Drift angle and its consequences in ship manoeuvres

2 4 .1111.1 1978

ARCH IEF

Lab. v. Scheefsbamikande PUBL. NO.528

Technische Hogeschool

OF THE N.S.M.B.

Reprinted from theJournal of Navigation, Bdit, No. 1, January £978

DRIFT ANGLE AND ITS

CONSEQUENCES IN SHIP

MANCEUVRES

K Meurs

(Netherlands Ship Model Basin)

Agi

Ii.0"

/

THE ROYAL INSTITUTE OF NAVIGATION

AT

THE ROYAL GEOGRAPHICAL SOCIETY

Drift Angle and its Consequences

in Ship Manoeuvres

K. Meurs

(Netherlands Ship Model Basin)

I . INTRODUCTION. When manceuvring ships, mariners usually pay a

great deal of attention to the rate at which theheading changes but the direction in which the ship actually moves may differ from the direction in which she is heading. This difference may be caused not only by cur-rent but also by the ship's drift velocity through the water in a direction perpendicular to the heading. This velocity is hard to recognize but can cause a turning moment on the ship, whether this is desired or not. In difficult manceuvres which cannot always be accomplished by changes of heading only, one can use the effects of this drift velocity. The drift angle, the angle between the heading and the direction in which the centre of gravity moves through the water, must not be confused with the course allowance necessary to make good a track over the ground when there is a

current.

FORCES EXERTED BY THE WATER. Besides the longitudinal resistance,

which is compensated by the propulsion, other forces will be exerted on a moving ship, including rudder forces, drift forces and forcesdue to the turning of the ship. When a ship sailing in still water has a certain lateral velocity, one can conceive the flow around the ship as the flow around a profile at an angle of attack that conforms to the drift angle (Fig. I).

The lift force L (the force perpendicular to the direction of flow) and

the induced resistance D (in the direction opposite to the ship's direction of motion), which are both caused by the drift angle 13, will result in a lateral force on the ship Y(B), a longitudinal force X($) and a turning

moment N(8) (Fig. 2).

Furthermore, when a ship sailing in still water has a certain rate of turn the resistance of the water will not only exert a turning moment on the ship, but there will also be a certain lateral force that must be compounded with the centrifugal force. This arises from the flow around the ship and its direction is mainly towards the centre of the turning circle.

DRIFT ANGLE ON A STRAIGHT COURSE IN STILL WATER. When a ship

is sailing straight in still water, with no external

clearly no drift angle. If however there is an external lateral force acting on the ship, for example the wind, the ship will pick up a lateral velocity

which will increase until the reaction force of the water equals

external lateral force. Consequently a symmetrically built ship that has

Resistance

4111-Lift force L

(A)

-"`

FIG . t. Flow round profile at an angle in relation to drift angle(u=longitudinal, = lateral velocities, relative to water)

"Y(A)

FIG. 2. Force components due to drift

Wind

FIG. 3. Turning moment due to a lateral force,

no forward speed, and lies with the wind abeam, always has a drift angle of 900. If, however, the ship is not symmetrical, for instance if the whole superstructure is aft, the wind will exert a moment which will make her turh, the tale of turn increasing to that at which the reaction moment of the Water equals the wind moment.

If an external lateral force (wind) is exerted on a moving ship the

water flow around the ship will change as a result of the lateral velocity. This change in flow also causes a large turning moment on the ship (Fig. 3). Where / is the distance between point of application and centre of gravity and Y the lateral force, the turning moment (N= /1 x Y) due to the drift angle will be additional to the moment caused by the wind, if the

.

Y(6)

Y_(c)-t-Y

(r)

(r)-Y()

Path of the centre of gravity

FIG. 4. Forces on a ship sailing a circular course

superstructure is aft. In order to sail straight (zero rate of turn) a com-pensatory rudder angle will have to be applied.

4. DRIFT ANGLE OF A SHIP TURNING IN STILL WATER. If lateral forces

other than the wind are exerted on a ship, these forces will also cause drift velocities. This can be the case if.the rudder, or a thruster, causes a lateral force, or if a ship sails along a circle. In the latter case there is also a centrifugal force. Sailing along the arc of a circle, or a series of arcs, may be intentional or unintentional. One may simply wish to change course, but the same thing happens unintentionally with careless steering. In both

cases drift angles are generated.

