Control Elements of Stability

[Music] property known as stability and since the elements of stability are so closely related to the laws that govern floating bodies it would serve us well to review those laws in order for any object to float it must displace a volume of water equal in weight to the weight of the object this may be demonstrated by collecting the water displaced by the ship and weighing it against the weight of the ship the small weight on the scale with the ship offsets the weight of the glass container obviously a sheet of metal placed in water will sink but the same sheet of metal shaped like a hole will remain a float because it now displaces a volume of water equal to its weight when weight or pressure is applied to a floating body the resistant force of the water is readily seen this resistant force is known as the force of buoyancy and its relation to weight or the force of gravity may also be demonstrated by suspending the metal sheet on a scale and immersing it in water we can see that the force of gravity meets Little Resistance the scale registers relatively small loss of weight yet shaped like a hull the sheet of metal meets enough resistance to keep it afloat the scale now registers zero the total weight or force of gravity of the metal is completely balanced by the force of buoyancy or upward pressure of the water this same rule applies to a ship and May explained diagrammatically with this sectional view of a vessel when lowered into the water the weight or gravitational force of the ship acting against the water is counteracted by a buoyant force as the vessel submerges displacing a larger volume of water the buoyant force increases when the force of buoyancy is equal to the force of gravity the ship is at the level at which it will float the buoyant volume of a ship is the entire watertight part of the hull the portion below the water level supports the full weight of the vessel the portion above the water level is the reserve buoyancy the reserve buoyancy is measured by the distance from the water line to the weather deck this height is called the freeboard as with a vessel the reserve buoyancy of any floating body determines the amount of weight that can be added before the vessel will sink as long as the body is watertight and retains some measure of Reserve buoyancy it will continue to float even when inclined or submerged by an outside force in considering the weight or gravitational force of a ship the weights of all parts of the ship are always calculated and dealt with as a single Force this resultant Force acts through the center of gravity a definite point at which the weights of all parts of the ship are balanced bed longitudinally as well as transversely the center of gravity of a ship may be compared with the center of gravity of any two or more weights balanced at a single point for example if two 5B weights are attached to a bar some distance apart the center of the gravitational forces or Center of GRA gra ity must be halfway between them and the resultant will be equal to 10 lb plus the weight of the bar if the weight is increased on one side the center of gravity will shift toward the center of the increased weight the same condition applies to a ship if a weight is added the center of gravity of the ship will shift to toward the center of gravity of the added weight any movement or shifting of the added weight will also cause a shift of position of the center of gravity of the ship in considering the stability of a ship the forces of buoyancy are also calculated as a resultant Force here the water pressure acts on the entire submerged portion of the hull the horizontal pressures being the same on both sides are not considered the pressure on one side offsets the pressure on the other side only the resultant of the upward pressure or buoyant force is considered this Force acts through the center of the displaced volume and is known as the center of buoyancy the location of the center of buoyancy is determined by the shape of the displaced volume it always acts through the geometric center of the submerged portion of the hull being the point at which the buoyant forces are assumed to be concentrated with the ship at rest the center of buoyancy remains stationary but when the ship is inclined the shape of the displaced volume changes this wedge-shaped portion of the ship is now above water and no longer contributes to buoyancy while the wedge on the opposite side is added to the buoyancy this transference of buoyancy from one side to the other causes the center of buoyancy to shift with each inclination of the vessel the center of buoyancy shifts to a new position depending upon the shape of the displaced volume in a Seaway the inclining force may be supplied by wave action and the constantly changing shape of the displaced volume causes a constant shifting of the center of buoyancy since the force of gravity and the force of buoyancy are opposing forces and both are at work on the ship their position in relation to each other has an important bearing on the stability characteristic of the vessel it should be remembered that the force of gravity always acts in a straight line downward while the force of buoyancy always acts in a straight line upward with the ship floating at rest the center of buoyancy is located directly below the center of gravity being equal and on the same vertical line one force Works directly against the other as a result the opposing forces are balanced and the ship is said to be in a state of equilibrium however when the ship is inclined by an outside force it tends to rotate and the balance is Disturbed since the weight of the ship is not changed the center of gravity remains at a fixed point point in the ship but the changing shape of the displaced volume changes the location of the center of buoyancy in relation to the center of gravity no longer on the same vertical line the two forces now parallel to each other tend to rotate the vessel returning it to an upright position the Rotary motion is similar to that produced by any two parallel forces acting in opposite directions on the same body when the forces are equal and directly opposed one balances the other the rotary motion occurs only when the forces are not acting on the same straight line as the ship returns to the upright position the forces move closer together when they reach the same vertical line the ship is again in its balanced position the writing of a ship may be compared to the writing of a rocker when the rocker is at rest the center of gravity is on one vertical line with the center of support of the rocker in other words the weight of the rocker is meant by an equal as the rocker is inclined the center of gravity remains