Preliminary study of the influence of controlled fins on ship pitching and heaving

,

7,56 = 379

.1"

Yr_ ,

Tievisoel Decethet

-4-5-EYEOS _{lt07411141E:w} TECX,NrOLOGIe

EXPEFOtifENt.431. To W WO TANK,

St)

3o kcal% Nrxr ir4

.816P--110

,AND Itr...;41UNG Ykk, I -

by

_ .0, 1

a-,/ dwa Lew t

-Jacpbs

_ 1.1

Proiteet

T.ToA GX I,

The wcYrkdeaOhibe

_{',L94....-.)leark b4r4 ingt. carried nut} 1270.1t7r the spi-A11024 _{tEt -L74, atiro,,aik of Sapp}

-'andel, the)

c01-2-rix::=; ..- 0 r ttln Dovii4,

_{Taylor Halle}

4

)3.aqirb Ooht1c1,';

' _Is 2,6312.,

.,..

,r---

_--,, e`"/JO

fri4 Fel: -tery- 8_, 1951

.}}^!'}rr"` 41414Nin..01,7,4 1 tf &

,

E 4 W.-4K a -4.1

;

litote,11

379

4 *'* Pk-,1417-liMPS STOX OF 2.1.}. r-.00110:OLLED TM ON

N-379

-STEVENS INSTITUTE OF TECHNOLOGY

NED.

EXPERIMENTAL TOWING

TANK

HOBOKEN, NEW JERSEY

PRELIM

ni fay

STUDY OF T INFLUENCE OF

CONTROLLED FINS ON SHIP PITCHING AND HEAVEZ by

Edward V. Lewis

and

Winnif red

R. Jacobs

177777777,71

This note summarizes initial analytical work undertaken as part of the project outlined in Ref. 1 for the study of possible _improvement

_in

ship motions by the use of controllable bow and/or stern _{fins. As} sug-gested in Ref. 2, the analytical studies have been used for planning a correlated experimental investigation which is also outlined herein.

In discussing the possibilities of the use of fixed or movable f:Hs for easing the motions of pitch and heave of a ship in a seaway, considera-tion must be given first to some general characteristics _{of ship motions}

and fin action. _{As pointed out in Ref 3, the most objectionable aspects}

of motions from the point of view of _{sea speed, possibility of damage,} etc., are the responses to near-synchronous _{waves or wave components.}

Approaching

_{synchronism results not only in large amplitudes of motion} but high vertical' accelerations at the ends of the ship and unfavorable phase

relationships which

_{lead to shipping of water forward and}

slamming.

Since

near-synchronous ship responses are of predominant _importance

_then,

it would be expected

_on

_{the basis of elementary vibration theory that}

simple damping would be

particularly

_{effective in reducing the amplitudes}

of motion.

This has been.00nfinned experimentally

_{both in regular}

and

Irregular waves (Ref. 3 and discussion by-Abkowitz)..

°,..tr,

- 1

ARLO4

. ,

Pimple Damping Devicesl

PART T _{ANALYTICAL STUDIES}

An obvious means for providing damping of pitching and heaving motions is to install fixed horizontal fins, which for effectiveness against pitching

should be located

as far

from amidships as possible. (Refs. 3 and 3A).

Fixed anti-pitching fins are analogous to bilge keels used to damp rolling

motion. At zero ship speed they act as pure damping devices, the fine being

like flat plates at right angles to the flow. (The only horizontal velocity

is the component of the orbital wave particle motions ,which can be neglected

here). The damping force results entirely from the drag of the fin, which

is proportional to the square of the relative, vertical velocity between fins and water. _{Hence, the fin action is quadratic damping, although it can}

perhaps be approximated as linear damping proportional to the first power of

velocity.

At forward speed, which is of primary interest, the situatice- is some-what different. _{In addition to relative vertical velocities, the forward}

velocity

of

the ship enters in. The combined effect of ship and wave velo-cities at bow and stern has been worked out from model _{test data (without} fins) and is presented in Fig. 1 for a typical condition of

_peak

pitching

.(near

synchronism) of

_{a 500-ft0 Series i4 ship (0.60 block coefficient).}

The speed is 12 knots, heading into a 750-ft. wave (1.5 L) of the moderate

height of 10.5 ft. _{If wave height is increased, the relative vertical} velocities 'will increase approximately in direct proportion. A similar.

picture is obtained at speeds for synchronism with

other

_{wave lengths.} With effective fins installed,the vertical velocities would of course

be reduced. _{Nevertheless, the figure shows that fixed fins would develop an}

appreciable angle of attack to the relative flow _direction,

_particularly

at the bow. _{In general the force which is effeCtive}

in reducing pitching (and heaving) is the vertical component Fv of the resultant Fr of the lift and drag forces on the fin. (See Fig. 1A). _{For the synchronous case} shown, the angle of attack e.C.,of the boy fins appears to be quite large,

and breakdown of flow would appear to be inleviteble. _{However, it should be}

borne in mind that with fins installed the

vertical

_{motion of the bow}

_and

stern would be

_considerably

_{less than shown in}

_{the figure, and the}

maximum

angle of attack

will

_{be correspondingly less.}

Hence, it appears tentatively

N-379

Fe

that in many cases the lift fo-rce can be assumed to give a good aonroxima-tion of the effective vertical force component. If the notions should be

so violent and the speed so low, however, that the angle of attack becomes large enough to result in breakdown of flow, the drag will increase and will contribute appreciably to the vertical force. The calculation of lift

and drag under these conditions is difficult, but it may be that the calcu-lation of lift on the assumption of no flow breakdown might still be a fairly good approximation to the resultant vertical force. In any case, it appears that even if breakdown occurs the vertical force may continue to increase with fin angle because both lift and drag contribute to it.

