran towboat pushing a 2 X 2 barge train--measured with propeller operating at 0.4D ahead of propeller plane

[12]

h= 5.OO m Tff 2.80 m

V :12.78 km/h

local velocity Va to the tow velocity V is plotted as contours of Va/V and wake fraction w in Figs. 4-6. Since the barge draft TL = 2.8 m is deeper than the towboat T = 1.75/2.0 m, the wake from the barge tow dominates the flow conditions at the propeller plane• The towboat hull tends to flatten the Va/V contours in the propeller plane. The tunnel top flattens the contours into nearly horizontal lines in Figs. 5 and 6.

When the operating propellers are present, there is a change in the flow pattern shown by contours of AV defined as

A V - Vwp -- Vnp V (3)

where

Vwp = local velocity with operating propeller Vnp = local velocity without propeller

V = tow velocity

in Figs. 7 and 8. The values of AW are larger for the conventional towboat (Fig. 7) in comparison to the values for the catamaran towboat (Fig. 8). This reflects the higher hull efficiency of the catamaran towboat.

VBD also completed an extensive study of triple and qua- druple-screw towboats pushing a six-barge train [13]. Table 2 summarizes the main particulars of the triple-screw towboat VBD Model 838 and Fig. 9 shows the hull lines. The self-pro- pulsion test results for the towboat are summarized in Figs. 10 and 11. The more streamlined tow arrangement (~ in these fig- ures accounts for the lower resistance and the higher towing speed

• attained. The improvement in the towboat performance from using nozzle propellers is evident in Fig. 10. Figure 11 shows the significant influence of the barge tow arrangement on the pro- pulsive factors. The propulsive coefficient ~H drops from 0.37 to 0.28 when the tow arrangement is changed from (J~) to (~).

The velocity distribution given by contours of VJV in Fig. 12 has the same horizontal pattern in the outboard propeller. The change caused by the operating propellers is evident when Figs. 12 and 13 are compared. Earlier VBD tests with the towboat fitted with ducted propellers also included wake measurements. Figure 14 shows measured Va/V for the conditions in Fig. 13. The high values of VJV approaching 2.0 illustrate the effectiveness

212 M A R I N E T E C H N O L O G Y

' 1 o _ _ . o o

I/ l i I TRA~ISQM 3

L : 3 5 . 0 0 m T : 1 . 7 0 m C~

B : t 4 . 9 5 m g : 5 5 3 . 5 m 3

... I 1 I 1 I li

:L 14 15 16 17 18 19 2 0

0 1 2 3 4 5 m

Fig. 9 Lines of VBD triple-screw towboat [13]

. ~ - / / / Lw.._&L

Table 2 Particulars of triple-screw towboat and barges [13]

Towboat Barge

Length LWL, m 35.00 74.00 Beam, B, m 14.95 11.33 Draft, T, m 1.70 3.00 Displ., v , m a 553.50 2359.70

P R O P E L L E R D E S I G N Diameter, D, m 2.10 Pitch/dia, P/D 1.052 Area Ratio, Ae/Ao 0.710 Blade No., z 4 Rotation direction

from aft:

4 0 0 0

G ~ I I i.J ~ ! 'l

P~ ~T~ BARE

PS 5000

n S rpm

3OO

200C - 1 0 0 4 - -

1 0 0 0

3000 .200

/ /

% I

- - 0 1

5.0 10.0 v s Km~

20

30

4O

HRUST Mp

I

Q r - q ' i ', ~,

o.2~- ~

t THRUST DEDUCTION

0.2 ~ ( ~ )

°-11- 1 I •

W T WAKE F R A C T I O N

/sTep I L

o . ~ -----~'t Q / " I

WT I MIDDLE 0.4 P.O," CfO..~----~ 0.3

I L _

10 17 14 VS km~l

Fig. 11 Self-propulsion test results showing influence of barge train ar- rangement [13]: Triple-screw towboat pushing six-barge train for test

conditions shown in Fig. 10

~ . . Fig. 10 Resistance and propulsion tests for six-barge train pushed by the triple-screw towboat in Fig. 9 [13]

213 JULY 1983

I it_...... - .,,x.. ~r ' ~ ] , ~ ~ ~ ~ , MEASU~EMEN, --~ ~ L . - - L . J ~ L . . . J

P L A N E I h = 5 . O 0 m

J

~ , 7 . g . t " t - o . , ' - 2 . - ~ < " - ~ ' - " " ~ " ~ ~ _.. j 7"9,-~ 1~ P.~.,o.,,k I,' l/,7 C'_-I--~C

-,

Fig. 12

-li Wake field Va/Vof triple-screw towboat pushing a 3 X 2 barge train--measured without propellers

at 0.4D ahead of propeller plane [ 13]

of the duct in accelerating the flow into the propeller. In closing this discussion we refer to the experimental s tudy

of Borozoni [14] on the influence of water depth h on the pro- peller characteristics. The single-screw shallow-draft tunnel stern model I is shown in Fig. 15 (CB = 0.595, L = 2.4 m, B = 0.28 m, T = 0.062 m). The propeller characteristics were D = 80 mm, z = 3, P / D = 1.04, and Ae/Ao = 0.63. The self-propulsion tests were completed at the Leningrad River Transpor t Insti tute, USSR. The results are shown for different depths h in Fig. 16. This figure indicates that the influence of the shallow water h i T < 6.0 is large in the range of advance coefficient J between 0.14 and 0.4:

Va J - n D (4)

where

Va = local velocity seen by propeller

n = propeller rps D = propeller diameter

This drop in the thrust deduction (1 -. t) when the advance ratio J is between 0.14 and 0.40 is similar t< the observations of Volker [10].

These various studies make it possible to grasp something of the operating conditions of the towboat propeller as well as the influences due to changes in barge wake, towboat hull, tow ar- rangement, nozzle propellers, and water depth.

Towboat tunnel stern designs

While operational requirements will dictate the barge number, draft Tt, and the water depth h, the designer can insure adequate water inflow to the propellers by proper design of the towboat tunnel stern. A comprehensive review of tunnel stern designs in

L ~ i I i

/ //l, rl/Jf ,I. " " F\ ~i ,k'J~ .x ~ / _ L Z L A _ / " I I \ I~ ',\1,"

\,~ ' t t ~ ~ t . . r l , , l / I 1 { ~ ~ /ill

o,.\~,] O.~o8~2~._v,~,.0 _ , '

/ ~ ~ I o,~

Fig. 13

M E A S U R E M E N T

.PLA"E~, I i ---'. A ' -- :-- / 8] h=~.OOr. VS : 1 2 . 5 7 k m h

~ [ . n = 2 2 8 r p r n

','1/,;17 ,f " ~ l \l ~ ~1 : t ' f l ,~, l~ ' , \ ' , l - " ', II i q i ~ L'~L'E~,~![I'~ . ~ ,I Ill ~7{~:7;! o,'~ ~ .~, ~ . 'E~ ' : '~ ' " j,.," I,'IIA Vf \",~\

