The high speed craft steering at off design motion regime

Intemational Confei-ence on Fast Sea Tvanspotiation FAST'2005. June 2005,St.Petersburg. Russia

T H E H I G H SPEED C R A F T S T E E R I N G AT O F F DESIGN MOTION

R E G I M E .

Marina P Lebedeva

N A V I C co.Obvodny emb, 14,192019, St. Petersburg, Russia

A B S T R A C T

The paper pi-esent the results of height-speed craft ttianoeuvering investigation at off-design motion regime. The results of craft see trail tests as well as the data of theoretical investigation of the problem are under consideration. The reasons of craft poor maneuverabilit)' at small speeds are discussed and the tnethod of craft stops maneuver realized is suggested.

I N T R O D U C T I O N

Every high speed craft has to have good manoeuvering characteristics even at o f f design motion regime, including the ship manoeuvering at small speed. The problem would be especially important for ships 25 - 30 meters long. These ships are large enough to provoke an accident at sea. It seems that i f the heknsman has opportunity to use all engine power for ship steering, he could solve problem he likes. But in reality it is not so easy. Such problem has to be solved during the high speed craft manoeuvering tests. The ship was 25 meters long. 4 water jet were installed to move and steering. The steering force of any direction could be generated. The problem to optimal mode of operation obtain has to be solved during tests. The ship moving at the beginning of manoeuver had to stay dead in water at the end of it. But all attempts to stop the ship were in vain.

The craft all of a sudden changed the direction, or began to rotate.

The center of gravity path registered durmg the test is shown on fig 1 as an example.

As the ship behavior was not ordinary the special measurements to obtain the reason of the phenomenon were fulfilled. The ship frack, the ship speed, the water jets thrusts and angle of steering device deflection were measured simultaneously.

The analysis of registered data was fulfilled. The test results were accompanied with the results of calculation to inteipret the measuring data.

The investigation results are shown in the paper.

Fig.l: The center of gravity track

1. T H E C R A F T M A T H E M A T I C A L M O D E L .

For ship motion description the set of 6 differential equation usually use. But i f the craft speed is small and Freud number is less than Fn < 0.2, and i f the ship is moving in calm water without heave and pitch, and the roll angle is small and not influence on kinematics parameters, then the number of equations in the set could be decrease. The sunplify mathemafical model would be the set of 3 differential equation. The similar mathematical model was used to craft motion analysis. The equations in non-dunensional fonn were as follows

d V , dT 2 B C B - ( l + k l l ) C,(P,r') + Fef(r').sinp + O.S-pV^LT (1) dV„ dT 2 B C B - ( l + k22) Cy(P,r') + F,f(r')-cosp-O.S-pV-'LT (2) dm _ 1 d T ~ O . M (l + k66) Cn,(P,r') + (3)

were

_E'^x

_E^-y

_E^z

_{- sum of}

longitudinal and transverse projection of water jet thrusts and the sum of moments, B = B/L - breadth to length ratio, CQ - block coefficient, k l l , k22, k66 added mass, , C y , C^, - non-dmiensional longitudmal and fransverse components of hydrodynamic al force and non-dimensional hydrodynamic moment., F^f = F^f/(O.SpV^LT) -non-dimensional centrifugal force, V x = V j , / V o ,

V y = V y / V o • non-dimensional components of velocity, p - drift angle, r' - non-dimensional craft cenhe o f gravity path, = o:) 2 • L / V Q , x = t • VQ / L -dimensional angular velocity and non-dimensional tune.

The longitudinal and fransverse projection of all water jet thrusts and the sum of moments would be called as steermg force and steering moment. The steering moment supposed to have two parts: the moment of the transverse steering force and additional moment due to couple of forces.

The equations (1) - (3) are written in Cartesian co-ordmate system connected with the ship. Forces acting in bow and in starboard direction and moment, acting in clockwise direction when look down the ship deck supposed to be positive.

The unknown values in equations set (1) - (3) are: two velocity components, angular velocity, two steering forces and moment. Thus the 3 - equations set has 6 unknown values. So the additional correlation equations are needed to fmd the solution.

