A mechanical system for reducing pitching and heaving of a surface piercing type hydrofoil boat

(1)

Reprinted from ,,EUROPEAN SHIPBUILDING" NO. 6, 1963, VOL. XII.

Lzb.

V.

t

DeUt

Norwegian Ship Model Experiment Tank

The Technical University of Norway

A MECHANICAL SYSTEM FOR REDUCING PITCHING AND HEAVING

OF A SURFACE PIERCING TYPE HYDROFOIL BOAT

BY

Harold Aa. Walderhaug

Norwegian Ship Model Experiment Tank Publication No. 73 January 1964

(2)

SHIP DESIGN

A MECHANICAL SYSTEM FOR REDUCING PITCHING AND

HEAVING OF A SURFACE-PIERCING TYPE HYDROFOIL BOAT

Introduction

A major difference between the two well-known

groups of hydrofoils, the surface piercing and the submerged, is the inherent stability of the former

as regards vertical displacement as well as heeling,

and the

indifference

of the

latter, practically speaking. The submerged hydrofoil must be steered from outside, either manually or automatically, but the foil is little influenced by the waves. On the

other hand the equipment for automatic foil

con-trol is expensive, and the question arises of whether it is snfficiently reliable. In the case of breakdown, it is expected that highly qualified experts with

first class equipment may be needed to undertake repair work. Under certain circumstances this may put a hydrofoil boat out of action for quite a long

time.

Different mechanical systems for controlling sur-face piercing hydrofoils may be suggested. For

example, it is feasible to equip a hydrofoil boat

with shock absorbers in order to reduce the wave impulses. However, such a system could not be applied to large hydrofoil boats since the weight of the shock absorbing system would probably be rather large. Another system which might be

feasible even for larger vessels consists of a ur-face piercing foil with s)ring controlled incidence, as suggested in Fig. S or 5. Instead of letting the

whole foil oscillate, it is also possible to equip a

fixed foil with spring controlled flaps. It is

con-venient to superimpose on such a system a means

of manually controlling the foil or the flap. This might be of value during take off or at certain

trim conditions. Such a mechanical system for

re-ducing the pitching and heaving of a hydrofoil boat, should he cheap, simple and robust, and it

Norwegian Ship Model Experiment Tank, Trondheim.

By

Harald Aa. Walderhaug1

should be possible to repair the system

at any

shipyard, small or large.

In the following are presented some theoretical

considerations and also results of a limited number

of model experiments in connection with a control

system based on the application of mechanical springs. The investigations are preliminary and it

is not expected that final conclusions can be drawn. But some of the results are encouraging and the

work should be carried further in a more

system-atic investigation. List a f h hA hF

hw

I k KA KF i LA LF L0 m M U z

1-of Symbols.

= distance from centre of gravity of boat to

centre of lift of after foil.

= distance from centre of gravity of boat to centre of lift of forward foil.

draught of foil.

= draught of after foil.

= draught of forward foil. = wave height.

= longitudinal moment of inertia of boat.

= spring constant.

= coefficient of viscosity for after foil.

Ver-tical force due to viscosity = K AZ.

= coefficient of viscosity for forward foil. = distance between forward and after foil =

a+f.

= lift on after foil. = lift on forward foil.

= wavelength of uperimposed oscillation. = wavelength.

= mass of hydrofoil boat. = trimming moment. = time.

= speed of advance of hydrofoil boat. = rise; heave.

(3)

z z a a5 Ez 9 9 9 dz dt d2z dt2

= angle of attack of foil at zero trim. = angle of attack at foil tip.

= lift phase angle relative to waves. = heave phase angle relative to waves. = pitch phase angle relative to waves.

= trim angle; pitch angle. d9 dt d20 dt2 140 mm COmm FOIL 1-2

Fig. 3. Dimensions foil 3.

The hydrofoil system

As shown in Figs. 1, 2, 3 and 4 the hydrofoil system is 'based on a balance between lift, drag

and spring forces. The expected results should be:

FOIL t-2

Fig. 1. Dimensions foils i and 2. Fig. 2.. Foils i and 2.

(4)

1) Increased lift during take-off, since the

relative-ly small lift and drag forces will lead to a

rather large angle of attack. This is most wel-come, because the resistance hump before the

take-off point may be critical, especially in a

seaway.