At the stern, it may be seen that the effective angles of attack are much less than at the bow, since the relative vertical velocities are so

much lower (See Ref. 4).

Hence,

fixed fins at the stern must be. much less

effectiVe than at the bow, as suggested in Ref. 3 and elsewhere. Any means that can be devised -- such as controllable fin angles -- to increase fin lift will therefore be helpful in the stern location, This possibility

appears promising enough for further investigation, and will be discussed

later on.

ICalculations for Fixed Fiq

The effect of fixed fins on motions can be calculated by the method of

Korvin-Kroukovsky (Refs. 5 and

SA),

provided that the equations of motion are modified to include the additional exciting force and moment due

_to

the

fins and the effect of the fins on the various hydrodynamic coefficients. Aerodynamic theory and recent work of Dr. Paul Kaplan are helpful here, and

the method

used In this investigation is outlined in

the

Appendix.

The

method is based on ideal potential flow and therefore neglects the effect of

any drag force. It assumes small angles of attack, and therefore is an

approximation when angles become large. The

calculations

have been carried

out

for the Series

60 model (0.60 block) with and without flat plate

fins

of the size used in model tests at the Stevens Experimental Towing Tank

(Ref. 3),

and also for smaller fins. Results are given in the accompanying

Table 1.

37

--TABLE 1

Effect of Fixed Flat Plate Fins on Motions in

Yaves

500-ft. Ship (Series 60 Lines, Cb = 0.60)

Synchronous Condition of 19-knot Speed

in Regular Waves of 1.5 x Ship Length and

Height = 10.5 ft.

EXPERDENTAL DATA, DDIB (3.9 knots)(Ref. 3A)

CALCULATED DATA

No fins

Pitch

_La,

7.18

4.03

-Heave

ft.

Pitch

deg.

Heave

ft.

15.1

Pair of fins, 21 x 21 ft.

At bow

At stern

6.27

15.1

0-91

0

At bow and stern

3077

11.4

3.41

3.7

Pair of fins, 6 x 12 ft.

At bow

6.02

13.6

1.16

1.5

At stern

6.93

15.20.25

-0.1

At bow and stern

5.84

114.3

1.34

0.8

EXTERMENTAL DATA, EIT

No fins (17.2 knots

_(19.0

"

(interp)

7.70

707

12.7

15.2

Pair of fins, 21 x 21 ft. (17.2 knots)

At Bow

4.15

11.7

3.55

1.0

At bow and stern

3.95

10.9

3.75

1.8

No fins

7.7

14.0

Pair of fins, 16.7 x 17.7 ft.

At bow

14.7

14.6

3.0

-o.6

Double

.Reduction in

Amplitude

Amplitude

N379

-Calculated figures in the table show the

g..

..eerefecetireateive-..

mess of bow fins for reducing both pitch

and heave.

The comparison of

calculated and experimental dataishows quite good agreement, particularly in

See

pitch, so that the method

e

celclulation Appendix) appears satisfactory for

the present.purooses, in'snite of the approximations involved.

Despite the effectiveness o fixed fins at the

shownby

calcula-tion and by model tests, major prctical difficulties present themselves.-

_{These arcs}

mainly struct=a problems resulting from the high impact forces to be expected..

if bow fins break the surface d

./ sible vtbration effects associated with

vortex formation if severe-ieparation occurs. These matters require further. study.

Fixed fins at the stern do

not

appear promising, but the possibility of using controllable fins at thir location

_seems

worthy of study.

Ftmllable Fins

at the Stern]

If a ship's forward speed is sufficient, there is a possibility of reducing motions by suitably-phased lift forces generated by movable fins

aft. _{This method has been successfully applied to reducing drastically the}

amplitude of rolling motions, but for pitching and heaving motions only

moderate reductions are sought or desired. _{In particular, the reduction of}

synchronous pitching oscillations is the objective, and hence the

_adjustable

fins

would., like fixed fins, function essentially as

_{danping.devices but}

making use of adjustable angles to increaseethe anr7le of attack

_and

hence the-lift.

As in the case of fixed fins, movable fins

_should

_be

located as

_2a7 from amidships as Possible in order to develop the maximum moment against

pitching. _{The flow at the fins will in all cases be the resultant of the}

forward velocity of the sh, the horizontal component of Wave particle velocities, and the relative vertical velocity between ship and wave, as shown in Fig. 1. _{Because of the relatively small vertical velocities at}

the

stern even at synchronism, the resultant velocity will vary moderately in magnitude and direction throughout a cycle of notion. _{This variation will} probably not make the fin control problem any more difficult than for

existing anti-rolling fins, using control based _{on lift or torque (Ref.}

_6).

The range of fin angles would not necessarily be large, and the high-lift characteristics of the so-called "flap-fin" or other similar devices could

probably

be utilized.

N-379

-

5

---On the other hand, the wake at the stern of the ship would reduce

some-what the net velocity and hence the forces produced by the ifins, although this effect would be smell

if-the fins were

placed near the keel.

Locating-fins abaft the propeller would increase their effectiveness, but mechanical

and structural problems would be very difficult. In summary then, an

effective installation might consist of carefully dbsiuned fixed fins forward

and

controllable fins aft.