The needed equations were obtauied using the results of craft steady motion investigation.

2. T H E C R A F T S T E A D Y IVIOTION

To stop the craft using the certain steering force and moment is possible i f the craft steady motion could exist.

The equations set to steady motion described could be obtained from equation (1) - (3) for zero left part. This equations set is as follows

Cx (P. r ' ) + F , f (!•')• sin p + ^ „ - = 0 0.5-pV^LT C,,(P,r') + F,f(r')cosp + -0.5-pV^LT = 0. (4) (5) Cn,(P,r') + O.S'pV^L^T " ' O.SpV^L^T = 0 . (6)

The equation (4) - (6) could be simplified using the non-dunensional expression of steering force and moment. New the equafions set doesn't contain the craft velocity. So the number of unknown values would reduce.

The new equation set is as follows C x ( P , r ' ) + F , f ( r ' ) . s i n p + P,, = 0 , C y ( P , r ' ) + F , f ( r ' ) . c o s P + Py = 0 , Cn,(P,r') + Py-lp + M , = 0 ,

E-x

E^.

The equation set (7) - (9) is the identity correspondence to equafion set (10) - (12)

(Cy (P, M ) + F,f (ÖJ) • cos P) • lp - C ^ (P, M ) - = 0

(10) P^ _ C^(P,m) + Fef(öJ).sinp

Py Cy(P,CE)) + F,f(CD)-COSP (11)

Cy (P, OJ) + F^.f (oy) • cos p + Py = 0 (12)

The equation (10) allowed to obtain the drift angle value for given craft path curvature and additional steering moment. The equation (11) allowed to obtain the ratio of longitudinal and transverse components of steering force. The equation (12) allowed to obtain non-dunensional curvature value for steady drift angle.

The craft inotion kinematics parameters for different C ^ ( P , r ' ) = 0 coinbination of steermg forces were obtained using

equation ( 1 0 ) - ( 1 2 ) C y ( P , r ' ) + F , K r ' ) - c o s p = 0 The investigation resuhs w i l l describe further. > VM= y ct \ J H " 1.1. Transverse steering force. The steering force

directs normal to craft centeiplane ?y ^0. The longitudinal component of steering force equals zero

Px = 0 , The additional steering moment equals zero Mz = 0 .

The equation set is as follows

(Cy (p,r') + F,f (r') • cosp) • lp - C „ , ( p , r ' ) = 0

C ^ ( p , r ' ) + F , f ( r ' ) - s i n p = 0

C y ( p , r ' ) + Frf(r')-cosP + Py = 0

The unknown values are: the drift angle p , the non-dimensional track curvature r ' , non-non-dimensional steering force Py .

The steady motion regime would exist when

Py > C y ( P „ , r ' ) + F , f ( r ' ) - c o s p „ (13)

I f condition (13) is fulfilled the equation set would have the only solution. The craft path would be the curvilinear path of constant curvature. The drift angle - bow-out to center of craft rotation. The drift angle and path cui-vature not depends on steering force value.

The craft velocity value can be calculate using the formula

Cy(P,r') + F(,f(r')-cosP ' O.SpLT'

So the craft velocity depends on steering force value. 1.2 Longitudinal steering force. The steering force directs along to craft centerplane Px ^ 0 . The transverse component of steering force equals zero

Py = 0 , The steering moment equals zero = 0 .

The equation set is as follows

C , ( P , r ' ) + F , f ( r ' ) - s i n p + P ^ = 0

The unknown values are: the drift angle p , the non-dimensional track curvature r', non-non-dimensional steering force P^,.

Two steady motion could exist. They are

the motion along strait line path with zero drift angle,

the steady tuming.

The craft path foim would depends on craft hull geometry and on her trim. The path would be the sh-aight Ime i f she has the sttaight Ime stability and would be curvilinear i f she has not.