FOIL 3

1W\/\/V\í\i\/\t_N

\/\/ / I\/\/\/\/

Fig. 4. Foil 3.

European Shipbuilding No. 6 - 1963 In connection with surface piercing foils, the suggested system will tend to reduce the lift variations in waves. At the same time the

trans-verse stability of the foil should be maintained

In a following sea, the system should counteract

the lift-reducing when the foil enters a wave,

Fig. 5. Foil 1: lift L as a function of draught h, speed U

and spring constant k.

Fig. 6. Foil 2: lift L as a function of draught h, speed U Fig. 7. Foil 2: lift L as a function of draught h, speed U

and spring constant k. and spring constant k.

FOIL i kg/cm 4-k-1,188

o--Lk9 10

--+-- k-oc

co2.1° h cm

-o

_--/

zzIv

-_-.--- ___+

-z

o 2 3 4 5 8 U rn/s 15 FOIL 2 1.188 kg/cIT

/

k

o____

-lo

-f k-Cm, '<2,7°

,j

//

/

/ /

/

,c

//

5

H

-7/

//////

//4

4 U rn/s 5 5 .1.5 FOIL 2

/

k - 2.945 kg/cm

o..---Lkg ... .4.. - k

h/

, « - 2.7 '

/

///

/////7

//

_7/

.1.:

I -,/

/

o .7

/71/

//

/

o 2 4 5 8 U rn/s

(5)

and so the tendency 'to crash 'should be di-minished.

It is possible to avoid the influence of the drag on the foil angle of attack by moving the pivoting

point down to 'the centre of drag in the foil. It would then be possible to make use of very weak

Fig. 8. Foil 2: lift L as a function of draught h, speed U, spring constant k and trim angle 8

Fig. 10. Foil 3: 'lift L as a function of draught h, speed I.,,

spring constant k and trim angle 9.

springs, 'since the lift could easily be balanced by

moving the pivoting point horizontally. In praotice.

however, 'such a system would create cavitation problems and there would be som.e reduction in the foil efficiency when the pivoting point is

situated below the water surface. A flap, on the other hand, may easily be controlled by a spring

system hidden in the main foil, and this system is,

in the author's opinion, to be preferred in con-nection with large 'hydrofoil boats with hollow

foils.

4

Fig. 9. Foil 3: lift L as a function of draught h, speed U

and spring constant k.

Fig. 11. Foil 2: lift variations in waves. Head sea.

2°. IO

o----k

FO/L2

_/

/

//-.

/1

/

2.945

/

'l-/

/

+

/

1o&5

+.

U

-k- ,-2.7

-525'vy's

hcm.i/'

/

//

Lkg

//

/

-

/

///

/

$ /+/

9

o - 0 2 3 4 Io FOIL 3

//

4: 1/ k-3,550 kg/cm k-oe o-34

-.0---

--+---//

///

Lkg

/

1'

/

h io

/

5

441 /+/

/

r

/

r'

V .

-í_t

---Û 0 2 3 4 5 5 UftVS ¡Q 5 FOIL 2 k - 2.945 k - 5.25 6.&cm kg/cm o ----f---U h L kg o 0 0 1 2 3 4 in 5 7 'O FOIL 3 .,_- -k-3.5SOkg/cm ,o-E .k

Lkgo

- 4- - - k -U-5.25 -r,1

o

-$ o

ii

_I' - o I 2 3 4

(6)

Fig. 12. Foil 2: phase angles.

Tests with single foils

In Figs. 5 to 10 some results of model tests in still water with the single foils are shown. The

possibilities of altering the foil characteristics are numerous, but it should be borne in mind that too large an angle of sweep back may upset the trans-verse stability of the foil.

As shown in Figs. 11, 12, 13 and 14 the very

simple spring system has effectively reduced the

lift variations in waves. At the same time the phase angle between lift and wave is increased, giving the foil more time to climb the waves.