-tift Obtainable from Controllable Fi7.71

The most effective controllable fins would be those which are maintained

at angles such that maximum lift is

always obtained either up

or down, as required. Actually such an ideal is not feasible in practice, and the actual variation of lift May be more nearly sinusoidal. In any case, the first

problem in estimating the effect of controllable fins on ship motions is to determine the maximum lift characteristics of the fins. The following

consi-derations must be taken int acc unt:

1. 'Maximum lift tbefo_e stalling) of a deeply

submerged

symmetrical hydrofoil of in miteaspect ratio at the operating.__.e._

Reynolds No.

- 2. Effect of finite aspect rati?.

/

Effects of pro ity 6 the surface, including

vie

possibilities

of cavita ion.

Effect of

non-uniform flow as a result of ship motion

and oscillation of fins.

Possible use of high lift devices such as flaps at the

trailing edge.

Assuming a shin of 500-ft, length, a reasonable size of fin might be x 12 ft., the size of typical fins used for control of rolling The

aspect ratio is 2, but if arranged with close

clearance to the hull an

effective aspect ratio of 4 may be assumed. Airfoil data and experience with fins and rudders (Ref. 7) indicate that a fairly thick, round-nosed section is most _suitable for high maxim= lift.

The effect nf Reynolds No. on maximum-lift is shown in Fig. 2--reprOdUced from Ref. 7. At a forward speed of 12 knots the Reynolds No.'

-

3.

07-4a

7

ffle

of the 6 x 12 ft. plate is 10 million and at 19 knots 15 million. Hence a

(C,) of 1.65 or above appears possible, with an infinite aspect ratio.

max

The original NACA report from which the figure was obtained (Ref. ti)

indicates

that- (C ) for the original test aspect ratio of 6 was approximately

7%

max- .

less, which would give a value of (CL)max =

1.54,

or say

1.5

for an aspect

ratio pf--4. Reference 7 shows that this-maximm lift would be obtained at an anale_of attack of 22 or,23.degrees'

for

aspect ratio

=L.

A check of

cavitation shows that _there is a possibility that the above

_

(C )- Would be reduced by cavitation. A large nose radius is helpful, and

mnx

increasing-the aspect ratio would be indirectly beneficial since it would

reduce the angle. of attack at stall without reducing (0 ) .

L max. Reference

7-shows for typical strut sections a critical

cavitation

index 6- = 2.5 at the largest angle of attack of 10° for a nose:

rad4us 6%

of the chord: This leads

to the following speeds for incipient cavitation as a function of depth:

Until data are

Depth, ft.

10 20 30

40 _///

found for the

. Critical Speed, Knots

13 14

15.5--17*

18

At the angles of attack mentioned above -- 22-23 degrees -- the critical

speeds would be much lower. Assuming tentatively and arbitrarily

r= 5

gives:

critl.cal cavitation index at large angles of

attack, it may be tentatively assumed that for a

chip speed of

19 knots

1

and an average fin immersion of

25 ft0

cavitation will begin at an angle of

attack of about 15°, where CT

= 1.5

x 15/22.5 = 1.00 Assuming that the

(C.,)

max taking into account cavitation

is midway between

the CL values at

-Depth, ft.- Critical Speed, Knots

5 21 10 22 20 22 30 2h 40 26 N-379

-7-I - ---- _-=

-1 ~

+1O

15

and 22.5 degrees, we have (0,)

e

max 2

Next free surface effects other than cavitation must be considered. A hydrofoil moving near the surface produces a wave disturbance. If the

angle of attack fluctuates this wave disturbance will fluctuate to some

extent. The indications are that at immereions of two chord-lengths or

more and at moderate angles of attack) the effect of free surface on

lift is negligible. Hence, it is

telit'AIely

assumed that in the present case, with an average immersion of about 25/6 = 4.1 x the chord, free surface

effects may be neglected.

Considering finally the non-uniform flow conditions at the fin,

calcu-, the circulatory portion of the

lations based on data in Ref. 9 give a factor of 0.8o to apply to ift for the 6 x 12 ft. fins on the 500-ft0 ship at 19 knots. If the fins were

doubled in size to 12 x 21 ft., this factor would become 0.80. On the basis of an average value of 0.85, and assuming that the

_angle

_{of attack for}

break-,

down does not change, the (CL) _{reduced further to 1.25 x 0.85 = 1.06.} On the other_hand, Kramer's effect (Ref. 12) night in some cases have a

favorable influence on the maximum lift,, and the virtual mass lift force would also increaseit.

The question remains as to whether some of the lift lost by the con-sideration mentioned above can be regained by the use of special high-lift

devices. _{Flaps have proved successful in connection with anti-rolling fins} (Refs.

6,

10), and airfoil data-suggests a possible gain of about 502 in (0L)max.---- However, Ref. 6 explains the control difficulties with a flap type

fin when the _{range of direction of flew is wide. It is veree} diffi-cult-to desi a mechanism to adjust the-flap

to the

_{optimum angle, and the} variation in the position of center of pressure _{m akes}

_use

_{of simple}

ifficult.

relationship

between lift

and

shaft torque in the control

_m=in,

It is

tentativeiy-COnelUdedethat conditions might be satisfactory at the stern

but not at the bow

for tete

of flap-fins. _{The estimated value of (C )}

L max

at the stern then becomes 1.06 x 1.5 = 1.6.

Attention has been directed in Ref. 11 to the high

lift

_{properties of}

fixed .oval hydrofoils with flap _{and the effect of boundary layer suction.}

The possibility of suction on more conventionalairfoil sections should-also be considered, or possibly outward _{plumping of water.}

PPrirrm, N-379 a 1 ' -er. .

kfrectq of Fins in Calm Water!