The steady haming regime would exists when

Px ^ C , ( P , t , r ' ) + Frf(r').sinp,t (14) I f condition (14) is fulfilled the equafion set has the

only solution. The craft path is the curvilinear path of constant curvature. The drift angle is bow-in to center of craft rotation. The drift angle and path curvature not depends on steering force value P^ .

The craft velocity value can be calculate usmg the formula

Cx ( p , CO)+ Fcf(öJ)-cos p'O.SpLT '

1.3. Steering moment. The both components of steering force are zero Px = 0, Py = 0 . The steering moment is not zero ^ 0.

The equation set is as follows C „ ( P , r ' ) + M , = 0

Cx(P,r') + F , f ( r ' ) - s i n p = 0 C y ( P , r ' ) + F c f ( r ' ) - c o s p = 0

The unknown values are: the drift angle p , the non-dimensional track curvature r', non-non-dimensional steering moment . The steady motion could not exist, as it is unpossible to ensure the balance of longifiidinal and fransverse forces simultaneously.

1.4. Steering force deflection. Tiie components of steering force are as follows = P • cos x , Py = P - s i n x , where % is water jets rudder device deflection angle. The additional steering moment equals zero M ^ = 0 .

The equation set is as follows

( C y (P, r') + F,f (r') • cos P) • lp - C ^ (p, r') = 0

Px _ C x ( p , r ' ) + F , f ( r ' ) . s i n p Py C y ( P , r ' ) + F , f ( r ' ) - c o s p

Cy(P,r') + F , f ( r ' ) - c o s p + P - s i n x = 0

The unknown values are: the drift angle p, the non-dimensional h-ack curvature r', non-non-dimensional water jet thrust P , water jets rudder device deflection angle

X-The steady motion is possible for all x values. X-The craft motion at lunit values o f angle ( X = 9 0 ' ' , x = 0 ° ) was ah-eady discussed (see 1.1 and

1.2).

The craft motion parameters could be obtained from two equation o f set. As it follows from equations the kinematics parameters not depends on water jet thrust

P , but depends on angle x •

The craft velocit}' value can be calculate usuig the formula

y 2 ^ P-cosx 1 _ Cx(P,r') + Fj.f(r') cosP O.SpLT'

1.5. Longitudinal and transverse steering forces. The both components of steering force are not zero

Px ^ 0 , Py 7^ 0 . The value of forces could changed independently The additional steering moment equals zero = 0 .

The equation set is as follows

( C y ( P , r ' ) + F r f ( r ' ) - c o s P ) - l p - C , „ ( P , r ' ) = 0

Px _ C x ( p , r ' ) + F , f ( r ' ) - s m P Py Cy(P,r') + F,f(r')-cosp

C „ ( p , r ' ) + P y . l p = 0

The unknown values are: the drift angle p , the non-dimensional frack ciu-vature r ' , longitudinal and transverse steering forces ratio Px/Py .

The steady motion is possible at small drift angles only. When drift angle work for 9 0 ° the hydrodynamic moment on the craft hull work for zero, and the hydrodynamic force work for it's maximal value. Thus one couldn't satisfy the force and the moment equilibrium conditions simultaneously. The craft motion parameters could be obtained from two equation o f set. The kinematics parameters not depends on Px/Py ratio.

The craft velocity value can be calculate using the formula

Px L _

CX (p, r ' ) + Fcf (!•')• cos P O.SpLT

1.6. Steering force to craft motion at large drift angle. The all components o f steering force and moments are not zero, i. e. Px ^ 0 , P 0 , * 0

At p ^ 9 0 ° and r'= 0 the equation set is as follows Cx(P) = 0

C y ( p ) + Py = 0

C n . ( P ) + P y T p + M , = 0

The unknown values are: the drift angle p , longitudinal steering force Py and additional steering moment .

The craft motion with large drift angles could be fulfilled using the steering force equal to hydrodynamic fransverse force and steering moment, equal to the sum of steermg force moment and hydrodynamic moment.