Static longitudinal stability

When the hydrofoil boat is given a change of

trim do, the restoring moment will be:

SLF SLF SLA dM

=

8h dhF f 8

dOf+

6h

dha

SLA

+ 8d9-a

(1) or, since

dhF= fd0

dhA a- dG, dM _SLF

SLFSLASLA

a ...(2)

dG 8h Sa 8h Sa

European Shipbuilding No. 6 - 1.963

Fig. 1:3. Foil 3: lift variaons in waves. Head sea. For the suggested foil system we find:

Foil 2, h = 6.5 cm Foil 3.

h=4 cm

Foil3,

h=5 cm

90 FOIL 2 kg/cm I cs-27 o- -- k-2.945 h-4cm

---1--k.o

Lf-5.25ri's 60 h-6.5cm EL

/

5

57 Lwm

.1_o FOIL 3 «-3.4 o k 3.550kg/cm

- +

LI-h4cm

-

k-5.25 rn/s 5 cm 5 N. h-o

o

o o 2 3 4 5 6 7 L k=294.5kp/m k= c U m/s 4.5 5.25

45

5.25

SLk/

₁₀ ₁₀ ₅₀ ₆₀ kp/rad 85 90 130 180 k3.55kp/m k= U rn/s 4.5 5.25 4.5 5.25 120 70 130 200 kp/rad 40 45 59 80 k=3.55kp!m ci U rn/s 4.5 5.25 4.5 5.25 SL -kp/m 40 20 80 130 SL kp/rad 40 45 59 80

(7)

Fig. 14. Foil 3: phase angles.

We hall further make use of the notation:

foil 3 forward, foil 2 aft foil 2 forward, foil 3 aft and

Ai, Bi:

both foils fixed

A2, B2: forward foil free, after foil fixed

AS, B3: forward foil fixed, after foil free

A4, B4: both foils free.

Design draught of foil 2 is 6.5 cm, whereas design draught of foil S is 4 cm as forward foil and 5 cm as after foil. At a speed of 4.5 rn/sec. we thus

obtain: = 147.9 kp m/rad Ai. dM dO dM Bi. dO «

According to this, all the systems should be

longi-tudinally stable in calm water. Mean values of 8L/8h and 8L/8a are used, however, and the

in-fluence of drag on the stability is not considered. 6

Fig. 15. Change of trim in still water.

In view of this, the safety margin of system B3 is probably rather .srnall, a fact which may explain

the recorded long-period oscillation of rise and trim of syste.m B3 in still water.

Dynamic longitudinal stability

In the present study the following

approxima-tions were introduced:

i) 8L/6h and SL/Sa are regarded as being

in-dependent of z, O and t, and equal to the static values.

The influence of the drag on the stability is

dis-regarded.

Surging is disregarded.

Downwash and waves from the forward foil

have negligible effects on the after foil. The horizontal component of the orbital wave

velocity is disregarded.

The orbital wave velocity is regarded as being

independent of heave and equal to the value at a mean draught of the foil.

The equations of motion in heave and pitch in

still water may be written:

SLF Of SLF SLA Oa SLA z mz+ _{Sa U}

-+

_{Sa U}

-- +

_{Sa U}

_{Sa U} SLF SLA 8TF SLF SLA Sa Sa 8h

z+

8h &f+ 8h Z SLA 8h

Oa+KFGf+KFZKAOa+KAz

0. (3) 8L óf2 _SLF _f SLA Ûa SLA za

8aU+SaU+8a

U

SaU

SLF SLA SLF SLF

Of+ &a+

zf+

Of2

Sa 5« 8h 8h SLA SLA 8h za+ 8h 0a9+KFOf2+KFzI

+KAa2_KAza=0

(4) FOIL 3 o k =3.55kg/cm

--+-- ko0

90 (J-5-25 rn/s _h4crn h-5 cm 60 N .... 30 O

/

-30 O 1 2 3 4 5 6 7 Lw m « « A2: « = i56.8 AS: «

= liii

A4: e = 120.0 « and e

= 71.8 kp m/rad

= 84.5

«

= i7.7

«

= 30.4

(8)

With the notation: a1 ao a3 a2 a1 ao O a3 a2 a1 O a4 a3

European Shipbuilding No. 6 - 1963

From (5) and (14) we find: a4 = ml

8LF I+mf2

8LA I+ma2

a:=

_6« _U

+

_8« _U +KF (I+mf2)+KA (I+ma2) 8LF 8LA

a =

8h (I+mf2)+ 8h (I+ma2) 6LF SLA 8« 8« 8LA 8LA 6LF 8a

+KFU-6 +KAU

8«

+

KFKAU2)()

¡8LF 8LA

6L' 6LA

6h 8« 8« 8h

+KFU 8hAU6h)

8LA 6LF 12

6LA 8LF

+(KF

_6« 8LF 8LA 18LF 8LA a0 8h 8h 8h 8« 8LF 8LA 6« 8h

Neglecting the viscosiity terms and also the added

mass, and inserting the values given for foil 2 and

3, we find that the determinants D1 and D2 are

positive for all the B systems as well as for system Al. However, a0 is negative for all the B systems.