The 0.60 block Series 60 _{lines were selected for the analytical study}

of ship motions with _movable

_{fins, since}

both analytical and _experimental

data on motions in head _{seas were available (Refs. 3, 5}

and 5A). As before a .ship of 500-ft. length was assumed, with 6 x 12 ft. fins. _{The location} should of course be as _{near the stern as possible, and it was assumed that}

the axis could be placed aboutl2Lof

the length from the A.P. (with fins on both sides of the ship acting together).

The assumption was made that a

type of fin could be used for which C, would vary linearly with _angle

_of

attack up to a tentative maximum _{value of 1.5.}

For a fin in undisturbed forward motion, i.e. not attached _{to a ship or model, sinusoidal}

fin

oscillation at the comparatively low frequencies associated _{with ship}

pitch-;94) 4)

ing could be expected to

produce approximately sinusoidal _{variation of lift}

N-379 9

-force. _{A more "rectangular" fin motion would produce a correspondingly}

rectangular variation of lift _{force. (Fig.}

3)-On the basis of the above

assumptions 'regarding CT, the lift force,

moment, and trim to be expected

from different .fixed fin anzles can be

readily computed, for different forward speeds:Ln calm _{water. assuming as}

a

first approximation that _{there is negligible}

interference between the

hull and the fin.

Results of such calculations are tabulated below for

6 x 12 ft. fins _{on a 500-ft0 ship at a speed of}

19 knots. (Note: "fin angle of attack" is angle of fin centerline to the _{local average flow} direction, not to any arbitrary reference line).

00 out

of

phase

TABLE 2

Effect Q4.L1,1,9d Fills in Calm Water,

(4.767,11 A

A

= "e. _{i2 Se4,22 IS-1'#)a* Z, 16:5ODD}

'At _la. ==

Increasing the size of the fins would theoretically increase

the force

and trim in direct proportion to area. Larger fins, giving more easily

measurable

effects, would be desirable for checking the calculations

expe-riplentally.

The next step

is to

determine the ship motion to be expected from the

sinusoidal motion of fins at forward speed

in calm water. A complication enters in here in the variation of the direction

and

velocity of flow at the fins as a result of the pitching and heaving oscillations of the ship.

convenience, sinusoidal variation of lift was assumed first. This may be

considered either as an approximation to sinusoidal fin motion or as a very close representation of the conditions obtainable with "lift control"

as

described in Ref. 6.

The amplitudes-of

pitch and heave calculated for a fin-equipped-ship

moving at 19 knots in calm water

on the basis of the coupled

_{equations of}

mOtion.(Refs. 5 and 515 are given 'below. These figures apply to a pair of 6 x 12 ft. bow or stern fins only, and the

period of oscillation is

_{in the}

vicinity of synchronism in pitch (0.79 sec.)). _{Figures are also given for a}

variation of lift which is

approximately

seuare, i.e., of the form shown by the heavy line in

Fig. 3,

The fundamental harmonic of the square periodic function is assumed to be equivalent to this lift variation for simple analytical solution of the equations of motion.

N-379 10 -Fin Angle

of Attack,

deg. Lift Force

One Pair of Fins, lbs.

Ship Trim, Degrees

One ?air Fins

For'd or Aft For'd

Two Pair Fins* and Aft 0 0 0 0 14

56,500

.04

.07 8 113,000 .07 015 12 170,500 .11 .22 16 227,000 .15 .30

For

-oscillation the amplitudes would

vary in

_{proportion to angle, provided that}

breakdown does not occur.

The results in

Table

3Aare

capable

of simple verification by

means

of

model tests, covering a range of

fin

angles in order to avoid breakdown of

flow.

N-379

TAE 3

Effect of

0Sci11ating.

Fins in Calm Water

Fin Location

Doubls_Amplitudeduble-Amplitude

---of ateh,-Deg. or Heave, rt.

Sinusoidal

variation of

lift _Forward' 7.0 2.0

0.9 _00/1

Approximately "square"

.variation of lift Fbr;iard 1.3 2.5

Aft 1.1

0.5

For future experimental work,

sinusoidal

variation of fin angle is much easier to reproduce than sinusoidal variation of torque or lift. Hence, calculations have been carried out for sinusoidal variation of fin angle,' using an extension of. the method used for fixed fins (see Appendix).

Results are given below, for a fin oscillation of - 200.

TABLE 3A

hrfect of Oscillating Fins in Calm Water (Cont.)

Fin Double Amplitude Double Amplitude

Location .. of Pitch, Deg. of. Heave, ft.

-Sinusoidal variation of

fin angle Forward 0.8 1.6

Aft 0.8 0.2

Forward and

Aft _{1.4 1.6}

Calculations indicate

that the

actual

_{angle of attack is less than 200} and hence breakdown of flow is

not anticipated

here. For other angles of fin

-The text-step-is-to nnSider the effects

to be expected from fin

-oscillation when the shipis-encountering

regular head seas. Here

the

velocity and direction of flow at the fin is further

-complicated by the

velocities in the encountered wave. (See Fig.' le) For convenience sinusoidal

variation is again assumed first' for the lift. force, and later for the fin angle with reference to the

The condition of ship motion of particular'interest'is that

nearsynchro-nism in pitch, since this involves

not only

the largest angles but

the

condi-tions for wet decks and.slaeuning

(Ref. 3).

