Intro to Naval Architecture 3E Episode 10 doc

a Figure 10.4 Spiral manoeuvre If the ship is stable there will be a unique rate of turn for eachrudder angle.. If the ship is unstable the plot has two 'arms' for thesmaller rudder angl

The spiral manoeuvre

This is a manoeuvre aimed at giving a feel for a ship's directionalstability From an initial straight course and steady speed the rudder isput over say 15° to starboard After a while the ship settles to a steadyrate of turn and this is noted The rudder angle is then reduced to 10°starboard and the new steady turn rate noted This is repeated forangles of 5°S, 5°P, 10°P, 15°P, 10°P and so on The resulting steady rates

of turn are plotted against rudder angle

(a)

Figure 10.4 Spiral manoeuvre

If the ship is stable there will be a unique rate of turn for eachrudder angle If the ship is unstable the plot has two 'arms' for thesmaller rudder angles, depending upon whether the rudder angle isapproached from above or below the value Within the rudder anglesfor which there is no unique response it is impossible to predict whichway the ship will turn, let alone the turn rate, as this will depend uponother disturbing factors present in the ocean The manoeuvre doesnot give a direct measure of the degree of stability, although the range

of rudder angles over which response is indeterminate is a roughguide To know the minimum rudder angle needed to ensure the shipturns in the desired direction is very useful

The pull-out manoeuvre

This manoeuvre1 is also related to the directional stability of the ship.The rudder is put over to a certain angle and held until the ship isturning at a steady rate The rudder is returned to amidships and thechange in the turn rate with time is noted For a stable ship the turnrate will reduce to zero and the ship takes up a new steady straight linecourse A plot of the log of the rate of turn against time is a straight lineafter a short transition period If the ship is unstable the turn rate willriot reduce to zero but there will remain some steady rate of turn Thearea under the plot of turn rate against time gives the total headingchange after the rudder angle is taken off The smaller this is the morestable the ship

If the ship is conducting turning trials it will be in a state of steadyturning at the end of the run If the rudder is centred the pull-outmanoeuvre can be carried out immediately for that speed and rudderangle

the hull f(a) increases roughly linearly with a up to the stall angle which is typically about 35° f(a) will then decrease.

Various approximate formulae have been proposed for calculating F.

An early one was:

In this an allowance was made for the effect of the propeller race bymultiplying Fby 1.3 for a rudder immediately behind a propeller and

by 1.2 for a centreline rudder behind twin screws Other formulationsbased on the true speed of the ship are:

The first two were proposed for twin rudders behind twin screws andthe third for a centreline rudder behind a single screw

If wind or water tunnel data is available for the rudder cross sectionthis should be used to calculate the lift and the centre of pressureposition

Typically the rudder area in merchant ships is between ^ and ^ of theproduct of length and draught

Rudder torques

To establish the torque needed to turn a rudder it is necessary to findthe position on the rudder at which the rudder force acts That

position is the centre of pressure For a rectangular flat plate of breadth B

at angle of attack a, this can be taken as (0.195 + 0.305 sin a) B aft of

the leading edge For a typical rudder section it has been suggested2that the centre of pressure for a rectangular rudder can be taken at

K X (chord length) aft of the leading edge, where:

The open water figure is used for both configurations for a ship goingastern

For a non-rectangular rudder an approximation to the centre ofpressure position can be obtained by dividing the rudder into anumber of rectangular sections and integrating the individual forcesand moments over the total area This method can also be used toestimate the vertical location of the centre of pressure, which dictatesthe bending moment on the rudder stock or forces on the supportingpintles

Example 10.1

A rudder with an area of 20 m2 when turned to 35° has the centre

of pressure 1.2m from the stock centreline If the ship speed is 15knots, and the rudder is located aft of the single propeller,calculate the diameter of the stock able to take this torque,assuming an allowable stress of 70 MN/m2

Using the simple formula from above to calculate the rudderforce and a factor of 1.3 to allow for the screw race:

This can be equated to qf/r where r is the stock radius, q is the

allowable stress, and/is the second moment of area about a polar

axis equal to Jtr 4 /^ Hence

In practice it would be necessary to take into account the shearforce and bending moment on the stock in checking that thestrength was adequate The bending moment and shear forces willdepend upon the way the rudder is supported If astern speeds arehigh enough the greatest torque can arise then as the rudder isless well balanced for movements astern

are termed balanced, semi-balanced or unbalanced The other method of

categorization is the arrangement for suspending the rudder from the

hull Some have a pintle at the bottom of the rudder, others one atabout mid depth and others have no lower pintle The last are termed

spade rudders and it is this type which is most commonly fitted in

Figure 10,6 Unbalanced rudder

Special rudders

A number of special rudders have been proposed and patented overthe years The aim is usually to improve the lift to drag ratio achieved