The craft velocity value can be calculate using the formula

V ^ = ^ ^ ^ ' C y ( P ^ ^ „ ) O.SpLT'

Thus

the craft steady motion exist for certain steering forces and moments; the steering forces ratio needed to steady motion provide depends on craft's hydrodynamic characteristics;

m most cases, the craft drift angle and craft path curvature are independent of fransverse steering force value but depends of longitudinal one; the craft velocity could depends of transverse steering force value

2. T H E C R A F T STOPPING T E S T S .

To stop the ship, it is enough to reveres the propeller thrust and after definite tune the ship would stopped dead in water.

To stop the craft moving along curvilinear path with drift angle and angular velocity one has to compensate all velocity components using steering forces and moments.

2.1 The craft stops using the consecutive turn of water jet thrust (Fig. 1. Region 1).

Water jet operation condition. Just before the record the craft had gone with the water jets thrust reveres. A t the beginnmg of the record the thrusts were tumed nomial to craft centerplane. The measure lasted for 150 seconds. The total thrust (transverse steering force) was permanent. Tlie value was equal R y = 2.3 kn . The moment of steering force was equal

= 4 3 . k n m .

Motion parameters at initial moment of registration. At the moment when record began the craft moves with longitudinal velocity equal to 0.07 m/s, fransverse velocity equal to 0.88 m/s, and angular velocity equal to 0.88 1/s.

Adotlon parameters during the stop manoeuver. The stopping procedure of the craft durmg the see frail had two phase. During the first phase the craft longitudinal component of velocity was tried to compensate by reversing the water jets thrust. During the second phase the transverse and angular velocity were tried to compensate by water jets thmst tums into position nomial to craft centerplane.

The craft path is shown on Fig. 2. The drift angle and angular velocity registered during manoeuver are shown on Fig. 3 and Fig. 4. Points on the craft path shows the craft position at moments when her kinematics parameters are changing. Kinematics parameters value at the moments are shown in table 1. They are

2 - the moment when angular velocity has the maximum value;

3 - the moment when transverse velocity became zero;

4 - the moment when longitudinal velocity became zero. Table 1. Time (s) Vx(ni/s) Vy _{(m/s) ö)z(l/s)} 1 10 -0.07 0.88 -0.200 2 50 -0.06 0.33 0.512 3 77 -0.04 0.00 0.401 4 90 0.00 -0.13 0.331 5 130 0.18 -0.40 0.187 -20 =0.000 „ ^ 40 Y(m)

X(m)

4 32

Fig. 2. The ship path during the craft stopped manoeuver.

Fig. 3. The drift angle value during the manoeuver.

m (1/s) 0.6 — I 0.4 D.2 -D.O -0.2 100 X ( S )

Fig. 4. The angular velocity value during the manoeuver.

The process of craft stops was as follows:

During 50 seconds from the beginning the craft circulated in clockwise direction with port ahead. Drift angle is aft-out. The value of drift angle was about

As it follows from table 1 both components of craft velocity were decreased and angular velocity increased.

At the end o f the period the craft path curvature suddenly changed. Then the drift angle was decreased to zero (point 3) and to « - 9 0 ° (point 4). After that craft began to circulate in opposite direction. So the craft try but could not stop.

The manoeuver "craft stops" was fulfilled using the fransverse steering force. After definite time value the craft has to move in steady turn with drift angle aft out to center of rotation (see p 1.1).

2.2 The craft stops using the simultaneous turn of water jets thrusts (Fig. 1. Region 2).

Water jet operation condition. A t record begins the sum of waters jet thrust value was equal to 0.9 kn and they were turned on 55° to craft centerplane. The water jets worked m this position during 100 seconds. After that the thrust was reversed and steermg force was placed in centerplane. the water jet tlirust value was increased to 9.5 kn.

Motion parameters at initia! moment of registration. At the moment when record began the craft moves with longitudinal velocity equal to -0.7 m/s, transverse velocity equal to 0.15 in/s, and angular velocity equal to -0.63 1/s.

Motion parameters during the stop irianoeuver. The craft path is shown on Fig. 5. Kinematics parameters value at different points are shown in table 2.