For a wave of length.eqUel to

_

-ship length,

the near-synchronous peak occurs in

the

vicinity-

of 8

knots

(Ref. 3), which is too low a-speed to expect

effective fin action. .-The

tear-synchronous peak for a wave of

1.5

L is in the vicinity of 19 knots, and this condition seemed of more

practical interest.

Calculations previously made for the

Series 60

model With 21 x 21 ft0

stationary bow fins (Table 1) were modified by the inclusion of sinusoidally

varying stern fin lift forces. The period

of

the forced variation was

assumed to be the sage as

the

period of encounter, but different phase

rela-tionships were considered in or,'er to find the optimum. Comparative reeulte with

and

without 6 x 12,fti-stex fins and fine x 17 ft. (double 'free)

are

tabulated below (Table 10 fo a chip speed of 19

knotsein_354wavaa.---

-

_-In these

calculations

it was as.umed that-the total effect of the fins was

-to produce a sinusoidally varyi

vvertiar force

with an amplitude given by

(cL)max1.

=-5,

/f

-including the efec -"of virtual mass, damping, etc. Hence

the motion

calculations we

car

ied out by considering the fin effect as a change in the exciting force oily. This method of course gives no clue

as to the amplitude of the fin mFtion

which

corresponded to the assumed

vertical

force.

IEffects of Fins on Ship Motion in

Waves-WO.

N-379

12

Stern fins

at optimum phase -wIth wave.

It will be noted by comparison with Table 1

that

_{the combination of}

fixed bow

fins

and small 6 x

1-2 ft. movable stern

fins night be expected to be slightly more effective in reducing pitch than

large

fixed fins at

-both ends. Doubling th:J. area of the

movable stern

_{fins, discloses the} possibility of appreciable further improvement. It 4s of intexest to note

purely static conditIons

f.,:r comparison that the

pitching angle under /to

_{be expected from simple}

---uncoupled

motion

theory (Ref.

18) is approximately 0.70 x wave slope .,(for,

this particular wave length) or

_3.o5

_{double amplitude.}

Variations

in

the stern- fins appear to

have

negligible effect on.

heaving.

Calculations also

indicated yery small effects'

fronthe

_stern

fins on the

phase relationship between motions

and waves.

For

future

comparisons

with

model tests, calculations have also been

definite maximum

made

on

the

basis of sinusoidal

_{variation up to a /fin angle instead ofa maximum}

lif-V.v4iig

method of calculation used is outlined in

_the

_{Appendix, and}

results are summarized in Table

in Waves with Sinusoidal Variation of Stern Fin orces

500-ft. Ship (Series 60 Lines, C 0.60)

:Synchronout

Condition of 19-Knot Speed in Regular Waves

of 1.5 x Ship Length and Height -= 10.5

ft.

-77.7

N-379

Calculated

Effect of

Fixed Bow and l'-',ovable Stern Fins

NO

Fixed bow fins only (Table 1)

t

Double Amplitude

Pitch, Def,;. Heave, Ft.

21 x 21 ft. L.03 11.6

Bow fins plus movable*

6 x 12 ft.

stern fins

_-3.43-

11.6

Bow fins plus movable *

x17. ft.

stern -fins

2.82

_11.5

TABLE

Regular'

-*Stern

fins at optimum phase with wave.

+ .

The results with fixed bow fins and 20o oscillaion of stern fins are seen to be roughly comparable to those obtained on

the basis

of sinu-soidal variation of lift (Table

4).

Experimental

Verification Of the

results in

Table

5

up to the condition of flow breakdown

is believed to

be desirable. The table also shows

that oscillating

stern fins alone are

not

very

effective.

TABLE 5

Calculated Effect of Fixed Bow and

Movable

Stern Fins in Waves

with Sinusoidal Variation of

Stern Fin Angles

500-ft. ship (Series 60 Lines, Cb =

0.60)

N-379

Synchronous Condition

in Regular 'waves of 1.5 x Ship

of 19-Knot Speed

Length and Height = 10.5

Ft.

Double Amplitude

Pitch

Heave, Ft.

No Fins (Table 1)

7.15

15.1

Fixed bow fins only (Table 1)

21 x

21 ft.

4.o3

11.6

Oscillating 6 x 12 ft.

_{+ o}

stern fins only -

10

+

-

200

6.56.

6.13

15.1

15.0

Bow fins

plus oscillating

x 12 ft.

stern fins"

.:

70°

3.72

11.5

+

-

20, 3.48

109

Bow fins plus oscillat4.3

8.5

x 17 ft. stern

fins

+

loo

3.46

11.6

4--20°

3.05

11.8

Deg.

Vonclusionsi

On the basis of the preliminary studies discussed above, it _appears that fixed and movable fins may under favorable

_assumptions

be of definite 'value in reducing the amplitudes of

_motion,

_{both in pitch and heave. No}

significant change in phase relationships between pitch and wave appears

possible, however.

In view of the fact that fixed fins are particularly effective forward

aid movable fins appear to be more

effective aft, a combination of

reason-ably large fixed fins at the bow and movable fins _{at the stern anpears}

particularlyDromisinq,, it must be realized that even a few degrees

reduc-tion in the pitching

amplitudes at

_{synchronism may have a very significant}

effect on reducing

'wetness of decks

_{and likelihood of}

_slamming.