This term does not contain visoosity or inertia

forces, so that the negleot of these should be of no consequence. By increasing 6LA /6« and decreas-ing 6LF/6a in the term a0, the stability could have

been improved. This is also self-evident from physi-cal considerations.

Model tests with sistems A and B

Some results of the model tests are presented in Figs. 16 to 23. As shown in Fig. 16, the foils were originally mounted on a boat model as system A,

which was tested in still water as well as in waves.

It appeared that the still water resistance hump at

the take-off point was indeed reduced for sytem A3.

The reduction was not large, but still sufficiently marked to make further experiments seem

worth-while. An unsuitable combination of foil

charac-teristics may on the other hand greatly increase the (18) A B C D E F G

₌

8LF1 6LA1 (5)

8aTJ+ 6aÙ+KF+KA

8LF SLA 8h

+

- 8h

8LFf

8LAa

+KF fKAa

8a U 6a 8LF 8LA 8LF 8LA

8hf__ia_

8a 8a 8LF f2 8LA a2

8aU+

6o -Ù+KFf2+KAa2 6LF ₂ 8LA 2 SLF 8LA

f+

a

f+

a 6h 8h 8a 8LF 8LA 8h 8h a we may write (3) and (4):

rnz+Az+Bz+C8+D = 0

(6)

I+EG+FO+Cz+Gz = 0

(7)

Introducing

z = z0

et

(8)

O = Ooet (9)

the system of differential equations is satisfied if:

2mz0+ wAz0+Bz0+ úCO0+ DO0 = 0 (10)

2 Io+ oE&0+ F90+Cz0+Gzo 0 (11)

For the

existence of non-trivial solutions it is necessary that:

o2m+wA+B, wC+D

2I+E±F

=0 ....(12)

giving the characteristic equation of the system:

a4o4 +a3Ú3 +a2o2+a10±a0 = 0 (13)

with:

a4 = ml

a3 = AI+Em

a2 = BI+F.m+AEC2

(14) a1

AF+BECDCC I

a0

BFDG

j

It has been shown, see refs. [1], [2],[3], [4] and

[5] for example, that the dynamic system is stable

when:

aj >0, where

i = 0, 1...4 .... (15)

=D1 >0

(16)

(9)

Fig. 16. Hydrofoil boat, system A. 9kg

r'

u

2 k V 95 an, SYSTEM 8

G=225kg

I

43 kg cm 55cm 13S kg

Fig. 17. Hydrofoil boat, system B.

(10)

8-take-off hump as shown for systems A2 and A4. System B was mounted on an aluminium frame,

shown in Fig. 17, and this system was therefore only tested in ifoil-borne condition at full speed.

Of the A systems only Al was tested in waves in

Fig. 18. Hyhofoil boat, system A in still water.

Fig. 20. Phase angles of heave.

European Shipbuilding No. 6 - 1963 head sea. This system was stable. All the B systems were tesed in waves in head sea conditions. The test results are presented in Figs. 19, 20, 21 and 22.

Superimposed on the ordinary heaving and pitch-ing motion, the hydrofoil boat also experienced a

long period motion in heave and pitch. This is

shown in Fig. 23. Arrows pointing upwards in this

figure indicate a stable motion, whereas arrows

pointing downwards indicate instability with fre-quent crashing. The wavy line of B.3 at Lw/i = O

Fig. 19 Recorded heave. Head sea.

Fig. 21. Recorded pitching. Head sea.

4 ¿ u Foil 2 CG. Foil 3 f 55cm -... fFoil2k.m 3 k-k.00 -.-- 3 k. Foil 2, k.2.945

[l2,

{Foil

I--3,

2 k.2..94559/cm k.3.550k'cm 3.550 kg/cm kg/cm 7 A I A2

A3----+---0 1-.--. I ¡

A4---'-X---4

ElF?; \'\ ,,L

'A__

I/A'

/

¡__

-125

Viii

"

!'-000

(

/

o

L--.