Wake field Va/V of triple-screw towboat pushing a 3 X 2 barge train--measured with operating propellers at 0.4D ahead of propeller plane [ 13]

214 MARINE TECHNOLOGY

MEASUREMENT

PLANE i 1 h = 5 , 0 m

' . , " , ~ 1 4 ~ '

Fig. 14 Wake field Va /V of triple-screw towboat pushing a 2 > 3 barge train--measured with propellers operating in ducts at 0.4D ahead of propeller plane [13]

the 1950's was published by Saunders in 1957 [5]. Allan has re- cently reviewed the design of multiple-screw tunnel sterns for operation in restricted water depths [9[. Several naval architects have developed schemes for the tunnel stern arrangement and .wL~ prepared design guidelines [6, 15, 19, 20[. Baier [6] used the scheme shown in Fig. 17(a). In Bogdanov's book [15] a similar scheme is adopted along with the design recommendations in Fig. z 17(b). Heuser [27] developed a more detailed scheme for the 0 tunnel stern with nozzle propellers. This scheme is shown in Figs. 17(c-1) and 17(c-2) along with the design recommendations. Lederer [19] has developed a tunnel stern arrangement based on the propeller diameter shown in Fig. 17(d).

Baier's 1959 paper [6] appears to be the main source of pub- lished data on tunnel stern designs used in contemporary U.S. towboat designs. However, it should be updated to reflect the

N b,,+,

I I I 7' ,111#1+ i i I I li']'i,I..,,

[ iZ

Fig. 15 Lines of Model 1 [14]

subsequent introduction of larger tows and more powerful tow- boats. This update was accomplished with the cooperation of several designers and towboat builders. Tunnel stern data fol- lowing the characterization in Fig. 17(a) were collected for over

0

Fig. 16

x L , . . , . I I I I I I I I I I I I ~

M I I ! ilr--'*.//////~" UOr! L : : : : i i A ~ - i . . . "

~r!!Itii ..-!! ~ i i

!l !! i ! ! ! i !

!i !i

b-.4,

J i l t !!

I i t l l i t l l l t l l i • C~ o.? O.8

i i i

i i '.i ! !

! ! !¢,0 , : 0 , j

: : 0,7

- - 0,~

Variation of propeller performance at different channel depths h [14]. Notation: K1 = KT, K2 = Ko, Ke = K ~ l _ t), X = J = Va/(nD), 1/prop = (Ke /K2 ) / (X /2~ r )

215 JULY 1983

A) TUNNEL STERN DESIGNI6] [151

I T I

i

A

PROPELLER PLANE

~ . , , , f ~ TUNNEL CE

FLECI'ION

12 --I Ii

W L - I - T t

L --TOWBOAT LENGTH -~..p

B) RECOMMENDED VALUES B.V. BOGDANOV[15]

0.33 ~ l l ~ S O.Z.5 6 _< ll/hT~ 7 0.I-< hT-T_<0.2 T

0.10_<12/{__< 0.20 12°_<O _< 15 ° O.05_<hTE-T<O.07 T

C-I)DUCTED PROPELLER TUNNEL STERN DESIGN H. HEUSER[27]

t ~ 1 1 ~ l - " 12~1-13-1 _ Y _ _ / I " 1 ,I

~t 4 ;-l~)-I z5 N9 ]

16 12 m_<L_<40 m 0,42 _< I6/L_< 0,58 5,4 -<16/D~:7,3

L/B_>I.60 0 .80- < 15116<-0.90 1.0_<14/D_<2.0 MINIMUM VALUES 13/~D_> 0.75 12/1~ 1.30 t = O. lOm hT-D = O.15m 15°-<O<'25° Oo<12°

IC

C-2) DUCTED PROPELLER TUNNEL STERN DESIGN H. HEUSER 1271

I I ZL-I. o2 i,

-w "WL--

propeller separation £ , [ . b2

0.02_< R/B<_ 0.04 0.52 <_ b2/B <_ 0.57 bl/D ~ 0.52 MINIMUM VALUES al_< 22° a2_< 19° t = O.10m tl = 0.20rn

D) DUCTED PROPELLER TUNNEL STERN DESIGN A.LEDERER [191

PROPELLER PITCH P/D = 1.094

Fi@. 17 Characterization of river towboat tunnel stern [6, 15-19, 27]

50 recently built towboats. The data are summarized in Table 3 [15-191.

The following discussion of the trends in towboat tunnel stern design makes use of the rsults from a subsequent study [20] completed after the original paper was presented at the Section meeting.

It was found that the preliminary sizing of the towboat length L and propeller diameter D can be estimated from the bhp/shaft [20]:

L = 62.0 + 7.5X - 0.235X 1.s (5)

D = 3.5 + 0.35X - 0.05X 2 (6)

where

X - bhp/shaft 100.0

300 < bhp/shaft < 3240 hp

The tunnel stern height hT and arrangement can be developed from the guidelines in Fig. 17. As Fig. 18(a) shows, there is a trend for the ratio D/hT to decrease from a value of 0.94 at 1500 bhp/shaft to 0.90 at 3200 bhp/shaft.

Vibration from inadequate water inflow/outflow in the tunnel is a design problem Baler treated [6]. Baler showed that two towboats which had excessive vibration, Nos. 42 and 62 in Table 3, could be isolated on a plot of (0 bhp/shaft)/T 2 versus bhp/shaft similar to the one shown in Fig. 18(b). The dashed line in Fig. 18(b) is given by [20]:

bhp/shaft [bhp/shaft] 0 T2 230.0 + 20.86 [ ~ I (7)

A simpler guideline developed by Latorre uses the "tunnel flow angles" 01 and 02 defined using the notation of Fig. 17(a) as

01 = tan-1 [ h/1 _-~-~j inflow tunnel angle (8)

Ih - q 02 = tan -1 [ - -1~-2 [ outflow tunnel angle (9)

The data in Table 3 were used to prepare Figs. 19(a) and 19(b). These figures indicate that contemporary towboat designs use 0 angles larger than Bagdonov's recommended 0 _< 15 deg. The data are in better agreement with Heuser's recommendation that 15 d e g < 0 _< 25 deg.

The limiting value of 01/0 in Fig. 19(a) is given by

01/0 < 1.14 - 0.018 0 < 1.0 (10)

The towboat designs exhibiting severe vibration are shown in this figure before and after redesign. For towboat 42, the value 01/0 = 0.56, which is below the guideline, and after redesign to towboat 43 the value 01/0 = 0.64, which is also under the guideline. For towboat 62, however, the value 01/0 -- 1.0, which is above the guideline. After the redesign to towboat 63, the value 01/0 -- 1.0, which is above the guideline given by equation (10). This is the reason why there was no improvement in towboat vibration after redesign.

The limiting value of 02/0 in Fig. 19(b) is given by

02/0 < 1.01 - 0.0486 0 - 0.00117 02 - 0.0000093 03 (11)

In Fig. 19(b) the value 02/0 = 0.518 for towboat 42, which is above the guideline given by equation (11). When the towboat is redesigned to towboat 43, the value 02/0 = 0.309, which is now under the guideline. This is why the vibration subsided to normal levels after the tunnel stern was redesigned to towboat 43.