_For

example, a reduction of only 2 degrees in double pitch

_amplitude

in a

500-ft. ship is equivalent to _{a L-1/2 ft. increase in freeboard and in draft,}

insofar as shipping water and emerging forefoot are concerned. Furthermore,

the important consideration is often the limiting speed or limiting sea

condition above which motions or accelerations _{become excessive. A moderate} reduction in average amplitude of motions _{may yield an appreciable extension} of the limit of speed or sea condition.

Accordingly, it is believed that further _experimental

_and

_analytical work under the present project should be _{directed primarily at the evaluatinT1}

of controllable stern

fins, particularly

_{in combination with fixed fins at}

the _bgl2T.

N-379

-It is believed that certain

experimental work would be of great value

next as a means of _{determining whether}

or not the above

_conclusions

_regarding ccntrollable stern fins are at all reasonable. _In

_planning

model tests in which fins are mounted on a model,

the

question of scale effect arises, since the model fins will operate _{at very low Reynolds No.}

As shown in Ref. 7 and elsewhere, the important _{scale effect is the variation of}

(CL)max

.

(and the stall angle) _{with Reynolds No. This is particularly}

significant

for this application because of the fact that it would _{be desirable to} operate the fins as _{near as}

_possible

to maximum lift at all times.

Typical model

fin

_{Reynolds Nos. for a ship speed of}

19 knots are as follows: G Model Model Scale Length,

1/25

20

1/50

10

1/100

₅

Ship

₅₀₀

PART II EXPERIMENTAL PROGRAM

-4 V Reynolds Nos. 6 ft. chord _{12 ft. chord} 111 x lob _{28 x}

_lol

5 x 10

10 x 10' 2 x 10 _{h x 10li}

6

15 x

106 _{30 x 10} N-379 -Revised 3/27/57

Reference to Fig. 2 suggests that within the _{possible range of model} size- it is impossible to

approach full scale conditions. It is believed,

therefore, that the model _{scale to be}

_{used should}

be

_determined

_{on the}

basis of other considerations and the scale

effect handled in some other

we)T. (Comparison of results for ETT

5

and DTMB 20-ft. Mariner _{models (Ref. 19)} with and without fins _{showed some scale effects.}

Except at low speeds where

exnerimental errors due to wave reflection were experienced, _{the small model}

fins are approximately _75%

as effective as the large model

_fins.)

Two possible solutions for the scaleeffect

Problem aopear. One is

to increase the maximum lift of the model fins

to full-scale level by increasing their size and/Or _{using slots, flaps,}

or other high-lift devices. The other possibility is to use fins of the

correct scale, restricting the operation to conditions _{in which no flow breakdown}

occurs. _{In predicting} full-,scale performance _{then, the higher maximum lift obtainable}

would be

taken care of by extrapolatiOn.

It seems at the _{Present time that the}

latter method would be _{preferable, If at the}

forces are measured, the scale-ef ect problem can

be completely bypassed.

The effect of a particular fluctu ting fin

force on mations'*iii" be known

.

---for the model; and

a

similar scal_d-up force_applied in some manner by

ship

fins would be

expected to produce// the same effect. The

problem

em of the. size and angular variat n

ac/tually

_{required to generate a}

parti-cular full-scale fin force c'n be,treated as a separate problem for

detailed study along the line of Part 1. _{(This is planned for 1958.)}

Accordingly,

the following 4ecific experimental work is planned, using

a 5-ft0 Series 60

(0.60 Block) model. _{This program is generally in}

accord-ance with Reference

Measure the trim angles and vertical force caused by stern fins set at different angles of attack at one forward speed in calm _water.

A plot of

these

results will

_{of course establish the. angle of attack}

at breakdown and permit the maximumI., obtainable with the model fins under steady conditions to be estimated for comparison _{with Fig. 2}

and Table 2.

Measure the model motions induced in calm water by the simple

harmonic oscillationof stern

fins

and measure the oscillating vertical

fin force. This will permit direct comparison with calculations of

- the effect of a lift force of known amplitude varying approximately

sinusoidally (Table 3). By covering a range of amplitudes of fin motion, the breakdown point can also be established. _{The period of} oscillation of the fins would correspond to the model's natural

pitching pericd.

Measure model motions and vertical fin force in regular _waves

of several lengths at the speed for maximum synchronous pitching,

without bow or stern fins,

with

fixed bow fins,

with a pair of moveable fins at stern arranged to

oscillate in different phase relationships to the

encountered waves, in addition to fixed bow _fins.

This will

provide direct evidence

of

_{theefectiveness of certain known} oscillating fin forces on model and ship behavior.

Tests in irregular waves will be deferred until the effectiveness of controllable fins in regular waves has been evaluated.

N-379 17

-References

Proposel IC, Stevens E.T.T. r'roposal for Research on the impr5ovement of

-Pitching,otions of-Ships by -Means of Contralable Bow and Stern Fin,

- -

-revised 21 June 1955 in accordance with conference at DTIB, 20 June 1955.

.Letter from Captain W.H.Leahy, C.O. and Director of DIMS. to Hugh W.

MacDoneld of L.T.T., 25 July 1955 (File: NCl/LIT Stevens, 587:WLA:js)0

"Ship Speeds in irregular Seas," by F.J.Lewis, Trans. SNANE, 1955.

_{_}

- 3A.

"Pitch Reduction

with Fixed Bow Fins

on aModel of the Series 60?.

0.60 Block Coefficient," by U.A.i'Ournaras, D1B

Report 1061, Oct._{_}

1956.

40

"Ship Sla-Taing in Head Seas," by V.G.Szebehely,.DTR76 Report 913,

Feb. 1955.