2 4 5 6 Urn/s .7 rn/s ¿J4.5

-'A

ri/Ari

V

pia_

1234

Lw/I

1.5 U= 4.5 rn/s 8 A -r

/

B3

720

.5 X o o 1 2

L/1

.90 U- 4.5 rn/s 60

+-B1

. D 82 X

0E;

B3 -30 -60 -120 -150 -180 1 2 3 4

Lw/I

(11)

indicates long period 'heave and pitch in still water As shown in Figs. 19 and 21, the heaving and pitching crE the hydrofoil boat in head sea has

been reduced by as much as 65-75 o/o by the

rather primitive application of spring controlled

hydrofoils. B'ut the hydrofoil boat, on the other

hand, has lost its longitudinal stability at some

wave lengths. Probably this can be overcome by introducing some kind of damping in the spring

system and by altering the foil

characteristics.

Further theoretical and experimental study is

need-ed to clarify this matter.

Equations of 7notion.s in regular waves

As shown in the experimental part, the equations

governing the dynamical stability in ca:lm water were insufficient to predict the 'stability of the

hydrofoil boat in waves. Referring to Fig. 24 we

may now write the equations 'of motions in regular waves as 6LFh 27r mz+Az+Bz+C0 +DO =

_8h2

L

r'VgL

] 8L h Ii

21t+f+

w II

-

J _8h ₂ L Lw) i

8LF1h

t

aI±

exp 27r _J

8ctu2

27rg 27r

cos

-L L

[(u±V

2ir hF

[L-[(u±j/'t+f1

LA

2j

- 8U 2

exp

[(u±V)t

-

a]

8LF h

2

sin-10+ E6+ FO+Cz±Gz _6h w

-

sin-2 Lw

[(u

8LF i h I

2irih'

11/2g

2îr

l---I----zOfIl II -

cos-L

Lw\2

!jVLw

L

u

gLw)

t+f]

8LA i h

pi

_z+8a)]

[

2rih

27rg 27r L

cos -

L !gL ]

Íu±/ta

2rj

lo

-Fig. 23. Recorded wave length of superimposed, long

period oscillation. Head sea. Fig. 22. Phase angles o'f pitching.

u CG IQLw' -c - /312 Orbital velocity. e _y

Fig. 24. Orbital velocities in semi-trochoidal wave

90

U4.5m/s

60 -30

/

-120 -150 -180 o i 2 3 4

L/1

Lw L:, .4 i ' L

3'

P,

u_a

4 F 27r/hA

I I z+9a11

- /';g

27r

cos-/ L

L L\2

!jd

L

Vertical component of orbital vcft

Forward: Lf(uc1/)t...fj

Aft _t ₂ _t-jL,

(12)

Fig. 25. Computed and recorded heave and pitch of system

Al, head sea.

where the upper and lower sign of ± or indicate head and following sea respectively, and where the orbital velocities at a mean draught of the foil, h/2, have been considered.

Approximating the amplitude of the orbital

vel-ocity by '/h exp[ rh/LwJ, and with the

no-tation:

Fig. 26. Computed and recorded heave and pitch of system

Bi, head sea.

P=

European Shipbuilding No. 6 - 1963

Fig. 27. Computed and recorded heave and pitch of system BZ, head sea.

6LF h 2rf 8LF h r rhF] 6h ¡27rg 27rf 6LA h 2ra

cos

-'L SUlL

w w L 6LAhw F TrhA11/

2a

---

ex-- 6e 2U

r [

_{Lw] V L} _L hF i 6LFhw . Lw] 6h 8e 2U / 2rg 27rf _8LAhw _2ra 6h

Slflj-±?