Like any other empirical approach, the use of 0 i and 02 and the preceding guidelines will require further verification and refinement. In the interterm they represent a simple way to check whether there will be adequate inflow and outflow in the tunnel stern.

216 MARINE TECHNOLOGY

Table 3 Summary of river towboat tunnel [6, 15-18] (notation in Fig. 17)

Towboat Prop. bhp Type Code L, T, ll, 12, hT, 0, Prop. Dia, No. No. Shaft Tunnel (Fig. 18) ft ft ft ft ft deg ft Notes

1 1 1500 ()pen [] 105.00 7.50 48.00 11.00 7.92 16 . . . 2 2 205 KN • 64.00 5.50 26.25 6.50 5.50 26.0 3 2 290 KN • 70.00 5.83 27.20 7.00 4.68 21.5 4125 4 2 300 open O 70.00 5.83 27.20 7.00 4.68 21.5 4.25 5 2 300 + 65.60 3.60 22.30 7.87 4.37 . . . 3.93 6 2 425 KN • 70.00 5.83 27.20 7.00 4.68 21.5 4.25 7 2 460 . . . + 84.00 5.24 40.30 11.35 5.67 . . . 4.92 8 2 465 . . . h 82.02 5.08 36.09 9.97 6.24 20.0 . . . 9 2 465 . . . ,x 49.21 4.92 26.80 6.23 5.37 25.0 . . .

10 2 470 . . . + 59.06 5.41 27.75 6.10 5.55 . . . 5.08 11 2 475 + 60.04 4.60 30.00 3.56 5.88 . . . 4.92 12 2 490 KI~ $ 90.00 7.50 40.00 8.75 6.56 18.5 6.00 13 2 500 KN • 146.00 6.00 58.00 10.00 6.25 11.0 14 2 525 + 142.72 4.10 57.10 9.50 4.75 . . . 4142 15 2 600 KI~ • 120.00 6.50 50.00 14.17 6.50 18.0 16 2 600 . . . + 74.15 6.40 33.37 8.21 6.80 . . . 17 2 620 . . . + 112.20 5.25 38.15 14.30 5.30 . . . 5.02 18 2 630 . . . + 118.11 5.41 53.15 15.69 6.81 . . . 5.74 19 2 630 . . . + 118.11 6.07 53.15 14.19 8.46 . . . 5.90 20 2 640 KN • 115.00 6.50 42.00 12.00 6.50 16.0 21 2 750 + 125.00 5.90 45.00 12.34 7.25 ... 6140 22 2 765 KI~ • 50.00 7.50 40.00 8.75 6.56 18.5 6.00 23 2 800 open [] 110.00 6.50 44.00 9.50 7.33 18.5 24 2 800 KN • 132.25 6.75 52.00 12.50 7.85 15.0 71()(J 25 2 877 . . . zx 114.70 5.74 49.63 12.60 7.17 17.5 6.89 26 2 877 . . . h 114.70 5.74 59.22 12.59 7.50 12.5 . . . 27 2 900 open [] 135.00 6.00 42.00 11.17 6.42 17.5 6.42 28 2 900 open [] 120.00 7.50 42.00 12.00 8.25 24.0 29 2 900 KN O 105.00 9.00 54.50 12.29 7.81 14.75 7166 30 2 900 . . . + 100.40 4.75 39.15 11.36 6.31 . . . 5.90 31 2 900 + 118.44 5.58 41.45 12.90 6.79 . . . 6.23 32 2 1200 K~q • 142.00 7.00 56,00 13.00 7.83 19.0 . . . 33 2 1200 open [] 130.00 7.00 44.00 12.00 7.75 20.0 34 2 1280 KN • 148.00 8.33 62.00 15.21 9.02 16.0 815() 35 2 1400 KN • 160.00 8.00 56.00 16.00 9.00 21.0 . . . 36 2 1475 open [] 117.50 7.50 47.50 15.00 7.50 14.0 37 2 1500 KN • 165.00 8.17 49.50 14.00 8.75 17.0 81]'i 38 2 1600 + 129.92 8.00 54.56 11.44 8.80 . . . 7.51 39 2 1640 K]~ • 140.00 7.50 58.00 18.00 9.25 15.0 40 2 1640 KN • 148.00 8.33 62.00 15.21 9.02 16.0 8:5" 41 2 1750 KN • 165.00 8.17 49.50 14.00 8.75 17.0 8.17 42 2 1920 ()pen O 150.00 6.58 53.00 12.00 9.0 22.0 . . . 43 2 1920 open O 166.00 7.38 69.00 17.00 8.76 15.0 . . . 44 2 2000 KN • 160.00 7.75 56.00 17.00 10.08 19.5 . 45 2 2000 KN • 200.00 9.00 80.00 20.00 10.79 17.5 101(J 46 2 2160 KN • 148.00 8.33 62.00 15.21 9.02 16.0 8.5 47 2 2160 KN • 168.00 8.44 70.92 14.17 10.02 14.0 9.0 48 2 2160 KN • 164.00 8.50 74.00 17.00 9.67 18.0 9.09 49 2 2160 KN • 150.00 8.35 64.50 15.33 9.85 15.0 9.0 50 2 2180 ()pen O 138.00 9.00 52.00 10.00 9.50 17.0 8.5 51 2 2240 open O 150.00 8.50 52.00 12.00 9.00 17.0 8.33 52 2 2500 KN • 170.00 9.06 63.50 16.50 10.25 17.0 9.16 53 2 2575 KN • 166.00 8.35 70.50 16.25 10.75 15.0 9.75 54 2 2600 KN • 168.00 8.44 70.92 14.17 10.02 14.0 9.00 55 2 2600 KN • 150.00 8.35 64.50 15.33 9.85 15.0 9,00 56 2 2875 KN • 145.00 9.00 54.90 15,50 10.50 20.5 9.16 57 2 3000 KN • 168.00 8.44 70.92 14.17 10.02 14.0 9.00 58 2 3000 KN • 200.00 9.00 80.00 20.00 10.79 17.5 10.00 59 2 3200 KN • 192.00 8.75 82.00 22.25 11.15 15.0 10.00 60 2 3225 KN • 180.00 8.85 73.50 19.00 11.04 15.0 10.00 61 2 3240 KN • 145.00 9.00 54.50 15.50 10.50 20.5 9.16 62 3 480 open ~ 115.00 3.50 39.42 14.78 4.83 11.0 . . . 63 3 480 open ~ 115.00 4.5 39.42 14.78 4.83 11.0 . . . 64 3 657.8 . . . v 114.83 7.35 55.77 14.37 7.82 16.5 65 3 953 v 114.83 6.89 45.21 12.41 7.81 19.0 6189 66 3 1600 i(I~l [] 150.00 8.00 59.00 16.50 8.75 16.5 67 3 2875 KN O 180.00 9.00 61.00 16.50 10.5 17.0 911'6

VBD Model i~: 815 VBD Model No. 816

VBD Model 1~o: 771 (Fig. 1 ) VBD Model No. 789

Serious Vibration [6] Redesign of 42 [6]

Serious Vibration [6] Redesign of 62 [6] VBD Model No. 863 VBD Model No. 838 (Fig. 9)

I~EY TO SYMBOL CODE

No. Ref. [61 [16], [17] [18] [15] Propellers open a K N b open KN

1 [] 2 D • 0 t A -}- 3 [] [] O v

a open: propeller without nozzle. b KN: propeller in Kort nozzle.