Figure 4 shows the forces exerted on a ship sailing along a circle ; at any point the centre of gravity moves in the direction of the tangent to the turning circle and the drift angle is always the angle between the tangent and the heading. This drift angle is a consequence of the lateral

force of the rudder Y,, the lateral force due to the rate of turn

and the centrifugal force Y have been initiated by the rudder mo-ment. In a state of equilibrium (rudder angle, drift velocity and rate of

turn remaining constant) the drift velocity and the rate

of turn are

defined by the rudder angle. From the combination of rate of turn and drift velocity, each point on the ship will describe its own turning circle, and each point situated further forward or aft will have a different lateral velocity.

E. THE RUDDER. If the rudder is considered as detached from the ship it can be conceived as having a profile similar to Fig. 1. The lift force L is generated because on the upper side of the profile (port when the rudder is seen from above) the pressure is less than on the lower side. This pressure difference can be explained by the consideration that water streaming along the upper side has to travel further than water streaming along the lower side and must still arrive at the far end simultaneously. Thus the water streams faster along the upper side than the lower and causes, according to hydrodynamic theory, less pressure on the upper side. If however the profile is not infinitely long, as is clearly the case

with a ship's rudder, the streams around the top and bottom of the

rudder will modify the total stream around the profile in such a way that the resulting force makes an angle with the lift force ; so that besides the

NO. I DRIFT ANGLE IN SHIP MANCEUVRES 129

lift force a resistance force is also induced. If the rudder is not in a free stream but located just behind a propeller, it will work on a different principle and can be regarded as a turbine blade that diverts the propeller-generated stream. Besides these two phenomena which will contribute to the lateral force working on the rudder (and thus on the ship), yet another lateral force will be exerted on the ship when the rudder has been laid at an angle, because of the different-slip stream velocities on the port and starboard quarters.

The need to consider the rudder as part of a ship-propeller-rudder

system is explained by the following reasoning-: If the rudder is con-sidered as a profile in an undisturbed stream, then too large a rudder angle would cause the lateral force on the ship to decrease as the stream in Fig. i (port side of the rudder) would not continue along the profile but break away. This condition is known as 'stalling' and occurs when the angle of attack (rudder angle) is larger than the 'stall angle', which is generally around

s°. However, with the rudder attached to the ship

the rudder angle can increase up to 600 before the lateral force on the ship starts to decrease progressively with an increase of the rudder angle (see Fig. 5). The lateral force due to a rudder angle, as shown by the upper curve in Fig. s-, is the total force by which the ship can be steered. Be-cause this force does not arise exclusively from component forces working on the rudder (and thus on the ship), the point of impact will not be on the rudder either, hut a certain small distance forward of it.

Rudder behind a ship Lateral force due to a rudder angle Rudder by Itself I 20 40 60

FIG. E. Rudder angle

6. DRIFT ANGLE AS ANGLE OF ATTACK. Looking once more at Fig. I,

in which the ship is schematized as a profile at rest in an homogeneous flow field (or the moving ship in a fluid at rest), it will be clear that the resistance induced by the drift angle will be large ; because the draught of the ship is small in relation to her length, the water not only moves around the ship but also underneath her.

This increaie in resistance contributes considerably to the speed-loss of the ship when manceuvring, and is so much 'larger than the resistance caused by the rudder angle alone that the latter is almost negligible.

130 K. MELIRS VOL. 31

Therefore, moving the rudder -back and forth quickly without allowing her to build up a drift angle, and a consequent induced resistance, is no effective way to get the speed off a ship. Only when the rudder angle is maintained for some time will she get a drift angle which will reduce her

speed.

-These phenomena change drastically when a ship sails in shallow water. In the .extreme case of 'a ship sailing on the bottom (keel clearance zero) no water will pass underneath her but only around her. The liftforce L is then maximal and will even create a longitudinal force in the direction of the ship's .heading; the induced drag, D, will be negligible as shown in

Fig. .6. sss, Deep water % h N.

\

no., 6. Drag in shallow water (h depth, I= draught)

If the ship in Fig. 4 is making a turn, points that are further aft will have a greater lateral velocity than the centre of gravity, while points forward of the centre of gravity will have a smaller lateral velocity. At point B in Fig. 4 the lateral velocity is zero and the heading will be the

tangent of the turning circle of this point; forward of the turning point the lateral velocity is reversed. The location of the turning point moves

further forward as the drift velocity increases. At the start of a turn,

just after the rudder has been laid, the turning point lies about a quarter of the ship's length aft of the forward perpendicular. As the turn pro-gresses the turning point moves forward until a condition of equilibrium has been reached.; in a tanker it then lies about a sixth of the ship's length aft of the forward perpendicular.