"Investigation of Ship

Motions in Regular Waves," by

V.B.Korvin-Kroukovsky,_

--- Trans.. SNJE,

1955.

.

5A.

"Recent

Developments

in the Theory of Ship notions and

Benai.n:: Moments

in Regular Waves," by

ETT Note No. 411.

"On the

Stabilization of Roll,"-by-j. H. Chadwick,- Tans..-SrAME,

_1955.

"Some Hydrodynamic Aspects of Appendage

Design,"

by Philip Mandel,

TY.ans. SNAME, 1953.

"Airfoil Section

Characteristics as

Affected by

Variations of

the Reynolds

rumber," by L. Jacobs and A. .1herman, NACA Report No. 586, 1937.

;

"Airfoil Theory for

_{1;onrbn,LIcrm Motion," by Th. Von Kaman and W.R.Sears,}

journal 'of the Aeronautieol-Lciences, Vol. 5,

August 1938.

"Experiences in the Stabilization of Ships -"y-Sir-William Wallace,

Trans. IES, 1955.

-

11,- "Oval Hydrofoils with TrailiAg Edge Flap and Boundary Layer

Suction,"-by Lee

Arnold Associates,

2Dr- Rpirt 55-2,

September

l95.

"Die Zunahme des Maxim

_{aufb;iebes:Ven Trae,flligeln bei}

p175'tz1icher

Anstellwinkelvergrsserung

(1473eneffekt),".by H. Kramer,

Z. Flugtech.

u. Notorluftschif. 23, 185-189 (1932).

Current Work on

Hydrofoil Stbility- by Dr. Paul Kaplan, under Contract

ONR-Nonr 263(01)(MB).

Tables of the Theodorsen Circulation

Function

for

Generalized

Motion,

by Y.L.Luke and M.A.Dengler, journal of the

Aerpnautical_Sciences,_.

July 1951.

15.

"Fluid Mechanics, Part II," by M.M.Hunk, Vol. 1 p.

286 Div. of

Aero-dynamic Theory, W.F.Durand, Editor;

Durand Reprinting Colniait-bee,

_California

institute of Technology,

_1943;

atev4(ii

N-379

18

-_2.

5.

Jacobs",

6.

7.'

---10.

---1/4:,----4

1.

References (Cont.)

16.

"Theoretical Analysis of the Longitudinal Stability

_{of a Tandem}

Hydrofoil System in Smooth 'elathr," by W. C. Hugh,

_{Jr. and Paul Kaplan,}

ET T Report No. 479, July 1953.

.17.

"The Forces and Moments Acting

_{on a Tandem Hydrofoil System in Waves,"}

by Paul Kaplan, El'!' Report No. 506, Dec. 1955.

18.

_{"On the Motions of Ships at Sea," by G. Weinblum}

_{and M. St.Denis,}

Trans. -SNAI`E, 1950.

19.. "A Study of the Seaworthinecs of a Mariner Class Ship Equipped with

Bow Anti-Pitching Fins," by V. A. Pourneras, DDIB Report (Preliminary)

1956.

N-379

-

-(1)

STEVENS INSTITUTE OF TECHNOLOGY

EXPERIMENTAL TOWING TANK

HOBOKEN. NEW JERSEY

APPENDIX

aucnATioN

OF _{THE EFFECT} OF FIXED FINS ON TIE RESPONSE

OF A SHIP TO REGULAR HEAD SEAS

The equations of

motion in pitch and heave for

the bare hull are r-7 Ot.

(

a

+

+ cz + dt3 + eG

g9

re

*\t,

AG + BG + C9 + Lt'z' +

+ Gz =

1,.cre the coefficients are as

defined in References

5

and 5a0

In

calculating

the effect of a pair of flat plate fins at the bow

and/or the

stern, the computed coefficients on the left hand side of these

equations must be

modified and a term

must

be added

to the right hand

side

for

the changes in fin lift

and

moment

due to waves.

".".'ect in Still Water

From Reference 13, the theoretical (unsteady

motion) hydrodynamic.

lift

L on a hydrofoil of large aspect ratio and its moment N .about the

center

of gravity of the system are, when the foil

is undergoing

oscillatory

rep

_{*(1- -0,97}

motion in still water,

onSV2 (k) + K Ptt,. Sc

-

Z9 _ 2 V Li. c

V

+ KPaSc3Z

-123

;here S = area of fin = bc for

a flat rectangular plate

c = chord of fin

b = span (effective or total span .here. in the case where a

pair

of fins

is attached nearti-e

keel of a ship

near

the bow or stern)

- AT

aspect'ratio'

= distance of "fin tO cg

_

(-+ if fin is forward of e.g. )

N-379 -(2) M - (71cSV2 ) E-4 r. E. Sc V 9 + ei-T, LC-)

ScEY

c(k)

-1 +

-2 ( A '1 Kc _ + L )

A1

-L

V. _{forward Velocity along x-axis, ft./sec.}

(.0=:- frequency of

encounter,*--rad.beci

k Vic

-reduced frequency

C(k) = frequency factor for a two-dimensional oscillating

_hydrofoil

.

'

(The

Theodorsen circulation

function)

iii(2)(1,)

C(k) =

( k ) i HoMR-17J

where

H

is the

Hankel function. (See Ref.

₁₁₎

K is the

coefficient of

_{accession to inertia of the fin, obtained} from Ref. 15 as the coefficient for. elliptic discs at aspect

ratios 1.168

times the aspect ratio of the fin (See Ref. 16).

ton SV,

Note

that (

-7-) is the steady state damping force of a fin per

1-,st

unit

vertical velocity by aerodynamic theory. Although limited to

fairly

large aspect ratios it may

still be considered

_{applicable to the case of}

1

aspect.

ratio 2.-

(lc Pi

_{Sc) is the virtual mass of a flat plate. (The}

actual mass of the

fins is insignificant.)