JULY 1983 217

..L CO

m

- - I m o "r Z 0 t -

O

.<

DpROP

' I i I i ! i u i i i i n I I

hT 'IRI~/EIR TOWBOAT DESIGN

1.0 ~ ) D p R ° P / h T VS B H P / s H A F T

z~

• , 0 O ,I- 4,

0.9 ~o '~ . o+

÷ ~ ~ +

0 . ~ , , , , , , , , , , , , . . . . 0 500 1000

0

• •

I I I I I I I I

1500 2000 2500

BH P/SHAF T

I i I ,

3O0O

O B H P / 2 ~ - # E p / T

i ~ i , , i n I f I I I I I I

1200 ,RIVER TOWBOA[ DES]GN (~) BHP

0. SHAF_~___~T vs BHP/sHAFT lO00 T2

BHP , ~ ,

_ _ ~ s ~ _ _ _ ~ : ~ o . o , ~ o . ~ q ~

800

60C

40C

200

I

, j i i r f -

J • J <

- 0 j

REDESIGN/ P • - ~ , ~ 1 •

~ 1 m m 0 I

e L " I

I i I I I I I I I I 1 I i I I I I I I

0

REDESIGN

3

• 0 q

• ) •

I I t I I I I I I

I 1 I I I v I I I

f J °

J I • J

°

• - - ° i ~ -

I

I I I I

500 1000 1500 2000 2500 3000

BHP//sHA F T

Fig. 18 Trends in river towboat tunnel stern design

l r , , i

e e~ X - - - ~-= ~.14- o.o18.e

I I I ,

1 . 0 ~ ---,,,,,,,,..,,~

0.9 " ~ --....

0.8

03

0.6

0.5

[ ]

- 'a- - -----_

o ~

[ ]

I I ~ I I I I

12 13 14 15 16 17 18 19 20 21 22 23 24 25

0 DEG.

1.0

0.8

.6 -

0 .4 i

0.2

' I ' E ' v T 'o ' ' ' ' ' ' ' ' ' - R R W B O A T D E S I G N . ® o2/o v ~ o

0 2 _ _ _ _ ~ . - - = 1 . 0 1 - 0 . 0 4 8 5 5 0 - 0 . 0 0 1 1 7 4 0 2 _ _ 0 . 0 0 0 0 0 9 3 e 3

REDESIGN []

• V I

• []

I

!

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

@ DEG

Fig. 19 Relationship of tunnel stern inflow angle O1 and outflow angle O 2

E s t i m a t i n g t o w r e s i s t a n c e and t o w b o a t p u s h

Rationale. Often the question is asked: "Why do we have to know the tow resistance and towboat push?" The answer to this is simply that they are required to est imate the prel iminary stil l-water speed.

The resistance of a given barge tow is a direct function of its speed. The effective push for a given towboat will also be a direct function of its total horsepower and speed.

For efficient operation the barge tow and towboat must be in equilibrium so

E P = R T (12)

where R T is the resistance of the barge train in pounds and E P

is the effective push of towboat in pounds. The speed resulting from equation (12) is the design speed for

the towboat-barge train. This speed will be used in determining the opt imum propeller and in making economic tradeoff studies for setting rates and estimating travel t ime [28].

Studies on barge train tow resistance. Researchers have developed mathematical models and equations to use in pre- dicting barge train tow resistance. Many of the major barge line companies have made model tests to predict the resistance of a part icular barge two used in a dedicated trade, to enable them to maximize the efficiency of the towboat to be used.

Comprehensive studies for predicting barge tow resistance where published by Howe [21] and Bronzini [22].

Howe deveh)ped a resistance equation where the two resistance is a quadratic function of tow speed. This equation was developed from data taken from tow movements, towboat log books, model tests, and tests with 195 by 95-ft barge tow arrangements. The equation is given as

R T = 0.07289e l"46/(h-T)V2TO6+50/(W-B)LO3sBl '19 (13)

where

R T = total barge train tow resistance, lb e = base of natural log = 2.71828 h = channel depth, ft T = uniform barge draft, ft V = sti l l-water tow speed, mph

W = width of waterway, ft B = overall width of barge tow, f t- L = overall length of barge tow, ft

Bronzini developed a resistance speed function combining both empirical and theoretical results [22]. The following is taken from [22]:

R T = r / V 2 = T F (14)

r/ = K / ~ ri (15) t

r = O . O l l 8 B T 2/5 L + 70.5 L - : ~ /V l _--2~RI K c (16)

K c = 2.42C~ - 3.43c~ + 1.34 (17)

K / = n~,K/,, + nlK/1 (18) n 3 + n]

where

R T = total barge train resistance, lb r~ = total specific barge train tow resistance, lb-sec2/ft 2

T F = thrust force of towboat, lb V = sti l l-water speed, fps

K / = fastening coefficient, Fig. 20 K/e = fastening empty barge coefficient, Fig. 20 K/1 = fastening loaded barge coefficient, Fig. 20

ne = number of empty barges

Kf 1.0

0.9

0.8

0.7

0.6

0.5

Fig. 20

FASTENING COEFE Kf

,,~,,,,,AS A FUNCTION OF BARGE TRAIN

i-= E FN-7 ~ BARGE

2- LOADED BARGE l i l i l .... I0 20 30

BARGE NUMBER

Fastening coefficient Kt as a function of tow size [22]

nl -- number of loaded barges ri = individual barge specific resistance, lb-sec2/ft 2 r = specific resistance of each vessel, towboat/barge, lb-

sec2/ft 2 B = beam (width) of vessel, ft T = draft of vessel, ft L = length of vessel, ft

CB = block coefficient = v / L B T K c = resistance coefficient

v = displacement of vessel, ft 3

This formula does not directly account for the waterway depth or channel width. There are corrections for shallow water to use with this formulation.

Figures 21, 22, and 23 are examples of model test results. Such tank tests are usually made to answer specific questions. This enables the sponsoring companies to maximize towboat efficiency during the prel iminary design.

Figure 24 presents the barge train resistance curves developed by one of the authors from empirical and full-scale test data. These curves show the tow resistance versus the theoretical sti l l-water speed for a semi-integrated 15-barge tow in deep (45 ft) and shallow (16 ft) water.

Studies on towboat push and thrust. It was pointed out earlier tha t the effective towboat push and thrus t are directly functions of towboat horsepower and speed.