, From the reasoning in the previous section it will be clear that any ship turning in a circle takes advantage of the drift force, which causes an extra turning moment to reinforce the moment generated by the rudder itself. Of course this is only possible because the rudder is attached to the stern. The magnitude of the drift angle depends on the form of the ship; a short ship with little draught-will-have a larger drift angle than a long and deep drawing ship on the same turning circle. From Fig. 6. it may be concluded that the same lateral force on the ship will cause a

NO. I DRIFT ANGLE IN SHIP MANCEUVRES 131

smaller drift angle in shallow water than in deep water. For the same rudder angle a ship in shallow water will experience a smaller decrease of speed than in deep water because of the smaller drift angle, and also

because of the smaller induced drag for a given drift angle.

DRIFT ANGLE AND COURSE CORRECTION ANGLE. In the preceding

sections we have discussed drift angles caused by intentionally or unin-tentionally sailing along arcs of circles and drift angles caused by winds more or less abeam. But what drift angle will a ship have when sailing in a current more or less abeam? The answer is that there is no drift angle at all if she sails straight in an unchanging homogeneous current in deep water. If, for instance, one wishes to sail from A to B at 7-g knots with a 2 knot current abeam one has only to find the course correction angle by drawing a vector diagram. This course correction angle (also called course allowance) is to be applied to the desired course to find the re-quired heading. The course allowance is often (erroneously) called drift angle, probably because the effects of wind and current have much in common. The presence or absence of a course correction angle depends only on the way the water, with the ship and all ships in the vicinity, moves in relation to the bottom.

If however the velocity of the current changes, a drift angle appears because initially, due to her inertia, the ship tends to make good exactly the same course over the ground as before. The drift angle caused by this imbalance will result in a lift force that makes the ship follow a new course over the ground. As soon as the ship makes good this new course the drift angle (and consequently the lift force) disappears. Changes in speed, as well as changes in current velocity occur when navigating in and out of harbour entrances. Both changes, because they involve the inertia of the ship, will influence her course over the ground, or track, only after some time. In large tankers this delay leads to an impression, going out, that the current change or gradient lies farther from the entrance, and going in closer to the entrance, while in reality there is an equal gradient in exactly the same place.

CROSS-CURRENTS IN SHALLOW WATER. When however a ship

sails in a cross-current in shallow water, she does experience a drift

angle. This phenomenon calls for an explanation. Even if the current velocity were equal at all depths one would still have to take into account

the resistance on the ship's bottom due to the close proximity of the

sea bed. The lateral force (although small) will result in a drift velocity in relation to the water.

But current velocity decreases towards the sea bottom because of

friction, and the lower parts of the ship move in an area of steeply

decreasing current velocities. This causes the flow along the upper part of the hull to come from the upstream side and the flow along the lower part of the hull to come from downstream. The drift angle due to the upper part of the hull causes a lateral force Y. The drift angle due to the

force-,V; ;the pOint, ofapplication Of'whiCh is fOr hydrodynainic:al

. reaSOris,a,,little:furtherlift-, This causes a-,rnoment to act on the ship that tendS...-to maki 'her, -turn -dominstream. A small :upstream rudder angle is

- thereforerequired,

The.lift,fcirce:Caused- bpthis-rudder angle. imist:be,:stiffiefent to

cOrnpensate ,for=the.,difference 'between the niornentsi due,,,, to T and V.. Both -lateral fOrcegTare'laSiusUal aCCOmpanied:b5cjOdUce&drags which, together with othe'ragsOciated phenomena;; result in leSS,,Speed hung fnade thati

dcep:water'.: If rybu :sail in a :2 -,-knot .crossTcUrient:and; Ositgirding the C`i,U;rent '.iiartre. bottom, apply::tlieiii,rsc 'correction for this tlifient Without- subtraCtiiig:i.litile drift angle, you il1 end up upstream: In conclusion it he said ;that the,---sea'licc.1 counteracts the set and alSO-rnaleS 'a ship falt4Off 's

also thekeel clearance, the

gtroriger'theS6'.effectS: When the".ikeePclearance,altctnately increases- and 'der.Creaiescai',it '46e.s7=in.sinile'Pdizts of the/Ii.ii-C-bafine-lAtic to submerge ---(hities; the ship may,: t4#,t(5 yaw. Anyrcidder,..:actiOn "Meant to "(Oolit'dfadt -,this, yaw Mac',be late in taking effect ancl-thUs:accentuatejthe yaW..instead;._

of counteracting it:.

tM E U R.2 L:'. 3