fixed but the center of support shifts to a new point away from the balanced position with the forces out of balance The Rocker tends to rotate until the forces Reg gain their balanced position and The Rocker comes to rest the relative positions of the lines of force may be Illustrated with the use of two arrows one of the arrows affixed at the center of gravity indicates the direction of the force of gravity a second arrow is used to indicate the direction and position of the resistant Force when the rocker is inclined the arrows representing the lines of force may be observed moving away from the position in which one force balances the other as the angle of inclination is increased the distance between the lines of force increases as The Rocker returns to the balanced position the distance between the lines of force decreases with the use of a measuring device it may be shown that as the distance between the lines of force increases the writing tendency of The Rocker increases as the lines of force move closer together the writing tendency diminishes it may also be shown that the value indicated on the scale increases in direct proportion to the distance between the lines of force when the lines of force are separated by a distance of 1 in the value of the writing tendency registers one unit on the scale at a separation of 2 in the scale registers a value of two units the distance between the lines of force is called the writing arm which is actually a measure of the writing tendency in determining the real value of the writing tendency however the weight of the rocker must also be considered if the weight of the rocker is doubled without changing the center of gravity the writing tendency is doubled with a writing arm of 1 in the writing tendency now registers two units on the scale exactly twice that of the lighter Rocker with a 2-in arm the scale registers a writing tendency of four units again twice that of the lighter rocker therefore the value of the writing tendency is obtained by multiplying the weight of the rocker by the length of the writing [Music] arm the writing tendency or writing moment of a ship as it is commonly called is also calculated in the same manner for instance here are two ships one weighing 10,000 tons the other 20,000 tons at the same angle of inclination both produce a writing arm of 3 ft therefore the writing moment of the lighter vessel is 10,000 tons multiplied by 3 ft or 30,000 ft tons while the writing moment of the heavier vessel is 20,000 tons time 3 ft or 60,000 foot tons but since the larger vessel requires a proportionately greater force to return it to the upright position the weight need not be considered and the writing arm alone can be used as the measure of the writing tendency for example when a ship has a writing arm of one foot at one angle of inclination and an AR of 3 ft at a greater angle the writing moment of the ship at this angle is three times as great as it was at the Lesser angle when the writing arm causes a vessel to return to the upright position from any angle of inclination the momentum of the vessel carries it past the upright position a writing arm is then produced on the opposite side resisting the momentum the shifting from one side to the other continues until the dampening effect of the water reduces the value of the writing arm to zero and the ship comes to rest in a c way however the equilibrium of the vessel is Disturbed continuously because the action of the Waves causes a constant shifting of the center of buoyancy in relation to the center of gravity and the movement of the center of buoyancy from one side to the other results in a rolling action of the vessel because of this rolling action the angle to which the ship may be inclined without cap sizing must also be considered this angle is known as the range of stability a rocker may be inclined without capsizing only up to a certain limit due to the form of The Rocker a point is reached where the movement of the center of support begins to diminish the center of gravity however continues to move with the rocker describing a path that causes it to overtake and pass to the opposite side of the point of support the arrows show clearly what happens the writing arm increases until a position is reached where the movement of the point of support is reduced at that time the force of gravity due to the rotary motion of the rocker moves closer to the resisting force and the arm begins to diminish this building up and diminishing of the writing tendency can also be demonstrated with the use of the measuring device the writing moment increases to a point where the maximum arm is reached after which the forces draw together and the value of the writing moment begins to diminish if the rotation is continued until the force of gravity passes to the opposite side of the resisting Force an upsetting moment is produced and The Rocker will capsize the range of stability of a vessel is limited in a similar manner due to the shape of the vessel the writing arm increases until after the deck Edge becomes a wash the maximum arm is then reached any further inclination of the vessel reduces the movement of the center of buoyancy and the writing arm begins to diminish when the center of gravity overtakes the center of buoyancy an upsetting moment is created and the ship capsizes it follows then that the writing arm as well as the range of stability is governed to a large extent by the shape of the vessel for that reason statical stability curves are provided for each vessel which show the length of the writing arm at any angle of inclination separate curves are plotted for every condition of loading the curves are obtained by calculating the length of the writing arm at various angles of inclination for instance at an inclination of 15° this particular ship produces a writing arm of 1.9 ft at 30° a writing arm of 3 fet is produced writing arms are similarly produced at further degrees of inclination and transferred to the Baseline of the graph when a point is reached at which the value of the arm is zero the limit of the range of stability is reached by drawing a line connecting the tops of the arms a curve is produced that will show the length of the writing arm at any angle of inclination for instance at an angle of 23° the writing arm produced is 2.6 ft the loading of a vessel however changes its stability characteristics this may be demonstrated with the use of this small scale boat model the statical stability curve for the model in a light condition shows that the maximum arm is produced when the model is tilted to an angle of 45° at 60° while the arm has begun to diminish it is still efficient to cause the model to return to equilibrium at 80° however the value