In [21] and [22] empirical formulas were published to estimate the towboat push. In [21] Howe's equation for the effective push appears as follows:

E P = 31.82 HP - 0.0039 hp 2 + (0.38 hp)h - 172.05 V 2 - 1.14V - HP (19)

where

EP = effective push, lb HP = towboat horsepower, hp

h = waterway depth, ft V = stil l-water equilibrium tow speed, mph

This equation was based on da ta from typical diesel-powered towboats.

In [22] the thrust force of the towboat is given by

T F = 26.4 hp (20)

where T F is the thrust fbrce produced by the towboat in pounds and hp is the towboat horsepower. Notice tha t this equation is not a direct function of the towboat speed.

Figure 25 was developed by one of the authors for a typical twin-screw 5600-hp towboat with l l0-in.-dia 5-bladed propellers operating in Kor t nozzles. This figure shows the towboat push

219 JULY 1983

150

100

~ 8 0 ",c

~ '60 C9 z ~ 4 o t~

a : 2 0

-50 4

Fig. 21

3000

EHP

20(%

I000

Fig. 22

RESISTANCE TEST WATER DEPTH h = 16 ft. BARGE DRAFTT = 9f t . /

/ KEY RESISTANCE OF - /

2 ~ TOWBOAT / (BEHIND BARGES) /

2

\

I 1 I I I 5 6 7 8 9 0

STILL WATER SPEED, MPH Model resistance test results for towboat with a fully integrated

barge tow 970 ft long by 105 ft wide

RESISTANCE TEST 6 x 3 TOW

TWIN SCREW TOWBOAT / LOADED BARGES T = 9 f t / WATER DEPTH h = 16ft / KEY /

I - -EHP CURVE / 2-RESISTA NCE / cuRv __/ /

I

R T

150

KIPS

- I00

50

t t I I I I 0 4 5 6 7 8 9 MPH

STILL WATER SPEED Model resistance test results for twin-screw towboat with a 6 X

3 barge tow

R T

150

KIPS

I00

50

Fig. 23

RESISTANCE TEST 6x 5 TOW

BARGE DRAFT T = 9 f t

I 2, 3,~

, 2\ 3\

/ / / i - - 1 2 f t RT r ~ . 1 " 2 - - / 6 f t .

L- / 3 - - 2 4 ft

EHP

2000

1000

- 0

i t 1 t t I 3 4 5 6 7 8 MPH

STILL WATER SPEED Model resistance test results for twin-screw towboat with a 6 X

5 barge tow at different water depths

as a function of still-water speed. It is based on empirical and full-scale data.

Es t ima t ing tow speed in sti l l water . It is possible for the designer to estimate the tow speed in still water using the fol- lowing:

1. Howe's equations (12), (13), and (19) 2. Bronzini's equations (14), (15) and (20) to obtain (21):

V = ~ . 4 _hp (21)

~/ KI ~i ri where V is the tow speed in unrestricted water. The speed V has to be then corrected for shallow water.

3. Model tank test results. 4. Empirical results such as Figs. 24 and 25 developed by the

author from full scale data. For comparison purposes of the resistance, push, and tow speed

from these various methods, we will consider a typical 5600-hp towboat pushing a 15-barge semi-integrated tow sketched in Fig. 24. The barges are typical raked hooper barges with L -- 195 ft, B = 35 ft, and D = 12 ft. The following will be assumed:

W = 1500 ft = width of waterway h = 45 ft = deep waterway depth h = 16 ft = shallow waterway depth

For the tow arrangement we have:

L = 975 ft = overall length of tow B = 105 ft = overall width of tow T --- 9 ft -- draft of loaded barges assumed to be uniform T = 1.5 ft = draft of empty barges assumed to be uniform

220 MARINE TECHNOLOGY

KIPS [

160

140

120

I00

80

60

40

20

0

ESTIMATED TOW RESISrANCE

I L I K E Y BARGE WATER

DRAFT DEPTH i

loaded sha l low I T = g f t h=16ft 2 loaded deep

T =9 ft h = 45ft 3 empty shallow

T= 1.5ft h=16ft 4 empty deep

T = 1.5 ft h = 45ft L =975 ft B = IO 5 ft

5 x 3 TOW

Fig. 24

2 4 6 8 10 12 14 STILL WATER SPEED MPH

Authors' resistance estimate for 5 X 3 barge tow

PUSH[ ESTIMATED TOWBOAT PUSH EP EP I

ITYPICAL 5600 HP TWIN SCREW TOWBOAT 1601 KORI" NOZZLE PROPELLERS IIOinch PROP. DIA

,

2 - - shallow h = 16ft

1 2 0 ~

6O

2O

I I I I t I 0 2 4 6 8 l0 12 14

STILL WATER SPEED MPH Fig, 25 Authors' estimate of towboat push for a typical 5600-bhp twin- screw towboat; five-bladed propellers 110 in. dia operating in a Kort

nozzle

For the approach in [22] it is necessary to specify the fol- lowing:

CB B T L Tempty Towboat 0.65 48.0 9.0 145 Barge 0.90 35.0 9.0 195 115

From Fig. 20:

K/loaded barge = 0.6 K/empty barge = 0.82 K/towboat = 0.6

Finally, the shallow-water correction eh is given by

Yshal tow water ---- eh V

where

(22)

( F eh = 1 + 0.0697T (23)

V = speed in unrestricted water, equation (21) h = depth of waterway, ft T = draft of barges, ft

Table 4 summarizes the results of the various towing speed es- timates. The tow speed functions have several shortcomings. Howe's function is questionable for higher towboat horsepower and higher towboat tow speed. Bronzini's equation for towboat thrust does not account for the towboat with nozzle propellers. Towboats fitted with nozzle propellers have improved tow speed in comparison with open propeller towboats of the same horse- power. Also, none of the methods give consideration to the pro-

Table 4 Comparison of 15-barge tow, still-water speed, mph

Deep Water, Shallow Water, Method h = 45 ft h = 16 ft

Loaded Empty Loaded Empty Barges Barges Barges Barges

Howe [20] a 10.9 7.9 12.9 Sronzini [21] b 10.68 13:36 8.68 12.55 Authors 'c 9.8 13.25 7.3 10.75

NOTES: a Deep water Fig. 26; shallow water, Fig. 27. b Speed with empty barges in unrestricted water = 13.5 mph; speed

with loaded barges in unrestricted water = 11.13 mph. c Deep water Fig. 28, shallow water Fig. 29.

peller characteristics, which as discussed earlier can improve towboat efficiency and increase the tow speed. Here 5-bladed propellers of 110 in. dia turning about 215 rpm are the reference point in this study. The towboat push and towing speed can be increased by using 4-bladed propellers if practical for the same horsepower.

P r e l i m i n a r y d e s i g n o f t o w b o a t p r o p e l l e r s

P h i l o s o p h y - - d e s i g n c r i t e r i a . With rising fuel prices, all the propeller design particulars have to be chosen carefully to obtain optimum and efficient propeller performance.

