The determination of appendage resistance of surface ships

(1)

ç) _t'i C)

(2)

4 = p = Notation Ships speed. Resistance. Effective power.

Mass density of water - normally at 15 degrees C

(59 degrees F).

s = Surface area.

A = Sectional area.

c = Mean chord length of appendage.

t = Maximum thickness of appendage.

CF = Frictional drag coefficient at a Reynolds Number (R) based on the length of the appendage and ships speed.

C = _{Drag coefficient based on the area of the maximum transverse}

I

section.

d = _{Mean diameter of shaft and shaft bracket barrels} 1

12d2+13d3

12+13

li = Total length of shaft and barrels (one side) = 12 + 13 12 = Length of shaft bracket barrels.

13 = Length of exposed shaft.

Diameter of shaft bracket barrels.

Diameter of exposed shaft.

h _{Vertical distance between centre of propeller boss} _{and hull.}

Note: _{Consistent units (ie Imperial or SI) should be ied} _throughout.

(3)

I L t ¡ i e

THE DETERNATION OF APPENDAGE _RESISTANCE

OF SURFACE SHIPS By R W Peck

1. _INTRODUCTION

The effective power _{due to arendage resistance}

represents a

considerable proportion of the total

E of a vessel. While it is important that the assessment

of appendage resistance should be

reasonably accurate consistency of method is probably _{more important.} Any short-comings in the _{actual values obtained}

can be taken into

account by use of correlation

factors derived from ship results and model predictions.

The methods of determining _{the resistance of}

appendages etc for

surface ships and submarines

were collated at AEW in 1968 _{(Reference i).}

Since then however with _{the advent of metrication and the adaption} of the ITTC model-ship _{correlation in determining}

ship resistance it is considered that

some revision and up dating of the previous methods is desirable.

2. _{The following appendages}

have been considered:-Bilge keels.

Rudders.

e. _{Stabiliser fins.}

Shaft bracket arms.

Shaft bracket barrels _{and shafts.}

Wind resistanc.

Condenser inlets and outlets. Sonar domes.

3.

_{DETAILS OF THOD OF ASSESS?NT}

3.1. _{Bilge Keels}

To date, resistance of the bilge keels has _{been arbitrarily}

taken as 12/3

times the calculated

skin friction (using the specific resistance

appropriate to length of keel) for the

exposed surface of the bilge keels, the skin

friction of the ships hull masked by the bilge _keel being deducted. _(References

i and 2.) Adopting a slightly

more rational approach, the _{bilge keel drag} may be considered in two

(4)

Interference drag reduces as the angle between the hull and bilge keel plating increases je as dimension z increases (see Figure 1).

In any intermediate situation

= Psv3 CF (2 2z y)

Figure 1 Figure 2

Thus when z = x + y le no bilge keel, additional drag = O and when 4 z = O le a plate keel, interference drag is taken as equal to skin

friction drag = psv2 Cr.,.

I

T

i

The accuracy requlred from such an empirical formula is such that it is not necessary to calculate S precisely and for normal bilge keels

S = L(x + y) where L is obtained as shown in Figure 2.

I

The formula then rethices to:- f

= pLV3 CF(x + y - z) in appropriate units

If the shape of the bilge keel is such that varies greatly, a

mean value may be found by

taking:-area of hull covered by bilce keel _I

wetted surface of bilge keel

Foul in g

¡

To obtain PE for the bilge keel of a vessel six months out of dock in

tropical waters an additional 0.56 CF should. be allowed on the skin friction portion of the (Reference 3).

le

E skin friction = pLV3 (x + y - z) x 1.56 CF

interference = _{pLV3 (x + y - z)CF}

Therefore ₆ MOD troncal = 1.28 pLy3 CF

Cx + y - z).

In temperate waters half the tropical allowance for fouling should be used

and the total is given by:

2

t

(5)

I t

6 MOD temperate =i.i1 pLV3 _CF

_{Cx + y - z)}

3.2. Rudders, Shaft Bracket Arms and Stabiliser Fins

Treating all these items as foil type sections _{a single formula has}

been devised based on Hoener (Reference 14). _{The drag coefficient}

appropriato.t

frontal area is given

by:-CD=Cf[1.25_

140(t

31 [ C(F) A C(A) j CçA Figure 3

where c = mean chord length

= C(F) + c(A)

S _{= surface area}

A _{= frontal area of maximum section}

t _{= maximum thickness}

-CF = skin friction coefficient from ITTC formulation

In the case of thin foils S/A _{can be taken as}

Then _{clean =}

pCD AV3 in appropriate units.