1hA1 1127rg

2a

6a U

expL

LWVLW

II cosL 6LF h 27rf _{6LF h} F rhF] cos H-R = 6h _L

f---expI--

L L_w l/27rg 27rf _8LAh 27ra ii

sin a

6h 2 COS VL L L

8LAhw l 7rhA]}/27rg 2-a sin

ex

8a2U

_LLW]VLW

L f6LFhw 2rf 8LFhw hF1

S

8h 2 Sifl_L

TI - exp r-

6a2U L

L wJ 27rg 27rf + 6LAh 27ra co's a 6h

sin

L L 2 '1 6LA h [

Ta

g cos27ra (21)

82

.5

/

iá

E

4

Theory 10

9

Theory

ii

_+.

.

-

-1 o

um

xper/men

2!

Al

_.4 . /-i-i:

o.w

I

--u_

-, --I 1-5 The. e

1'

.er, ents -1 2 LW//I

81

.5 . 4 Theory_ o 2.0 1'S Lxperiments -. . Theory -o 2 3 4

(13)

Fig. 28. Computed and recorded heave and pitch of

system B3, head sea. we may write (19) and (20) as:

/27rU 1127rg\

mz+Az+Bz+CO+D9Psin

±/

)t

where the factor V27rg/L

is the circular

fre-quency of the wave motion.

These equations were studied on the analog com-puter ANITA of the Chr. Micheisen Institute, Ber-gen, for systems Al and Bi, B2, B3 and B4 for the conditions:

U

=

4.5 rn/sec.

h

=4cm

L/L

=

i - 1.88 - 2-2.67 - 4.

The computed pitch and heave are shown in Figs. 25 to 29 compared with the model results. The computer also clearly showed the stability of

system Al, a slight instability of the systems Bi and B3 and great instability for the systems B2 and

B4 at most wave lengths.

To improve the agreement between theoretical and experimental results, the lift derivatives 8L/8h

and 8L/ a should be determined by dynamic

ex-periments in still water, by dipping and oscillating the foiLs. Further the viscous and added mass terms

should be determined by similar experimeith, and all these terms should be included in the equations

- 12

Fig. 29. Computed and recorded heave and pitch of

system B4, head sea. of motion.

Further due regard should be taken to the fact that at least L/6h is not a constant and is not independent of z. Probably 8L1 a can be

regard-ed as constant for some hydrofoils.

REFERENCES

Kaplan, P.: «Longitudinal Stability and Motions

of a Tandem Hydrofoil System in a Regular

Seaway.» Stevens Institite of Technology, Re-port No. 517, Dec., 1959.

Kaplan, P., Hu, P. N. and Tsakonas, S.: Methods

for Estimating the Longitudinal and Lateral Dynamic Stability of Hydrofoil Craft.» Stevens Institute of Technology, Report No. 691, May.

1958.

[31 Friedsma, G.: «Longiludinal Stability of

Surface-Piercing Hydrofoil Systems for Water-Based

Aircraf t.» Stevens Institute of Technology,

Re-port No. 732, Oct., 1959.

Uspensky, J. V.: «Theory of Equations.» McGraw-Hill Book Company, Inc., 1948.

Sponder, E.: «Ort the Representation of the

Sta-bility Region in Oscillation Problems with the

Aid of the Hurwitz Determinants.» NACA Tech-nical Memorandum 1348, August, 1952.

[61 Weinbium, G.: «Uber eine angenäherte

Behand-lung des Tauchens und Stampfens von

Trag-flächensyst em en in regelmässigem Seegang.»

Schiffstechnik, 25. Heft, 5. Band, Februar, 1958, pp. 2-5.

[71 Ogilvie, T. F.: «The Theoretical Prediction of the

Longitudinal Motions of Hydrofoil Craf t.» David Taylor Model Basin, Report No. 1138, Nov., 1958.

[8] Schiott, H.: ASEA, Västerás, Sweden. Private

talks at the ship technical meeting in Abo,

Fin-land, Oct.. 1963.

B4

z,

¿eots

per o --+.,._._ _{4..:,,___'} 2.0 10 Theory

---1

.5 ¿rimen(s o 2

L/

3 4

83

.6

V

.4 5' e.

,-Experiments o Theory 2.0 15 Theor

+'

1/ExPeriments

.5 o 1 2 3 4

L/

+Qcos(

-1-/2rg

II -\

t (22) L

LJ

IO+EÓ+F9+Cz+Gz =

Rsin

i /

2rg\ ¡ 27rU i

/

2rg\ + S

_±

(23) (2mrU

L ±

COS Lw V _{Lw )} V

Lw)t