Different river trades determine the number and type of barges which make up a given barge tow train (dedicated tow). Then the total horsepower and type of engines to be used on a given tow- boat are established. The operational area is also normally specified.

JULY 1983 221

EP RT

160

KIPS

140

120

100

80

60

HOWE'S SPEED FUNCTION[21] DEEP WATER 5600 HPTOWBOAT WITH 5x3TOW

I L I /

/ I ~ . ~ , . _ E P = R T eq.(12)

V= 10.9 mDh

KEY

I TOWBOAT EP eq.(t9)

2 TOWR T T=gfteq.(13) loaded 3 TOWR T T=l .5 f t eq.(13)empty

L=975 ft B = 105 i t h = 45 ft 2 \

40

20

I - ~ - - - - - r - - - I I I I I 0 2 4 6 8 10 12 MPHI4

STILL WATER SPEED Fig. 26 Howe's speed function (towboat push and resistance estimate) for a 5 X 3 barge tow in deep water, h = 45 ft, pushed by a 5600-hp

towboat

The power produced by the engines minus transmission losses must match the power absorbed by the propeller. This engine- propeller matching specifies the propeller rpm at which the propeller will absorb the horsepower delivered by the engines to propel the tow at a fixed towing speed.

For this discussion we will consider a common coal-moving operation on the Ohio River. The 5600-hp towboat pushes a t5-barge tow (5 long by 3 wide due to lock and dam size restric- tions). The towboat and barge characteristics are summarized in Table 5.

Choice of tow res i s tance , t owboa t push and towing speed. Consider the author 's speed function in Fig. 28 for deep-water operation. As this figure indicates, the towboat will be able to push the loaded barges at 9.8 mph and the empty barges at 13.25

Table 5 Towboat and barge particulars

Towboat Barge

Length, L, ft 145.0 195.0 Beam, B, ft 48.0 35.0 Depth, D, ft 11.5 12.0 Draft, T, ft 9.0 9.0

PROPELLER 5 blades Diameter in 110 Twin-screw fixed-pitch, with Kort nozzles Wake fraction, w = 0.18 Thrust Ded., t = 0.145

ENGINES Two Alco 16V-251F diesel engines Rating: 2915 bhp at 900 rpm (MCR) Gear: Falk 3040 MR

4.192:1 reduction ratio

EP

R T

100

KIPSI

HOWE'S SPEED FUNCTION[21] SHALLOW WATER 5600 HP TOWBOAT W1TH 5x3TOW

KEg

I TOWBOAT EP eq.(19) 2 TOW R T T=gfteq.(13) loaded

3 TOWR 1 T=l.5ft eq.(13)empty

L=975 ft B= 105It h = l g f t

I

8o : R T eq.(12)

60

40

2O

--.-'~-----i~-~ I I I I I 0 2 4 6 8 10 12 14

MPH STILL WATER SPEED

Fig. 27 Howe's speed function (towboat push and resistance estimate) for a 5 X 3 barge tow in shallow water, h = 16 ft, pushed by a 5600-hp

towboat

mph. The question is: Which speed will we select as the design speed for the towboat barge system and propeller(s) design?

(a) If we design for 13.25 mph, the towboat is going to push the empty barge train at that speed. When the towboat pushes the loaded barge tow, the tow resistance will be much higher than the towboat push.

(b) If we design for the 9.8 mph, the towboat is going to push the loaded barge train only at that speed. When the towboat pushes the empty barges then at 9.8 mph, the towboat push ca- pabil i ty will be much higher than the tow resistance.

In both cases, one condition will not be satisfied. The solution to this problem is given in the following subsection on matching the engine and propeller.

M a t c h i n g eng ine and p rope l l e r . Since diesel engines have already been selected in this example, all the engine character- istics, l imitations, and power curves are known. Some propeller characteristics can be established. Normally the diameter is made as large as the space behind the hull allows, the nmnber of pro- peller blades is chosen to minimize vibration excitation, and the area ratio is selected for satisfactory loading and minimum cav- itation.

In the present example the propeller diameter is 9.16 ft, the number of blades is 5, and to maintain a low blade tip speed the gear ratio is 4.192:1, giving a propeller rpm = 215. Assuming 2.5 percent losses at the gear, then the shaft horsepower is

shp = 2915 × 0.975 = 2842 hp

Because of the high horsepower it can be ant ic ipated tha t the blade area of the propeller will be large. A 4-bladed propeller is not practical and for this reason the 5-bladed propeller is used.

222 M A R I N E T E C H N O L O G Y

EP R[

160

KIPS

140

120

I00

80

60

40

20

0

Fig. 28

AUTHOR'S SPEED FUNCTION DEEP WATER 5600 HPTOWBOAT WITH 5x3 TOW

_ l - - L l

V=9.SMPH

KEY FIG I TOWBOAT EP 26 \

2 TOW R T T : 9 f t 25 loaded

3 TOWR T T= l . 5 f t 25 empty

L=975f t B = 105ft h = 45 ft

2 V=

EP= R T

l I I I I 2 4 6 8 10 12Mp H 14

STILL WATER SPEED Authors' speed function (towboat push and resistance estimate)

for a 5 X 3 barge tow in deep water, h --- 45 ft, pushed by a 5600-hp towboat

EP R[

120

KIPS

100

AUTHOR'S SPEED FUNCTION SHALLOW WATER 5600 HPTOWBOAT WITH 5x3 TOW

KEY FIG I TOW BOAT EP 26 2 TOW R T T = 9 f t 25 loaded

3 TOWR T T=1.5 25 empty

L=975 f t B= 105ft h= 16ft

- i -

EP =R T ~ / ~ . . _ . _ _ _ _ _ _ _ . _ _ _ eq (12)

80 V=

60 2

40 3

20

I 0 2 4 6 8 I0 12Mp H 14

STILL WATER SPEED Fig, 29 Authors' speed function (towboat push and resistance estimate) for a 5 X 3 barge tow in shallow water, h = 16 ft, pushed by a 5600-hp

towboat

For the intended deep-water, ice-free operation, propellers in nozzles are specified to obtain the highest towboat efficiency with the same engine power. As mentioned earlier, at equilibrium the power produced by the engine equals the power absorbed by the propeller. Matching the engine and propeller involves finding the operating point where propeller and engine torque, power, and rpm are equal. This insures that the power produced by the en- gine at maximum output equals the power absorbed by the load--in this case, the propeller.

If the propeller and engine power-rpm curves are plotted to- gether the propeller-engine matching can be done graphically. This is illustrated in Fig. 30 where the intersection of the engine and propeller curves at Point (~ shows the engine propeller match point. This point should be the most efficient horsepower output of the engine at rated rpm when matched on the properly pitched propeller to absorb the engine output and propel the tow and towboat at the given design speed.

Typically for towboats, engine-propeller matching involves only the choice of the propeller pitcb. In this example the pro- peller pitch will be selected so the propeller can absorb the 2845 maximum rated horsepower at the engine speed of 900 rpm or 215 propeller rpm, Fig. 30.