Note: _{In the case of rudders 1.1V should be used in obtaining}

Reynolds number and resistance, hence for rudders _{PCD AV3 x (1.1)2}

Foulin

cH

To allow for fouling the skin friction portion of the _formula

(ie or -) should be increased by _{the appropriate amount.}

For six months out of dock in tropical

_conditions

this would be

_0.56.

i

t

(6)

1 25 c

+ 1.56 () + 140

(

t

)

Such that

6

D tropical

_{= CF [}

c(F)

_C(A)

In temperate conditions the corresponding formula is

6 MDD texrrnerate = CF

14

3

+ 1.28 (-) + 140 (_

_A

C(A)

Note:

_{Fast Patrol Boats should be}

_{treated as a special}

_case.

fl-ien

estimating the shaft bracket

_{resistance for these and similar}

_craft

Reference 5 should be consulted

_{since the resistance}

_{measured on}

full scale model FF3 brackets

_{was considerably in excess of that}

obtained from the then

_{current formula and the formula detailed herein.}

3.3. _{Shaft Bracket Barrels and Shafts}

Twin Shafts

The following formula, deduced by R E Froude from model experiments has

been used at AEW to estimate

_{the resistance of shaft}

_{bracket barrels}

and shafts.

t

b d V2

t

R tons (for 2 shafts)

10,000

where

b = distance of centreline of shaft from centreline plane of

_{ship in feet.}

= mean diameter of shaft and

_{barrels in feet.}

V = ship speed (in knots in above formula).

If R

_{= CD}

_{pAV2 it}

_{can be shown that from the above}

formula

CD

= 0.019

where i is the length of the shaft and barrels and

_{A = ld1.}

In deriving his formula Froude took the ratio

_{as a measure of the}

'fineness of run' of

_{the shaft relative to the}

_{hull and this gave}

him a measure

_{of the cross flow.}

_{It may be argued that in}

present

warship desis the

_{vertical distance h between}

_{the centre of}

propeller and the hull

_{would be a. better measure of cross flow.}

Comparing several

_{recent twin screw warship}

_{desis the value}

varies between 0.9

_{and 1.0 (except for}

_{wide beam vessels)}

so

that in using h instead of b the estimate of resistance is not greatly

affected.

I

1.25

C

C(F)

(7)

i

Froude also considered that the ship appendage resistance was

approximately 0.5 that scaled from model whereas opinion expressed

in more recent papers (References

6

and 7) indicates that perhaps

an appendage coefficient of 0.7 may be nearer.

0.7 (b or h

This would make CD

= 0.079 x

_0.5

¿

-

(b or h)

-.

i

It is therefore considered that in estimating the resistance of shafts

(2 in nunber) the following formula should be used.

R = CD

pAV2 in appropriate units

_01h

h

CD

-.

- 10

R

phd1 V2

SinQle Shafts

A CD

value of half that for twin shafts should be

_{taken ie}

h

iCD =20

or

hd1 V2

Fouij0

To allow for fouling

_{at the tropical rate for}

6

months out of dock

1.56 times the

clean

should be assumed.

In temperate conditions 1.28

times the clean

should be assuned.

h

_{= vertical distance between centre of propeller and hull.}

11

total length of shafting and barrels (one side).

d1 = mean diameter of shafts and barrels.

A

= d1 x l.

V = ship speed.

The resistance may then be written

as

20 using appropriate units

ii

(8)

6

L

Note: In estimating the resistance of shafts for Fast Patrol Boats

Reference 8 should be consulted. Values of CD obtained from

f'ull-scale experiments for various angles of shaft inclination are quoted

therein.

3.14 _{Wind Resistance}

Pn assessment of the wind resistance to the forward motion of a

vessel is required to be made. In calculating the wind resistance for a given trial condition the method described in Reference 11 in

con5unction with the serni-emperical relationship between drag

coefficient and aspect ratio given in Figure 4.

When making standard corrections for wind it is usual to allow for a 10 knot wind up and down the measured course, such that the relative velocity becomes V . + 10 or

ship

-(V + 10)2 + (y - 10)2

S

V 2 _{+ loo}

2 s

The source of the information from which Figure 4 was obtained can

be found in Reference 9.

3.5.

Condenser Inlets and Outlets

An allowance for these items is only made where the circulating water is induced without the use of main circulating purrrps.