A flap rudder, Figure 10.8, uses a flap at the trailing edge to improve the

lift by changing aerofoil shape Typically, as the rudder turns, the flapgoes to twice the angle of the main rudder but in some rudders the

flaps can be moved independently A variant is the Flettner rudder which

uses two narrow flaps at the trailing edge The flaps move so as to assistthe main rudder movement reducing the torque required of thesteering gear

Figure 10.7 Semi-balanced rudder

Figure 10.8 Flap rudder

In semi-balanced and unbalanced rudders the fixed structure ahead

of the rudder can be shaped to help augment the lateral force at therudder

Active rudders

These are usually spade type rudders but incorporating a fairedhousing with a small electric motor driving a small propeller Thisprovides a 'rudder' force even when the ship is at rest when thehydrodynamic forces on the rudder would be zero It is used in shipsrequiring good manoeuvrability at very low speeds

The Kitchen rudder

This rudder is a two-part tube shrouding the propeller and turningabout a vertical axis For ahead propulsion the two halves of the tubeare opened to fore and aft flow For turning the two halves can bemoved together to deflect the propeller race The two halves can bemoved to block the propeller race and reverse its flow

Figure 10,9 Kitchen rudder

Vertical axis propeller

This type of propeller is essentially a horizontal disc carrying a number

of aerofoil shaped vertical blades As the disc turns the blades arecaused to turn about their vertical axes so that they create a thrust Fornormal propulsion the blades are set so that the thrust is fore and aft.When the ship wishes to turn the blades are adjusted so that the thrust

is at an angle They can produce lateral thrust even at low shipspeed

Lateral thrust units

It is sometimes desirable to be able to control a ship's head and courseindependently This situation can arise in mine countermeasure vesselswhich need to follow a certain path relative to the ground in conditions

Figure 10.10 Vertical axis rudder (a) Construction (b) Operation

of wind and tide Other vessels demanding good positional control areoffshore rigs This leads to a desire to have the ability to produce lateralthrusts at the bow as well as the stern It has been seen that bow ruddersare likely to be ineffective because of their proximity to the neutralpoint The alternative is to put a thrust unit, usually a contra-rotating

propeller, in a transverse tube Such devices are called lateral thrust units

or bow thrust units when fitted forward Their efficiency is seriously

reduced by a ship's forward speed, the thrust being roughly halved atabout two knots Some offshore rigs have dynamic positional controlprovided by a number of computer controlled lateral thrust units

SHIP HANDLING

Several aspects of the handling of a ship are not brought out by thevarious manoeuvres discussed above

Handling at low speed

At low speed any hydrodynamic forces on the hull and rudders aresmall since they vary as the square of the speed The master must useother means to manoeuvre the ship, including:

(1) Using one shaft, in a twin shaft ship, to go ahead while the othergoes astern

(2) When leaving, or arriving at, the dockside a stern or head ropecan be used as a pivot while going ahead or astern on thepropeller,

(3) Using the so-called paddle wheel effect which is a lateral force

arising from the non-axial flow through the propeller The forceacts so as to cause the stern to swing in the direction it wouldmove had the propeller been a wheel running on a hard surface

In twin screws the effects generally balance out when both shaftsare acting to provide ahead or astern thrust In comingalongside a jetty a short burst astern on one shaft can 'kick' thestern in towards the jetty or away from it depending which shaft

is used

(4) Using one of the special devices described above For instance aKitchen rudder, a vertical axis propeller or a lateral thruster

Interaction between ships

As discussed in Chapter 8 on resistance a ship creates a pressure field

as it moves through the water The field shows a marked increase inpressure near the bow and stern with a suction over the centralportion of the ship This pressure field acts for quite an area around

the ship Anything entering and disturbing the pressure field willcause a change in the forces on the ship, and suffer forces on itself.

If one ship passes close to another in overtaking it, the ships initiallyrepel each other This repulsion force reduces to zero as the bow ofthe overtaking ship reaches the other's amidships and an attractionforce builds up This is at a maximum soon after the ships are abreastafter which it reduces and becomes a repelling force as the two shipspart company When running abreast the ships experience bowoutward moments As they approach or break away they suffer a bowinward moment3 Such forces are very important for ships when theyare replenishing at sea4

Similar considerations apply when a ship approaches a fixed object.For a vertical canal bank or jetty the ship experiences a lateral forceand yaw moment Open structure jetties will have much less effectthan a solid one In shallow water the reaction is with the sea bed andthe ship experiences a vertical force and trimming moment resulting

in a bodily sinkage and trim by the stern This can cause a ship toground in water which is nominally several feet deeper than thedraught5

The sinkage is known as squat This phenomenon has become more

important with the increasing size of tankers and bulk carriers Squat ispresent even in deep water due to the different pressure field aroundthe ship at speed It is accentuated, as well as being more significant, in

shallow water In a confined waterway a blockage effect occurs once the

ship's sectional area exceeds a certain percentage of the waterway'scross section This is due to the increased speed of the water which istrying to move past the ship

For narrow channels a blockage factor mid a velocity-return factor 6 havebeen defined as:

A formula for estimating squat at speed Vin open or confined waters

is:

Cg being the block coefficient

A simplified formula for open water7 is:

Other approximate approaches8 are to take squat as 10 per cent ofthe draught or as 0.3 metres for every five knots of speed

DYNAMIC STABILITY AND CONTROL OF SUBMARINESModern submarines can travel at high speed although sometimes theirfunction requires them to move very slowly These two speed regimes

pose quite different situations as regards their dynamic stability and

control in the vertical plane The submarine's static stability dominatesthe low speed performance but has negligible influence at high speed.For motions in the horizontal plane the submarine's problems aresimilar to those of a surface ship except that the submarine, when deep,experiences no free surface effects At periscope depth the free surfacebecomes important as it affects the forces and moments the submarineexperiences, but again mainly in the vertical plane

A submarine must avoid hitting the sea bed or exceeding its safediving depth and, to remain covert, must not break surface It has alayer of water in which to manoeuvre which is only about two or threeship lengths deep At high speed there is little time to take correctiveaction should anything go wrong By convention submarines use theterm pitch angle for inclinations about a transverse horizontal axis (thetrim for surface ships) and the term trim is used to denote the state ofequilibrium when submerged To trim a submarine it is brought toneutral buoyancy with the centres of gravity and buoyancy in line.The approach to the problem is like that used for the directionalstability of surface ships but bearing in mind that:

(1) The submarine is positively stable in pitch angle So if it isdisturbed in pitch while at rest it will return to its original trimangle

(2) The submarine is unstable for depth changes due to thecompressibility of the hull

(3) It is not possible to maintain a precise balance between weightand buoyancy as fuel and stores are used up

The last two considerations mean that the control surfaces must be able

to provide a vertical force to counter any out of balance force andmoment in the vertical plane To control depth and pitch separately

Figure 10.11 Submarine in vertical plane

requires two sets of control surface, the hydroplanes, one forward and

mqV'm a centrifugal force term

mgBQB is a statical stability term, BG being the distance between B

andG

This stability term is constant for all speeds whereas the moments Mvary with the square of the velocity The stability term can normally beignored at speeds greater than 10 knots Ignoring this term for the time

being and eliminating w between the two equations leads to the

condition that for the submarine to have positive dynamic stability:

This is termed the high speed stability criterion If this criterion is met and

the submarine is statically stable, it will be stable at all speeds If thecriterion is not met then a statically stable submarine will develop adiverging oscillation at forward speeds above some critical value

The equations can be manipulated9 to derive a number of interestingrelationships:

(1) The steady path in the vertical plane cannot be a circle unless BG

is zero

(2) The rate of change of depth is zero if

(3) The pitch angle is zero if M$ H /Z$ H ~ M^/Z^ but the depth rate is

not zero but given by <5HZ3H/^v

(4) The ratio M W /Z W defines the distance forward of G of a point

known as the neutral point A vertical force applied at this point

causes a depth change but no change in pitch angle

(5) A second point, known as the critical point, is distant mgBG/VZ^

aft of the neutral point A vertical force applied at the criticalpoint will cause no change of depth but will change the pitchangle A downward force forward of the critical point willincrease depth, a downward force aft of the critical point willreduce depth Thus at this point there is a reversal of theexpected result of applying a vertical force

(6) As speed drops the critical point moves aft At some speed,perhaps two or three knots, the critical point will fall on the afterhydroplane position The speed at which this happens is termed

the critical speed.

Figim 10.12 Neutral and critical points

MODIFYING THE MANOEUVRING PERFORMANCE

As with other aspects of ship performance it is difficult, and sometimesdangerous, to generalize on the effect of design changes on a ship'smanoeuvring qualities This is because so many factors interact andwhat is true for one form may not be true for another Broadly however

it can be expected that:

(1) Stern trim improves directional stability and increases turningdiameter

(2) A larger rudder can improve directional stability and give betterturning

(3) Decrease in draught can increase turning rate and improvedirectional stability This is perhaps due to the rudder becomingmore dominant relative to the immersed hull

(4) Higher length to beam ratios lead to a more stable ship andgreater directional stability

(5) Quite marked changes in metacentric height, whilst affectingthe heel during a turn, have little effect on turning rate ordirectional stability

(6) For surface ships at a given rudder angle the turning circleincreases in diameter with increasing speed but rate of turn canincrease For submarines turning diameters are little affected byspeed

(7) A large skeg aft will increase directional stability and turningcircle diameter

(8) Cutting away the below water profile forward can increasedirectional stability

By and large the hull design of both a surface ship and a submarine isdictated by considerations other than manoeuvring If model tests show

a need to change the manoeuvring performance this would normally

be achieved by modifying the areas and positions of the controlsurfaces and skegs

SUMMARY

The reasons a ship requires certain levels of manoeuvrability have beendiscussed and the difficulties in defining any standard parameters forstudying the matter pointed out Various standard manoeuvres used indefining a vessel's directional stability and turning performance havebeen described A number of rudder types and other devices formanoeuvring ships have been reviewed The special case of a