We now return to the earlier question of which of the two barge tow conditions, empty or loaded, will be used in the propeller design. These corresponded to 13.25- and 9.8-mph equilibrium speeds. The two different loads and speeds require two different propeller pitch values. Since the propellers are fixed pitch, we can only select a single design pitch. A compromise must be made to satisfy the two different loads determined by the best oper- ating efficiency.

(a) First, consider designing the propeller pitch for 13.25 mph

with the empty tow. Figure 31 shows the engine-propeller design (match) Point ~ when pushing the loaded barge tow. Clearly the propeller would require less pitch since the speed would be lower. Therefore the existing high-pitch propeller would tend to drop engine hp and rpm to an engine overload at Point (~, resulting in maximum fuel consumption. Equilibrium does not exist, and worst yet the speed of the loaded tow will drop below 9.8 mph. This is evident because the propeller curve is to the left of the optimum curve. So the diesel engine operation is now limited by the diesel engine's overload limits for engine power and rpm. This is caused by the higher pitch of the propeller designed for 13.25-mph operation.

(b) Now consider designing the propeller pitch for the 9.8-mph loaded barge tow speed. Figure 32 shows the engine-propeller design or match Point ~ when the towboat pushes the empty barges. Clearly the propeller would require a larger pitch, since the tow speed will be higher. Nevertheless with the existing low-pitch propeller, the engine could operate at the rated 900 engine rpm and develop less engine horsepower. Again the equilibrium conditions are not satisfied, but the diesel engines are not overloaded and the towboat will push the empty barge tow at a speed below 13.25 mph.

Engine manufacturers recommend that the engines not be overloaded in operation and 50% of the anticipated towboat op- eration will be pushing the loaded barge tow. Therefore, the recommended still-water speed to use in the propeller design is the 9.8 mph estimated when pushing the 15 loaded barges.

Propeller design and features of towboat propellers. Having selected a rational still-water speed for the towboat pushing the barge tow, it is now possible to proceed with the propeller design. With towboat propellers, most of the design

J U L Y 1 9 8 3 2 2 3

3200 HP

2800

2400

2000

1600

1200

800

400

0

Fig. 30

ENGINE-PROPELLER MATCHING DESIGN PROPELLER PITCH PROPELLER ABSORBS AT(~')

2842 HP

KEY I DIESE

2 PROPE

DESIGN MATCH

:POINT@

900 ENGINE , , , I RtPM

50 I00 150 200215 250 300 PROPELLER RPM

Illustration of towboat engine-propeller matching hp versus rpm plot

3200 HP

2800

2400

2000

1600

1200

800

400

ENGINE-PROPELLER MATCHING

OFF-DESIGN OPERATION MATC H POINT (~(OVERLOAD) TOWBOAT PUSHING LOADED 5x3TOW

MATCH POINT (~)

KEY

I DIESEL SHP 2 OFF-DESIGN

PROPELLER LOAD

/ ) /

DESIGN MArC H PO 'NT(~) EMPTY TOW

V=I3.25MPP

900 ENGINE 1 I I i I RIPM

0 50 100 150 200 215 250 300 PROPELLER RPM

Fig. 31 Illustration of engine being overloaded (torque limited) when pushing 5 X 3 loaded barge tow in deep water. Propeller pitch selected

for 13.25 mph with 5 X 3 empty barge tow in deep water

3200 HP

2800

2400

2000

1600

1200

800

400

ENGINE-PROPELLER MATCHING

OFF-DESIGN OPERATION -MATCH POINT (~(RPM LIMITED)

TOWBOAT PUSHING EMPTY 5x3 TOW

KEY /

I DIESEL SHP / 2 OFF-DESIGN /

PROPELLER L O A D /

I c

DESIGN MATC H

, PO I N_____[[ ( ~ LOADED TOW V=9.8 MPH

/ MATCH

900 ENGINE I I l I I RPMI

0 50 100 150 200 215 250 300 PROPELLER RPM

Fig. 32 Engine-propeller match with propeller pitch selected for 9.8 mph with 5 X 3 loaded barge tow in deep water. Engine is rpm limited (but not

overloaded) when pushing the 5 X 3 empty barge tow

factors are fixed so the propeller pitch has to be selected to match the propel ler to the m a x i m u m ou tpu t of the engines.

Wi th the following data, the propel ler design can be com- pleted:

shp = 2842 hp tIT - - 97 percent (3 percen t loss in shaft ing)

dhp = shp ~T = 2759 hp towboat

speed V = 9.8 mph or 9.8 × 0.8684 = 8.5 knots w = 0.18

T h e following are calculated:

Va = V(1 - w) = 8.5(1 - 0.18) = 6.97 knots

N - dhp °5 _ 88 (24) Bp - Va2.5

N P = ~ = 282 .77 (25)

With the aid of systematic ducted propeller tests of the B-series propel ler design in nozzles [7, 8], the op t imum p i t ch /d i ame te r rat io is obtained:

P / D = 0.93

So the propel ler p i tch for D = 110 in. is 102.3 in. To comple te the design, rout ine cavi ta t ion and s t rength cal-

culat ions are required. F rom Fig. 28 at 9.8 m p h the total resis- tance or towboat push is 93 000 lb or 46 500 lb/shaft .

F r o m equat ion (7):

R = E P = (1 - t ) T (26)

where

224 MARINE TECHNOLOGY

- - I . 0 R

- - 0 . 9 R

_ _ o / - - 0 . 7

- - 0 . 6

- - 0 . 5

- - 0 . 4 R

- - 0 . 3

- - 0 . 2 R

I I

/ /

',, / ] PITCH DISTRIBUTION / ! ~ 1 p(R)/%a× ± ; . . . . . L

Fig. 33 Typical towboat propeller

R = resistance, lb t = thrust deduction

T = thrust = R/ (1 - t) = 54.386 lb/shaft The static pressure taken at the propeller centerline is given by

Po - Pv = 14.45 + 0.45h psi (27)

where h is the head of water at the propeller centerline, ft. For this example h = 3.86 ft, so from (27) Po - Pv = 16.187 psi.

The dynamic pressure corresponding to the relative velocity VR at 0.7 radius is

qT = 1/2pVR 2 = (Va)2 I- (nD)2 (28) (7.12) (329)

= 36.85 psi

where

Va = local velocity, knots n = propeller rpm D = propeller diameter, ft

The local cavitation number is then [23]:

Po - P~ 16.187 o - - = 0.439 (29)

q r 36.85

For the twin-screw towboat with such highly loaded propellers operating inside Kort nozzles, it will be assumed that there is a 7.5 percent cavitation on the back of the propeller blades. Keeping the propeller blade loading within 6.5 to 7.5 psi and using the Burrill chart [23], the value of ~" is

T / A p T - - 0.198 (30)

QT

where T is the thrust in pounds and Ap is the projected area in square feet.