In evaluating the lift and moment of _{a pair of flat plate fins attached}

at the keel

near

the bow or the

stern of the 500-ft. ,Series 60

_{ship, the}

quarter-chord E

of tha fin can be

neglected as

_{insignificant when compared} with t = 239 ft. The

equations can then be written as

(4 bc V (./

-(

. ) C(k) - - t

eii+

1 + (3) 1 .Kfq41 bc2

t

M=L t

-N-379

A2

-ker = L

Modification of the Coefficients of the Motion Equations

The increments to be added to the coefficients of equations (1)

for the effect of a pair of fins on the notion in still water are from

equations (3):

Aa = K

bc2

4

AA = (Aa)

1,2

Ad = AD = (La)

Ab = (P.

bc V) C(1,-.)

2

'

-(Ab) t2 -(Aa) VZ

= (.4b)

- (La) V =

AE = (Lb) t

4g = -(Ab) V

AC = -(Ab) V

= -(A E) V

Go = A G = 0

Changes in Fin Lift and Moment Due to daves

From Reference 17, the additional lift force and moment due to waves

acting on the forward hydrofoil of a system moving in regular head seas

are,-neglecting second-order terms,

AT/ ; LT,w

t (AL )

2 n

-hk

where

I

- A(

7--u)e-9:T/

the ratio of the amplitude of

th

e vertical

77-component of orbit,,' velocity to velocity

along the x-axis

Aw = wave amplitude

k = wave length

c

= wave celerity

h = submergence of the foil below still water level

#,,Dn sy- wo (1-7._

)e1tr_pt4-0)

_I-Jo(

v)

J1c,15-1

L_

_x

2

C(k) + iK(1 + cw Ji

. (

-

3

-=

_

-and the other Symbols are as- defined before.

(t = 0 when the wave nodal point

before the crest is at the c.g

of the system

-If the dash effect is neglected, which it may be i

the case of the

-'

two. sets of fins .at bow and stern of the 500-ft, ship since the effect of

ship' wavemaking is also neglbcted4 equation (4) applies also to the tear foil

.

with 4

negative.

-and AM

are to be added to the right hand sides_pf .the force and

W

moment equations respectively.

_-'

I

-,Effect' of Finn Oscillating About Fin Midpoint

_

-When, fins oscillate' about their own -midpoint

calculated above there are the following lift and pitching

_

(5)

II

0S!s

= steady ,angle of attack of foil, (without orbital motion) c",<.;-= 0

0

2IZ

for the. case-of the flat plate fins

_{to the. Series 60 Ship.}

attached

-,

- X.

,

))

X

,

J( '0

''' Bessel functions of argument ))'

ship's c.g. due to this oscillation,. derived as in eq. (2):

-3 V2

0,

+.2

C"'//-1

X m 'e 9 2 4- (

v.() 0(k)

.

1

-tr.°

in addition to the effects

mbment about the

-r

-49-'777 . -rrtrrsnr--;";"2,.2.nr:iwn.CW17-77.'Ft7M7Fr, +())141:K Sc Z V ...Z

+ (.) it

K Sc3

(;:14_

Where cK='"4nZi" is. the an

of 1..tation of the foil, positiVe with up,

pitching moment M.

.

-., -.,

--- ___._ M =:"Z L.

This force and moment must be adder to

the, right hand side o

equations (1):

1

_

I

FC,v2.L en r! A )t4

-r

Sc. v.. c

<,.

FR

"rt,r-id

or

iT

f-,-41 114 s

rv

RE:."1-7 Avvr

FOrqe.C.-(

cdA?otsie--Tv

T-A (r p,

p1-i)1iNfr

awn,.

N-379

F-r

, -.I.8 1.6 (-3 1.4 u. UJ

0

1.0 ! 70:8 J00,000 REYNOLDS NUMBER L.,{ :71.41r7.771.r! n

23 4.-75

6

89

, 1,000,000 _ a .5 - r.-11 v, t i17; ...-4. 4.4.,,.. a

t '

4 5

6 789

10,000,000 ILo

14- 31Y

F 1.Cr. 2. 5 F ';.,"''55.4,e-flr7...'fr,"...1.;.'

_,

Fig. 2 THE EFFECT OF REYNOLDS NU, BER ON MAXIMUM LIFT COE,FFICIENT FOR VARIOUS ASPECT

RATIO FOILS WITH A CHORD /T ICKNESS RATIO OF 6.7 '( Figure 13 reproduced from re erence 7. )

I I I . . _____. .. '11' 1 11

I-,. ..,... . ' . 1 -. _ 4 1 -ASPECT RATIO= ... oo r. , , ' ';! II ...,

-SS21r--11.

'

-0

.-':,,,- ./ _I

--1

11 ..,,,,,,---,--7. ''---,I 4( ..1 / , 1 .

:

---,

./

....1

0 ' ASPECT ASPECT ___ASPECT-RATi0-=-RATIO RATIO = I = 2 3- --:.-

[i

''' , 1 J a 3 2

4

7-UiVa(ewe- /.17 C

Car

ve

-ASstimED

-5-00 ARE

V

A

RI

A- 7? o/p/

AMP

Etge./IV44LE-A77---

/v

R15

)

A

37 9