of the writing arm is zero and the slightest inclination Beyond this point will cause the model to cap size with the same model weighted to represent a loaded condition the stability characteristics are considerably improved the curve for the model in this condition of loading shows that the writing arm is so much greater than that of the light model that at the angle at which the light model will cap size the model in the loaded condition possesses a considerable writing arm at this angle the loaded model will return readily to equilibrium it will not cap size until it is tilted to an angle of more than 135° but while the improved stability of the loaded model as shown by by these two curves is a result of added weight the location of the weight is extremely important the same weight placed high in the model will cause it to caps sizee at an angle of inclination smaller than that of the light model it will be recalled that when the heavy rocker was inclined to produce an arm of 2 in the value on the scale registered four units by measuring the angle of inclination and lowering the center of gravity by Shifting the weight downward it may be demonstrated that both the writing arm and the writing tendency are materially increased inclined to the same angle the writing arm is now 2 and 1/2 in in length and the writing tendency is correspondingly increased the same is true with a vessel by Shifting the center of gravity downward it may readily be seen how the writing arm is increased therefore weight added low in a ship will improve stability by while weight placed high in the vessel decreases the length of the writing arm impairing its stability in distributing weights transversely so long as the center of gravity of the load remains on the center line The Vessel will remain in an upright position if weight is shifted to one side the center of gravity will shift to that side and a new state of equilibrium is produced at rest in this new position it may be seen that the forces of gravity and buoyancy are again in the same vertical line if a weight is shifted to one side of a v vessel producing an appreciable amount of heal a great deal of stability will be lost in the new state of equilibrium the writing arm would be zero at the angle of heel in this case 10° and the curve would show a considerable loss of stability at all angles of inclination in this condition the small arm remaining at greater angles of heel May not be sufficient to overcome an outside force in which case The Vessel would capsize the stability of a vessel can be determined by shifting a heavyweight outboard and noting the angle of heel with the load placed low in the model shifting of the weight produces only a small angle of heel indicating good stability with the same load placed high in the model the angle of heel is great indicating poor stability a rough indication of stability can be obtained by determining the period of roll which is the average time required for a vessel to roll from one side to the other and back again with a load placed low in the model the period of roll is rapid indicating good stability with the same load placed high in the model the period is slow indicating that stability is poor these two methods of judging stability may be used to Advantage in demonstrating the effect of liquid loads by completely filling the bottom tank of the model with liquid a condition known as solid flooding it may be shown that the period of roll with solid flooding is the same as that with a solid load of the same weight but with a tank tank top removed the period is slow stability is considerably impaired the liquid shifting in the direction of the Roll opposes the tendency of the vessel to WR itself the difference in stability between solid and partial flooding may also be shown by inclining the model by means of a weight with solid flooding there is only a small angle of heel with free surface the liquid shifting in the direction of the list produces a large angle of heel when the ship is in motion the constant shifting of the liquid load causes is a constant shifting of the center of gravity in this unstable condition the center of gravity May shift so far to one side that at a relatively small angle of heel The Vessel will cap siiz any increase of surface area increases the free surface effect here the same amount of liquid with twice the surface area produces twice the free surface effect the effect of the shifting liquid weight in this condition is so great that the vessel will no longer maintain an upright position it tends to heal to one side or the other it is not until an angle is reached at which the writing tendency is equal to the healing tendency that the ship comes to rest in a new state of equilibrium in this position the center of gravity and the center of buoyancy are once again on the same vertical line if any attempt is made to correct this list by shifting of weight to the opposite side it will result in an even greater list in the opposite direction the same amount of free surface on the upper decks of the vessel will combine the ill effects of free surface and high weight in this condition the ship is unstable at all angles and will capsize since all vessels carry large amounts of fresh water and liquid fuels longitudinal bulkheads are built into the fuel and water tanks to minimize the free surface effect the greater the number of subdivisions the smaller the free surface effect the same principles that apply to transverse stability also apply to longitudinal stability however a weight that produces a list has very little effect upon trim due to its length The Vessel possesses such good stability for and a that a relative ly large weight is required to produce any considerable change of trim but in view of the fact that transverse stability can be seriously affected by distribution of weight or by free surface effect it is extremely important to consider these factors in relation to the stability characteristics built into each vessel the statical stability curves supplied to each vessel indicate the stability characteristics for certain conditions of loading if it is found desirable to improve stability it can be accomplished by transferring heavy weights to lower levels thereby lowering the center of gravity and lengthening the writing arm should a list develop as a result of flooding or the excessive use of water in fir fighting it can be corrected by pumping the excess water overboard or draining it to a lower level thereby lowering the center of gravity in every case however do consideration must be given to all the elements that govern stability but an attempt to correct one undesirable condition may result in a worse condition that would further impair stability I