Therefore

T / A p = QT X 0.198

= 7.3 psi (blade loading)

and

T 54 386 - - =

Ap QT X 0.198 36.85 X 0.198 X 144

= 51.76~2

The propeller disk area is then

KTrD 2 A o ~ - -

4

where K = 1.04 with nozzle and K = 1 without nozzle:

Ao = 1.04 X 7r × 9.1672 = 68.63 ft 2 4

So the projected area ratio equals

Ap = 51.7__6_6 = 0.754 Ao 68.63

From Taylor's approximate formula [23]:

A__~p = 1.067 - 0.229 X P AD D

AD is the developed area of the blades in feet:

Ap 1.067 X 0.229 X 0.93 0.854 AD

S O

(31)

Ao = ~ = 60.61 ft 2 (32) 0.854

and the developed area ratio:

AD 60.61 - = 0.883

Ao 68.63

Figure 33 shows a typical towboat propeller designed from these criteria. Unlike recent oceangoing ship propellers, there is no blade skew or rake used in order to have good backing per- formance. In conventional towboat propeller designs the pitch at the blade tip is reduced as in Fig. 33 on the assumption that the blade tip speed could cause excessive cavitation. This still requires clarification. With the potential higher performance from loading the blade tip, there is an incentive not to reduce the pitch at the blade tip. For propellers designed for higher horse- power, the blade tip area increases and the tip region becomes more square, resembling a Kaplan-type blade with rounded corners.

Conclus ions

This paper presents a discussion on towboat hull and propul- sion design. A review of recent European research on towboat hull form is presented to illustrate the influences of limited water depth, the barge train wake, nozzle propellers, and the arrange- ment of the barges on the towboat propulsive performance.

JULY 1983 225

Tunnel stern designs are characterized following Fig. 17 for over 60 towboats. The authors introduced the tunnel inflow tunnel angle 01 and outflow tunnel angle 02 to characterize the tunnel geometry.

Since there has been little published on towboat propeller design procedure, a design example for a twin-screw, 5600-hp towboat pushing a 15-barge tow in deep (45 ft) and shallow (16 ft) is presented. Beginning with published techniques [21, 22] for estimating tow resistance, a comparison is made with the authors' empirical data, showing a good agreement in deep water. Then the selection of the design conditions, namely, the tow speed, is presented. This is governed by the requirement of avoiding an overload of the diesel engine. Finally, the selection of propeller pitch is illustrated along with the cavitation and strength cal- culations.

From the various points addressed, it is possible to make the following conclusions:

1. The towboat propulsive coefficient np ranges between 30 and 35 percent, which is lower than the values found on con- ventional merchant ships. This is due to

(a) towboat operating in barge train wake, (b) high thrust loading on propellers, (e) propeller diameter being limited by water depth,

and (d) propeller operation in tunnels and presence of ahead.

and astern rudders. 2. Comparison of model tests of a conventional and catamaran

towboat with open propellers indicate that the catamaran hull requires 10 percent less power to maintain the same tow speed. Later model tests with propeller nozzles and rudders fitted were inconclusive because of the nonoptional rudder setting on the catamaran hulls.

3. The arrangement and design recommendations for the towboat tunnel stern are summarized in Fig. 17. As a means to insure adequate inflow and outflow from the tunnel, the tunnel flow angles 01 and 02 along with design guidelines are intro- duced.

4. A comparison of a typical 15-barge tow resistance indicates that the previously published formulas under-estimate the tow resistance and over-estimate the towboat performance, which results in a higher equilibrium speed.

5. A design philosophy for selecting the propeller operating point is summarized and it is pointed out that the design point should be taken at the condition corresponding to the operation with loaded barges.

6. In the preliminary towboat propeller design example, a technique for designing the towboat propellers is illustrated.

Metric Conversion Table

1 in. = 25.4 mm 1 ft = 0.3048 m

1 ft 2 = 0.0929 m 2 1 ft 3 = 0.0283 m 3

1 mile = 1.6 km 1 ton = 0.9 metric tons

1 lb = 0.45 kg 1 hhp = 0.7457 kW 1 ft/s 1.689 knots

1 mph = 1.151 knots

Acknowledgments

The authors would like to acknowledge the assistance of Mr. Han-Herbert Dunow, DAAD program student in translating the German language materials and the cooperation of Dr. Heuser and Mr. Luthra, VBD.

The tunnel stern information supplied by Mr. C. Van Mook, Dravo Corp., Professor Lederer, University of Louvain, and Dr. Muller, VBD, is deeply appreciated. Finally, the authors are

grateful to Mr. Sidney Bond and Ms. Mayrene Haehl for their assistance in preparing the paper.

References

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3 Parsons, A. R. and Renshaw, E., "A Review of Modern River Towboat Design," SNAME Gulf Section, May 3, 1957.

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14 Basin, A. M., "Influence of Shallow Water on Hull Propeller In- teraction of Passenger Vessels," Ship Hydrodynamics In Shallow Water, Sudostroyeniye, Leningrad, 1976, pp. 150-163 (in Russian); English translation: [25].

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16 Van Mook, C., Dravo Corp., private communication, June 4, 1981.

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18 Muller, L., Versuchsanstalt fur Binnenschiffbau, Duisburg, West Germany, private communication, May 12, 1981.

19 Lederer, A., Universite Catholique de Louvain, Louvain, Belgium, private communication, April 30, 1981.

20 Latorre, R., "River Towboat Tunnel Stern," International Shipbuilding Progress, Vol. 29, No. 338, Oct. 1982.

21 Howe, C. W., Inland Waterway Transportation, Johns Hopkins Press, Baltimore, Md., 1969, pp. 23-27.

22 Bronzini, M. S., Lopez, L. A., and Stammer, R. E., "Inland Wa- terway Port Model: Design, Development, and Methodology," Trans- portation Center, University of Tennessee, Final Report Contract MA- 79-SAC-00183, Jan. 1981, pp. 408-409.

23 Principles of Naval Architecture, J. P. Comstock, Ed., SNAME, revised edition, 1977.

24 Latorre, R., "Flow Around Full Ship Stern; Translations of S-e- lected Japanese and German Technical Articles," Department of Naval Architecture and Marine Engineering, University of Michigan Report No. 198, Ann Arbor, May 1976.

25 Latorre, R. and Dunow, H., "Improvement of River Towboat Propulsion; Translations of Selected German and Russian Technical Articles," Department of Naval Architecture and Marine Engineering, University of Michigan Report No. 243, Ann Arbor, Nov. 1981.

26 Latorre, R., Luthra, G., and Tang, K., "Improvement of Inland Waterway Vessel and Barge Tow Performance; Translations of Selected Chinese, German, and Russian Technical Articles," Department of Naval Architecture and Marine Engineering, University of Michigan Report No. 249, Ann Arbor, Sept. 1982.

27 Heuser, H., "Optimierung Der Hinterschiffsform Von Schub- booten Versuchsanstalt fur Binnenschiffbau e.V.," Bericht No. 853a, Dec. 1977.

28 Marbury, F., "Least-Energy Operation of River Shipping," MA- RINE TECHNOLOGY, Vol. 16, No. 2, April 1979, pp. 136-155.

226 MARINE TECHNOLOGY