Not many ships are capable of producing sufficient head naturally and hence pumps are invariably in use at the maximum desi-i speed end therefore no additional allowance is made.

Where it is necessary to estimate the additional due to main circulating water systems the following is calculated.

Resistance due to change of momentum of water entering the

inlet from the boundary layer.

Resista-ice due to loss of available head through the system. Resistance due to outlet lip if fitted.

Resistance due to change of momentum of flow leaving the

outlet end entering the boundary layer.

Methods for obtaining this resistance are detailed in Reference 10.

3.6.

Sonar Domes

Resistance experiments _{are progrenmed with double models of sonar domes}

and the results of these experiments will be _{reDorted separately.}

Meanwhile the formula in _{paragraph 3.2 should be used and where}

(9)

i

I

Reference 2.

_{AEW Report dated iii May}

_1923.

_{Notes on Methods of}

Estimating Resistance of

_{Appendages at Haslar.}

Reference 3.

AEW Technical Memorandum

_{No 13/73.}

_{Analysis of}

Surface Ship Resistance

_Experiments.

_{UNCLASSIFIED.}

Reference 14.

_{Aerodynamic Drag by S F Hoerner.}

Reference 5.

PEW Report No 69/5I.

_{Resistance of Shaft Brackets}

of Fast Patrol Boats.

_{CONFIDENTIAL.}

Reference 6.

_{An informal Note on the Appendage. Scale Factor}

.

British Hovercraft Corporation.

_{EEL/5246014 dated}

15 June 1973.

Reference 7.

Reference 8.

Reference

References

PEW Technical Memorandum No 141/68.

The Determination of Appendage

_Resistance.

UNCLASSIFIED.

An Investigation of the Scale

_{Effect of Appendage}

Resistance of a Geometrically

_{Similar Series of}

Models of the DD71O Class

_{by Klemm and Buckingham,}

Webb Institute of Naval Architecture.

CONFIDENTIAL.

PEW Report No 1414/514.

_{Resistance of Propeller}

_Shafts.

CONFIDENTIAL.

PEW Technical Memorandum No 114/68.

Wind on Tide

Drags on Various Geometric

_{and Ship Superstructure}

Shapes.

UNCLASSIFIED.

Reference 10.

_{PEW Technical Memorandum}

_No55/57.

Apendage Resistance.

Main Circulating Water

Systems.

UNCLASSIFIED.

Reference 11.

_{PEW Technical Memorandum No 76018.}

Calculation of Power Due to Wind Forces.

UNCLASSIFIED. I

i

(10)

Io- o

9-0

9-O

70 -0

50 4-0

30

2-O O-6

o-5

o-ç

o-e

0-,

j

NOTES

O

.4 -

fr'AX-.

. ALL

3 ASPECT

OVERALL.

R.SPET

(JE.

54 iS

Wi7ERL

,A/N

HO VE I R

5T7/O,V4L

(ASCL

PROFILE ARPR

AReL

1.5

LENCTH.

OF PROFILE PER/t-7ETER

TI-f.

THE PROF/LE

SU.°ERSTRUCTURE

3UCI-I /TEt'IS

SLCTIOA' oJEC7S

TR'SVEÁ'SC

PLAN,

NOT

14REA

/RE FOR

1$ THE PROF/LE

HALF OVERALL

AS FIRSTS,

Sud-I

PCRIfr7E

FUNNELS

YAW ANCLE

PLAN

LENGTH (EX.

TER TO

L TC,

$PARS OÊRR/CXS

AS TAIL FINS

AREA

IN

OF

I.J.L.)/

/NCL

O,V THE ¿IDE -CMSE

ETC.

O Z'ECR.EES.

OP .5W/PS,

- STREAP'-YL/NE

R,qTlO

RATIO

ro

)/ovE/'ALL

TI-lE RATIO

INE

ITEMS

BUT

RC RA P T. i i

DR,iC COEFFJC/ENT.

¿EA/CTH.

L.ENC

OP

o 04 O-

_{0-06 0-07}

_0-0.9

_0-20

_0-30

_{0 40 0-50 0 O O-70}

_{O - 9o/}

O-08

O-IO

0.o

ASPECT RATiO PROF/LE (PÑ)

FIG. 4 DRAG COEFFICIENTS

_{FOR SHIP FORMS}

AND GEOMETRIC

_{SHAPES. WIND OR TIDE FORE & AFT}

&

¡

I