They are

2 - the moment when fransverse velocity became zero;

3 - the moment when thrust reversed;

4 - the moment when transverse velocity became zero again. Table 2. Time (s) _{Vx(m/s) Vy (m/s)} C 0 z ( l / S ) 1 450 0.73 0.15 -0.630 2 495 0.35 0.00 -0.714 3 559 0.33 -0.68 -0.628 4 657 0.39 0.00 -0.293 5 641 0.32 -0.12 -0.164 6 700 0.33 0.16 0.974

velocity compensates the craft path and craft angular velocity began to increase.

Y ( m )

-50

Fig. 5. The ship path during the craft stopped manoeuver.

The conunon for all craft stop tests are the impossibility to decreased the velocities value to zero. The reason of experience failure is the steady value of steermg force during manoeuver.

The hydrodynamic force and moments on craft hull decrees as square of craft velocity, but steering forces and moments stay constant. So the steering force effectiveness w i l l increase while the craft speed decrease and craft kmematics parameters changed. This can explain the failure of craft stop tests mentioned above.

3. T H E M O D E L S I M U L A T I O N R E S U L T S . The motion parameters values at craft stop manoeuver were computed using the equation set (1) - (3). The hydrodynamic forces and moments of schematize ship were use for the purpose. Thefr sfructural formulas were as follows

non-dimensional longitudinal force Cx(P,oJ) = C^ + c P . p + C J

+cr

+

The manoeuver "craft stops" was fulfilled using the steering force deflection (p. 2.4).

So the craft w i l l move in steady tum with drift angle bow-in and bow-out to center of craft rotation in accordance with craft velocity value.

The process was as follows:

Duruig 100 seconds from the beginning the craft was cu-culating with decreasing drift angle (from 10° to

- 70° ) and transverse craft velocity as well (see table 2). When steering force being reversed to craft

non-dunensional transverse force

Cy(P,cö)

C^

_•P

non-dimensional moment

C,„

(P,

+cr

+ c P f .p.ro + cPP^ -p^.ro + c P f ^ . p . r o ^

+ cPP^" • p 2 _ 2 .

The calculations were fulfdled for different combination of steering force mentioned above. They showed

the craft steering motion is possible i f the steady motion regime exists;

it is impossible to stop the craft using the constant steering force; the craft motion parameters at small craft velocity depends on craft stability and steering force value.

As it follows from calculation results it is possible to fulfilled the craft stop maneuver i f changing the steering force and moments values simultaneously with squared craft velocity.

The calculation results are shown on Fig. 6. A l l parameters on the graph are shown in non-dimensional form as follows

non-dimensional longifridmal velocity V x = V j V o

non-dimensional fransverse velocity V y = V 3 , / V o

non-dunensional angular velocity

55 = C02 -(L/Vo)

non-dunensional time T = t / ( L / V o )

The calculafion was ftilfilled for follow initial conditions

Vx = 1 ; Vy = - 0 . 1 ; 53 = -0.3

The suggested method is not the only method to successful craft steering provide.

C O N C L U S I O N

1. The craft steady motion exist for certain steering forces and moments; the steering forces values and their combination depends on craft's hydrodynamic characteristics.

2. In most cases, the craft drift angle and craft path curvature are independent o f fransverse steering force value but depends of longitudinal one; but the craft velocity could depends of transverse steering force value.

3. It is impossible to stop the craft using the constant steering force; the craft motion parameters at small craft velocity depends from craft stability and steering force value.

4. To ftilfilled the craft stop maneuver the steering force and moments values have to be decreased simultaneously with decreasing of craft velocity.

R E F E R E N C E S

1. Ship theory guide, vol. I , I I , I I I edited by Voitlfunsky Ya. I . , St.Petersburg , Shipbuilding, 1985. (in Russion).

2. Lebedeva M . P., 2003, Ships M'ith the separate operate steering force. ManoeuvrabiHty and steering. Proceedings 2333 312, St.Petersburg, (in Russion).

Fig. 6. The time history of craft kinematics parameters changing (calculation resuhs)